diff --git a/llmeval-env/lib/python3.10/site-packages/nvidia_curand_cu12-10.3.2.106.dist-info/METADATA b/llmeval-env/lib/python3.10/site-packages/nvidia_curand_cu12-10.3.2.106.dist-info/METADATA new file mode 100644 index 0000000000000000000000000000000000000000..301ffe540f0242521617353143a2ee3ad715a44e --- /dev/null +++ b/llmeval-env/lib/python3.10/site-packages/nvidia_curand_cu12-10.3.2.106.dist-info/METADATA @@ -0,0 +1,35 @@ +Metadata-Version: 2.1 +Name: nvidia-curand-cu12 +Version: 10.3.2.106 +Summary: CURAND native runtime libraries +Home-page: https://developer.nvidia.com/cuda-zone +Author: Nvidia CUDA Installer Team +Author-email: cuda_installer@nvidia.com +License: NVIDIA Proprietary Software +Keywords: cuda,nvidia,runtime,machine learning,deep learning +Classifier: Development Status :: 4 - Beta +Classifier: Intended Audience :: Developers +Classifier: Intended Audience :: Education +Classifier: Intended Audience :: Science/Research +Classifier: License :: Other/Proprietary License +Classifier: Natural Language :: English +Classifier: Programming Language :: Python :: 3 +Classifier: Programming Language :: Python :: 3.5 +Classifier: Programming Language :: Python :: 3.6 +Classifier: Programming Language :: Python :: 3.7 +Classifier: Programming Language :: Python :: 3.8 +Classifier: Programming Language :: Python :: 3.9 +Classifier: Programming Language :: Python :: 3.10 +Classifier: Programming Language :: Python :: 3.11 +Classifier: Programming Language :: Python :: 3 :: Only +Classifier: Topic :: Scientific/Engineering +Classifier: Topic :: Scientific/Engineering :: Mathematics +Classifier: Topic :: Scientific/Engineering :: Artificial Intelligence +Classifier: Topic :: Software Development +Classifier: Topic :: Software Development :: Libraries +Classifier: Operating System :: Microsoft :: Windows +Classifier: Operating System :: POSIX :: Linux +Requires-Python: >=3 +License-File: License.txt + +CURAND native runtime libraries diff --git a/llmeval-env/lib/python3.10/site-packages/pkg_resources/__init__.py b/llmeval-env/lib/python3.10/site-packages/pkg_resources/__init__.py new file mode 100644 index 0000000000000000000000000000000000000000..955fdc48b60cc6f9bc03916039a379a741a7d93a --- /dev/null +++ b/llmeval-env/lib/python3.10/site-packages/pkg_resources/__init__.py @@ -0,0 +1,3303 @@ +""" +Package resource API +-------------------- + +A resource is a logical file contained within a package, or a logical +subdirectory thereof. The package resource API expects resource names +to have their path parts separated with ``/``, *not* whatever the local +path separator is. Do not use os.path operations to manipulate resource +names being passed into the API. + +The package resource API is designed to work with normal filesystem packages, +.egg files, and unpacked .egg files. It can also work in a limited way with +.zip files and with custom PEP 302 loaders that support the ``get_data()`` +method. +""" + +import sys +import os +import io +import time +import re +import types +import zipfile +import zipimport +import warnings +import stat +import functools +import pkgutil +import operator +import platform +import collections +import plistlib +import email.parser +import errno +import tempfile +import textwrap +import itertools +import inspect +import ntpath +import posixpath +import importlib +from pkgutil import get_importer + +try: + import _imp +except ImportError: + # Python 3.2 compatibility + import imp as _imp + +try: + FileExistsError +except NameError: + FileExistsError = OSError + +# capture these to bypass sandboxing +from os import utime +try: + from os import mkdir, rename, unlink + WRITE_SUPPORT = True +except ImportError: + # no write support, probably under GAE + WRITE_SUPPORT = False + +from os import open as os_open +from os.path import isdir, split + +try: + import importlib.machinery as importlib_machinery + # access attribute to force import under delayed import mechanisms. + importlib_machinery.__name__ +except ImportError: + importlib_machinery = None + +from pkg_resources.extern import appdirs +from pkg_resources.extern import packaging +__import__('pkg_resources.extern.packaging.version') +__import__('pkg_resources.extern.packaging.specifiers') +__import__('pkg_resources.extern.packaging.requirements') +__import__('pkg_resources.extern.packaging.markers') + +if sys.version_info < (3, 5): + raise RuntimeError("Python 3.5 or later is required") + +# declare some globals that will be defined later to +# satisfy the linters. +require = None +working_set = None +add_activation_listener = None +resources_stream = None +cleanup_resources = None +resource_dir = None +resource_stream = None +set_extraction_path = None +resource_isdir = None +resource_string = None +iter_entry_points = None +resource_listdir = None +resource_filename = None +resource_exists = None +_distribution_finders = None +_namespace_handlers = None +_namespace_packages = None + + +class PEP440Warning(RuntimeWarning): + """ + Used when there is an issue with a version or specifier not complying with + PEP 440. + """ + + +def parse_version(v): + try: + return packaging.version.Version(v) + except packaging.version.InvalidVersion: + warnings.warn( + f"{v} is an invalid version and will not be supported in " + "a future release", + PkgResourcesDeprecationWarning, + ) + return packaging.version.LegacyVersion(v) + + +_state_vars = {} + + +def _declare_state(vartype, **kw): + globals().update(kw) + _state_vars.update(dict.fromkeys(kw, vartype)) + + +def __getstate__(): + state = {} + g = globals() + for k, v in _state_vars.items(): + state[k] = g['_sget_' + v](g[k]) + return state + + +def __setstate__(state): + g = globals() + for k, v in state.items(): + g['_sset_' + _state_vars[k]](k, g[k], v) + return state + + +def _sget_dict(val): + return val.copy() + + +def _sset_dict(key, ob, state): + ob.clear() + ob.update(state) + + +def _sget_object(val): + return val.__getstate__() + + +def _sset_object(key, ob, state): + ob.__setstate__(state) + + +_sget_none = _sset_none = lambda *args: None + + +def get_supported_platform(): + """Return this platform's maximum compatible version. + + distutils.util.get_platform() normally reports the minimum version + of macOS that would be required to *use* extensions produced by + distutils. But what we want when checking compatibility is to know the + version of macOS that we are *running*. To allow usage of packages that + explicitly require a newer version of macOS, we must also know the + current version of the OS. + + If this condition occurs for any other platform with a version in its + platform strings, this function should be extended accordingly. + """ + plat = get_build_platform() + m = macosVersionString.match(plat) + if m is not None and sys.platform == "darwin": + try: + plat = 'macosx-%s-%s' % ('.'.join(_macos_vers()[:2]), m.group(3)) + except ValueError: + # not macOS + pass + return plat + + +__all__ = [ + # Basic resource access and distribution/entry point discovery + 'require', 'run_script', 'get_provider', 'get_distribution', + 'load_entry_point', 'get_entry_map', 'get_entry_info', + 'iter_entry_points', + 'resource_string', 'resource_stream', 'resource_filename', + 'resource_listdir', 'resource_exists', 'resource_isdir', + + # Environmental control + 'declare_namespace', 'working_set', 'add_activation_listener', + 'find_distributions', 'set_extraction_path', 'cleanup_resources', + 'get_default_cache', + + # Primary implementation classes + 'Environment', 'WorkingSet', 'ResourceManager', + 'Distribution', 'Requirement', 'EntryPoint', + + # Exceptions + 'ResolutionError', 'VersionConflict', 'DistributionNotFound', + 'UnknownExtra', 'ExtractionError', + + # Warnings + 'PEP440Warning', + + # Parsing functions and string utilities + 'parse_requirements', 'parse_version', 'safe_name', 'safe_version', + 'get_platform', 'compatible_platforms', 'yield_lines', 'split_sections', + 'safe_extra', 'to_filename', 'invalid_marker', 'evaluate_marker', + + # filesystem utilities + 'ensure_directory', 'normalize_path', + + # Distribution "precedence" constants + 'EGG_DIST', 'BINARY_DIST', 'SOURCE_DIST', 'CHECKOUT_DIST', 'DEVELOP_DIST', + + # "Provider" interfaces, implementations, and registration/lookup APIs + 'IMetadataProvider', 'IResourceProvider', 'FileMetadata', + 'PathMetadata', 'EggMetadata', 'EmptyProvider', 'empty_provider', + 'NullProvider', 'EggProvider', 'DefaultProvider', 'ZipProvider', + 'register_finder', 'register_namespace_handler', 'register_loader_type', + 'fixup_namespace_packages', 'get_importer', + + # Warnings + 'PkgResourcesDeprecationWarning', + + # Deprecated/backward compatibility only + 'run_main', 'AvailableDistributions', +] + + +class ResolutionError(Exception): + """Abstract base for dependency resolution errors""" + + def __repr__(self): + return self.__class__.__name__ + repr(self.args) + + +class VersionConflict(ResolutionError): + """ + An already-installed version conflicts with the requested version. + + Should be initialized with the installed Distribution and the requested + Requirement. + """ + + _template = "{self.dist} is installed but {self.req} is required" + + @property + def dist(self): + return self.args[0] + + @property + def req(self): + return self.args[1] + + def report(self): + return self._template.format(**locals()) + + def with_context(self, required_by): + """ + If required_by is non-empty, return a version of self that is a + ContextualVersionConflict. + """ + if not required_by: + return self + args = self.args + (required_by,) + return ContextualVersionConflict(*args) + + +class ContextualVersionConflict(VersionConflict): + """ + A VersionConflict that accepts a third parameter, the set of the + requirements that required the installed Distribution. + """ + + _template = VersionConflict._template + ' by {self.required_by}' + + @property + def required_by(self): + return self.args[2] + + +class DistributionNotFound(ResolutionError): + """A requested distribution was not found""" + + _template = ("The '{self.req}' distribution was not found " + "and is required by {self.requirers_str}") + + @property + def req(self): + return self.args[0] + + @property + def requirers(self): + return self.args[1] + + @property + def requirers_str(self): + if not self.requirers: + return 'the application' + return ', '.join(self.requirers) + + def report(self): + return self._template.format(**locals()) + + def __str__(self): + return self.report() + + +class UnknownExtra(ResolutionError): + """Distribution doesn't have an "extra feature" of the given name""" + + +_provider_factories = {} + +PY_MAJOR = '{}.{}'.format(*sys.version_info) +EGG_DIST = 3 +BINARY_DIST = 2 +SOURCE_DIST = 1 +CHECKOUT_DIST = 0 +DEVELOP_DIST = -1 + + +def register_loader_type(loader_type, provider_factory): + """Register `provider_factory` to make providers for `loader_type` + + `loader_type` is the type or class of a PEP 302 ``module.__loader__``, + and `provider_factory` is a function that, passed a *module* object, + returns an ``IResourceProvider`` for that module. + """ + _provider_factories[loader_type] = provider_factory + + +def get_provider(moduleOrReq): + """Return an IResourceProvider for the named module or requirement""" + if isinstance(moduleOrReq, Requirement): + return working_set.find(moduleOrReq) or require(str(moduleOrReq))[0] + try: + module = sys.modules[moduleOrReq] + except KeyError: + __import__(moduleOrReq) + module = sys.modules[moduleOrReq] + loader = getattr(module, '__loader__', None) + return _find_adapter(_provider_factories, loader)(module) + + +def _macos_vers(_cache=[]): + if not _cache: + version = platform.mac_ver()[0] + # fallback for MacPorts + if version == '': + plist = '/System/Library/CoreServices/SystemVersion.plist' + if os.path.exists(plist): + if hasattr(plistlib, 'readPlist'): + plist_content = plistlib.readPlist(plist) + if 'ProductVersion' in plist_content: + version = plist_content['ProductVersion'] + + _cache.append(version.split('.')) + return _cache[0] + + +def _macos_arch(machine): + return {'PowerPC': 'ppc', 'Power_Macintosh': 'ppc'}.get(machine, machine) + + +def get_build_platform(): + """Return this platform's string for platform-specific distributions + + XXX Currently this is the same as ``distutils.util.get_platform()``, but it + needs some hacks for Linux and macOS. + """ + from sysconfig import get_platform + + plat = get_platform() + if sys.platform == "darwin" and not plat.startswith('macosx-'): + try: + version = _macos_vers() + machine = os.uname()[4].replace(" ", "_") + return "macosx-%d.%d-%s" % ( + int(version[0]), int(version[1]), + _macos_arch(machine), + ) + except ValueError: + # if someone is running a non-Mac darwin system, this will fall + # through to the default implementation + pass + return plat + + +macosVersionString = re.compile(r"macosx-(\d+)\.(\d+)-(.*)") +darwinVersionString = re.compile(r"darwin-(\d+)\.(\d+)\.(\d+)-(.*)") +# XXX backward compat +get_platform = get_build_platform + + +def compatible_platforms(provided, required): + """Can code for the `provided` platform run on the `required` platform? + + Returns true if either platform is ``None``, or the platforms are equal. + + XXX Needs compatibility checks for Linux and other unixy OSes. + """ + if provided is None or required is None or provided == required: + # easy case + return True + + # macOS special cases + reqMac = macosVersionString.match(required) + if reqMac: + provMac = macosVersionString.match(provided) + + # is this a Mac package? + if not provMac: + # this is backwards compatibility for packages built before + # setuptools 0.6. All packages built after this point will + # use the new macOS designation. + provDarwin = darwinVersionString.match(provided) + if provDarwin: + dversion = int(provDarwin.group(1)) + macosversion = "%s.%s" % (reqMac.group(1), reqMac.group(2)) + if dversion == 7 and macosversion >= "10.3" or \ + dversion == 8 and macosversion >= "10.4": + return True + # egg isn't macOS or legacy darwin + return False + + # are they the same major version and machine type? + if provMac.group(1) != reqMac.group(1) or \ + provMac.group(3) != reqMac.group(3): + return False + + # is the required OS major update >= the provided one? + if int(provMac.group(2)) > int(reqMac.group(2)): + return False + + return True + + # XXX Linux and other platforms' special cases should go here + return False + + +def run_script(dist_spec, script_name): + """Locate distribution `dist_spec` and run its `script_name` script""" + ns = sys._getframe(1).f_globals + name = ns['__name__'] + ns.clear() + ns['__name__'] = name + require(dist_spec)[0].run_script(script_name, ns) + + +# backward compatibility +run_main = run_script + + +def get_distribution(dist): + """Return a current distribution object for a Requirement or string""" + if isinstance(dist, str): + dist = Requirement.parse(dist) + if isinstance(dist, Requirement): + dist = get_provider(dist) + if not isinstance(dist, Distribution): + raise TypeError("Expected string, Requirement, or Distribution", dist) + return dist + + +def load_entry_point(dist, group, name): + """Return `name` entry point of `group` for `dist` or raise ImportError""" + return get_distribution(dist).load_entry_point(group, name) + + +def get_entry_map(dist, group=None): + """Return the entry point map for `group`, or the full entry map""" + return get_distribution(dist).get_entry_map(group) + + +def get_entry_info(dist, group, name): + """Return the EntryPoint object for `group`+`name`, or ``None``""" + return get_distribution(dist).get_entry_info(group, name) + + +class IMetadataProvider: + def has_metadata(name): + """Does the package's distribution contain the named metadata?""" + + def get_metadata(name): + """The named metadata resource as a string""" + + def get_metadata_lines(name): + """Yield named metadata resource as list of non-blank non-comment lines + + Leading and trailing whitespace is stripped from each line, and lines + with ``#`` as the first non-blank character are omitted.""" + + def metadata_isdir(name): + """Is the named metadata a directory? (like ``os.path.isdir()``)""" + + def metadata_listdir(name): + """List of metadata names in the directory (like ``os.listdir()``)""" + + def run_script(script_name, namespace): + """Execute the named script in the supplied namespace dictionary""" + + +class IResourceProvider(IMetadataProvider): + """An object that provides access to package resources""" + + def get_resource_filename(manager, resource_name): + """Return a true filesystem path for `resource_name` + + `manager` must be an ``IResourceManager``""" + + def get_resource_stream(manager, resource_name): + """Return a readable file-like object for `resource_name` + + `manager` must be an ``IResourceManager``""" + + def get_resource_string(manager, resource_name): + """Return a string containing the contents of `resource_name` + + `manager` must be an ``IResourceManager``""" + + def has_resource(resource_name): + """Does the package contain the named resource?""" + + def resource_isdir(resource_name): + """Is the named resource a directory? (like ``os.path.isdir()``)""" + + def resource_listdir(resource_name): + """List of resource names in the directory (like ``os.listdir()``)""" + + +class WorkingSet: + """A collection of active distributions on sys.path (or a similar list)""" + + def __init__(self, entries=None): + """Create working set from list of path entries (default=sys.path)""" + self.entries = [] + self.entry_keys = {} + self.by_key = {} + self.callbacks = [] + + if entries is None: + entries = sys.path + + for entry in entries: + self.add_entry(entry) + + @classmethod + def _build_master(cls): + """ + Prepare the master working set. + """ + ws = cls() + try: + from __main__ import __requires__ + except ImportError: + # The main program does not list any requirements + return ws + + # ensure the requirements are met + try: + ws.require(__requires__) + except VersionConflict: + return cls._build_from_requirements(__requires__) + + return ws + + @classmethod + def _build_from_requirements(cls, req_spec): + """ + Build a working set from a requirement spec. Rewrites sys.path. + """ + # try it without defaults already on sys.path + # by starting with an empty path + ws = cls([]) + reqs = parse_requirements(req_spec) + dists = ws.resolve(reqs, Environment()) + for dist in dists: + ws.add(dist) + + # add any missing entries from sys.path + for entry in sys.path: + if entry not in ws.entries: + ws.add_entry(entry) + + # then copy back to sys.path + sys.path[:] = ws.entries + return ws + + def add_entry(self, entry): + """Add a path item to ``.entries``, finding any distributions on it + + ``find_distributions(entry, True)`` is used to find distributions + corresponding to the path entry, and they are added. `entry` is + always appended to ``.entries``, even if it is already present. + (This is because ``sys.path`` can contain the same value more than + once, and the ``.entries`` of the ``sys.path`` WorkingSet should always + equal ``sys.path``.) + """ + self.entry_keys.setdefault(entry, []) + self.entries.append(entry) + for dist in find_distributions(entry, True): + self.add(dist, entry, False) + + def __contains__(self, dist): + """True if `dist` is the active distribution for its project""" + return self.by_key.get(dist.key) == dist + + def find(self, req): + """Find a distribution matching requirement `req` + + If there is an active distribution for the requested project, this + returns it as long as it meets the version requirement specified by + `req`. But, if there is an active distribution for the project and it + does *not* meet the `req` requirement, ``VersionConflict`` is raised. + If there is no active distribution for the requested project, ``None`` + is returned. + """ + dist = self.by_key.get(req.key) + if dist is not None and dist not in req: + # XXX add more info + raise VersionConflict(dist, req) + return dist + + def iter_entry_points(self, group, name=None): + """Yield entry point objects from `group` matching `name` + + If `name` is None, yields all entry points in `group` from all + distributions in the working set, otherwise only ones matching + both `group` and `name` are yielded (in distribution order). + """ + return ( + entry + for dist in self + for entry in dist.get_entry_map(group).values() + if name is None or name == entry.name + ) + + def run_script(self, requires, script_name): + """Locate distribution for `requires` and run `script_name` script""" + ns = sys._getframe(1).f_globals + name = ns['__name__'] + ns.clear() + ns['__name__'] = name + self.require(requires)[0].run_script(script_name, ns) + + def __iter__(self): + """Yield distributions for non-duplicate projects in the working set + + The yield order is the order in which the items' path entries were + added to the working set. + """ + seen = {} + for item in self.entries: + if item not in self.entry_keys: + # workaround a cache issue + continue + + for key in self.entry_keys[item]: + if key not in seen: + seen[key] = 1 + yield self.by_key[key] + + def add(self, dist, entry=None, insert=True, replace=False): + """Add `dist` to working set, associated with `entry` + + If `entry` is unspecified, it defaults to the ``.location`` of `dist`. + On exit from this routine, `entry` is added to the end of the working + set's ``.entries`` (if it wasn't already present). + + `dist` is only added to the working set if it's for a project that + doesn't already have a distribution in the set, unless `replace=True`. + If it's added, any callbacks registered with the ``subscribe()`` method + will be called. + """ + if insert: + dist.insert_on(self.entries, entry, replace=replace) + + if entry is None: + entry = dist.location + keys = self.entry_keys.setdefault(entry, []) + keys2 = self.entry_keys.setdefault(dist.location, []) + if not replace and dist.key in self.by_key: + # ignore hidden distros + return + + self.by_key[dist.key] = dist + if dist.key not in keys: + keys.append(dist.key) + if dist.key not in keys2: + keys2.append(dist.key) + self._added_new(dist) + + # FIXME: 'WorkingSet.resolve' is too complex (11) + def resolve(self, requirements, env=None, installer=None, # noqa: C901 + replace_conflicting=False, extras=None): + """List all distributions needed to (recursively) meet `requirements` + + `requirements` must be a sequence of ``Requirement`` objects. `env`, + if supplied, should be an ``Environment`` instance. If + not supplied, it defaults to all distributions available within any + entry or distribution in the working set. `installer`, if supplied, + will be invoked with each requirement that cannot be met by an + already-installed distribution; it should return a ``Distribution`` or + ``None``. + + Unless `replace_conflicting=True`, raises a VersionConflict exception + if + any requirements are found on the path that have the correct name but + the wrong version. Otherwise, if an `installer` is supplied it will be + invoked to obtain the correct version of the requirement and activate + it. + + `extras` is a list of the extras to be used with these requirements. + This is important because extra requirements may look like `my_req; + extra = "my_extra"`, which would otherwise be interpreted as a purely + optional requirement. Instead, we want to be able to assert that these + requirements are truly required. + """ + + # set up the stack + requirements = list(requirements)[::-1] + # set of processed requirements + processed = {} + # key -> dist + best = {} + to_activate = [] + + req_extras = _ReqExtras() + + # Mapping of requirement to set of distributions that required it; + # useful for reporting info about conflicts. + required_by = collections.defaultdict(set) + + while requirements: + # process dependencies breadth-first + req = requirements.pop(0) + if req in processed: + # Ignore cyclic or redundant dependencies + continue + + if not req_extras.markers_pass(req, extras): + continue + + dist = best.get(req.key) + if dist is None: + # Find the best distribution and add it to the map + dist = self.by_key.get(req.key) + if dist is None or (dist not in req and replace_conflicting): + ws = self + if env is None: + if dist is None: + env = Environment(self.entries) + else: + # Use an empty environment and workingset to avoid + # any further conflicts with the conflicting + # distribution + env = Environment([]) + ws = WorkingSet([]) + dist = best[req.key] = env.best_match( + req, ws, installer, + replace_conflicting=replace_conflicting + ) + if dist is None: + requirers = required_by.get(req, None) + raise DistributionNotFound(req, requirers) + to_activate.append(dist) + if dist not in req: + # Oops, the "best" so far conflicts with a dependency + dependent_req = required_by[req] + raise VersionConflict(dist, req).with_context(dependent_req) + + # push the new requirements onto the stack + new_requirements = dist.requires(req.extras)[::-1] + requirements.extend(new_requirements) + + # Register the new requirements needed by req + for new_requirement in new_requirements: + required_by[new_requirement].add(req.project_name) + req_extras[new_requirement] = req.extras + + processed[req] = True + + # return list of distros to activate + return to_activate + + def find_plugins( + self, plugin_env, full_env=None, installer=None, fallback=True): + """Find all activatable distributions in `plugin_env` + + Example usage:: + + distributions, errors = working_set.find_plugins( + Environment(plugin_dirlist) + ) + # add plugins+libs to sys.path + map(working_set.add, distributions) + # display errors + print('Could not load', errors) + + The `plugin_env` should be an ``Environment`` instance that contains + only distributions that are in the project's "plugin directory" or + directories. The `full_env`, if supplied, should be an ``Environment`` + contains all currently-available distributions. If `full_env` is not + supplied, one is created automatically from the ``WorkingSet`` this + method is called on, which will typically mean that every directory on + ``sys.path`` will be scanned for distributions. + + `installer` is a standard installer callback as used by the + ``resolve()`` method. The `fallback` flag indicates whether we should + attempt to resolve older versions of a plugin if the newest version + cannot be resolved. + + This method returns a 2-tuple: (`distributions`, `error_info`), where + `distributions` is a list of the distributions found in `plugin_env` + that were loadable, along with any other distributions that are needed + to resolve their dependencies. `error_info` is a dictionary mapping + unloadable plugin distributions to an exception instance describing the + error that occurred. Usually this will be a ``DistributionNotFound`` or + ``VersionConflict`` instance. + """ + + plugin_projects = list(plugin_env) + # scan project names in alphabetic order + plugin_projects.sort() + + error_info = {} + distributions = {} + + if full_env is None: + env = Environment(self.entries) + env += plugin_env + else: + env = full_env + plugin_env + + shadow_set = self.__class__([]) + # put all our entries in shadow_set + list(map(shadow_set.add, self)) + + for project_name in plugin_projects: + + for dist in plugin_env[project_name]: + + req = [dist.as_requirement()] + + try: + resolvees = shadow_set.resolve(req, env, installer) + + except ResolutionError as v: + # save error info + error_info[dist] = v + if fallback: + # try the next older version of project + continue + else: + # give up on this project, keep going + break + + else: + list(map(shadow_set.add, resolvees)) + distributions.update(dict.fromkeys(resolvees)) + + # success, no need to try any more versions of this project + break + + distributions = list(distributions) + distributions.sort() + + return distributions, error_info + + def require(self, *requirements): + """Ensure that distributions matching `requirements` are activated + + `requirements` must be a string or a (possibly-nested) sequence + thereof, specifying the distributions and versions required. The + return value is a sequence of the distributions that needed to be + activated to fulfill the requirements; all relevant distributions are + included, even if they were already activated in this working set. + """ + needed = self.resolve(parse_requirements(requirements)) + + for dist in needed: + self.add(dist) + + return needed + + def subscribe(self, callback, existing=True): + """Invoke `callback` for all distributions + + If `existing=True` (default), + call on all existing ones, as well. + """ + if callback in self.callbacks: + return + self.callbacks.append(callback) + if not existing: + return + for dist in self: + callback(dist) + + def _added_new(self, dist): + for callback in self.callbacks: + callback(dist) + + def __getstate__(self): + return ( + self.entries[:], self.entry_keys.copy(), self.by_key.copy(), + self.callbacks[:] + ) + + def __setstate__(self, e_k_b_c): + entries, keys, by_key, callbacks = e_k_b_c + self.entries = entries[:] + self.entry_keys = keys.copy() + self.by_key = by_key.copy() + self.callbacks = callbacks[:] + + +class _ReqExtras(dict): + """ + Map each requirement to the extras that demanded it. + """ + + def markers_pass(self, req, extras=None): + """ + Evaluate markers for req against each extra that + demanded it. + + Return False if the req has a marker and fails + evaluation. Otherwise, return True. + """ + extra_evals = ( + req.marker.evaluate({'extra': extra}) + for extra in self.get(req, ()) + (extras or (None,)) + ) + return not req.marker or any(extra_evals) + + +class Environment: + """Searchable snapshot of distributions on a search path""" + + def __init__( + self, search_path=None, platform=get_supported_platform(), + python=PY_MAJOR): + """Snapshot distributions available on a search path + + Any distributions found on `search_path` are added to the environment. + `search_path` should be a sequence of ``sys.path`` items. If not + supplied, ``sys.path`` is used. + + `platform` is an optional string specifying the name of the platform + that platform-specific distributions must be compatible with. If + unspecified, it defaults to the current platform. `python` is an + optional string naming the desired version of Python (e.g. ``'3.6'``); + it defaults to the current version. + + You may explicitly set `platform` (and/or `python`) to ``None`` if you + wish to map *all* distributions, not just those compatible with the + running platform or Python version. + """ + self._distmap = {} + self.platform = platform + self.python = python + self.scan(search_path) + + def can_add(self, dist): + """Is distribution `dist` acceptable for this environment? + + The distribution must match the platform and python version + requirements specified when this environment was created, or False + is returned. + """ + py_compat = ( + self.python is None + or dist.py_version is None + or dist.py_version == self.python + ) + return py_compat and compatible_platforms(dist.platform, self.platform) + + def remove(self, dist): + """Remove `dist` from the environment""" + self._distmap[dist.key].remove(dist) + + def scan(self, search_path=None): + """Scan `search_path` for distributions usable in this environment + + Any distributions found are added to the environment. + `search_path` should be a sequence of ``sys.path`` items. If not + supplied, ``sys.path`` is used. Only distributions conforming to + the platform/python version defined at initialization are added. + """ + if search_path is None: + search_path = sys.path + + for item in search_path: + for dist in find_distributions(item): + self.add(dist) + + def __getitem__(self, project_name): + """Return a newest-to-oldest list of distributions for `project_name` + + Uses case-insensitive `project_name` comparison, assuming all the + project's distributions use their project's name converted to all + lowercase as their key. + + """ + distribution_key = project_name.lower() + return self._distmap.get(distribution_key, []) + + def add(self, dist): + """Add `dist` if we ``can_add()`` it and it has not already been added + """ + if self.can_add(dist) and dist.has_version(): + dists = self._distmap.setdefault(dist.key, []) + if dist not in dists: + dists.append(dist) + dists.sort(key=operator.attrgetter('hashcmp'), reverse=True) + + def best_match( + self, req, working_set, installer=None, replace_conflicting=False): + """Find distribution best matching `req` and usable on `working_set` + + This calls the ``find(req)`` method of the `working_set` to see if a + suitable distribution is already active. (This may raise + ``VersionConflict`` if an unsuitable version of the project is already + active in the specified `working_set`.) If a suitable distribution + isn't active, this method returns the newest distribution in the + environment that meets the ``Requirement`` in `req`. If no suitable + distribution is found, and `installer` is supplied, then the result of + calling the environment's ``obtain(req, installer)`` method will be + returned. + """ + try: + dist = working_set.find(req) + except VersionConflict: + if not replace_conflicting: + raise + dist = None + if dist is not None: + return dist + for dist in self[req.key]: + if dist in req: + return dist + # try to download/install + return self.obtain(req, installer) + + def obtain(self, requirement, installer=None): + """Obtain a distribution matching `requirement` (e.g. via download) + + Obtain a distro that matches requirement (e.g. via download). In the + base ``Environment`` class, this routine just returns + ``installer(requirement)``, unless `installer` is None, in which case + None is returned instead. This method is a hook that allows subclasses + to attempt other ways of obtaining a distribution before falling back + to the `installer` argument.""" + if installer is not None: + return installer(requirement) + + def __iter__(self): + """Yield the unique project names of the available distributions""" + for key in self._distmap.keys(): + if self[key]: + yield key + + def __iadd__(self, other): + """In-place addition of a distribution or environment""" + if isinstance(other, Distribution): + self.add(other) + elif isinstance(other, Environment): + for project in other: + for dist in other[project]: + self.add(dist) + else: + raise TypeError("Can't add %r to environment" % (other,)) + return self + + def __add__(self, other): + """Add an environment or distribution to an environment""" + new = self.__class__([], platform=None, python=None) + for env in self, other: + new += env + return new + + +# XXX backward compatibility +AvailableDistributions = Environment + + +class ExtractionError(RuntimeError): + """An error occurred extracting a resource + + The following attributes are available from instances of this exception: + + manager + The resource manager that raised this exception + + cache_path + The base directory for resource extraction + + original_error + The exception instance that caused extraction to fail + """ + + +class ResourceManager: + """Manage resource extraction and packages""" + extraction_path = None + + def __init__(self): + self.cached_files = {} + + def resource_exists(self, package_or_requirement, resource_name): + """Does the named resource exist?""" + return get_provider(package_or_requirement).has_resource(resource_name) + + def resource_isdir(self, package_or_requirement, resource_name): + """Is the named resource an existing directory?""" + return get_provider(package_or_requirement).resource_isdir( + resource_name + ) + + def resource_filename(self, package_or_requirement, resource_name): + """Return a true filesystem path for specified resource""" + return get_provider(package_or_requirement).get_resource_filename( + self, resource_name + ) + + def resource_stream(self, package_or_requirement, resource_name): + """Return a readable file-like object for specified resource""" + return get_provider(package_or_requirement).get_resource_stream( + self, resource_name + ) + + def resource_string(self, package_or_requirement, resource_name): + """Return specified resource as a string""" + return get_provider(package_or_requirement).get_resource_string( + self, resource_name + ) + + def resource_listdir(self, package_or_requirement, resource_name): + """List the contents of the named resource directory""" + return get_provider(package_or_requirement).resource_listdir( + resource_name + ) + + def extraction_error(self): + """Give an error message for problems extracting file(s)""" + + old_exc = sys.exc_info()[1] + cache_path = self.extraction_path or get_default_cache() + + tmpl = textwrap.dedent(""" + Can't extract file(s) to egg cache + + The following error occurred while trying to extract file(s) + to the Python egg cache: + + {old_exc} + + The Python egg cache directory is currently set to: + + {cache_path} + + Perhaps your account does not have write access to this directory? + You can change the cache directory by setting the PYTHON_EGG_CACHE + environment variable to point to an accessible directory. + """).lstrip() + err = ExtractionError(tmpl.format(**locals())) + err.manager = self + err.cache_path = cache_path + err.original_error = old_exc + raise err + + def get_cache_path(self, archive_name, names=()): + """Return absolute location in cache for `archive_name` and `names` + + The parent directory of the resulting path will be created if it does + not already exist. `archive_name` should be the base filename of the + enclosing egg (which may not be the name of the enclosing zipfile!), + including its ".egg" extension. `names`, if provided, should be a + sequence of path name parts "under" the egg's extraction location. + + This method should only be called by resource providers that need to + obtain an extraction location, and only for names they intend to + extract, as it tracks the generated names for possible cleanup later. + """ + extract_path = self.extraction_path or get_default_cache() + target_path = os.path.join(extract_path, archive_name + '-tmp', *names) + try: + _bypass_ensure_directory(target_path) + except Exception: + self.extraction_error() + + self._warn_unsafe_extraction_path(extract_path) + + self.cached_files[target_path] = 1 + return target_path + + @staticmethod + def _warn_unsafe_extraction_path(path): + """ + If the default extraction path is overridden and set to an insecure + location, such as /tmp, it opens up an opportunity for an attacker to + replace an extracted file with an unauthorized payload. Warn the user + if a known insecure location is used. + + See Distribute #375 for more details. + """ + if os.name == 'nt' and not path.startswith(os.environ['windir']): + # On Windows, permissions are generally restrictive by default + # and temp directories are not writable by other users, so + # bypass the warning. + return + mode = os.stat(path).st_mode + if mode & stat.S_IWOTH or mode & stat.S_IWGRP: + msg = ( + "Extraction path is writable by group/others " + "and vulnerable to attack when " + "used with get_resource_filename ({path}). " + "Consider a more secure " + "location (set with .set_extraction_path or the " + "PYTHON_EGG_CACHE environment variable)." + ).format(**locals()) + warnings.warn(msg, UserWarning) + + def postprocess(self, tempname, filename): + """Perform any platform-specific postprocessing of `tempname` + + This is where Mac header rewrites should be done; other platforms don't + have anything special they should do. + + Resource providers should call this method ONLY after successfully + extracting a compressed resource. They must NOT call it on resources + that are already in the filesystem. + + `tempname` is the current (temporary) name of the file, and `filename` + is the name it will be renamed to by the caller after this routine + returns. + """ + + if os.name == 'posix': + # Make the resource executable + mode = ((os.stat(tempname).st_mode) | 0o555) & 0o7777 + os.chmod(tempname, mode) + + def set_extraction_path(self, path): + """Set the base path where resources will be extracted to, if needed. + + If you do not call this routine before any extractions take place, the + path defaults to the return value of ``get_default_cache()``. (Which + is based on the ``PYTHON_EGG_CACHE`` environment variable, with various + platform-specific fallbacks. See that routine's documentation for more + details.) + + Resources are extracted to subdirectories of this path based upon + information given by the ``IResourceProvider``. You may set this to a + temporary directory, but then you must call ``cleanup_resources()`` to + delete the extracted files when done. There is no guarantee that + ``cleanup_resources()`` will be able to remove all extracted files. + + (Note: you may not change the extraction path for a given resource + manager once resources have been extracted, unless you first call + ``cleanup_resources()``.) + """ + if self.cached_files: + raise ValueError( + "Can't change extraction path, files already extracted" + ) + + self.extraction_path = path + + def cleanup_resources(self, force=False): + """ + Delete all extracted resource files and directories, returning a list + of the file and directory names that could not be successfully removed. + This function does not have any concurrency protection, so it should + generally only be called when the extraction path is a temporary + directory exclusive to a single process. This method is not + automatically called; you must call it explicitly or register it as an + ``atexit`` function if you wish to ensure cleanup of a temporary + directory used for extractions. + """ + # XXX + + +def get_default_cache(): + """ + Return the ``PYTHON_EGG_CACHE`` environment variable + or a platform-relevant user cache dir for an app + named "Python-Eggs". + """ + return ( + os.environ.get('PYTHON_EGG_CACHE') + or appdirs.user_cache_dir(appname='Python-Eggs') + ) + + +def safe_name(name): + """Convert an arbitrary string to a standard distribution name + + Any runs of non-alphanumeric/. characters are replaced with a single '-'. + """ + return re.sub('[^A-Za-z0-9.]+', '-', name) + + +def safe_version(version): + """ + Convert an arbitrary string to a standard version string + """ + try: + # normalize the version + return str(packaging.version.Version(version)) + except packaging.version.InvalidVersion: + version = version.replace(' ', '.') + return re.sub('[^A-Za-z0-9.]+', '-', version) + + +def safe_extra(extra): + """Convert an arbitrary string to a standard 'extra' name + + Any runs of non-alphanumeric characters are replaced with a single '_', + and the result is always lowercased. + """ + return re.sub('[^A-Za-z0-9.-]+', '_', extra).lower() + + +def to_filename(name): + """Convert a project or version name to its filename-escaped form + + Any '-' characters are currently replaced with '_'. + """ + return name.replace('-', '_') + + +def invalid_marker(text): + """ + Validate text as a PEP 508 environment marker; return an exception + if invalid or False otherwise. + """ + try: + evaluate_marker(text) + except SyntaxError as e: + e.filename = None + e.lineno = None + return e + return False + + +def evaluate_marker(text, extra=None): + """ + Evaluate a PEP 508 environment marker. + Return a boolean indicating the marker result in this environment. + Raise SyntaxError if marker is invalid. + + This implementation uses the 'pyparsing' module. + """ + try: + marker = packaging.markers.Marker(text) + return marker.evaluate() + except packaging.markers.InvalidMarker as e: + raise SyntaxError(e) from e + + +class NullProvider: + """Try to implement resources and metadata for arbitrary PEP 302 loaders""" + + egg_name = None + egg_info = None + loader = None + + def __init__(self, module): + self.loader = getattr(module, '__loader__', None) + self.module_path = os.path.dirname(getattr(module, '__file__', '')) + + def get_resource_filename(self, manager, resource_name): + return self._fn(self.module_path, resource_name) + + def get_resource_stream(self, manager, resource_name): + return io.BytesIO(self.get_resource_string(manager, resource_name)) + + def get_resource_string(self, manager, resource_name): + return self._get(self._fn(self.module_path, resource_name)) + + def has_resource(self, resource_name): + return self._has(self._fn(self.module_path, resource_name)) + + def _get_metadata_path(self, name): + return self._fn(self.egg_info, name) + + def has_metadata(self, name): + if not self.egg_info: + return self.egg_info + + path = self._get_metadata_path(name) + return self._has(path) + + def get_metadata(self, name): + if not self.egg_info: + return "" + path = self._get_metadata_path(name) + value = self._get(path) + try: + return value.decode('utf-8') + except UnicodeDecodeError as exc: + # Include the path in the error message to simplify + # troubleshooting, and without changing the exception type. + exc.reason += ' in {} file at path: {}'.format(name, path) + raise + + def get_metadata_lines(self, name): + return yield_lines(self.get_metadata(name)) + + def resource_isdir(self, resource_name): + return self._isdir(self._fn(self.module_path, resource_name)) + + def metadata_isdir(self, name): + return self.egg_info and self._isdir(self._fn(self.egg_info, name)) + + def resource_listdir(self, resource_name): + return self._listdir(self._fn(self.module_path, resource_name)) + + def metadata_listdir(self, name): + if self.egg_info: + return self._listdir(self._fn(self.egg_info, name)) + return [] + + def run_script(self, script_name, namespace): + script = 'scripts/' + script_name + if not self.has_metadata(script): + raise ResolutionError( + "Script {script!r} not found in metadata at {self.egg_info!r}" + .format(**locals()), + ) + script_text = self.get_metadata(script).replace('\r\n', '\n') + script_text = script_text.replace('\r', '\n') + script_filename = self._fn(self.egg_info, script) + namespace['__file__'] = script_filename + if os.path.exists(script_filename): + with open(script_filename) as fid: + source = fid.read() + code = compile(source, script_filename, 'exec') + exec(code, namespace, namespace) + else: + from linecache import cache + cache[script_filename] = ( + len(script_text), 0, script_text.split('\n'), script_filename + ) + script_code = compile(script_text, script_filename, 'exec') + exec(script_code, namespace, namespace) + + def _has(self, path): + raise NotImplementedError( + "Can't perform this operation for unregistered loader type" + ) + + def _isdir(self, path): + raise NotImplementedError( + "Can't perform this operation for unregistered loader type" + ) + + def _listdir(self, path): + raise NotImplementedError( + "Can't perform this operation for unregistered loader type" + ) + + def _fn(self, base, resource_name): + self._validate_resource_path(resource_name) + if resource_name: + return os.path.join(base, *resource_name.split('/')) + return base + + @staticmethod + def _validate_resource_path(path): + """ + Validate the resource paths according to the docs. + https://setuptools.pypa.io/en/latest/pkg_resources.html#basic-resource-access + + >>> warned = getfixture('recwarn') + >>> warnings.simplefilter('always') + >>> vrp = NullProvider._validate_resource_path + >>> vrp('foo/bar.txt') + >>> bool(warned) + False + >>> vrp('../foo/bar.txt') + >>> bool(warned) + True + >>> warned.clear() + >>> vrp('/foo/bar.txt') + >>> bool(warned) + True + >>> vrp('foo/../../bar.txt') + >>> bool(warned) + True + >>> warned.clear() + >>> vrp('foo/f../bar.txt') + >>> bool(warned) + False + + Windows path separators are straight-up disallowed. + >>> vrp(r'\\foo/bar.txt') + Traceback (most recent call last): + ... + ValueError: Use of .. or absolute path in a resource path \ +is not allowed. + + >>> vrp(r'C:\\foo/bar.txt') + Traceback (most recent call last): + ... + ValueError: Use of .. or absolute path in a resource path \ +is not allowed. + + Blank values are allowed + + >>> vrp('') + >>> bool(warned) + False + + Non-string values are not. + + >>> vrp(None) + Traceback (most recent call last): + ... + AttributeError: ... + """ + invalid = ( + os.path.pardir in path.split(posixpath.sep) or + posixpath.isabs(path) or + ntpath.isabs(path) + ) + if not invalid: + return + + msg = "Use of .. or absolute path in a resource path is not allowed." + + # Aggressively disallow Windows absolute paths + if ntpath.isabs(path) and not posixpath.isabs(path): + raise ValueError(msg) + + # for compatibility, warn; in future + # raise ValueError(msg) + warnings.warn( + msg[:-1] + " and will raise exceptions in a future release.", + DeprecationWarning, + stacklevel=4, + ) + + def _get(self, path): + if hasattr(self.loader, 'get_data'): + return self.loader.get_data(path) + raise NotImplementedError( + "Can't perform this operation for loaders without 'get_data()'" + ) + + +register_loader_type(object, NullProvider) + + +def _parents(path): + """ + yield all parents of path including path + """ + last = None + while path != last: + yield path + last = path + path, _ = os.path.split(path) + + +class EggProvider(NullProvider): + """Provider based on a virtual filesystem""" + + def __init__(self, module): + NullProvider.__init__(self, module) + self._setup_prefix() + + def _setup_prefix(self): + # Assume that metadata may be nested inside a "basket" + # of multiple eggs and use module_path instead of .archive. + eggs = filter(_is_egg_path, _parents(self.module_path)) + egg = next(eggs, None) + egg and self._set_egg(egg) + + def _set_egg(self, path): + self.egg_name = os.path.basename(path) + self.egg_info = os.path.join(path, 'EGG-INFO') + self.egg_root = path + + +class DefaultProvider(EggProvider): + """Provides access to package resources in the filesystem""" + + def _has(self, path): + return os.path.exists(path) + + def _isdir(self, path): + return os.path.isdir(path) + + def _listdir(self, path): + return os.listdir(path) + + def get_resource_stream(self, manager, resource_name): + return open(self._fn(self.module_path, resource_name), 'rb') + + def _get(self, path): + with open(path, 'rb') as stream: + return stream.read() + + @classmethod + def _register(cls): + loader_names = 'SourceFileLoader', 'SourcelessFileLoader', + for name in loader_names: + loader_cls = getattr(importlib_machinery, name, type(None)) + register_loader_type(loader_cls, cls) + + +DefaultProvider._register() + + +class EmptyProvider(NullProvider): + """Provider that returns nothing for all requests""" + + module_path = None + + _isdir = _has = lambda self, path: False + + def _get(self, path): + return '' + + def _listdir(self, path): + return [] + + def __init__(self): + pass + + +empty_provider = EmptyProvider() + + +class ZipManifests(dict): + """ + zip manifest builder + """ + + @classmethod + def build(cls, path): + """ + Build a dictionary similar to the zipimport directory + caches, except instead of tuples, store ZipInfo objects. + + Use a platform-specific path separator (os.sep) for the path keys + for compatibility with pypy on Windows. + """ + with zipfile.ZipFile(path) as zfile: + items = ( + ( + name.replace('/', os.sep), + zfile.getinfo(name), + ) + for name in zfile.namelist() + ) + return dict(items) + + load = build + + +class MemoizedZipManifests(ZipManifests): + """ + Memoized zipfile manifests. + """ + manifest_mod = collections.namedtuple('manifest_mod', 'manifest mtime') + + def load(self, path): + """ + Load a manifest at path or return a suitable manifest already loaded. + """ + path = os.path.normpath(path) + mtime = os.stat(path).st_mtime + + if path not in self or self[path].mtime != mtime: + manifest = self.build(path) + self[path] = self.manifest_mod(manifest, mtime) + + return self[path].manifest + + +class ZipProvider(EggProvider): + """Resource support for zips and eggs""" + + eagers = None + _zip_manifests = MemoizedZipManifests() + + def __init__(self, module): + EggProvider.__init__(self, module) + self.zip_pre = self.loader.archive + os.sep + + def _zipinfo_name(self, fspath): + # Convert a virtual filename (full path to file) into a zipfile subpath + # usable with the zipimport directory cache for our target archive + fspath = fspath.rstrip(os.sep) + if fspath == self.loader.archive: + return '' + if fspath.startswith(self.zip_pre): + return fspath[len(self.zip_pre):] + raise AssertionError( + "%s is not a subpath of %s" % (fspath, self.zip_pre) + ) + + def _parts(self, zip_path): + # Convert a zipfile subpath into an egg-relative path part list. + # pseudo-fs path + fspath = self.zip_pre + zip_path + if fspath.startswith(self.egg_root + os.sep): + return fspath[len(self.egg_root) + 1:].split(os.sep) + raise AssertionError( + "%s is not a subpath of %s" % (fspath, self.egg_root) + ) + + @property + def zipinfo(self): + return self._zip_manifests.load(self.loader.archive) + + def get_resource_filename(self, manager, resource_name): + if not self.egg_name: + raise NotImplementedError( + "resource_filename() only supported for .egg, not .zip" + ) + # no need to lock for extraction, since we use temp names + zip_path = self._resource_to_zip(resource_name) + eagers = self._get_eager_resources() + if '/'.join(self._parts(zip_path)) in eagers: + for name in eagers: + self._extract_resource(manager, self._eager_to_zip(name)) + return self._extract_resource(manager, zip_path) + + @staticmethod + def _get_date_and_size(zip_stat): + size = zip_stat.file_size + # ymdhms+wday, yday, dst + date_time = zip_stat.date_time + (0, 0, -1) + # 1980 offset already done + timestamp = time.mktime(date_time) + return timestamp, size + + # FIXME: 'ZipProvider._extract_resource' is too complex (12) + def _extract_resource(self, manager, zip_path): # noqa: C901 + + if zip_path in self._index(): + for name in self._index()[zip_path]: + last = self._extract_resource( + manager, os.path.join(zip_path, name) + ) + # return the extracted directory name + return os.path.dirname(last) + + timestamp, size = self._get_date_and_size(self.zipinfo[zip_path]) + + if not WRITE_SUPPORT: + raise IOError('"os.rename" and "os.unlink" are not supported ' + 'on this platform') + try: + + real_path = manager.get_cache_path( + self.egg_name, self._parts(zip_path) + ) + + if self._is_current(real_path, zip_path): + return real_path + + outf, tmpnam = _mkstemp( + ".$extract", + dir=os.path.dirname(real_path), + ) + os.write(outf, self.loader.get_data(zip_path)) + os.close(outf) + utime(tmpnam, (timestamp, timestamp)) + manager.postprocess(tmpnam, real_path) + + try: + rename(tmpnam, real_path) + + except os.error: + if os.path.isfile(real_path): + if self._is_current(real_path, zip_path): + # the file became current since it was checked above, + # so proceed. + return real_path + # Windows, del old file and retry + elif os.name == 'nt': + unlink(real_path) + rename(tmpnam, real_path) + return real_path + raise + + except os.error: + # report a user-friendly error + manager.extraction_error() + + return real_path + + def _is_current(self, file_path, zip_path): + """ + Return True if the file_path is current for this zip_path + """ + timestamp, size = self._get_date_and_size(self.zipinfo[zip_path]) + if not os.path.isfile(file_path): + return False + stat = os.stat(file_path) + if stat.st_size != size or stat.st_mtime != timestamp: + return False + # check that the contents match + zip_contents = self.loader.get_data(zip_path) + with open(file_path, 'rb') as f: + file_contents = f.read() + return zip_contents == file_contents + + def _get_eager_resources(self): + if self.eagers is None: + eagers = [] + for name in ('native_libs.txt', 'eager_resources.txt'): + if self.has_metadata(name): + eagers.extend(self.get_metadata_lines(name)) + self.eagers = eagers + return self.eagers + + def _index(self): + try: + return self._dirindex + except AttributeError: + ind = {} + for path in self.zipinfo: + parts = path.split(os.sep) + while parts: + parent = os.sep.join(parts[:-1]) + if parent in ind: + ind[parent].append(parts[-1]) + break + else: + ind[parent] = [parts.pop()] + self._dirindex = ind + return ind + + def _has(self, fspath): + zip_path = self._zipinfo_name(fspath) + return zip_path in self.zipinfo or zip_path in self._index() + + def _isdir(self, fspath): + return self._zipinfo_name(fspath) in self._index() + + def _listdir(self, fspath): + return list(self._index().get(self._zipinfo_name(fspath), ())) + + def _eager_to_zip(self, resource_name): + return self._zipinfo_name(self._fn(self.egg_root, resource_name)) + + def _resource_to_zip(self, resource_name): + return self._zipinfo_name(self._fn(self.module_path, resource_name)) + + +register_loader_type(zipimport.zipimporter, ZipProvider) + + +class FileMetadata(EmptyProvider): + """Metadata handler for standalone PKG-INFO files + + Usage:: + + metadata = FileMetadata("/path/to/PKG-INFO") + + This provider rejects all data and metadata requests except for PKG-INFO, + which is treated as existing, and will be the contents of the file at + the provided location. + """ + + def __init__(self, path): + self.path = path + + def _get_metadata_path(self, name): + return self.path + + def has_metadata(self, name): + return name == 'PKG-INFO' and os.path.isfile(self.path) + + def get_metadata(self, name): + if name != 'PKG-INFO': + raise KeyError("No metadata except PKG-INFO is available") + + with io.open(self.path, encoding='utf-8', errors="replace") as f: + metadata = f.read() + self._warn_on_replacement(metadata) + return metadata + + def _warn_on_replacement(self, metadata): + replacement_char = '�' + if replacement_char in metadata: + tmpl = "{self.path} could not be properly decoded in UTF-8" + msg = tmpl.format(**locals()) + warnings.warn(msg) + + def get_metadata_lines(self, name): + return yield_lines(self.get_metadata(name)) + + +class PathMetadata(DefaultProvider): + """Metadata provider for egg directories + + Usage:: + + # Development eggs: + + egg_info = "/path/to/PackageName.egg-info" + base_dir = os.path.dirname(egg_info) + metadata = PathMetadata(base_dir, egg_info) + dist_name = os.path.splitext(os.path.basename(egg_info))[0] + dist = Distribution(basedir, project_name=dist_name, metadata=metadata) + + # Unpacked egg directories: + + egg_path = "/path/to/PackageName-ver-pyver-etc.egg" + metadata = PathMetadata(egg_path, os.path.join(egg_path,'EGG-INFO')) + dist = Distribution.from_filename(egg_path, metadata=metadata) + """ + + def __init__(self, path, egg_info): + self.module_path = path + self.egg_info = egg_info + + +class EggMetadata(ZipProvider): + """Metadata provider for .egg files""" + + def __init__(self, importer): + """Create a metadata provider from a zipimporter""" + + self.zip_pre = importer.archive + os.sep + self.loader = importer + if importer.prefix: + self.module_path = os.path.join(importer.archive, importer.prefix) + else: + self.module_path = importer.archive + self._setup_prefix() + + +_declare_state('dict', _distribution_finders={}) + + +def register_finder(importer_type, distribution_finder): + """Register `distribution_finder` to find distributions in sys.path items + + `importer_type` is the type or class of a PEP 302 "Importer" (sys.path item + handler), and `distribution_finder` is a callable that, passed a path + item and the importer instance, yields ``Distribution`` instances found on + that path item. See ``pkg_resources.find_on_path`` for an example.""" + _distribution_finders[importer_type] = distribution_finder + + +def find_distributions(path_item, only=False): + """Yield distributions accessible via `path_item`""" + importer = get_importer(path_item) + finder = _find_adapter(_distribution_finders, importer) + return finder(importer, path_item, only) + + +def find_eggs_in_zip(importer, path_item, only=False): + """ + Find eggs in zip files; possibly multiple nested eggs. + """ + if importer.archive.endswith('.whl'): + # wheels are not supported with this finder + # they don't have PKG-INFO metadata, and won't ever contain eggs + return + metadata = EggMetadata(importer) + if metadata.has_metadata('PKG-INFO'): + yield Distribution.from_filename(path_item, metadata=metadata) + if only: + # don't yield nested distros + return + for subitem in metadata.resource_listdir(''): + if _is_egg_path(subitem): + subpath = os.path.join(path_item, subitem) + dists = find_eggs_in_zip(zipimport.zipimporter(subpath), subpath) + for dist in dists: + yield dist + elif subitem.lower().endswith(('.dist-info', '.egg-info')): + subpath = os.path.join(path_item, subitem) + submeta = EggMetadata(zipimport.zipimporter(subpath)) + submeta.egg_info = subpath + yield Distribution.from_location(path_item, subitem, submeta) + + +register_finder(zipimport.zipimporter, find_eggs_in_zip) + + +def find_nothing(importer, path_item, only=False): + return () + + +register_finder(object, find_nothing) + + +def _by_version_descending(names): + """ + Given a list of filenames, return them in descending order + by version number. + + >>> names = 'bar', 'foo', 'Python-2.7.10.egg', 'Python-2.7.2.egg' + >>> _by_version_descending(names) + ['Python-2.7.10.egg', 'Python-2.7.2.egg', 'bar', 'foo'] + >>> names = 'Setuptools-1.2.3b1.egg', 'Setuptools-1.2.3.egg' + >>> _by_version_descending(names) + ['Setuptools-1.2.3.egg', 'Setuptools-1.2.3b1.egg'] + >>> names = 'Setuptools-1.2.3b1.egg', 'Setuptools-1.2.3.post1.egg' + >>> _by_version_descending(names) + ['Setuptools-1.2.3.post1.egg', 'Setuptools-1.2.3b1.egg'] + """ + def try_parse(name): + """ + Attempt to parse as a version or return a null version. + """ + try: + return packaging.version.Version(name) + except Exception: + return packaging.version.Version('0') + + def _by_version(name): + """ + Parse each component of the filename + """ + name, ext = os.path.splitext(name) + parts = itertools.chain(name.split('-'), [ext]) + return [try_parse(part) for part in parts] + + return sorted(names, key=_by_version, reverse=True) + + +def find_on_path(importer, path_item, only=False): + """Yield distributions accessible on a sys.path directory""" + path_item = _normalize_cached(path_item) + + if _is_unpacked_egg(path_item): + yield Distribution.from_filename( + path_item, metadata=PathMetadata( + path_item, os.path.join(path_item, 'EGG-INFO') + ) + ) + return + + entries = ( + os.path.join(path_item, child) + for child in safe_listdir(path_item) + ) + + # for performance, before sorting by version, + # screen entries for only those that will yield + # distributions + filtered = ( + entry + for entry in entries + if dist_factory(path_item, entry, only) + ) + + # scan for .egg and .egg-info in directory + path_item_entries = _by_version_descending(filtered) + for entry in path_item_entries: + fullpath = os.path.join(path_item, entry) + factory = dist_factory(path_item, entry, only) + for dist in factory(fullpath): + yield dist + + +def dist_factory(path_item, entry, only): + """Return a dist_factory for the given entry.""" + lower = entry.lower() + is_egg_info = lower.endswith('.egg-info') + is_dist_info = ( + lower.endswith('.dist-info') and + os.path.isdir(os.path.join(path_item, entry)) + ) + is_meta = is_egg_info or is_dist_info + return ( + distributions_from_metadata + if is_meta else + find_distributions + if not only and _is_egg_path(entry) else + resolve_egg_link + if not only and lower.endswith('.egg-link') else + NoDists() + ) + + +class NoDists: + """ + >>> bool(NoDists()) + False + + >>> list(NoDists()('anything')) + [] + """ + def __bool__(self): + return False + + def __call__(self, fullpath): + return iter(()) + + +def safe_listdir(path): + """ + Attempt to list contents of path, but suppress some exceptions. + """ + try: + return os.listdir(path) + except (PermissionError, NotADirectoryError): + pass + except OSError as e: + # Ignore the directory if does not exist, not a directory or + # permission denied + if e.errno not in (errno.ENOTDIR, errno.EACCES, errno.ENOENT): + raise + return () + + +def distributions_from_metadata(path): + root = os.path.dirname(path) + if os.path.isdir(path): + if len(os.listdir(path)) == 0: + # empty metadata dir; skip + return + metadata = PathMetadata(root, path) + else: + metadata = FileMetadata(path) + entry = os.path.basename(path) + yield Distribution.from_location( + root, entry, metadata, precedence=DEVELOP_DIST, + ) + + +def non_empty_lines(path): + """ + Yield non-empty lines from file at path + """ + with open(path) as f: + for line in f: + line = line.strip() + if line: + yield line + + +def resolve_egg_link(path): + """ + Given a path to an .egg-link, resolve distributions + present in the referenced path. + """ + referenced_paths = non_empty_lines(path) + resolved_paths = ( + os.path.join(os.path.dirname(path), ref) + for ref in referenced_paths + ) + dist_groups = map(find_distributions, resolved_paths) + return next(dist_groups, ()) + + +register_finder(pkgutil.ImpImporter, find_on_path) + +if hasattr(importlib_machinery, 'FileFinder'): + register_finder(importlib_machinery.FileFinder, find_on_path) + +_declare_state('dict', _namespace_handlers={}) +_declare_state('dict', _namespace_packages={}) + + +def register_namespace_handler(importer_type, namespace_handler): + """Register `namespace_handler` to declare namespace packages + + `importer_type` is the type or class of a PEP 302 "Importer" (sys.path item + handler), and `namespace_handler` is a callable like this:: + + def namespace_handler(importer, path_entry, moduleName, module): + # return a path_entry to use for child packages + + Namespace handlers are only called if the importer object has already + agreed that it can handle the relevant path item, and they should only + return a subpath if the module __path__ does not already contain an + equivalent subpath. For an example namespace handler, see + ``pkg_resources.file_ns_handler``. + """ + _namespace_handlers[importer_type] = namespace_handler + + +def _handle_ns(packageName, path_item): + """Ensure that named package includes a subpath of path_item (if needed)""" + + importer = get_importer(path_item) + if importer is None: + return None + + # use find_spec (PEP 451) and fall-back to find_module (PEP 302) + try: + loader = importer.find_spec(packageName).loader + except AttributeError: + # capture warnings due to #1111 + with warnings.catch_warnings(): + warnings.simplefilter("ignore") + loader = importer.find_module(packageName) + + if loader is None: + return None + module = sys.modules.get(packageName) + if module is None: + module = sys.modules[packageName] = types.ModuleType(packageName) + module.__path__ = [] + _set_parent_ns(packageName) + elif not hasattr(module, '__path__'): + raise TypeError("Not a package:", packageName) + handler = _find_adapter(_namespace_handlers, importer) + subpath = handler(importer, path_item, packageName, module) + if subpath is not None: + path = module.__path__ + path.append(subpath) + importlib.import_module(packageName) + _rebuild_mod_path(path, packageName, module) + return subpath + + +def _rebuild_mod_path(orig_path, package_name, module): + """ + Rebuild module.__path__ ensuring that all entries are ordered + corresponding to their sys.path order + """ + sys_path = [_normalize_cached(p) for p in sys.path] + + def safe_sys_path_index(entry): + """ + Workaround for #520 and #513. + """ + try: + return sys_path.index(entry) + except ValueError: + return float('inf') + + def position_in_sys_path(path): + """ + Return the ordinal of the path based on its position in sys.path + """ + path_parts = path.split(os.sep) + module_parts = package_name.count('.') + 1 + parts = path_parts[:-module_parts] + return safe_sys_path_index(_normalize_cached(os.sep.join(parts))) + + new_path = sorted(orig_path, key=position_in_sys_path) + new_path = [_normalize_cached(p) for p in new_path] + + if isinstance(module.__path__, list): + module.__path__[:] = new_path + else: + module.__path__ = new_path + + +def declare_namespace(packageName): + """Declare that package 'packageName' is a namespace package""" + + _imp.acquire_lock() + try: + if packageName in _namespace_packages: + return + + path = sys.path + parent, _, _ = packageName.rpartition('.') + + if parent: + declare_namespace(parent) + if parent not in _namespace_packages: + __import__(parent) + try: + path = sys.modules[parent].__path__ + except AttributeError as e: + raise TypeError("Not a package:", parent) from e + + # Track what packages are namespaces, so when new path items are added, + # they can be updated + _namespace_packages.setdefault(parent or None, []).append(packageName) + _namespace_packages.setdefault(packageName, []) + + for path_item in path: + # Ensure all the parent's path items are reflected in the child, + # if they apply + _handle_ns(packageName, path_item) + + finally: + _imp.release_lock() + + +def fixup_namespace_packages(path_item, parent=None): + """Ensure that previously-declared namespace packages include path_item""" + _imp.acquire_lock() + try: + for package in _namespace_packages.get(parent, ()): + subpath = _handle_ns(package, path_item) + if subpath: + fixup_namespace_packages(subpath, package) + finally: + _imp.release_lock() + + +def file_ns_handler(importer, path_item, packageName, module): + """Compute an ns-package subpath for a filesystem or zipfile importer""" + + subpath = os.path.join(path_item, packageName.split('.')[-1]) + normalized = _normalize_cached(subpath) + for item in module.__path__: + if _normalize_cached(item) == normalized: + break + else: + # Only return the path if it's not already there + return subpath + + +register_namespace_handler(pkgutil.ImpImporter, file_ns_handler) +register_namespace_handler(zipimport.zipimporter, file_ns_handler) + +if hasattr(importlib_machinery, 'FileFinder'): + register_namespace_handler(importlib_machinery.FileFinder, file_ns_handler) + + +def null_ns_handler(importer, path_item, packageName, module): + return None + + +register_namespace_handler(object, null_ns_handler) + + +def normalize_path(filename): + """Normalize a file/dir name for comparison purposes""" + return os.path.normcase(os.path.realpath(os.path.normpath( + _cygwin_patch(filename)))) + + +def _cygwin_patch(filename): # pragma: nocover + """ + Contrary to POSIX 2008, on Cygwin, getcwd (3) contains + symlink components. Using + os.path.abspath() works around this limitation. A fix in os.getcwd() + would probably better, in Cygwin even more so, except + that this seems to be by design... + """ + return os.path.abspath(filename) if sys.platform == 'cygwin' else filename + + +def _normalize_cached(filename, _cache={}): + try: + return _cache[filename] + except KeyError: + _cache[filename] = result = normalize_path(filename) + return result + + +def _is_egg_path(path): + """ + Determine if given path appears to be an egg. + """ + return _is_zip_egg(path) or _is_unpacked_egg(path) + + +def _is_zip_egg(path): + return ( + path.lower().endswith('.egg') and + os.path.isfile(path) and + zipfile.is_zipfile(path) + ) + + +def _is_unpacked_egg(path): + """ + Determine if given path appears to be an unpacked egg. + """ + return ( + path.lower().endswith('.egg') and + os.path.isfile(os.path.join(path, 'EGG-INFO', 'PKG-INFO')) + ) + + +def _set_parent_ns(packageName): + parts = packageName.split('.') + name = parts.pop() + if parts: + parent = '.'.join(parts) + setattr(sys.modules[parent], name, sys.modules[packageName]) + + +def _nonblank(str): + return str and not str.startswith('#') + + +@functools.singledispatch +def yield_lines(iterable): + """Yield valid lines of a string or iterable""" + return itertools.chain.from_iterable(map(yield_lines, iterable)) + + +@yield_lines.register(str) +def _(text): + return filter(_nonblank, map(str.strip, text.splitlines())) + + +MODULE = re.compile(r"\w+(\.\w+)*$").match +EGG_NAME = re.compile( + r""" + (?P[^-]+) ( + -(?P[^-]+) ( + -py(?P[^-]+) ( + -(?P.+) + )? + )? + )? + """, + re.VERBOSE | re.IGNORECASE, +).match + + +class EntryPoint: + """Object representing an advertised importable object""" + + def __init__(self, name, module_name, attrs=(), extras=(), dist=None): + if not MODULE(module_name): + raise ValueError("Invalid module name", module_name) + self.name = name + self.module_name = module_name + self.attrs = tuple(attrs) + self.extras = tuple(extras) + self.dist = dist + + def __str__(self): + s = "%s = %s" % (self.name, self.module_name) + if self.attrs: + s += ':' + '.'.join(self.attrs) + if self.extras: + s += ' [%s]' % ','.join(self.extras) + return s + + def __repr__(self): + return "EntryPoint.parse(%r)" % str(self) + + def load(self, require=True, *args, **kwargs): + """ + Require packages for this EntryPoint, then resolve it. + """ + if not require or args or kwargs: + warnings.warn( + "Parameters to load are deprecated. Call .resolve and " + ".require separately.", + PkgResourcesDeprecationWarning, + stacklevel=2, + ) + if require: + self.require(*args, **kwargs) + return self.resolve() + + def resolve(self): + """ + Resolve the entry point from its module and attrs. + """ + module = __import__(self.module_name, fromlist=['__name__'], level=0) + try: + return functools.reduce(getattr, self.attrs, module) + except AttributeError as exc: + raise ImportError(str(exc)) from exc + + def require(self, env=None, installer=None): + if self.extras and not self.dist: + raise UnknownExtra("Can't require() without a distribution", self) + + # Get the requirements for this entry point with all its extras and + # then resolve them. We have to pass `extras` along when resolving so + # that the working set knows what extras we want. Otherwise, for + # dist-info distributions, the working set will assume that the + # requirements for that extra are purely optional and skip over them. + reqs = self.dist.requires(self.extras) + items = working_set.resolve(reqs, env, installer, extras=self.extras) + list(map(working_set.add, items)) + + pattern = re.compile( + r'\s*' + r'(?P.+?)\s*' + r'=\s*' + r'(?P[\w.]+)\s*' + r'(:\s*(?P[\w.]+))?\s*' + r'(?P\[.*\])?\s*$' + ) + + @classmethod + def parse(cls, src, dist=None): + """Parse a single entry point from string `src` + + Entry point syntax follows the form:: + + name = some.module:some.attr [extra1, extra2] + + The entry name and module name are required, but the ``:attrs`` and + ``[extras]`` parts are optional + """ + m = cls.pattern.match(src) + if not m: + msg = "EntryPoint must be in 'name=module:attrs [extras]' format" + raise ValueError(msg, src) + res = m.groupdict() + extras = cls._parse_extras(res['extras']) + attrs = res['attr'].split('.') if res['attr'] else () + return cls(res['name'], res['module'], attrs, extras, dist) + + @classmethod + def _parse_extras(cls, extras_spec): + if not extras_spec: + return () + req = Requirement.parse('x' + extras_spec) + if req.specs: + raise ValueError() + return req.extras + + @classmethod + def parse_group(cls, group, lines, dist=None): + """Parse an entry point group""" + if not MODULE(group): + raise ValueError("Invalid group name", group) + this = {} + for line in yield_lines(lines): + ep = cls.parse(line, dist) + if ep.name in this: + raise ValueError("Duplicate entry point", group, ep.name) + this[ep.name] = ep + return this + + @classmethod + def parse_map(cls, data, dist=None): + """Parse a map of entry point groups""" + if isinstance(data, dict): + data = data.items() + else: + data = split_sections(data) + maps = {} + for group, lines in data: + if group is None: + if not lines: + continue + raise ValueError("Entry points must be listed in groups") + group = group.strip() + if group in maps: + raise ValueError("Duplicate group name", group) + maps[group] = cls.parse_group(group, lines, dist) + return maps + + +def _version_from_file(lines): + """ + Given an iterable of lines from a Metadata file, return + the value of the Version field, if present, or None otherwise. + """ + def is_version_line(line): + return line.lower().startswith('version:') + version_lines = filter(is_version_line, lines) + line = next(iter(version_lines), '') + _, _, value = line.partition(':') + return safe_version(value.strip()) or None + + +class Distribution: + """Wrap an actual or potential sys.path entry w/metadata""" + PKG_INFO = 'PKG-INFO' + + def __init__( + self, location=None, metadata=None, project_name=None, + version=None, py_version=PY_MAJOR, platform=None, + precedence=EGG_DIST): + self.project_name = safe_name(project_name or 'Unknown') + if version is not None: + self._version = safe_version(version) + self.py_version = py_version + self.platform = platform + self.location = location + self.precedence = precedence + self._provider = metadata or empty_provider + + @classmethod + def from_location(cls, location, basename, metadata=None, **kw): + project_name, version, py_version, platform = [None] * 4 + basename, ext = os.path.splitext(basename) + if ext.lower() in _distributionImpl: + cls = _distributionImpl[ext.lower()] + + match = EGG_NAME(basename) + if match: + project_name, version, py_version, platform = match.group( + 'name', 'ver', 'pyver', 'plat' + ) + return cls( + location, metadata, project_name=project_name, version=version, + py_version=py_version, platform=platform, **kw + )._reload_version() + + def _reload_version(self): + return self + + @property + def hashcmp(self): + return ( + self.parsed_version, + self.precedence, + self.key, + self.location, + self.py_version or '', + self.platform or '', + ) + + def __hash__(self): + return hash(self.hashcmp) + + def __lt__(self, other): + return self.hashcmp < other.hashcmp + + def __le__(self, other): + return self.hashcmp <= other.hashcmp + + def __gt__(self, other): + return self.hashcmp > other.hashcmp + + def __ge__(self, other): + return self.hashcmp >= other.hashcmp + + def __eq__(self, other): + if not isinstance(other, self.__class__): + # It's not a Distribution, so they are not equal + return False + return self.hashcmp == other.hashcmp + + def __ne__(self, other): + return not self == other + + # These properties have to be lazy so that we don't have to load any + # metadata until/unless it's actually needed. (i.e., some distributions + # may not know their name or version without loading PKG-INFO) + + @property + def key(self): + try: + return self._key + except AttributeError: + self._key = key = self.project_name.lower() + return key + + @property + def parsed_version(self): + if not hasattr(self, "_parsed_version"): + self._parsed_version = parse_version(self.version) + + return self._parsed_version + + def _warn_legacy_version(self): + LV = packaging.version.LegacyVersion + is_legacy = isinstance(self._parsed_version, LV) + if not is_legacy: + return + + # While an empty version is technically a legacy version and + # is not a valid PEP 440 version, it's also unlikely to + # actually come from someone and instead it is more likely that + # it comes from setuptools attempting to parse a filename and + # including it in the list. So for that we'll gate this warning + # on if the version is anything at all or not. + if not self.version: + return + + tmpl = textwrap.dedent(""" + '{project_name} ({version})' is being parsed as a legacy, + non PEP 440, + version. You may find odd behavior and sort order. + In particular it will be sorted as less than 0.0. It + is recommended to migrate to PEP 440 compatible + versions. + """).strip().replace('\n', ' ') + + warnings.warn(tmpl.format(**vars(self)), PEP440Warning) + + @property + def version(self): + try: + return self._version + except AttributeError as e: + version = self._get_version() + if version is None: + path = self._get_metadata_path_for_display(self.PKG_INFO) + msg = ( + "Missing 'Version:' header and/or {} file at path: {}" + ).format(self.PKG_INFO, path) + raise ValueError(msg, self) from e + + return version + + @property + def _dep_map(self): + """ + A map of extra to its list of (direct) requirements + for this distribution, including the null extra. + """ + try: + return self.__dep_map + except AttributeError: + self.__dep_map = self._filter_extras(self._build_dep_map()) + return self.__dep_map + + @staticmethod + def _filter_extras(dm): + """ + Given a mapping of extras to dependencies, strip off + environment markers and filter out any dependencies + not matching the markers. + """ + for extra in list(filter(None, dm)): + new_extra = extra + reqs = dm.pop(extra) + new_extra, _, marker = extra.partition(':') + fails_marker = marker and ( + invalid_marker(marker) + or not evaluate_marker(marker) + ) + if fails_marker: + reqs = [] + new_extra = safe_extra(new_extra) or None + + dm.setdefault(new_extra, []).extend(reqs) + return dm + + def _build_dep_map(self): + dm = {} + for name in 'requires.txt', 'depends.txt': + for extra, reqs in split_sections(self._get_metadata(name)): + dm.setdefault(extra, []).extend(parse_requirements(reqs)) + return dm + + def requires(self, extras=()): + """List of Requirements needed for this distro if `extras` are used""" + dm = self._dep_map + deps = [] + deps.extend(dm.get(None, ())) + for ext in extras: + try: + deps.extend(dm[safe_extra(ext)]) + except KeyError as e: + raise UnknownExtra( + "%s has no such extra feature %r" % (self, ext) + ) from e + return deps + + def _get_metadata_path_for_display(self, name): + """ + Return the path to the given metadata file, if available. + """ + try: + # We need to access _get_metadata_path() on the provider object + # directly rather than through this class's __getattr__() + # since _get_metadata_path() is marked private. + path = self._provider._get_metadata_path(name) + + # Handle exceptions e.g. in case the distribution's metadata + # provider doesn't support _get_metadata_path(). + except Exception: + return '[could not detect]' + + return path + + def _get_metadata(self, name): + if self.has_metadata(name): + for line in self.get_metadata_lines(name): + yield line + + def _get_version(self): + lines = self._get_metadata(self.PKG_INFO) + version = _version_from_file(lines) + + return version + + def activate(self, path=None, replace=False): + """Ensure distribution is importable on `path` (default=sys.path)""" + if path is None: + path = sys.path + self.insert_on(path, replace=replace) + if path is sys.path: + fixup_namespace_packages(self.location) + for pkg in self._get_metadata('namespace_packages.txt'): + if pkg in sys.modules: + declare_namespace(pkg) + + def egg_name(self): + """Return what this distribution's standard .egg filename should be""" + filename = "%s-%s-py%s" % ( + to_filename(self.project_name), to_filename(self.version), + self.py_version or PY_MAJOR + ) + + if self.platform: + filename += '-' + self.platform + return filename + + def __repr__(self): + if self.location: + return "%s (%s)" % (self, self.location) + else: + return str(self) + + def __str__(self): + try: + version = getattr(self, 'version', None) + except ValueError: + version = None + version = version or "[unknown version]" + return "%s %s" % (self.project_name, version) + + def __getattr__(self, attr): + """Delegate all unrecognized public attributes to .metadata provider""" + if attr.startswith('_'): + raise AttributeError(attr) + return getattr(self._provider, attr) + + def __dir__(self): + return list( + set(super(Distribution, self).__dir__()) + | set( + attr for attr in self._provider.__dir__() + if not attr.startswith('_') + ) + ) + + @classmethod + def from_filename(cls, filename, metadata=None, **kw): + return cls.from_location( + _normalize_cached(filename), os.path.basename(filename), metadata, + **kw + ) + + def as_requirement(self): + """Return a ``Requirement`` that matches this distribution exactly""" + if isinstance(self.parsed_version, packaging.version.Version): + spec = "%s==%s" % (self.project_name, self.parsed_version) + else: + spec = "%s===%s" % (self.project_name, self.parsed_version) + + return Requirement.parse(spec) + + def load_entry_point(self, group, name): + """Return the `name` entry point of `group` or raise ImportError""" + ep = self.get_entry_info(group, name) + if ep is None: + raise ImportError("Entry point %r not found" % ((group, name),)) + return ep.load() + + def get_entry_map(self, group=None): + """Return the entry point map for `group`, or the full entry map""" + try: + ep_map = self._ep_map + except AttributeError: + ep_map = self._ep_map = EntryPoint.parse_map( + self._get_metadata('entry_points.txt'), self + ) + if group is not None: + return ep_map.get(group, {}) + return ep_map + + def get_entry_info(self, group, name): + """Return the EntryPoint object for `group`+`name`, or ``None``""" + return self.get_entry_map(group).get(name) + + # FIXME: 'Distribution.insert_on' is too complex (13) + def insert_on(self, path, loc=None, replace=False): # noqa: C901 + """Ensure self.location is on path + + If replace=False (default): + - If location is already in path anywhere, do nothing. + - Else: + - If it's an egg and its parent directory is on path, + insert just ahead of the parent. + - Else: add to the end of path. + If replace=True: + - If location is already on path anywhere (not eggs) + or higher priority than its parent (eggs) + do nothing. + - Else: + - If it's an egg and its parent directory is on path, + insert just ahead of the parent, + removing any lower-priority entries. + - Else: add it to the front of path. + """ + + loc = loc or self.location + if not loc: + return + + nloc = _normalize_cached(loc) + bdir = os.path.dirname(nloc) + npath = [(p and _normalize_cached(p) or p) for p in path] + + for p, item in enumerate(npath): + if item == nloc: + if replace: + break + else: + # don't modify path (even removing duplicates) if + # found and not replace + return + elif item == bdir and self.precedence == EGG_DIST: + # if it's an .egg, give it precedence over its directory + # UNLESS it's already been added to sys.path and replace=False + if (not replace) and nloc in npath[p:]: + return + if path is sys.path: + self.check_version_conflict() + path.insert(p, loc) + npath.insert(p, nloc) + break + else: + if path is sys.path: + self.check_version_conflict() + if replace: + path.insert(0, loc) + else: + path.append(loc) + return + + # p is the spot where we found or inserted loc; now remove duplicates + while True: + try: + np = npath.index(nloc, p + 1) + except ValueError: + break + else: + del npath[np], path[np] + # ha! + p = np + + return + + def check_version_conflict(self): + if self.key == 'setuptools': + # ignore the inevitable setuptools self-conflicts :( + return + + nsp = dict.fromkeys(self._get_metadata('namespace_packages.txt')) + loc = normalize_path(self.location) + for modname in self._get_metadata('top_level.txt'): + if (modname not in sys.modules or modname in nsp + or modname in _namespace_packages): + continue + if modname in ('pkg_resources', 'setuptools', 'site'): + continue + fn = getattr(sys.modules[modname], '__file__', None) + if fn and (normalize_path(fn).startswith(loc) or + fn.startswith(self.location)): + continue + issue_warning( + "Module %s was already imported from %s, but %s is being added" + " to sys.path" % (modname, fn, self.location), + ) + + def has_version(self): + try: + self.version + except ValueError: + issue_warning("Unbuilt egg for " + repr(self)) + return False + return True + + def clone(self, **kw): + """Copy this distribution, substituting in any changed keyword args""" + names = 'project_name version py_version platform location precedence' + for attr in names.split(): + kw.setdefault(attr, getattr(self, attr, None)) + kw.setdefault('metadata', self._provider) + return self.__class__(**kw) + + @property + def extras(self): + return [dep for dep in self._dep_map if dep] + + +class EggInfoDistribution(Distribution): + def _reload_version(self): + """ + Packages installed by distutils (e.g. numpy or scipy), + which uses an old safe_version, and so + their version numbers can get mangled when + converted to filenames (e.g., 1.11.0.dev0+2329eae to + 1.11.0.dev0_2329eae). These distributions will not be + parsed properly + downstream by Distribution and safe_version, so + take an extra step and try to get the version number from + the metadata file itself instead of the filename. + """ + md_version = self._get_version() + if md_version: + self._version = md_version + return self + + +class DistInfoDistribution(Distribution): + """ + Wrap an actual or potential sys.path entry + w/metadata, .dist-info style. + """ + PKG_INFO = 'METADATA' + EQEQ = re.compile(r"([\(,])\s*(\d.*?)\s*([,\)])") + + @property + def _parsed_pkg_info(self): + """Parse and cache metadata""" + try: + return self._pkg_info + except AttributeError: + metadata = self.get_metadata(self.PKG_INFO) + self._pkg_info = email.parser.Parser().parsestr(metadata) + return self._pkg_info + + @property + def _dep_map(self): + try: + return self.__dep_map + except AttributeError: + self.__dep_map = self._compute_dependencies() + return self.__dep_map + + def _compute_dependencies(self): + """Recompute this distribution's dependencies.""" + dm = self.__dep_map = {None: []} + + reqs = [] + # Including any condition expressions + for req in self._parsed_pkg_info.get_all('Requires-Dist') or []: + reqs.extend(parse_requirements(req)) + + def reqs_for_extra(extra): + for req in reqs: + if not req.marker or req.marker.evaluate({'extra': extra}): + yield req + + common = frozenset(reqs_for_extra(None)) + dm[None].extend(common) + + for extra in self._parsed_pkg_info.get_all('Provides-Extra') or []: + s_extra = safe_extra(extra.strip()) + dm[s_extra] = list(frozenset(reqs_for_extra(extra)) - common) + + return dm + + +_distributionImpl = { + '.egg': Distribution, + '.egg-info': EggInfoDistribution, + '.dist-info': DistInfoDistribution, +} + + +def issue_warning(*args, **kw): + level = 1 + g = globals() + try: + # find the first stack frame that is *not* code in + # the pkg_resources module, to use for the warning + while sys._getframe(level).f_globals is g: + level += 1 + except ValueError: + pass + warnings.warn(stacklevel=level + 1, *args, **kw) + + +def parse_requirements(strs): + """Yield ``Requirement`` objects for each specification in `strs` + + `strs` must be a string, or a (possibly-nested) iterable thereof. + """ + # create a steppable iterator, so we can handle \-continuations + lines = iter(yield_lines(strs)) + + for line in lines: + # Drop comments -- a hash without a space may be in a URL. + if ' #' in line: + line = line[:line.find(' #')] + # If there is a line continuation, drop it, and append the next line. + if line.endswith('\\'): + line = line[:-2].strip() + try: + line += next(lines) + except StopIteration: + return + yield Requirement(line) + + +class RequirementParseError(packaging.requirements.InvalidRequirement): + "Compatibility wrapper for InvalidRequirement" + + +class Requirement(packaging.requirements.Requirement): + def __init__(self, requirement_string): + """DO NOT CALL THIS UNDOCUMENTED METHOD; use Requirement.parse()!""" + super(Requirement, self).__init__(requirement_string) + self.unsafe_name = self.name + project_name = safe_name(self.name) + self.project_name, self.key = project_name, project_name.lower() + self.specs = [ + (spec.operator, spec.version) for spec in self.specifier] + self.extras = tuple(map(safe_extra, self.extras)) + self.hashCmp = ( + self.key, + self.url, + self.specifier, + frozenset(self.extras), + str(self.marker) if self.marker else None, + ) + self.__hash = hash(self.hashCmp) + + def __eq__(self, other): + return ( + isinstance(other, Requirement) and + self.hashCmp == other.hashCmp + ) + + def __ne__(self, other): + return not self == other + + def __contains__(self, item): + if isinstance(item, Distribution): + if item.key != self.key: + return False + + item = item.version + + # Allow prereleases always in order to match the previous behavior of + # this method. In the future this should be smarter and follow PEP 440 + # more accurately. + return self.specifier.contains(item, prereleases=True) + + def __hash__(self): + return self.__hash + + def __repr__(self): + return "Requirement.parse(%r)" % str(self) + + @staticmethod + def parse(s): + req, = parse_requirements(s) + return req + + +def _always_object(classes): + """ + Ensure object appears in the mro even + for old-style classes. + """ + if object not in classes: + return classes + (object,) + return classes + + +def _find_adapter(registry, ob): + """Return an adapter factory for `ob` from `registry`""" + types = _always_object(inspect.getmro(getattr(ob, '__class__', type(ob)))) + for t in types: + if t in registry: + return registry[t] + + +def ensure_directory(path): + """Ensure that the parent directory of `path` exists""" + dirname = os.path.dirname(path) + os.makedirs(dirname, exist_ok=True) + + +def _bypass_ensure_directory(path): + """Sandbox-bypassing version of ensure_directory()""" + if not WRITE_SUPPORT: + raise IOError('"os.mkdir" not supported on this platform.') + dirname, filename = split(path) + if dirname and filename and not isdir(dirname): + _bypass_ensure_directory(dirname) + try: + mkdir(dirname, 0o755) + except FileExistsError: + pass + + +def split_sections(s): + """Split a string or iterable thereof into (section, content) pairs + + Each ``section`` is a stripped version of the section header ("[section]") + and each ``content`` is a list of stripped lines excluding blank lines and + comment-only lines. If there are any such lines before the first section + header, they're returned in a first ``section`` of ``None``. + """ + section = None + content = [] + for line in yield_lines(s): + if line.startswith("["): + if line.endswith("]"): + if section or content: + yield section, content + section = line[1:-1].strip() + content = [] + else: + raise ValueError("Invalid section heading", line) + else: + content.append(line) + + # wrap up last segment + yield section, content + + +def _mkstemp(*args, **kw): + old_open = os.open + try: + # temporarily bypass sandboxing + os.open = os_open + return tempfile.mkstemp(*args, **kw) + finally: + # and then put it back + os.open = old_open + + +# Silence the PEP440Warning by default, so that end users don't get hit by it +# randomly just because they use pkg_resources. We want to append the rule +# because we want earlier uses of filterwarnings to take precedence over this +# one. +warnings.filterwarnings("ignore", category=PEP440Warning, append=True) + + +# from jaraco.functools 1.3 +def _call_aside(f, *args, **kwargs): + f(*args, **kwargs) + return f + + +@_call_aside +def _initialize(g=globals()): + "Set up global resource manager (deliberately not state-saved)" + manager = ResourceManager() + g['_manager'] = manager + g.update( + (name, getattr(manager, name)) + for name in dir(manager) + if not name.startswith('_') + ) + + +class PkgResourcesDeprecationWarning(Warning): + """ + Base class for warning about deprecations in ``pkg_resources`` + + This class is not derived from ``DeprecationWarning``, and as such is + visible by default. + """ + + +@_call_aside +def _initialize_master_working_set(): + """ + Prepare the master working set and make the ``require()`` + API available. + + This function has explicit effects on the global state + of pkg_resources. It is intended to be invoked once at + the initialization of this module. + + Invocation by other packages is unsupported and done + at their own risk. + """ + working_set = WorkingSet._build_master() + _declare_state('object', working_set=working_set) + + require = working_set.require + iter_entry_points = working_set.iter_entry_points + add_activation_listener = working_set.subscribe + run_script = working_set.run_script + # backward compatibility + run_main = run_script + # Activate all distributions already on sys.path with replace=False and + # ensure that all distributions added to the working set in the future + # (e.g. by calling ``require()``) will get activated as well, + # with higher priority (replace=True). + tuple( + dist.activate(replace=False) + for dist in working_set + ) + add_activation_listener( + lambda dist: dist.activate(replace=True), + existing=False, + ) + working_set.entries = [] + # match order + list(map(working_set.add_entry, sys.path)) + globals().update(locals()) diff --git a/llmeval-env/lib/python3.10/site-packages/pkg_resources/__pycache__/__init__.cpython-310.pyc b/llmeval-env/lib/python3.10/site-packages/pkg_resources/__pycache__/__init__.cpython-310.pyc new file mode 100644 index 0000000000000000000000000000000000000000..16d07c0742dbc7fa31a81de7a85f6c274d1104ea Binary files /dev/null and b/llmeval-env/lib/python3.10/site-packages/pkg_resources/__pycache__/__init__.cpython-310.pyc differ diff --git a/llmeval-env/lib/python3.10/site-packages/pkg_resources/_vendor/__init__.py b/llmeval-env/lib/python3.10/site-packages/pkg_resources/_vendor/__init__.py new file mode 100644 index 0000000000000000000000000000000000000000..e69de29bb2d1d6434b8b29ae775ad8c2e48c5391 diff --git a/llmeval-env/lib/python3.10/site-packages/pkg_resources/_vendor/appdirs.py b/llmeval-env/lib/python3.10/site-packages/pkg_resources/_vendor/appdirs.py new file mode 100644 index 0000000000000000000000000000000000000000..ae67001af8b661373edeee2eb327b9f63e630d62 --- /dev/null +++ b/llmeval-env/lib/python3.10/site-packages/pkg_resources/_vendor/appdirs.py @@ -0,0 +1,608 @@ +#!/usr/bin/env python +# -*- coding: utf-8 -*- +# Copyright (c) 2005-2010 ActiveState Software Inc. +# Copyright (c) 2013 Eddy Petrișor + +"""Utilities for determining application-specific dirs. + +See for details and usage. +""" +# Dev Notes: +# - MSDN on where to store app data files: +# http://support.microsoft.com/default.aspx?scid=kb;en-us;310294#XSLTH3194121123120121120120 +# - Mac OS X: http://developer.apple.com/documentation/MacOSX/Conceptual/BPFileSystem/index.html +# - XDG spec for Un*x: http://standards.freedesktop.org/basedir-spec/basedir-spec-latest.html + +__version_info__ = (1, 4, 3) +__version__ = '.'.join(map(str, __version_info__)) + + +import sys +import os + +PY3 = sys.version_info[0] == 3 + +if PY3: + unicode = str + +if sys.platform.startswith('java'): + import platform + os_name = platform.java_ver()[3][0] + if os_name.startswith('Windows'): # "Windows XP", "Windows 7", etc. + system = 'win32' + elif os_name.startswith('Mac'): # "Mac OS X", etc. + system = 'darwin' + else: # "Linux", "SunOS", "FreeBSD", etc. + # Setting this to "linux2" is not ideal, but only Windows or Mac + # are actually checked for and the rest of the module expects + # *sys.platform* style strings. + system = 'linux2' +else: + system = sys.platform + + + +def user_data_dir(appname=None, appauthor=None, version=None, roaming=False): + r"""Return full path to the user-specific data dir for this application. + + "appname" is the name of application. + If None, just the system directory is returned. + "appauthor" (only used on Windows) is the name of the + appauthor or distributing body for this application. Typically + it is the owning company name. This falls back to appname. You may + pass False to disable it. + "version" is an optional version path element to append to the + path. You might want to use this if you want multiple versions + of your app to be able to run independently. If used, this + would typically be ".". + Only applied when appname is present. + "roaming" (boolean, default False) can be set True to use the Windows + roaming appdata directory. That means that for users on a Windows + network setup for roaming profiles, this user data will be + sync'd on login. See + + for a discussion of issues. + + Typical user data directories are: + Mac OS X: ~/Library/Application Support/ + Unix: ~/.local/share/ # or in $XDG_DATA_HOME, if defined + Win XP (not roaming): C:\Documents and Settings\\Application Data\\ + Win XP (roaming): C:\Documents and Settings\\Local Settings\Application Data\\ + Win 7 (not roaming): C:\Users\\AppData\Local\\ + Win 7 (roaming): C:\Users\\AppData\Roaming\\ + + For Unix, we follow the XDG spec and support $XDG_DATA_HOME. + That means, by default "~/.local/share/". + """ + if system == "win32": + if appauthor is None: + appauthor = appname + const = roaming and "CSIDL_APPDATA" or "CSIDL_LOCAL_APPDATA" + path = os.path.normpath(_get_win_folder(const)) + if appname: + if appauthor is not False: + path = os.path.join(path, appauthor, appname) + else: + path = os.path.join(path, appname) + elif system == 'darwin': + path = os.path.expanduser('~/Library/Application Support/') + if appname: + path = os.path.join(path, appname) + else: + path = os.getenv('XDG_DATA_HOME', os.path.expanduser("~/.local/share")) + if appname: + path = os.path.join(path, appname) + if appname and version: + path = os.path.join(path, version) + return path + + +def site_data_dir(appname=None, appauthor=None, version=None, multipath=False): + r"""Return full path to the user-shared data dir for this application. + + "appname" is the name of application. + If None, just the system directory is returned. + "appauthor" (only used on Windows) is the name of the + appauthor or distributing body for this application. Typically + it is the owning company name. This falls back to appname. You may + pass False to disable it. + "version" is an optional version path element to append to the + path. You might want to use this if you want multiple versions + of your app to be able to run independently. If used, this + would typically be ".". + Only applied when appname is present. + "multipath" is an optional parameter only applicable to *nix + which indicates that the entire list of data dirs should be + returned. By default, the first item from XDG_DATA_DIRS is + returned, or '/usr/local/share/', + if XDG_DATA_DIRS is not set + + Typical site data directories are: + Mac OS X: /Library/Application Support/ + Unix: /usr/local/share/ or /usr/share/ + Win XP: C:\Documents and Settings\All Users\Application Data\\ + Vista: (Fail! "C:\ProgramData" is a hidden *system* directory on Vista.) + Win 7: C:\ProgramData\\ # Hidden, but writeable on Win 7. + + For Unix, this is using the $XDG_DATA_DIRS[0] default. + + WARNING: Do not use this on Windows. See the Vista-Fail note above for why. + """ + if system == "win32": + if appauthor is None: + appauthor = appname + path = os.path.normpath(_get_win_folder("CSIDL_COMMON_APPDATA")) + if appname: + if appauthor is not False: + path = os.path.join(path, appauthor, appname) + else: + path = os.path.join(path, appname) + elif system == 'darwin': + path = os.path.expanduser('/Library/Application Support') + if appname: + path = os.path.join(path, appname) + else: + # XDG default for $XDG_DATA_DIRS + # only first, if multipath is False + path = os.getenv('XDG_DATA_DIRS', + os.pathsep.join(['/usr/local/share', '/usr/share'])) + pathlist = [os.path.expanduser(x.rstrip(os.sep)) for x in path.split(os.pathsep)] + if appname: + if version: + appname = os.path.join(appname, version) + pathlist = [os.sep.join([x, appname]) for x in pathlist] + + if multipath: + path = os.pathsep.join(pathlist) + else: + path = pathlist[0] + return path + + if appname and version: + path = os.path.join(path, version) + return path + + +def user_config_dir(appname=None, appauthor=None, version=None, roaming=False): + r"""Return full path to the user-specific config dir for this application. + + "appname" is the name of application. + If None, just the system directory is returned. + "appauthor" (only used on Windows) is the name of the + appauthor or distributing body for this application. Typically + it is the owning company name. This falls back to appname. You may + pass False to disable it. + "version" is an optional version path element to append to the + path. You might want to use this if you want multiple versions + of your app to be able to run independently. If used, this + would typically be ".". + Only applied when appname is present. + "roaming" (boolean, default False) can be set True to use the Windows + roaming appdata directory. That means that for users on a Windows + network setup for roaming profiles, this user data will be + sync'd on login. See + + for a discussion of issues. + + Typical user config directories are: + Mac OS X: same as user_data_dir + Unix: ~/.config/ # or in $XDG_CONFIG_HOME, if defined + Win *: same as user_data_dir + + For Unix, we follow the XDG spec and support $XDG_CONFIG_HOME. + That means, by default "~/.config/". + """ + if system in ["win32", "darwin"]: + path = user_data_dir(appname, appauthor, None, roaming) + else: + path = os.getenv('XDG_CONFIG_HOME', os.path.expanduser("~/.config")) + if appname: + path = os.path.join(path, appname) + if appname and version: + path = os.path.join(path, version) + return path + + +def site_config_dir(appname=None, appauthor=None, version=None, multipath=False): + r"""Return full path to the user-shared data dir for this application. + + "appname" is the name of application. + If None, just the system directory is returned. + "appauthor" (only used on Windows) is the name of the + appauthor or distributing body for this application. Typically + it is the owning company name. This falls back to appname. You may + pass False to disable it. + "version" is an optional version path element to append to the + path. You might want to use this if you want multiple versions + of your app to be able to run independently. If used, this + would typically be ".". + Only applied when appname is present. + "multipath" is an optional parameter only applicable to *nix + which indicates that the entire list of config dirs should be + returned. By default, the first item from XDG_CONFIG_DIRS is + returned, or '/etc/xdg/', if XDG_CONFIG_DIRS is not set + + Typical site config directories are: + Mac OS X: same as site_data_dir + Unix: /etc/xdg/ or $XDG_CONFIG_DIRS[i]/ for each value in + $XDG_CONFIG_DIRS + Win *: same as site_data_dir + Vista: (Fail! "C:\ProgramData" is a hidden *system* directory on Vista.) + + For Unix, this is using the $XDG_CONFIG_DIRS[0] default, if multipath=False + + WARNING: Do not use this on Windows. See the Vista-Fail note above for why. + """ + if system in ["win32", "darwin"]: + path = site_data_dir(appname, appauthor) + if appname and version: + path = os.path.join(path, version) + else: + # XDG default for $XDG_CONFIG_DIRS + # only first, if multipath is False + path = os.getenv('XDG_CONFIG_DIRS', '/etc/xdg') + pathlist = [os.path.expanduser(x.rstrip(os.sep)) for x in path.split(os.pathsep)] + if appname: + if version: + appname = os.path.join(appname, version) + pathlist = [os.sep.join([x, appname]) for x in pathlist] + + if multipath: + path = os.pathsep.join(pathlist) + else: + path = pathlist[0] + return path + + +def user_cache_dir(appname=None, appauthor=None, version=None, opinion=True): + r"""Return full path to the user-specific cache dir for this application. + + "appname" is the name of application. + If None, just the system directory is returned. + "appauthor" (only used on Windows) is the name of the + appauthor or distributing body for this application. Typically + it is the owning company name. This falls back to appname. You may + pass False to disable it. + "version" is an optional version path element to append to the + path. You might want to use this if you want multiple versions + of your app to be able to run independently. If used, this + would typically be ".". + Only applied when appname is present. + "opinion" (boolean) can be False to disable the appending of + "Cache" to the base app data dir for Windows. See + discussion below. + + Typical user cache directories are: + Mac OS X: ~/Library/Caches/ + Unix: ~/.cache/ (XDG default) + Win XP: C:\Documents and Settings\\Local Settings\Application Data\\\Cache + Vista: C:\Users\\AppData\Local\\\Cache + + On Windows the only suggestion in the MSDN docs is that local settings go in + the `CSIDL_LOCAL_APPDATA` directory. This is identical to the non-roaming + app data dir (the default returned by `user_data_dir` above). Apps typically + put cache data somewhere *under* the given dir here. Some examples: + ...\Mozilla\Firefox\Profiles\\Cache + ...\Acme\SuperApp\Cache\1.0 + OPINION: This function appends "Cache" to the `CSIDL_LOCAL_APPDATA` value. + This can be disabled with the `opinion=False` option. + """ + if system == "win32": + if appauthor is None: + appauthor = appname + path = os.path.normpath(_get_win_folder("CSIDL_LOCAL_APPDATA")) + if appname: + if appauthor is not False: + path = os.path.join(path, appauthor, appname) + else: + path = os.path.join(path, appname) + if opinion: + path = os.path.join(path, "Cache") + elif system == 'darwin': + path = os.path.expanduser('~/Library/Caches') + if appname: + path = os.path.join(path, appname) + else: + path = os.getenv('XDG_CACHE_HOME', os.path.expanduser('~/.cache')) + if appname: + path = os.path.join(path, appname) + if appname and version: + path = os.path.join(path, version) + return path + + +def user_state_dir(appname=None, appauthor=None, version=None, roaming=False): + r"""Return full path to the user-specific state dir for this application. + + "appname" is the name of application. + If None, just the system directory is returned. + "appauthor" (only used on Windows) is the name of the + appauthor or distributing body for this application. Typically + it is the owning company name. This falls back to appname. You may + pass False to disable it. + "version" is an optional version path element to append to the + path. You might want to use this if you want multiple versions + of your app to be able to run independently. If used, this + would typically be ".". + Only applied when appname is present. + "roaming" (boolean, default False) can be set True to use the Windows + roaming appdata directory. That means that for users on a Windows + network setup for roaming profiles, this user data will be + sync'd on login. See + + for a discussion of issues. + + Typical user state directories are: + Mac OS X: same as user_data_dir + Unix: ~/.local/state/ # or in $XDG_STATE_HOME, if defined + Win *: same as user_data_dir + + For Unix, we follow this Debian proposal + to extend the XDG spec and support $XDG_STATE_HOME. + + That means, by default "~/.local/state/". + """ + if system in ["win32", "darwin"]: + path = user_data_dir(appname, appauthor, None, roaming) + else: + path = os.getenv('XDG_STATE_HOME', os.path.expanduser("~/.local/state")) + if appname: + path = os.path.join(path, appname) + if appname and version: + path = os.path.join(path, version) + return path + + +def user_log_dir(appname=None, appauthor=None, version=None, opinion=True): + r"""Return full path to the user-specific log dir for this application. + + "appname" is the name of application. + If None, just the system directory is returned. + "appauthor" (only used on Windows) is the name of the + appauthor or distributing body for this application. Typically + it is the owning company name. This falls back to appname. You may + pass False to disable it. + "version" is an optional version path element to append to the + path. You might want to use this if you want multiple versions + of your app to be able to run independently. If used, this + would typically be ".". + Only applied when appname is present. + "opinion" (boolean) can be False to disable the appending of + "Logs" to the base app data dir for Windows, and "log" to the + base cache dir for Unix. See discussion below. + + Typical user log directories are: + Mac OS X: ~/Library/Logs/ + Unix: ~/.cache//log # or under $XDG_CACHE_HOME if defined + Win XP: C:\Documents and Settings\\Local Settings\Application Data\\\Logs + Vista: C:\Users\\AppData\Local\\\Logs + + On Windows the only suggestion in the MSDN docs is that local settings + go in the `CSIDL_LOCAL_APPDATA` directory. (Note: I'm interested in + examples of what some windows apps use for a logs dir.) + + OPINION: This function appends "Logs" to the `CSIDL_LOCAL_APPDATA` + value for Windows and appends "log" to the user cache dir for Unix. + This can be disabled with the `opinion=False` option. + """ + if system == "darwin": + path = os.path.join( + os.path.expanduser('~/Library/Logs'), + appname) + elif system == "win32": + path = user_data_dir(appname, appauthor, version) + version = False + if opinion: + path = os.path.join(path, "Logs") + else: + path = user_cache_dir(appname, appauthor, version) + version = False + if opinion: + path = os.path.join(path, "log") + if appname and version: + path = os.path.join(path, version) + return path + + +class AppDirs(object): + """Convenience wrapper for getting application dirs.""" + def __init__(self, appname=None, appauthor=None, version=None, + roaming=False, multipath=False): + self.appname = appname + self.appauthor = appauthor + self.version = version + self.roaming = roaming + self.multipath = multipath + + @property + def user_data_dir(self): + return user_data_dir(self.appname, self.appauthor, + version=self.version, roaming=self.roaming) + + @property + def site_data_dir(self): + return site_data_dir(self.appname, self.appauthor, + version=self.version, multipath=self.multipath) + + @property + def user_config_dir(self): + return user_config_dir(self.appname, self.appauthor, + version=self.version, roaming=self.roaming) + + @property + def site_config_dir(self): + return site_config_dir(self.appname, self.appauthor, + version=self.version, multipath=self.multipath) + + @property + def user_cache_dir(self): + return user_cache_dir(self.appname, self.appauthor, + version=self.version) + + @property + def user_state_dir(self): + return user_state_dir(self.appname, self.appauthor, + version=self.version) + + @property + def user_log_dir(self): + return user_log_dir(self.appname, self.appauthor, + version=self.version) + + +#---- internal support stuff + +def _get_win_folder_from_registry(csidl_name): + """This is a fallback technique at best. I'm not sure if using the + registry for this guarantees us the correct answer for all CSIDL_* + names. + """ + if PY3: + import winreg as _winreg + else: + import _winreg + + shell_folder_name = { + "CSIDL_APPDATA": "AppData", + "CSIDL_COMMON_APPDATA": "Common AppData", + "CSIDL_LOCAL_APPDATA": "Local AppData", + }[csidl_name] + + key = _winreg.OpenKey( + _winreg.HKEY_CURRENT_USER, + r"Software\Microsoft\Windows\CurrentVersion\Explorer\Shell Folders" + ) + dir, type = _winreg.QueryValueEx(key, shell_folder_name) + return dir + + +def _get_win_folder_with_pywin32(csidl_name): + from win32com.shell import shellcon, shell + dir = shell.SHGetFolderPath(0, getattr(shellcon, csidl_name), 0, 0) + # Try to make this a unicode path because SHGetFolderPath does + # not return unicode strings when there is unicode data in the + # path. + try: + dir = unicode(dir) + + # Downgrade to short path name if have highbit chars. See + # . + has_high_char = False + for c in dir: + if ord(c) > 255: + has_high_char = True + break + if has_high_char: + try: + import win32api + dir = win32api.GetShortPathName(dir) + except ImportError: + pass + except UnicodeError: + pass + return dir + + +def _get_win_folder_with_ctypes(csidl_name): + import ctypes + + csidl_const = { + "CSIDL_APPDATA": 26, + "CSIDL_COMMON_APPDATA": 35, + "CSIDL_LOCAL_APPDATA": 28, + }[csidl_name] + + buf = ctypes.create_unicode_buffer(1024) + ctypes.windll.shell32.SHGetFolderPathW(None, csidl_const, None, 0, buf) + + # Downgrade to short path name if have highbit chars. See + # . + has_high_char = False + for c in buf: + if ord(c) > 255: + has_high_char = True + break + if has_high_char: + buf2 = ctypes.create_unicode_buffer(1024) + if ctypes.windll.kernel32.GetShortPathNameW(buf.value, buf2, 1024): + buf = buf2 + + return buf.value + +def _get_win_folder_with_jna(csidl_name): + import array + from com.sun import jna + from com.sun.jna.platform import win32 + + buf_size = win32.WinDef.MAX_PATH * 2 + buf = array.zeros('c', buf_size) + shell = win32.Shell32.INSTANCE + shell.SHGetFolderPath(None, getattr(win32.ShlObj, csidl_name), None, win32.ShlObj.SHGFP_TYPE_CURRENT, buf) + dir = jna.Native.toString(buf.tostring()).rstrip("\0") + + # Downgrade to short path name if have highbit chars. See + # . + has_high_char = False + for c in dir: + if ord(c) > 255: + has_high_char = True + break + if has_high_char: + buf = array.zeros('c', buf_size) + kernel = win32.Kernel32.INSTANCE + if kernel.GetShortPathName(dir, buf, buf_size): + dir = jna.Native.toString(buf.tostring()).rstrip("\0") + + return dir + +if system == "win32": + try: + import win32com.shell + _get_win_folder = _get_win_folder_with_pywin32 + except ImportError: + try: + from ctypes import windll + _get_win_folder = _get_win_folder_with_ctypes + except ImportError: + try: + import com.sun.jna + _get_win_folder = _get_win_folder_with_jna + except ImportError: + _get_win_folder = _get_win_folder_from_registry + + +#---- self test code + +if __name__ == "__main__": + appname = "MyApp" + appauthor = "MyCompany" + + props = ("user_data_dir", + "user_config_dir", + "user_cache_dir", + "user_state_dir", + "user_log_dir", + "site_data_dir", + "site_config_dir") + + print("-- app dirs %s --" % __version__) + + print("-- app dirs (with optional 'version')") + dirs = AppDirs(appname, appauthor, version="1.0") + for prop in props: + print("%s: %s" % (prop, getattr(dirs, prop))) + + print("\n-- app dirs (without optional 'version')") + dirs = AppDirs(appname, appauthor) + for prop in props: + print("%s: %s" % (prop, getattr(dirs, prop))) + + print("\n-- app dirs (without optional 'appauthor')") + dirs = AppDirs(appname) + for prop in props: + print("%s: %s" % (prop, getattr(dirs, prop))) + + print("\n-- app dirs (with disabled 'appauthor')") + dirs = AppDirs(appname, appauthor=False) + for prop in props: + print("%s: %s" % (prop, getattr(dirs, prop))) diff --git a/llmeval-env/lib/python3.10/site-packages/pkg_resources/_vendor/packaging/__about__.py b/llmeval-env/lib/python3.10/site-packages/pkg_resources/_vendor/packaging/__about__.py new file mode 100644 index 0000000000000000000000000000000000000000..c359122f97125ed630760029f7fd0689f1caefd3 --- /dev/null +++ b/llmeval-env/lib/python3.10/site-packages/pkg_resources/_vendor/packaging/__about__.py @@ -0,0 +1,26 @@ +# This file is dual licensed under the terms of the Apache License, Version +# 2.0, and the BSD License. See the LICENSE file in the root of this repository +# for complete details. + +__all__ = [ + "__title__", + "__summary__", + "__uri__", + "__version__", + "__author__", + "__email__", + "__license__", + "__copyright__", +] + +__title__ = "packaging" +__summary__ = "Core utilities for Python packages" +__uri__ = "https://github.com/pypa/packaging" + +__version__ = "21.2" + +__author__ = "Donald Stufft and individual contributors" +__email__ = "donald@stufft.io" + +__license__ = "BSD-2-Clause or Apache-2.0" +__copyright__ = "2014-2019 %s" % __author__ diff --git a/llmeval-env/lib/python3.10/site-packages/pkg_resources/_vendor/packaging/__init__.py b/llmeval-env/lib/python3.10/site-packages/pkg_resources/_vendor/packaging/__init__.py new file mode 100644 index 0000000000000000000000000000000000000000..3c50c5dcfeeda2efed282200a5c5cc8c5f7542f7 --- /dev/null +++ b/llmeval-env/lib/python3.10/site-packages/pkg_resources/_vendor/packaging/__init__.py @@ -0,0 +1,25 @@ +# This file is dual licensed under the terms of the Apache License, Version +# 2.0, and the BSD License. See the LICENSE file in the root of this repository +# for complete details. + +from .__about__ import ( + __author__, + __copyright__, + __email__, + __license__, + __summary__, + __title__, + __uri__, + __version__, +) + +__all__ = [ + "__title__", + "__summary__", + "__uri__", + "__version__", + "__author__", + "__email__", + "__license__", + "__copyright__", +] diff --git a/llmeval-env/lib/python3.10/site-packages/pkg_resources/_vendor/packaging/__pycache__/__about__.cpython-310.pyc b/llmeval-env/lib/python3.10/site-packages/pkg_resources/_vendor/packaging/__pycache__/__about__.cpython-310.pyc new file mode 100644 index 0000000000000000000000000000000000000000..b98a881e16da616d8038c2e66f28ebfdacc7190e Binary files /dev/null and b/llmeval-env/lib/python3.10/site-packages/pkg_resources/_vendor/packaging/__pycache__/__about__.cpython-310.pyc differ diff --git a/llmeval-env/lib/python3.10/site-packages/pkg_resources/_vendor/packaging/__pycache__/__init__.cpython-310.pyc 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a/llmeval-env/lib/python3.10/site-packages/pkg_resources/_vendor/packaging/_manylinux.py b/llmeval-env/lib/python3.10/site-packages/pkg_resources/_vendor/packaging/_manylinux.py new file mode 100644 index 0000000000000000000000000000000000000000..4c379aa6f69ff56c8f19612002c6e3e939ea6012 --- /dev/null +++ b/llmeval-env/lib/python3.10/site-packages/pkg_resources/_vendor/packaging/_manylinux.py @@ -0,0 +1,301 @@ +import collections +import functools +import os +import re +import struct +import sys +import warnings +from typing import IO, Dict, Iterator, NamedTuple, Optional, Tuple + + +# Python does not provide platform information at sufficient granularity to +# identify the architecture of the running executable in some cases, so we +# determine it dynamically by reading the information from the running +# process. This only applies on Linux, which uses the ELF format. +class _ELFFileHeader: + # https://en.wikipedia.org/wiki/Executable_and_Linkable_Format#File_header + class _InvalidELFFileHeader(ValueError): + """ + An invalid ELF file header was found. + """ + + ELF_MAGIC_NUMBER = 0x7F454C46 + ELFCLASS32 = 1 + ELFCLASS64 = 2 + ELFDATA2LSB = 1 + ELFDATA2MSB = 2 + EM_386 = 3 + EM_S390 = 22 + EM_ARM = 40 + EM_X86_64 = 62 + EF_ARM_ABIMASK = 0xFF000000 + EF_ARM_ABI_VER5 = 0x05000000 + EF_ARM_ABI_FLOAT_HARD = 0x00000400 + + def __init__(self, file: IO[bytes]) -> None: + def unpack(fmt: str) -> int: + try: + data = file.read(struct.calcsize(fmt)) + result: Tuple[int, ...] = struct.unpack(fmt, data) + except struct.error: + raise _ELFFileHeader._InvalidELFFileHeader() + return result[0] + + self.e_ident_magic = unpack(">I") + if self.e_ident_magic != self.ELF_MAGIC_NUMBER: + raise _ELFFileHeader._InvalidELFFileHeader() + self.e_ident_class = unpack("B") + if self.e_ident_class not in {self.ELFCLASS32, self.ELFCLASS64}: + raise _ELFFileHeader._InvalidELFFileHeader() + self.e_ident_data = unpack("B") + if self.e_ident_data not in {self.ELFDATA2LSB, self.ELFDATA2MSB}: + raise _ELFFileHeader._InvalidELFFileHeader() + self.e_ident_version = unpack("B") + self.e_ident_osabi = unpack("B") + self.e_ident_abiversion = unpack("B") + self.e_ident_pad = file.read(7) + format_h = "H" + format_i = "I" + format_q = "Q" + format_p = format_i if self.e_ident_class == self.ELFCLASS32 else format_q + self.e_type = unpack(format_h) + self.e_machine = unpack(format_h) + self.e_version = unpack(format_i) + self.e_entry = unpack(format_p) + self.e_phoff = unpack(format_p) + self.e_shoff = unpack(format_p) + self.e_flags = unpack(format_i) + self.e_ehsize = unpack(format_h) + self.e_phentsize = unpack(format_h) + self.e_phnum = unpack(format_h) + self.e_shentsize = unpack(format_h) + self.e_shnum = unpack(format_h) + self.e_shstrndx = unpack(format_h) + + +def _get_elf_header() -> Optional[_ELFFileHeader]: + try: + with open(sys.executable, "rb") as f: + elf_header = _ELFFileHeader(f) + except (OSError, TypeError, _ELFFileHeader._InvalidELFFileHeader): + return None + return elf_header + + +def _is_linux_armhf() -> bool: + # hard-float ABI can be detected from the ELF header of the running + # process + # https://static.docs.arm.com/ihi0044/g/aaelf32.pdf + elf_header = _get_elf_header() + if elf_header is None: + return False + result = elf_header.e_ident_class == elf_header.ELFCLASS32 + result &= elf_header.e_ident_data == elf_header.ELFDATA2LSB + result &= elf_header.e_machine == elf_header.EM_ARM + result &= ( + elf_header.e_flags & elf_header.EF_ARM_ABIMASK + ) == elf_header.EF_ARM_ABI_VER5 + result &= ( + elf_header.e_flags & elf_header.EF_ARM_ABI_FLOAT_HARD + ) == elf_header.EF_ARM_ABI_FLOAT_HARD + return result + + +def _is_linux_i686() -> bool: + elf_header = _get_elf_header() + if elf_header is None: + return False + result = elf_header.e_ident_class == elf_header.ELFCLASS32 + result &= elf_header.e_ident_data == elf_header.ELFDATA2LSB + result &= elf_header.e_machine == elf_header.EM_386 + return result + + +def _have_compatible_abi(arch: str) -> bool: + if arch == "armv7l": + return _is_linux_armhf() + if arch == "i686": + return _is_linux_i686() + return arch in {"x86_64", "aarch64", "ppc64", "ppc64le", "s390x"} + + +# If glibc ever changes its major version, we need to know what the last +# minor version was, so we can build the complete list of all versions. +# For now, guess what the highest minor version might be, assume it will +# be 50 for testing. Once this actually happens, update the dictionary +# with the actual value. +_LAST_GLIBC_MINOR: Dict[int, int] = collections.defaultdict(lambda: 50) + + +class _GLibCVersion(NamedTuple): + major: int + minor: int + + +def _glibc_version_string_confstr() -> Optional[str]: + """ + Primary implementation of glibc_version_string using os.confstr. + """ + # os.confstr is quite a bit faster than ctypes.DLL. It's also less likely + # to be broken or missing. This strategy is used in the standard library + # platform module. + # https://github.com/python/cpython/blob/fcf1d003bf4f0100c/Lib/platform.py#L175-L183 + try: + # os.confstr("CS_GNU_LIBC_VERSION") returns a string like "glibc 2.17". + version_string = os.confstr("CS_GNU_LIBC_VERSION") + assert version_string is not None + _, version = version_string.split() + except (AssertionError, AttributeError, OSError, ValueError): + # os.confstr() or CS_GNU_LIBC_VERSION not available (or a bad value)... + return None + return version + + +def _glibc_version_string_ctypes() -> Optional[str]: + """ + Fallback implementation of glibc_version_string using ctypes. + """ + try: + import ctypes + except ImportError: + return None + + # ctypes.CDLL(None) internally calls dlopen(NULL), and as the dlopen + # manpage says, "If filename is NULL, then the returned handle is for the + # main program". This way we can let the linker do the work to figure out + # which libc our process is actually using. + # + # We must also handle the special case where the executable is not a + # dynamically linked executable. This can occur when using musl libc, + # for example. In this situation, dlopen() will error, leading to an + # OSError. Interestingly, at least in the case of musl, there is no + # errno set on the OSError. The single string argument used to construct + # OSError comes from libc itself and is therefore not portable to + # hard code here. In any case, failure to call dlopen() means we + # can proceed, so we bail on our attempt. + try: + process_namespace = ctypes.CDLL(None) + except OSError: + return None + + try: + gnu_get_libc_version = process_namespace.gnu_get_libc_version + except AttributeError: + # Symbol doesn't exist -> therefore, we are not linked to + # glibc. + return None + + # Call gnu_get_libc_version, which returns a string like "2.5" + gnu_get_libc_version.restype = ctypes.c_char_p + version_str: str = gnu_get_libc_version() + # py2 / py3 compatibility: + if not isinstance(version_str, str): + version_str = version_str.decode("ascii") + + return version_str + + +def _glibc_version_string() -> Optional[str]: + """Returns glibc version string, or None if not using glibc.""" + return _glibc_version_string_confstr() or _glibc_version_string_ctypes() + + +def _parse_glibc_version(version_str: str) -> Tuple[int, int]: + """Parse glibc version. + + We use a regexp instead of str.split because we want to discard any + random junk that might come after the minor version -- this might happen + in patched/forked versions of glibc (e.g. Linaro's version of glibc + uses version strings like "2.20-2014.11"). See gh-3588. + """ + m = re.match(r"(?P[0-9]+)\.(?P[0-9]+)", version_str) + if not m: + warnings.warn( + "Expected glibc version with 2 components major.minor," + " got: %s" % version_str, + RuntimeWarning, + ) + return -1, -1 + return int(m.group("major")), int(m.group("minor")) + + +@functools.lru_cache() +def _get_glibc_version() -> Tuple[int, int]: + version_str = _glibc_version_string() + if version_str is None: + return (-1, -1) + return _parse_glibc_version(version_str) + + +# From PEP 513, PEP 600 +def _is_compatible(name: str, arch: str, version: _GLibCVersion) -> bool: + sys_glibc = _get_glibc_version() + if sys_glibc < version: + return False + # Check for presence of _manylinux module. + try: + import _manylinux # noqa + except ImportError: + return True + if hasattr(_manylinux, "manylinux_compatible"): + result = _manylinux.manylinux_compatible(version[0], version[1], arch) + if result is not None: + return bool(result) + return True + if version == _GLibCVersion(2, 5): + if hasattr(_manylinux, "manylinux1_compatible"): + return bool(_manylinux.manylinux1_compatible) + if version == _GLibCVersion(2, 12): + if hasattr(_manylinux, "manylinux2010_compatible"): + return bool(_manylinux.manylinux2010_compatible) + if version == _GLibCVersion(2, 17): + if hasattr(_manylinux, "manylinux2014_compatible"): + return bool(_manylinux.manylinux2014_compatible) + return True + + +_LEGACY_MANYLINUX_MAP = { + # CentOS 7 w/ glibc 2.17 (PEP 599) + (2, 17): "manylinux2014", + # CentOS 6 w/ glibc 2.12 (PEP 571) + (2, 12): "manylinux2010", + # CentOS 5 w/ glibc 2.5 (PEP 513) + (2, 5): "manylinux1", +} + + +def platform_tags(linux: str, arch: str) -> Iterator[str]: + if not _have_compatible_abi(arch): + return + # Oldest glibc to be supported regardless of architecture is (2, 17). + too_old_glibc2 = _GLibCVersion(2, 16) + if arch in {"x86_64", "i686"}: + # On x86/i686 also oldest glibc to be supported is (2, 5). + too_old_glibc2 = _GLibCVersion(2, 4) + current_glibc = _GLibCVersion(*_get_glibc_version()) + glibc_max_list = [current_glibc] + # We can assume compatibility across glibc major versions. + # https://sourceware.org/bugzilla/show_bug.cgi?id=24636 + # + # Build a list of maximum glibc versions so that we can + # output the canonical list of all glibc from current_glibc + # down to too_old_glibc2, including all intermediary versions. + for glibc_major in range(current_glibc.major - 1, 1, -1): + glibc_minor = _LAST_GLIBC_MINOR[glibc_major] + glibc_max_list.append(_GLibCVersion(glibc_major, glibc_minor)) + for glibc_max in glibc_max_list: + if glibc_max.major == too_old_glibc2.major: + min_minor = too_old_glibc2.minor + else: + # For other glibc major versions oldest supported is (x, 0). + min_minor = -1 + for glibc_minor in range(glibc_max.minor, min_minor, -1): + glibc_version = _GLibCVersion(glibc_max.major, glibc_minor) + tag = "manylinux_{}_{}".format(*glibc_version) + if _is_compatible(tag, arch, glibc_version): + yield linux.replace("linux", tag) + # Handle the legacy manylinux1, manylinux2010, manylinux2014 tags. + if glibc_version in _LEGACY_MANYLINUX_MAP: + legacy_tag = _LEGACY_MANYLINUX_MAP[glibc_version] + if _is_compatible(legacy_tag, arch, glibc_version): + yield linux.replace("linux", legacy_tag) diff --git a/llmeval-env/lib/python3.10/site-packages/pkg_resources/_vendor/packaging/_musllinux.py b/llmeval-env/lib/python3.10/site-packages/pkg_resources/_vendor/packaging/_musllinux.py new file mode 100644 index 0000000000000000000000000000000000000000..85450fafa34733d81dd8d5c52637a464e5399efa --- /dev/null +++ b/llmeval-env/lib/python3.10/site-packages/pkg_resources/_vendor/packaging/_musllinux.py @@ -0,0 +1,136 @@ +"""PEP 656 support. + +This module implements logic to detect if the currently running Python is +linked against musl, and what musl version is used. +""" + +import contextlib +import functools +import operator +import os +import re +import struct +import subprocess +import sys +from typing import IO, Iterator, NamedTuple, Optional, Tuple + + +def _read_unpacked(f: IO[bytes], fmt: str) -> Tuple[int, ...]: + return struct.unpack(fmt, f.read(struct.calcsize(fmt))) + + +def _parse_ld_musl_from_elf(f: IO[bytes]) -> Optional[str]: + """Detect musl libc location by parsing the Python executable. + + Based on: https://gist.github.com/lyssdod/f51579ae8d93c8657a5564aefc2ffbca + ELF header: https://refspecs.linuxfoundation.org/elf/gabi4+/ch4.eheader.html + """ + f.seek(0) + try: + ident = _read_unpacked(f, "16B") + except struct.error: + return None + if ident[:4] != tuple(b"\x7fELF"): # Invalid magic, not ELF. + return None + f.seek(struct.calcsize("HHI"), 1) # Skip file type, machine, and version. + + try: + # e_fmt: Format for program header. + # p_fmt: Format for section header. + # p_idx: Indexes to find p_type, p_offset, and p_filesz. + e_fmt, p_fmt, p_idx = { + 1: ("IIIIHHH", "IIIIIIII", (0, 1, 4)), # 32-bit. + 2: ("QQQIHHH", "IIQQQQQQ", (0, 2, 5)), # 64-bit. + }[ident[4]] + except KeyError: + return None + else: + p_get = operator.itemgetter(*p_idx) + + # Find the interpreter section and return its content. + try: + _, e_phoff, _, _, _, e_phentsize, e_phnum = _read_unpacked(f, e_fmt) + except struct.error: + return None + for i in range(e_phnum + 1): + f.seek(e_phoff + e_phentsize * i) + try: + p_type, p_offset, p_filesz = p_get(_read_unpacked(f, p_fmt)) + except struct.error: + return None + if p_type != 3: # Not PT_INTERP. + continue + f.seek(p_offset) + interpreter = os.fsdecode(f.read(p_filesz)).strip("\0") + if "musl" not in interpreter: + return None + return interpreter + return None + + +class _MuslVersion(NamedTuple): + major: int + minor: int + + +def _parse_musl_version(output: str) -> Optional[_MuslVersion]: + lines = [n for n in (n.strip() for n in output.splitlines()) if n] + if len(lines) < 2 or lines[0][:4] != "musl": + return None + m = re.match(r"Version (\d+)\.(\d+)", lines[1]) + if not m: + return None + return _MuslVersion(major=int(m.group(1)), minor=int(m.group(2))) + + +@functools.lru_cache() +def _get_musl_version(executable: str) -> Optional[_MuslVersion]: + """Detect currently-running musl runtime version. + + This is done by checking the specified executable's dynamic linking + information, and invoking the loader to parse its output for a version + string. If the loader is musl, the output would be something like:: + + musl libc (x86_64) + Version 1.2.2 + Dynamic Program Loader + """ + with contextlib.ExitStack() as stack: + try: + f = stack.enter_context(open(executable, "rb")) + except IOError: + return None + ld = _parse_ld_musl_from_elf(f) + if not ld: + return None + proc = subprocess.run([ld], stderr=subprocess.PIPE, universal_newlines=True) + return _parse_musl_version(proc.stderr) + + +def platform_tags(arch: str) -> Iterator[str]: + """Generate musllinux tags compatible to the current platform. + + :param arch: Should be the part of platform tag after the ``linux_`` + prefix, e.g. ``x86_64``. The ``linux_`` prefix is assumed as a + prerequisite for the current platform to be musllinux-compatible. + + :returns: An iterator of compatible musllinux tags. + """ + sys_musl = _get_musl_version(sys.executable) + if sys_musl is None: # Python not dynamically linked against musl. + return + for minor in range(sys_musl.minor, -1, -1): + yield f"musllinux_{sys_musl.major}_{minor}_{arch}" + + +if __name__ == "__main__": # pragma: no cover + import sysconfig + + plat = sysconfig.get_platform() + assert plat.startswith("linux-"), "not linux" + + print("plat:", plat) + print("musl:", _get_musl_version(sys.executable)) + print("tags:", end=" ") + for t in platform_tags(re.sub(r"[.-]", "_", plat.split("-", 1)[-1])): + print(t, end="\n ") diff --git a/llmeval-env/lib/python3.10/site-packages/pkg_resources/_vendor/packaging/_structures.py b/llmeval-env/lib/python3.10/site-packages/pkg_resources/_vendor/packaging/_structures.py new file mode 100644 index 0000000000000000000000000000000000000000..951549753afa255148c7c60d868303963f8c1813 --- /dev/null +++ b/llmeval-env/lib/python3.10/site-packages/pkg_resources/_vendor/packaging/_structures.py @@ -0,0 +1,67 @@ +# This file is dual licensed under the terms of the Apache License, Version +# 2.0, and the BSD License. See the LICENSE file in the root of this repository +# for complete details. + + +class InfinityType: + def __repr__(self) -> str: + return "Infinity" + + def __hash__(self) -> int: + return hash(repr(self)) + + def __lt__(self, other: object) -> bool: + return False + + def __le__(self, other: object) -> bool: + return False + + def __eq__(self, other: object) -> bool: + return isinstance(other, self.__class__) + + def __ne__(self, other: object) -> bool: + return not isinstance(other, self.__class__) + + def __gt__(self, other: object) -> bool: + return True + + def __ge__(self, other: object) -> bool: + return True + + def __neg__(self: object) -> "NegativeInfinityType": + return NegativeInfinity + + +Infinity = InfinityType() + + +class NegativeInfinityType: + def __repr__(self) -> str: + return "-Infinity" + + def __hash__(self) -> int: + return hash(repr(self)) + + def __lt__(self, other: object) -> bool: + return True + + def __le__(self, other: object) -> bool: + return True + + def __eq__(self, other: object) -> bool: + return isinstance(other, self.__class__) + + def __ne__(self, other: object) -> bool: + return not isinstance(other, self.__class__) + + def __gt__(self, other: object) -> bool: + return False + + def __ge__(self, other: object) -> bool: + return False + + def __neg__(self: object) -> InfinityType: + return Infinity + + +NegativeInfinity = NegativeInfinityType() diff --git a/llmeval-env/lib/python3.10/site-packages/pkg_resources/_vendor/packaging/markers.py b/llmeval-env/lib/python3.10/site-packages/pkg_resources/_vendor/packaging/markers.py new file mode 100644 index 0000000000000000000000000000000000000000..18769b09a8a34f1e7d63cc61e62cd128ff5f9484 --- /dev/null +++ b/llmeval-env/lib/python3.10/site-packages/pkg_resources/_vendor/packaging/markers.py @@ -0,0 +1,304 @@ +# This file is dual licensed under the terms of the Apache License, Version +# 2.0, and the BSD License. See the LICENSE file in the root of this repository +# for complete details. + +import operator +import os +import platform +import sys +from typing import Any, Callable, Dict, List, Optional, Tuple, Union + +from pkg_resources.extern.pyparsing import ( # noqa: N817 + Forward, + Group, + Literal as L, + ParseException, + ParseResults, + QuotedString, + ZeroOrMore, + stringEnd, + stringStart, +) + +from .specifiers import InvalidSpecifier, Specifier + +__all__ = [ + "InvalidMarker", + "UndefinedComparison", + "UndefinedEnvironmentName", + "Marker", + "default_environment", +] + +Operator = Callable[[str, str], bool] + + +class InvalidMarker(ValueError): + """ + An invalid marker was found, users should refer to PEP 508. + """ + + +class UndefinedComparison(ValueError): + """ + An invalid operation was attempted on a value that doesn't support it. + """ + + +class UndefinedEnvironmentName(ValueError): + """ + A name was attempted to be used that does not exist inside of the + environment. + """ + + +class Node: + def __init__(self, value: Any) -> None: + self.value = value + + def __str__(self) -> str: + return str(self.value) + + def __repr__(self) -> str: + return f"<{self.__class__.__name__}('{self}')>" + + def serialize(self) -> str: + raise NotImplementedError + + +class Variable(Node): + def serialize(self) -> str: + return str(self) + + +class Value(Node): + def serialize(self) -> str: + return f'"{self}"' + + +class Op(Node): + def serialize(self) -> str: + return str(self) + + +VARIABLE = ( + L("implementation_version") + | L("platform_python_implementation") + | L("implementation_name") + | L("python_full_version") + | L("platform_release") + | L("platform_version") + | L("platform_machine") + | L("platform_system") + | L("python_version") + | L("sys_platform") + | L("os_name") + | L("os.name") # PEP-345 + | L("sys.platform") # PEP-345 + | L("platform.version") # PEP-345 + | L("platform.machine") # PEP-345 + | L("platform.python_implementation") # PEP-345 + | L("python_implementation") # undocumented setuptools legacy + | L("extra") # PEP-508 +) +ALIASES = { + "os.name": "os_name", + "sys.platform": "sys_platform", + "platform.version": "platform_version", + "platform.machine": "platform_machine", + "platform.python_implementation": "platform_python_implementation", + "python_implementation": "platform_python_implementation", +} +VARIABLE.setParseAction(lambda s, l, t: Variable(ALIASES.get(t[0], t[0]))) + +VERSION_CMP = ( + L("===") | L("==") | L(">=") | L("<=") | L("!=") | L("~=") | L(">") | L("<") +) + +MARKER_OP = VERSION_CMP | L("not in") | L("in") +MARKER_OP.setParseAction(lambda s, l, t: Op(t[0])) + +MARKER_VALUE = QuotedString("'") | QuotedString('"') +MARKER_VALUE.setParseAction(lambda s, l, t: Value(t[0])) + +BOOLOP = L("and") | L("or") + +MARKER_VAR = VARIABLE | MARKER_VALUE + +MARKER_ITEM = Group(MARKER_VAR + MARKER_OP + MARKER_VAR) +MARKER_ITEM.setParseAction(lambda s, l, t: tuple(t[0])) + +LPAREN = L("(").suppress() +RPAREN = L(")").suppress() + +MARKER_EXPR = Forward() +MARKER_ATOM = MARKER_ITEM | Group(LPAREN + MARKER_EXPR + RPAREN) +MARKER_EXPR << MARKER_ATOM + ZeroOrMore(BOOLOP + MARKER_EXPR) + +MARKER = stringStart + MARKER_EXPR + stringEnd + + +def _coerce_parse_result(results: Union[ParseResults, List[Any]]) -> List[Any]: + if isinstance(results, ParseResults): + return [_coerce_parse_result(i) for i in results] + else: + return results + + +def _format_marker( + marker: Union[List[str], Tuple[Node, ...], str], first: Optional[bool] = True +) -> str: + + assert isinstance(marker, (list, tuple, str)) + + # Sometimes we have a structure like [[...]] which is a single item list + # where the single item is itself it's own list. In that case we want skip + # the rest of this function so that we don't get extraneous () on the + # outside. + if ( + isinstance(marker, list) + and len(marker) == 1 + and isinstance(marker[0], (list, tuple)) + ): + return _format_marker(marker[0]) + + if isinstance(marker, list): + inner = (_format_marker(m, first=False) for m in marker) + if first: + return " ".join(inner) + else: + return "(" + " ".join(inner) + ")" + elif isinstance(marker, tuple): + return " ".join([m.serialize() for m in marker]) + else: + return marker + + +_operators: Dict[str, Operator] = { + "in": lambda lhs, rhs: lhs in rhs, + "not in": lambda lhs, rhs: lhs not in rhs, + "<": operator.lt, + "<=": operator.le, + "==": operator.eq, + "!=": operator.ne, + ">=": operator.ge, + ">": operator.gt, +} + + +def _eval_op(lhs: str, op: Op, rhs: str) -> bool: + try: + spec = Specifier("".join([op.serialize(), rhs])) + except InvalidSpecifier: + pass + else: + return spec.contains(lhs) + + oper: Optional[Operator] = _operators.get(op.serialize()) + if oper is None: + raise UndefinedComparison(f"Undefined {op!r} on {lhs!r} and {rhs!r}.") + + return oper(lhs, rhs) + + +class Undefined: + pass + + +_undefined = Undefined() + + +def _get_env(environment: Dict[str, str], name: str) -> str: + value: Union[str, Undefined] = environment.get(name, _undefined) + + if isinstance(value, Undefined): + raise UndefinedEnvironmentName( + f"{name!r} does not exist in evaluation environment." + ) + + return value + + +def _evaluate_markers(markers: List[Any], environment: Dict[str, str]) -> bool: + groups: List[List[bool]] = [[]] + + for marker in markers: + assert isinstance(marker, (list, tuple, str)) + + if isinstance(marker, list): + groups[-1].append(_evaluate_markers(marker, environment)) + elif isinstance(marker, tuple): + lhs, op, rhs = marker + + if isinstance(lhs, Variable): + lhs_value = _get_env(environment, lhs.value) + rhs_value = rhs.value + else: + lhs_value = lhs.value + rhs_value = _get_env(environment, rhs.value) + + groups[-1].append(_eval_op(lhs_value, op, rhs_value)) + else: + assert marker in ["and", "or"] + if marker == "or": + groups.append([]) + + return any(all(item) for item in groups) + + +def format_full_version(info: "sys._version_info") -> str: + version = "{0.major}.{0.minor}.{0.micro}".format(info) + kind = info.releaselevel + if kind != "final": + version += kind[0] + str(info.serial) + return version + + +def default_environment() -> Dict[str, str]: + iver = format_full_version(sys.implementation.version) + implementation_name = sys.implementation.name + return { + "implementation_name": implementation_name, + "implementation_version": iver, + "os_name": os.name, + "platform_machine": platform.machine(), + "platform_release": platform.release(), + "platform_system": platform.system(), + "platform_version": platform.version(), + "python_full_version": platform.python_version(), + "platform_python_implementation": platform.python_implementation(), + "python_version": ".".join(platform.python_version_tuple()[:2]), + "sys_platform": sys.platform, + } + + +class Marker: + def __init__(self, marker: str) -> None: + try: + self._markers = _coerce_parse_result(MARKER.parseString(marker)) + except ParseException as e: + raise InvalidMarker( + f"Invalid marker: {marker!r}, parse error at " + f"{marker[e.loc : e.loc + 8]!r}" + ) + + def __str__(self) -> str: + return _format_marker(self._markers) + + def __repr__(self) -> str: + return f"" + + def evaluate(self, environment: Optional[Dict[str, str]] = None) -> bool: + """Evaluate a marker. + + Return the boolean from evaluating the given marker against the + environment. environment is an optional argument to override all or + part of the determined environment. + + The environment is determined from the current Python process. + """ + current_environment = default_environment() + if environment is not None: + current_environment.update(environment) + + return _evaluate_markers(self._markers, current_environment) diff --git a/llmeval-env/lib/python3.10/site-packages/pkg_resources/_vendor/packaging/requirements.py b/llmeval-env/lib/python3.10/site-packages/pkg_resources/_vendor/packaging/requirements.py new file mode 100644 index 0000000000000000000000000000000000000000..6af14ec4ce49e633d030611c26f0bd9beaf13e6a --- /dev/null +++ b/llmeval-env/lib/python3.10/site-packages/pkg_resources/_vendor/packaging/requirements.py @@ -0,0 +1,146 @@ +# This file is dual licensed under the terms of the Apache License, Version +# 2.0, and the BSD License. See the LICENSE file in the root of this repository +# for complete details. + +import re +import string +import urllib.parse +from typing import List, Optional as TOptional, Set + +from pkg_resources.extern.pyparsing import ( # noqa + Combine, + Literal as L, + Optional, + ParseException, + Regex, + Word, + ZeroOrMore, + originalTextFor, + stringEnd, + stringStart, +) + +from .markers import MARKER_EXPR, Marker +from .specifiers import LegacySpecifier, Specifier, SpecifierSet + + +class InvalidRequirement(ValueError): + """ + An invalid requirement was found, users should refer to PEP 508. + """ + + +ALPHANUM = Word(string.ascii_letters + string.digits) + +LBRACKET = L("[").suppress() +RBRACKET = L("]").suppress() +LPAREN = L("(").suppress() +RPAREN = L(")").suppress() +COMMA = L(",").suppress() +SEMICOLON = L(";").suppress() +AT = L("@").suppress() + +PUNCTUATION = Word("-_.") +IDENTIFIER_END = ALPHANUM | (ZeroOrMore(PUNCTUATION) + ALPHANUM) +IDENTIFIER = Combine(ALPHANUM + ZeroOrMore(IDENTIFIER_END)) + +NAME = IDENTIFIER("name") +EXTRA = IDENTIFIER + +URI = Regex(r"[^ ]+")("url") +URL = AT + URI + +EXTRAS_LIST = EXTRA + ZeroOrMore(COMMA + EXTRA) +EXTRAS = (LBRACKET + Optional(EXTRAS_LIST) + RBRACKET)("extras") + +VERSION_PEP440 = Regex(Specifier._regex_str, re.VERBOSE | re.IGNORECASE) +VERSION_LEGACY = Regex(LegacySpecifier._regex_str, re.VERBOSE | re.IGNORECASE) + +VERSION_ONE = VERSION_PEP440 ^ VERSION_LEGACY +VERSION_MANY = Combine( + VERSION_ONE + ZeroOrMore(COMMA + VERSION_ONE), joinString=",", adjacent=False +)("_raw_spec") +_VERSION_SPEC = Optional((LPAREN + VERSION_MANY + RPAREN) | VERSION_MANY) +_VERSION_SPEC.setParseAction(lambda s, l, t: t._raw_spec or "") + +VERSION_SPEC = originalTextFor(_VERSION_SPEC)("specifier") +VERSION_SPEC.setParseAction(lambda s, l, t: t[1]) + +MARKER_EXPR = originalTextFor(MARKER_EXPR())("marker") +MARKER_EXPR.setParseAction( + lambda s, l, t: Marker(s[t._original_start : t._original_end]) +) +MARKER_SEPARATOR = SEMICOLON +MARKER = MARKER_SEPARATOR + MARKER_EXPR + +VERSION_AND_MARKER = VERSION_SPEC + Optional(MARKER) +URL_AND_MARKER = URL + Optional(MARKER) + +NAMED_REQUIREMENT = NAME + Optional(EXTRAS) + (URL_AND_MARKER | VERSION_AND_MARKER) + +REQUIREMENT = stringStart + NAMED_REQUIREMENT + stringEnd +# pkg_resources.extern.pyparsing isn't thread safe during initialization, so we do it eagerly, see +# issue #104 +REQUIREMENT.parseString("x[]") + + +class Requirement: + """Parse a requirement. + + Parse a given requirement string into its parts, such as name, specifier, + URL, and extras. Raises InvalidRequirement on a badly-formed requirement + string. + """ + + # TODO: Can we test whether something is contained within a requirement? + # If so how do we do that? Do we need to test against the _name_ of + # the thing as well as the version? What about the markers? + # TODO: Can we normalize the name and extra name? + + def __init__(self, requirement_string: str) -> None: + try: + req = REQUIREMENT.parseString(requirement_string) + except ParseException as e: + raise InvalidRequirement( + f'Parse error at "{ requirement_string[e.loc : e.loc + 8]!r}": {e.msg}' + ) + + self.name: str = req.name + if req.url: + parsed_url = urllib.parse.urlparse(req.url) + if parsed_url.scheme == "file": + if urllib.parse.urlunparse(parsed_url) != req.url: + raise InvalidRequirement("Invalid URL given") + elif not (parsed_url.scheme and parsed_url.netloc) or ( + not parsed_url.scheme and not parsed_url.netloc + ): + raise InvalidRequirement(f"Invalid URL: {req.url}") + self.url: TOptional[str] = req.url + else: + self.url = None + self.extras: Set[str] = set(req.extras.asList() if req.extras else []) + self.specifier: SpecifierSet = SpecifierSet(req.specifier) + self.marker: TOptional[Marker] = req.marker if req.marker else None + + def __str__(self) -> str: + parts: List[str] = [self.name] + + if self.extras: + formatted_extras = ",".join(sorted(self.extras)) + parts.append(f"[{formatted_extras}]") + + if self.specifier: + parts.append(str(self.specifier)) + + if self.url: + parts.append(f"@ {self.url}") + if self.marker: + parts.append(" ") + + if self.marker: + parts.append(f"; {self.marker}") + + return "".join(parts) + + def __repr__(self) -> str: + return f"" diff --git a/llmeval-env/lib/python3.10/site-packages/pkg_resources/_vendor/packaging/specifiers.py b/llmeval-env/lib/python3.10/site-packages/pkg_resources/_vendor/packaging/specifiers.py new file mode 100644 index 0000000000000000000000000000000000000000..ce66bd4addbde1e332e9a42f6eb62adc471193e5 --- /dev/null +++ b/llmeval-env/lib/python3.10/site-packages/pkg_resources/_vendor/packaging/specifiers.py @@ -0,0 +1,828 @@ +# This file is dual licensed under the terms of the Apache License, Version +# 2.0, and the BSD License. See the LICENSE file in the root of this repository +# for complete details. + +import abc +import functools +import itertools +import re +import warnings +from typing import ( + Callable, + Dict, + Iterable, + Iterator, + List, + Optional, + Pattern, + Set, + Tuple, + TypeVar, + Union, +) + +from .utils import canonicalize_version +from .version import LegacyVersion, Version, parse + +ParsedVersion = Union[Version, LegacyVersion] +UnparsedVersion = Union[Version, LegacyVersion, str] +VersionTypeVar = TypeVar("VersionTypeVar", bound=UnparsedVersion) +CallableOperator = Callable[[ParsedVersion, str], bool] + + +class InvalidSpecifier(ValueError): + """ + An invalid specifier was found, users should refer to PEP 440. + """ + + +class BaseSpecifier(metaclass=abc.ABCMeta): + @abc.abstractmethod + def __str__(self) -> str: + """ + Returns the str representation of this Specifier like object. This + should be representative of the Specifier itself. + """ + + @abc.abstractmethod + def __hash__(self) -> int: + """ + Returns a hash value for this Specifier like object. + """ + + @abc.abstractmethod + def __eq__(self, other: object) -> bool: + """ + Returns a boolean representing whether or not the two Specifier like + objects are equal. + """ + + @abc.abstractmethod + def __ne__(self, other: object) -> bool: + """ + Returns a boolean representing whether or not the two Specifier like + objects are not equal. + """ + + @abc.abstractproperty + def prereleases(self) -> Optional[bool]: + """ + Returns whether or not pre-releases as a whole are allowed by this + specifier. + """ + + @prereleases.setter + def prereleases(self, value: bool) -> None: + """ + Sets whether or not pre-releases as a whole are allowed by this + specifier. + """ + + @abc.abstractmethod + def contains(self, item: str, prereleases: Optional[bool] = None) -> bool: + """ + Determines if the given item is contained within this specifier. + """ + + @abc.abstractmethod + def filter( + self, iterable: Iterable[VersionTypeVar], prereleases: Optional[bool] = None + ) -> Iterable[VersionTypeVar]: + """ + Takes an iterable of items and filters them so that only items which + are contained within this specifier are allowed in it. + """ + + +class _IndividualSpecifier(BaseSpecifier): + + _operators: Dict[str, str] = {} + _regex: Pattern[str] + + def __init__(self, spec: str = "", prereleases: Optional[bool] = None) -> None: + match = self._regex.search(spec) + if not match: + raise InvalidSpecifier(f"Invalid specifier: '{spec}'") + + self._spec: Tuple[str, str] = ( + match.group("operator").strip(), + match.group("version").strip(), + ) + + # Store whether or not this Specifier should accept prereleases + self._prereleases = prereleases + + def __repr__(self) -> str: + pre = ( + f", prereleases={self.prereleases!r}" + if self._prereleases is not None + else "" + ) + + return "<{}({!r}{})>".format(self.__class__.__name__, str(self), pre) + + def __str__(self) -> str: + return "{}{}".format(*self._spec) + + @property + def _canonical_spec(self) -> Tuple[str, str]: + return self._spec[0], canonicalize_version(self._spec[1]) + + def __hash__(self) -> int: + return hash(self._canonical_spec) + + def __eq__(self, other: object) -> bool: + if isinstance(other, str): + try: + other = self.__class__(str(other)) + except InvalidSpecifier: + return NotImplemented + elif not isinstance(other, self.__class__): + return NotImplemented + + return self._canonical_spec == other._canonical_spec + + def __ne__(self, other: object) -> bool: + if isinstance(other, str): + try: + other = self.__class__(str(other)) + except InvalidSpecifier: + return NotImplemented + elif not isinstance(other, self.__class__): + return NotImplemented + + return self._spec != other._spec + + def _get_operator(self, op: str) -> CallableOperator: + operator_callable: CallableOperator = getattr( + self, f"_compare_{self._operators[op]}" + ) + return operator_callable + + def _coerce_version(self, version: UnparsedVersion) -> ParsedVersion: + if not isinstance(version, (LegacyVersion, Version)): + version = parse(version) + return version + + @property + def operator(self) -> str: + return self._spec[0] + + @property + def version(self) -> str: + return self._spec[1] + + @property + def prereleases(self) -> Optional[bool]: + return self._prereleases + + @prereleases.setter + def prereleases(self, value: bool) -> None: + self._prereleases = value + + def __contains__(self, item: str) -> bool: + return self.contains(item) + + def contains( + self, item: UnparsedVersion, prereleases: Optional[bool] = None + ) -> bool: + + # Determine if prereleases are to be allowed or not. + if prereleases is None: + prereleases = self.prereleases + + # Normalize item to a Version or LegacyVersion, this allows us to have + # a shortcut for ``"2.0" in Specifier(">=2") + normalized_item = self._coerce_version(item) + + # Determine if we should be supporting prereleases in this specifier + # or not, if we do not support prereleases than we can short circuit + # logic if this version is a prereleases. + if normalized_item.is_prerelease and not prereleases: + return False + + # Actually do the comparison to determine if this item is contained + # within this Specifier or not. + operator_callable: CallableOperator = self._get_operator(self.operator) + return operator_callable(normalized_item, self.version) + + def filter( + self, iterable: Iterable[VersionTypeVar], prereleases: Optional[bool] = None + ) -> Iterable[VersionTypeVar]: + + yielded = False + found_prereleases = [] + + kw = {"prereleases": prereleases if prereleases is not None else True} + + # Attempt to iterate over all the values in the iterable and if any of + # them match, yield them. + for version in iterable: + parsed_version = self._coerce_version(version) + + if self.contains(parsed_version, **kw): + # If our version is a prerelease, and we were not set to allow + # prereleases, then we'll store it for later in case nothing + # else matches this specifier. + if parsed_version.is_prerelease and not ( + prereleases or self.prereleases + ): + found_prereleases.append(version) + # Either this is not a prerelease, or we should have been + # accepting prereleases from the beginning. + else: + yielded = True + yield version + + # Now that we've iterated over everything, determine if we've yielded + # any values, and if we have not and we have any prereleases stored up + # then we will go ahead and yield the prereleases. + if not yielded and found_prereleases: + for version in found_prereleases: + yield version + + +class LegacySpecifier(_IndividualSpecifier): + + _regex_str = r""" + (?P(==|!=|<=|>=|<|>)) + \s* + (?P + [^,;\s)]* # Since this is a "legacy" specifier, and the version + # string can be just about anything, we match everything + # except for whitespace, a semi-colon for marker support, + # a closing paren since versions can be enclosed in + # them, and a comma since it's a version separator. + ) + """ + + _regex = re.compile(r"^\s*" + _regex_str + r"\s*$", re.VERBOSE | re.IGNORECASE) + + _operators = { + "==": "equal", + "!=": "not_equal", + "<=": "less_than_equal", + ">=": "greater_than_equal", + "<": "less_than", + ">": "greater_than", + } + + def __init__(self, spec: str = "", prereleases: Optional[bool] = None) -> None: + super().__init__(spec, prereleases) + + warnings.warn( + "Creating a LegacyVersion has been deprecated and will be " + "removed in the next major release", + DeprecationWarning, + ) + + def _coerce_version(self, version: UnparsedVersion) -> LegacyVersion: + if not isinstance(version, LegacyVersion): + version = LegacyVersion(str(version)) + return version + + def _compare_equal(self, prospective: LegacyVersion, spec: str) -> bool: + return prospective == self._coerce_version(spec) + + def _compare_not_equal(self, prospective: LegacyVersion, spec: str) -> bool: + return prospective != self._coerce_version(spec) + + def _compare_less_than_equal(self, prospective: LegacyVersion, spec: str) -> bool: + return prospective <= self._coerce_version(spec) + + def _compare_greater_than_equal( + self, prospective: LegacyVersion, spec: str + ) -> bool: + return prospective >= self._coerce_version(spec) + + def _compare_less_than(self, prospective: LegacyVersion, spec: str) -> bool: + return prospective < self._coerce_version(spec) + + def _compare_greater_than(self, prospective: LegacyVersion, spec: str) -> bool: + return prospective > self._coerce_version(spec) + + +def _require_version_compare( + fn: Callable[["Specifier", ParsedVersion, str], bool] +) -> Callable[["Specifier", ParsedVersion, str], bool]: + @functools.wraps(fn) + def wrapped(self: "Specifier", prospective: ParsedVersion, spec: str) -> bool: + if not isinstance(prospective, Version): + return False + return fn(self, prospective, spec) + + return wrapped + + +class Specifier(_IndividualSpecifier): + + _regex_str = r""" + (?P(~=|==|!=|<=|>=|<|>|===)) + (?P + (?: + # The identity operators allow for an escape hatch that will + # do an exact string match of the version you wish to install. + # This will not be parsed by PEP 440 and we cannot determine + # any semantic meaning from it. This operator is discouraged + # but included entirely as an escape hatch. + (?<====) # Only match for the identity operator + \s* + [^\s]* # We just match everything, except for whitespace + # since we are only testing for strict identity. + ) + | + (?: + # The (non)equality operators allow for wild card and local + # versions to be specified so we have to define these two + # operators separately to enable that. + (?<===|!=) # Only match for equals and not equals + + \s* + v? + (?:[0-9]+!)? # epoch + [0-9]+(?:\.[0-9]+)* # release + (?: # pre release + [-_\.]? + (a|b|c|rc|alpha|beta|pre|preview) + [-_\.]? + [0-9]* + )? + (?: # post release + (?:-[0-9]+)|(?:[-_\.]?(post|rev|r)[-_\.]?[0-9]*) + )? + + # You cannot use a wild card and a dev or local version + # together so group them with a | and make them optional. + (?: + (?:[-_\.]?dev[-_\.]?[0-9]*)? # dev release + (?:\+[a-z0-9]+(?:[-_\.][a-z0-9]+)*)? # local + | + \.\* # Wild card syntax of .* + )? + ) + | + (?: + # The compatible operator requires at least two digits in the + # release segment. + (?<=~=) # Only match for the compatible operator + + \s* + v? + (?:[0-9]+!)? # epoch + [0-9]+(?:\.[0-9]+)+ # release (We have a + instead of a *) + (?: # pre release + [-_\.]? + (a|b|c|rc|alpha|beta|pre|preview) + [-_\.]? + [0-9]* + )? + (?: # post release + (?:-[0-9]+)|(?:[-_\.]?(post|rev|r)[-_\.]?[0-9]*) + )? + (?:[-_\.]?dev[-_\.]?[0-9]*)? # dev release + ) + | + (?: + # All other operators only allow a sub set of what the + # (non)equality operators do. Specifically they do not allow + # local versions to be specified nor do they allow the prefix + # matching wild cards. + (?=": "greater_than_equal", + "<": "less_than", + ">": "greater_than", + "===": "arbitrary", + } + + @_require_version_compare + def _compare_compatible(self, prospective: ParsedVersion, spec: str) -> bool: + + # Compatible releases have an equivalent combination of >= and ==. That + # is that ~=2.2 is equivalent to >=2.2,==2.*. This allows us to + # implement this in terms of the other specifiers instead of + # implementing it ourselves. The only thing we need to do is construct + # the other specifiers. + + # We want everything but the last item in the version, but we want to + # ignore suffix segments. + prefix = ".".join( + list(itertools.takewhile(_is_not_suffix, _version_split(spec)))[:-1] + ) + + # Add the prefix notation to the end of our string + prefix += ".*" + + return self._get_operator(">=")(prospective, spec) and self._get_operator("==")( + prospective, prefix + ) + + @_require_version_compare + def _compare_equal(self, prospective: ParsedVersion, spec: str) -> bool: + + # We need special logic to handle prefix matching + if spec.endswith(".*"): + # In the case of prefix matching we want to ignore local segment. + prospective = Version(prospective.public) + # Split the spec out by dots, and pretend that there is an implicit + # dot in between a release segment and a pre-release segment. + split_spec = _version_split(spec[:-2]) # Remove the trailing .* + + # Split the prospective version out by dots, and pretend that there + # is an implicit dot in between a release segment and a pre-release + # segment. + split_prospective = _version_split(str(prospective)) + + # Shorten the prospective version to be the same length as the spec + # so that we can determine if the specifier is a prefix of the + # prospective version or not. + shortened_prospective = split_prospective[: len(split_spec)] + + # Pad out our two sides with zeros so that they both equal the same + # length. + padded_spec, padded_prospective = _pad_version( + split_spec, shortened_prospective + ) + + return padded_prospective == padded_spec + else: + # Convert our spec string into a Version + spec_version = Version(spec) + + # If the specifier does not have a local segment, then we want to + # act as if the prospective version also does not have a local + # segment. + if not spec_version.local: + prospective = Version(prospective.public) + + return prospective == spec_version + + @_require_version_compare + def _compare_not_equal(self, prospective: ParsedVersion, spec: str) -> bool: + return not self._compare_equal(prospective, spec) + + @_require_version_compare + def _compare_less_than_equal(self, prospective: ParsedVersion, spec: str) -> bool: + + # NB: Local version identifiers are NOT permitted in the version + # specifier, so local version labels can be universally removed from + # the prospective version. + return Version(prospective.public) <= Version(spec) + + @_require_version_compare + def _compare_greater_than_equal( + self, prospective: ParsedVersion, spec: str + ) -> bool: + + # NB: Local version identifiers are NOT permitted in the version + # specifier, so local version labels can be universally removed from + # the prospective version. + return Version(prospective.public) >= Version(spec) + + @_require_version_compare + def _compare_less_than(self, prospective: ParsedVersion, spec_str: str) -> bool: + + # Convert our spec to a Version instance, since we'll want to work with + # it as a version. + spec = Version(spec_str) + + # Check to see if the prospective version is less than the spec + # version. If it's not we can short circuit and just return False now + # instead of doing extra unneeded work. + if not prospective < spec: + return False + + # This special case is here so that, unless the specifier itself + # includes is a pre-release version, that we do not accept pre-release + # versions for the version mentioned in the specifier (e.g. <3.1 should + # not match 3.1.dev0, but should match 3.0.dev0). + if not spec.is_prerelease and prospective.is_prerelease: + if Version(prospective.base_version) == Version(spec.base_version): + return False + + # If we've gotten to here, it means that prospective version is both + # less than the spec version *and* it's not a pre-release of the same + # version in the spec. + return True + + @_require_version_compare + def _compare_greater_than(self, prospective: ParsedVersion, spec_str: str) -> bool: + + # Convert our spec to a Version instance, since we'll want to work with + # it as a version. + spec = Version(spec_str) + + # Check to see if the prospective version is greater than the spec + # version. If it's not we can short circuit and just return False now + # instead of doing extra unneeded work. + if not prospective > spec: + return False + + # This special case is here so that, unless the specifier itself + # includes is a post-release version, that we do not accept + # post-release versions for the version mentioned in the specifier + # (e.g. >3.1 should not match 3.0.post0, but should match 3.2.post0). + if not spec.is_postrelease and prospective.is_postrelease: + if Version(prospective.base_version) == Version(spec.base_version): + return False + + # Ensure that we do not allow a local version of the version mentioned + # in the specifier, which is technically greater than, to match. + if prospective.local is not None: + if Version(prospective.base_version) == Version(spec.base_version): + return False + + # If we've gotten to here, it means that prospective version is both + # greater than the spec version *and* it's not a pre-release of the + # same version in the spec. + return True + + def _compare_arbitrary(self, prospective: Version, spec: str) -> bool: + return str(prospective).lower() == str(spec).lower() + + @property + def prereleases(self) -> bool: + + # If there is an explicit prereleases set for this, then we'll just + # blindly use that. + if self._prereleases is not None: + return self._prereleases + + # Look at all of our specifiers and determine if they are inclusive + # operators, and if they are if they are including an explicit + # prerelease. + operator, version = self._spec + if operator in ["==", ">=", "<=", "~=", "==="]: + # The == specifier can include a trailing .*, if it does we + # want to remove before parsing. + if operator == "==" and version.endswith(".*"): + version = version[:-2] + + # Parse the version, and if it is a pre-release than this + # specifier allows pre-releases. + if parse(version).is_prerelease: + return True + + return False + + @prereleases.setter + def prereleases(self, value: bool) -> None: + self._prereleases = value + + +_prefix_regex = re.compile(r"^([0-9]+)((?:a|b|c|rc)[0-9]+)$") + + +def _version_split(version: str) -> List[str]: + result: List[str] = [] + for item in version.split("."): + match = _prefix_regex.search(item) + if match: + result.extend(match.groups()) + else: + result.append(item) + return result + + +def _is_not_suffix(segment: str) -> bool: + return not any( + segment.startswith(prefix) for prefix in ("dev", "a", "b", "rc", "post") + ) + + +def _pad_version(left: List[str], right: List[str]) -> Tuple[List[str], List[str]]: + left_split, right_split = [], [] + + # Get the release segment of our versions + left_split.append(list(itertools.takewhile(lambda x: x.isdigit(), left))) + right_split.append(list(itertools.takewhile(lambda x: x.isdigit(), right))) + + # Get the rest of our versions + left_split.append(left[len(left_split[0]) :]) + right_split.append(right[len(right_split[0]) :]) + + # Insert our padding + left_split.insert(1, ["0"] * max(0, len(right_split[0]) - len(left_split[0]))) + right_split.insert(1, ["0"] * max(0, len(left_split[0]) - len(right_split[0]))) + + return (list(itertools.chain(*left_split)), list(itertools.chain(*right_split))) + + +class SpecifierSet(BaseSpecifier): + def __init__( + self, specifiers: str = "", prereleases: Optional[bool] = None + ) -> None: + + # Split on , to break each individual specifier into it's own item, and + # strip each item to remove leading/trailing whitespace. + split_specifiers = [s.strip() for s in specifiers.split(",") if s.strip()] + + # Parsed each individual specifier, attempting first to make it a + # Specifier and falling back to a LegacySpecifier. + parsed: Set[_IndividualSpecifier] = set() + for specifier in split_specifiers: + try: + parsed.add(Specifier(specifier)) + except InvalidSpecifier: + parsed.add(LegacySpecifier(specifier)) + + # Turn our parsed specifiers into a frozen set and save them for later. + self._specs = frozenset(parsed) + + # Store our prereleases value so we can use it later to determine if + # we accept prereleases or not. + self._prereleases = prereleases + + def __repr__(self) -> str: + pre = ( + f", prereleases={self.prereleases!r}" + if self._prereleases is not None + else "" + ) + + return "".format(str(self), pre) + + def __str__(self) -> str: + return ",".join(sorted(str(s) for s in self._specs)) + + def __hash__(self) -> int: + return hash(self._specs) + + def __and__(self, other: Union["SpecifierSet", str]) -> "SpecifierSet": + if isinstance(other, str): + other = SpecifierSet(other) + elif not isinstance(other, SpecifierSet): + return NotImplemented + + specifier = SpecifierSet() + specifier._specs = frozenset(self._specs | other._specs) + + if self._prereleases is None and other._prereleases is not None: + specifier._prereleases = other._prereleases + elif self._prereleases is not None and other._prereleases is None: + specifier._prereleases = self._prereleases + elif self._prereleases == other._prereleases: + specifier._prereleases = self._prereleases + else: + raise ValueError( + "Cannot combine SpecifierSets with True and False prerelease " + "overrides." + ) + + return specifier + + def __eq__(self, other: object) -> bool: + if isinstance(other, (str, _IndividualSpecifier)): + other = SpecifierSet(str(other)) + elif not isinstance(other, SpecifierSet): + return NotImplemented + + return self._specs == other._specs + + def __ne__(self, other: object) -> bool: + if isinstance(other, (str, _IndividualSpecifier)): + other = SpecifierSet(str(other)) + elif not isinstance(other, SpecifierSet): + return NotImplemented + + return self._specs != other._specs + + def __len__(self) -> int: + return len(self._specs) + + def __iter__(self) -> Iterator[_IndividualSpecifier]: + return iter(self._specs) + + @property + def prereleases(self) -> Optional[bool]: + + # If we have been given an explicit prerelease modifier, then we'll + # pass that through here. + if self._prereleases is not None: + return self._prereleases + + # If we don't have any specifiers, and we don't have a forced value, + # then we'll just return None since we don't know if this should have + # pre-releases or not. + if not self._specs: + return None + + # Otherwise we'll see if any of the given specifiers accept + # prereleases, if any of them do we'll return True, otherwise False. + return any(s.prereleases for s in self._specs) + + @prereleases.setter + def prereleases(self, value: bool) -> None: + self._prereleases = value + + def __contains__(self, item: UnparsedVersion) -> bool: + return self.contains(item) + + def contains( + self, item: UnparsedVersion, prereleases: Optional[bool] = None + ) -> bool: + + # Ensure that our item is a Version or LegacyVersion instance. + if not isinstance(item, (LegacyVersion, Version)): + item = parse(item) + + # Determine if we're forcing a prerelease or not, if we're not forcing + # one for this particular filter call, then we'll use whatever the + # SpecifierSet thinks for whether or not we should support prereleases. + if prereleases is None: + prereleases = self.prereleases + + # We can determine if we're going to allow pre-releases by looking to + # see if any of the underlying items supports them. If none of them do + # and this item is a pre-release then we do not allow it and we can + # short circuit that here. + # Note: This means that 1.0.dev1 would not be contained in something + # like >=1.0.devabc however it would be in >=1.0.debabc,>0.0.dev0 + if not prereleases and item.is_prerelease: + return False + + # We simply dispatch to the underlying specs here to make sure that the + # given version is contained within all of them. + # Note: This use of all() here means that an empty set of specifiers + # will always return True, this is an explicit design decision. + return all(s.contains(item, prereleases=prereleases) for s in self._specs) + + def filter( + self, iterable: Iterable[VersionTypeVar], prereleases: Optional[bool] = None + ) -> Iterable[VersionTypeVar]: + + # Determine if we're forcing a prerelease or not, if we're not forcing + # one for this particular filter call, then we'll use whatever the + # SpecifierSet thinks for whether or not we should support prereleases. + if prereleases is None: + prereleases = self.prereleases + + # If we have any specifiers, then we want to wrap our iterable in the + # filter method for each one, this will act as a logical AND amongst + # each specifier. + if self._specs: + for spec in self._specs: + iterable = spec.filter(iterable, prereleases=bool(prereleases)) + return iterable + # If we do not have any specifiers, then we need to have a rough filter + # which will filter out any pre-releases, unless there are no final + # releases, and which will filter out LegacyVersion in general. + else: + filtered: List[VersionTypeVar] = [] + found_prereleases: List[VersionTypeVar] = [] + + item: UnparsedVersion + parsed_version: Union[Version, LegacyVersion] + + for item in iterable: + # Ensure that we some kind of Version class for this item. + if not isinstance(item, (LegacyVersion, Version)): + parsed_version = parse(item) + else: + parsed_version = item + + # Filter out any item which is parsed as a LegacyVersion + if isinstance(parsed_version, LegacyVersion): + continue + + # Store any item which is a pre-release for later unless we've + # already found a final version or we are accepting prereleases + if parsed_version.is_prerelease and not prereleases: + if not filtered: + found_prereleases.append(item) + else: + filtered.append(item) + + # If we've found no items except for pre-releases, then we'll go + # ahead and use the pre-releases + if not filtered and found_prereleases and prereleases is None: + return found_prereleases + + return filtered diff --git a/llmeval-env/lib/python3.10/site-packages/pkg_resources/_vendor/packaging/tags.py b/llmeval-env/lib/python3.10/site-packages/pkg_resources/_vendor/packaging/tags.py new file mode 100644 index 0000000000000000000000000000000000000000..e65890a90cd709489865750e953bf347720c75cd --- /dev/null +++ b/llmeval-env/lib/python3.10/site-packages/pkg_resources/_vendor/packaging/tags.py @@ -0,0 +1,484 @@ +# This file is dual licensed under the terms of the Apache License, Version +# 2.0, and the BSD License. See the LICENSE file in the root of this repository +# for complete details. + +import logging +import platform +import sys +import sysconfig +from importlib.machinery import EXTENSION_SUFFIXES +from typing import ( + Dict, + FrozenSet, + Iterable, + Iterator, + List, + Optional, + Sequence, + Tuple, + Union, + cast, +) + +from . import _manylinux, _musllinux + +logger = logging.getLogger(__name__) + +PythonVersion = Sequence[int] +MacVersion = Tuple[int, int] + +INTERPRETER_SHORT_NAMES: Dict[str, str] = { + "python": "py", # Generic. + "cpython": "cp", + "pypy": "pp", + "ironpython": "ip", + "jython": "jy", +} + + +_32_BIT_INTERPRETER = sys.maxsize <= 2 ** 32 + + +class Tag: + """ + A representation of the tag triple for a wheel. + + Instances are considered immutable and thus are hashable. Equality checking + is also supported. + """ + + __slots__ = ["_interpreter", "_abi", "_platform", "_hash"] + + def __init__(self, interpreter: str, abi: str, platform: str) -> None: + self._interpreter = interpreter.lower() + self._abi = abi.lower() + self._platform = platform.lower() + # The __hash__ of every single element in a Set[Tag] will be evaluated each time + # that a set calls its `.disjoint()` method, which may be called hundreds of + # times when scanning a page of links for packages with tags matching that + # Set[Tag]. Pre-computing the value here produces significant speedups for + # downstream consumers. + self._hash = hash((self._interpreter, self._abi, self._platform)) + + @property + def interpreter(self) -> str: + return self._interpreter + + @property + def abi(self) -> str: + return self._abi + + @property + def platform(self) -> str: + return self._platform + + def __eq__(self, other: object) -> bool: + if not isinstance(other, Tag): + return NotImplemented + + return ( + (self._hash == other._hash) # Short-circuit ASAP for perf reasons. + and (self._platform == other._platform) + and (self._abi == other._abi) + and (self._interpreter == other._interpreter) + ) + + def __hash__(self) -> int: + return self._hash + + def __str__(self) -> str: + return f"{self._interpreter}-{self._abi}-{self._platform}" + + def __repr__(self) -> str: + return "<{self} @ {self_id}>".format(self=self, self_id=id(self)) + + +def parse_tag(tag: str) -> FrozenSet[Tag]: + """ + Parses the provided tag (e.g. `py3-none-any`) into a frozenset of Tag instances. + + Returning a set is required due to the possibility that the tag is a + compressed tag set. + """ + tags = set() + interpreters, abis, platforms = tag.split("-") + for interpreter in interpreters.split("."): + for abi in abis.split("."): + for platform_ in platforms.split("."): + tags.add(Tag(interpreter, abi, platform_)) + return frozenset(tags) + + +def _get_config_var(name: str, warn: bool = False) -> Union[int, str, None]: + value = sysconfig.get_config_var(name) + if value is None and warn: + logger.debug( + "Config variable '%s' is unset, Python ABI tag may be incorrect", name + ) + return value + + +def _normalize_string(string: str) -> str: + return string.replace(".", "_").replace("-", "_") + + +def _abi3_applies(python_version: PythonVersion) -> bool: + """ + Determine if the Python version supports abi3. + + PEP 384 was first implemented in Python 3.2. + """ + return len(python_version) > 1 and tuple(python_version) >= (3, 2) + + +def _cpython_abis(py_version: PythonVersion, warn: bool = False) -> List[str]: + py_version = tuple(py_version) # To allow for version comparison. + abis = [] + version = _version_nodot(py_version[:2]) + debug = pymalloc = ucs4 = "" + with_debug = _get_config_var("Py_DEBUG", warn) + has_refcount = hasattr(sys, "gettotalrefcount") + # Windows doesn't set Py_DEBUG, so checking for support of debug-compiled + # extension modules is the best option. + # https://github.com/pypa/pip/issues/3383#issuecomment-173267692 + has_ext = "_d.pyd" in EXTENSION_SUFFIXES + if with_debug or (with_debug is None and (has_refcount or has_ext)): + debug = "d" + if py_version < (3, 8): + with_pymalloc = _get_config_var("WITH_PYMALLOC", warn) + if with_pymalloc or with_pymalloc is None: + pymalloc = "m" + if py_version < (3, 3): + unicode_size = _get_config_var("Py_UNICODE_SIZE", warn) + if unicode_size == 4 or ( + unicode_size is None and sys.maxunicode == 0x10FFFF + ): + ucs4 = "u" + elif debug: + # Debug builds can also load "normal" extension modules. + # We can also assume no UCS-4 or pymalloc requirement. + abis.append(f"cp{version}") + abis.insert( + 0, + "cp{version}{debug}{pymalloc}{ucs4}".format( + version=version, debug=debug, pymalloc=pymalloc, ucs4=ucs4 + ), + ) + return abis + + +def cpython_tags( + python_version: Optional[PythonVersion] = None, + abis: Optional[Iterable[str]] = None, + platforms: Optional[Iterable[str]] = None, + *, + warn: bool = False, +) -> Iterator[Tag]: + """ + Yields the tags for a CPython interpreter. + + The tags consist of: + - cp-- + - cp-abi3- + - cp-none- + - cp-abi3- # Older Python versions down to 3.2. + + If python_version only specifies a major version then user-provided ABIs and + the 'none' ABItag will be used. + + If 'abi3' or 'none' are specified in 'abis' then they will be yielded at + their normal position and not at the beginning. + """ + if not python_version: + python_version = sys.version_info[:2] + + interpreter = "cp{}".format(_version_nodot(python_version[:2])) + + if abis is None: + if len(python_version) > 1: + abis = _cpython_abis(python_version, warn) + else: + abis = [] + abis = list(abis) + # 'abi3' and 'none' are explicitly handled later. + for explicit_abi in ("abi3", "none"): + try: + abis.remove(explicit_abi) + except ValueError: + pass + + platforms = list(platforms or platform_tags()) + for abi in abis: + for platform_ in platforms: + yield Tag(interpreter, abi, platform_) + if _abi3_applies(python_version): + yield from (Tag(interpreter, "abi3", platform_) for platform_ in platforms) + yield from (Tag(interpreter, "none", platform_) for platform_ in platforms) + + if _abi3_applies(python_version): + for minor_version in range(python_version[1] - 1, 1, -1): + for platform_ in platforms: + interpreter = "cp{version}".format( + version=_version_nodot((python_version[0], minor_version)) + ) + yield Tag(interpreter, "abi3", platform_) + + +def _generic_abi() -> Iterator[str]: + abi = sysconfig.get_config_var("SOABI") + if abi: + yield _normalize_string(abi) + + +def generic_tags( + interpreter: Optional[str] = None, + abis: Optional[Iterable[str]] = None, + platforms: Optional[Iterable[str]] = None, + *, + warn: bool = False, +) -> Iterator[Tag]: + """ + Yields the tags for a generic interpreter. + + The tags consist of: + - -- + + The "none" ABI will be added if it was not explicitly provided. + """ + if not interpreter: + interp_name = interpreter_name() + interp_version = interpreter_version(warn=warn) + interpreter = "".join([interp_name, interp_version]) + if abis is None: + abis = _generic_abi() + platforms = list(platforms or platform_tags()) + abis = list(abis) + if "none" not in abis: + abis.append("none") + for abi in abis: + for platform_ in platforms: + yield Tag(interpreter, abi, platform_) + + +def _py_interpreter_range(py_version: PythonVersion) -> Iterator[str]: + """ + Yields Python versions in descending order. + + After the latest version, the major-only version will be yielded, and then + all previous versions of that major version. + """ + if len(py_version) > 1: + yield "py{version}".format(version=_version_nodot(py_version[:2])) + yield "py{major}".format(major=py_version[0]) + if len(py_version) > 1: + for minor in range(py_version[1] - 1, -1, -1): + yield "py{version}".format(version=_version_nodot((py_version[0], minor))) + + +def compatible_tags( + python_version: Optional[PythonVersion] = None, + interpreter: Optional[str] = None, + platforms: Optional[Iterable[str]] = None, +) -> Iterator[Tag]: + """ + Yields the sequence of tags that are compatible with a specific version of Python. + + The tags consist of: + - py*-none- + - -none-any # ... if `interpreter` is provided. + - py*-none-any + """ + if not python_version: + python_version = sys.version_info[:2] + platforms = list(platforms or platform_tags()) + for version in _py_interpreter_range(python_version): + for platform_ in platforms: + yield Tag(version, "none", platform_) + if interpreter: + yield Tag(interpreter, "none", "any") + for version in _py_interpreter_range(python_version): + yield Tag(version, "none", "any") + + +def _mac_arch(arch: str, is_32bit: bool = _32_BIT_INTERPRETER) -> str: + if not is_32bit: + return arch + + if arch.startswith("ppc"): + return "ppc" + + return "i386" + + +def _mac_binary_formats(version: MacVersion, cpu_arch: str) -> List[str]: + formats = [cpu_arch] + if cpu_arch == "x86_64": + if version < (10, 4): + return [] + formats.extend(["intel", "fat64", "fat32"]) + + elif cpu_arch == "i386": + if version < (10, 4): + return [] + formats.extend(["intel", "fat32", "fat"]) + + elif cpu_arch == "ppc64": + # TODO: Need to care about 32-bit PPC for ppc64 through 10.2? + if version > (10, 5) or version < (10, 4): + return [] + formats.append("fat64") + + elif cpu_arch == "ppc": + if version > (10, 6): + return [] + formats.extend(["fat32", "fat"]) + + if cpu_arch in {"arm64", "x86_64"}: + formats.append("universal2") + + if cpu_arch in {"x86_64", "i386", "ppc64", "ppc", "intel"}: + formats.append("universal") + + return formats + + +def mac_platforms( + version: Optional[MacVersion] = None, arch: Optional[str] = None +) -> Iterator[str]: + """ + Yields the platform tags for a macOS system. + + The `version` parameter is a two-item tuple specifying the macOS version to + generate platform tags for. The `arch` parameter is the CPU architecture to + generate platform tags for. Both parameters default to the appropriate value + for the current system. + """ + version_str, _, cpu_arch = platform.mac_ver() + if version is None: + version = cast("MacVersion", tuple(map(int, version_str.split(".")[:2]))) + else: + version = version + if arch is None: + arch = _mac_arch(cpu_arch) + else: + arch = arch + + if (10, 0) <= version and version < (11, 0): + # Prior to Mac OS 11, each yearly release of Mac OS bumped the + # "minor" version number. The major version was always 10. + for minor_version in range(version[1], -1, -1): + compat_version = 10, minor_version + binary_formats = _mac_binary_formats(compat_version, arch) + for binary_format in binary_formats: + yield "macosx_{major}_{minor}_{binary_format}".format( + major=10, minor=minor_version, binary_format=binary_format + ) + + if version >= (11, 0): + # Starting with Mac OS 11, each yearly release bumps the major version + # number. The minor versions are now the midyear updates. + for major_version in range(version[0], 10, -1): + compat_version = major_version, 0 + binary_formats = _mac_binary_formats(compat_version, arch) + for binary_format in binary_formats: + yield "macosx_{major}_{minor}_{binary_format}".format( + major=major_version, minor=0, binary_format=binary_format + ) + + if version >= (11, 0): + # Mac OS 11 on x86_64 is compatible with binaries from previous releases. + # Arm64 support was introduced in 11.0, so no Arm binaries from previous + # releases exist. + # + # However, the "universal2" binary format can have a + # macOS version earlier than 11.0 when the x86_64 part of the binary supports + # that version of macOS. + if arch == "x86_64": + for minor_version in range(16, 3, -1): + compat_version = 10, minor_version + binary_formats = _mac_binary_formats(compat_version, arch) + for binary_format in binary_formats: + yield "macosx_{major}_{minor}_{binary_format}".format( + major=compat_version[0], + minor=compat_version[1], + binary_format=binary_format, + ) + else: + for minor_version in range(16, 3, -1): + compat_version = 10, minor_version + binary_format = "universal2" + yield "macosx_{major}_{minor}_{binary_format}".format( + major=compat_version[0], + minor=compat_version[1], + binary_format=binary_format, + ) + + +def _linux_platforms(is_32bit: bool = _32_BIT_INTERPRETER) -> Iterator[str]: + linux = _normalize_string(sysconfig.get_platform()) + if is_32bit: + if linux == "linux_x86_64": + linux = "linux_i686" + elif linux == "linux_aarch64": + linux = "linux_armv7l" + _, arch = linux.split("_", 1) + yield from _manylinux.platform_tags(linux, arch) + yield from _musllinux.platform_tags(arch) + yield linux + + +def _generic_platforms() -> Iterator[str]: + yield _normalize_string(sysconfig.get_platform()) + + +def platform_tags() -> Iterator[str]: + """ + Provides the platform tags for this installation. + """ + if platform.system() == "Darwin": + return mac_platforms() + elif platform.system() == "Linux": + return _linux_platforms() + else: + return _generic_platforms() + + +def interpreter_name() -> str: + """ + Returns the name of the running interpreter. + """ + name = sys.implementation.name + return INTERPRETER_SHORT_NAMES.get(name) or name + + +def interpreter_version(*, warn: bool = False) -> str: + """ + Returns the version of the running interpreter. + """ + version = _get_config_var("py_version_nodot", warn=warn) + if version: + version = str(version) + else: + version = _version_nodot(sys.version_info[:2]) + return version + + +def _version_nodot(version: PythonVersion) -> str: + return "".join(map(str, version)) + + +def sys_tags(*, warn: bool = False) -> Iterator[Tag]: + """ + Returns the sequence of tag triples for the running interpreter. + + The order of the sequence corresponds to priority order for the + interpreter, from most to least important. + """ + + interp_name = interpreter_name() + if interp_name == "cp": + yield from cpython_tags(warn=warn) + else: + yield from generic_tags() + + yield from compatible_tags() diff --git a/llmeval-env/lib/python3.10/site-packages/pkg_resources/_vendor/packaging/utils.py b/llmeval-env/lib/python3.10/site-packages/pkg_resources/_vendor/packaging/utils.py new file mode 100644 index 0000000000000000000000000000000000000000..bab11b80c60f10a4f3bccb12eb5b17c48a449767 --- /dev/null +++ b/llmeval-env/lib/python3.10/site-packages/pkg_resources/_vendor/packaging/utils.py @@ -0,0 +1,136 @@ +# This file is dual licensed under the terms of the Apache License, Version +# 2.0, and the BSD License. See the LICENSE file in the root of this repository +# for complete details. + +import re +from typing import FrozenSet, NewType, Tuple, Union, cast + +from .tags import Tag, parse_tag +from .version import InvalidVersion, Version + +BuildTag = Union[Tuple[()], Tuple[int, str]] +NormalizedName = NewType("NormalizedName", str) + + +class InvalidWheelFilename(ValueError): + """ + An invalid wheel filename was found, users should refer to PEP 427. + """ + + +class InvalidSdistFilename(ValueError): + """ + An invalid sdist filename was found, users should refer to the packaging user guide. + """ + + +_canonicalize_regex = re.compile(r"[-_.]+") +# PEP 427: The build number must start with a digit. +_build_tag_regex = re.compile(r"(\d+)(.*)") + + +def canonicalize_name(name: str) -> NormalizedName: + # This is taken from PEP 503. + value = _canonicalize_regex.sub("-", name).lower() + return cast(NormalizedName, value) + + +def canonicalize_version(version: Union[Version, str]) -> str: + """ + This is very similar to Version.__str__, but has one subtle difference + with the way it handles the release segment. + """ + if isinstance(version, str): + try: + parsed = Version(version) + except InvalidVersion: + # Legacy versions cannot be normalized + return version + else: + parsed = version + + parts = [] + + # Epoch + if parsed.epoch != 0: + parts.append(f"{parsed.epoch}!") + + # Release segment + # NB: This strips trailing '.0's to normalize + parts.append(re.sub(r"(\.0)+$", "", ".".join(str(x) for x in parsed.release))) + + # Pre-release + if parsed.pre is not None: + parts.append("".join(str(x) for x in parsed.pre)) + + # Post-release + if parsed.post is not None: + parts.append(f".post{parsed.post}") + + # Development release + if parsed.dev is not None: + parts.append(f".dev{parsed.dev}") + + # Local version segment + if parsed.local is not None: + parts.append(f"+{parsed.local}") + + return "".join(parts) + + +def parse_wheel_filename( + filename: str, +) -> Tuple[NormalizedName, Version, BuildTag, FrozenSet[Tag]]: + if not filename.endswith(".whl"): + raise InvalidWheelFilename( + f"Invalid wheel filename (extension must be '.whl'): {filename}" + ) + + filename = filename[:-4] + dashes = filename.count("-") + if dashes not in (4, 5): + raise InvalidWheelFilename( + f"Invalid wheel filename (wrong number of parts): {filename}" + ) + + parts = filename.split("-", dashes - 2) + name_part = parts[0] + # See PEP 427 for the rules on escaping the project name + if "__" in name_part or re.match(r"^[\w\d._]*$", name_part, re.UNICODE) is None: + raise InvalidWheelFilename(f"Invalid project name: {filename}") + name = canonicalize_name(name_part) + version = Version(parts[1]) + if dashes == 5: + build_part = parts[2] + build_match = _build_tag_regex.match(build_part) + if build_match is None: + raise InvalidWheelFilename( + f"Invalid build number: {build_part} in '{filename}'" + ) + build = cast(BuildTag, (int(build_match.group(1)), build_match.group(2))) + else: + build = () + tags = parse_tag(parts[-1]) + return (name, version, build, tags) + + +def parse_sdist_filename(filename: str) -> Tuple[NormalizedName, Version]: + if filename.endswith(".tar.gz"): + file_stem = filename[: -len(".tar.gz")] + elif filename.endswith(".zip"): + file_stem = filename[: -len(".zip")] + else: + raise InvalidSdistFilename( + f"Invalid sdist filename (extension must be '.tar.gz' or '.zip'):" + f" {filename}" + ) + + # We are requiring a PEP 440 version, which cannot contain dashes, + # so we split on the last dash. + name_part, sep, version_part = file_stem.rpartition("-") + if not sep: + raise InvalidSdistFilename(f"Invalid sdist filename: {filename}") + + name = canonicalize_name(name_part) + version = Version(version_part) + return (name, version) diff --git a/llmeval-env/lib/python3.10/site-packages/pkg_resources/_vendor/packaging/version.py b/llmeval-env/lib/python3.10/site-packages/pkg_resources/_vendor/packaging/version.py new file mode 100644 index 0000000000000000000000000000000000000000..de9a09a4ed3b078b37e7490a6686f660ae935aca --- /dev/null +++ b/llmeval-env/lib/python3.10/site-packages/pkg_resources/_vendor/packaging/version.py @@ -0,0 +1,504 @@ +# This file is dual licensed under the terms of the Apache License, Version +# 2.0, and the BSD License. See the LICENSE file in the root of this repository +# for complete details. + +import collections +import itertools +import re +import warnings +from typing import Callable, Iterator, List, Optional, SupportsInt, Tuple, Union + +from ._structures import Infinity, InfinityType, NegativeInfinity, NegativeInfinityType + +__all__ = ["parse", "Version", "LegacyVersion", "InvalidVersion", "VERSION_PATTERN"] + +InfiniteTypes = Union[InfinityType, NegativeInfinityType] +PrePostDevType = Union[InfiniteTypes, Tuple[str, int]] +SubLocalType = Union[InfiniteTypes, int, str] +LocalType = Union[ + NegativeInfinityType, + Tuple[ + Union[ + SubLocalType, + Tuple[SubLocalType, str], + Tuple[NegativeInfinityType, SubLocalType], + ], + ..., + ], +] +CmpKey = Tuple[ + int, Tuple[int, ...], PrePostDevType, PrePostDevType, PrePostDevType, LocalType +] +LegacyCmpKey = Tuple[int, Tuple[str, ...]] +VersionComparisonMethod = Callable[ + [Union[CmpKey, LegacyCmpKey], Union[CmpKey, LegacyCmpKey]], bool +] + +_Version = collections.namedtuple( + "_Version", ["epoch", "release", "dev", "pre", "post", "local"] +) + + +def parse(version: str) -> Union["LegacyVersion", "Version"]: + """ + Parse the given version string and return either a :class:`Version` object + or a :class:`LegacyVersion` object depending on if the given version is + a valid PEP 440 version or a legacy version. + """ + try: + return Version(version) + except InvalidVersion: + return LegacyVersion(version) + + +class InvalidVersion(ValueError): + """ + An invalid version was found, users should refer to PEP 440. + """ + + +class _BaseVersion: + _key: Union[CmpKey, LegacyCmpKey] + + def __hash__(self) -> int: + return hash(self._key) + + # Please keep the duplicated `isinstance` check + # in the six comparisons hereunder + # unless you find a way to avoid adding overhead function calls. + def __lt__(self, other: "_BaseVersion") -> bool: + if not isinstance(other, _BaseVersion): + return NotImplemented + + return self._key < other._key + + def __le__(self, other: "_BaseVersion") -> bool: + if not isinstance(other, _BaseVersion): + return NotImplemented + + return self._key <= other._key + + def __eq__(self, other: object) -> bool: + if not isinstance(other, _BaseVersion): + return NotImplemented + + return self._key == other._key + + def __ge__(self, other: "_BaseVersion") -> bool: + if not isinstance(other, _BaseVersion): + return NotImplemented + + return self._key >= other._key + + def __gt__(self, other: "_BaseVersion") -> bool: + if not isinstance(other, _BaseVersion): + return NotImplemented + + return self._key > other._key + + def __ne__(self, other: object) -> bool: + if not isinstance(other, _BaseVersion): + return NotImplemented + + return self._key != other._key + + +class LegacyVersion(_BaseVersion): + def __init__(self, version: str) -> None: + self._version = str(version) + self._key = _legacy_cmpkey(self._version) + + warnings.warn( + "Creating a LegacyVersion has been deprecated and will be " + "removed in the next major release", + DeprecationWarning, + ) + + def __str__(self) -> str: + return self._version + + def __repr__(self) -> str: + return f"" + + @property + def public(self) -> str: + return self._version + + @property + def base_version(self) -> str: + return self._version + + @property + def epoch(self) -> int: + return -1 + + @property + def release(self) -> None: + return None + + @property + def pre(self) -> None: + return None + + @property + def post(self) -> None: + return None + + @property + def dev(self) -> None: + return None + + @property + def local(self) -> None: + return None + + @property + def is_prerelease(self) -> bool: + return False + + @property + def is_postrelease(self) -> bool: + return False + + @property + def is_devrelease(self) -> bool: + return False + + +_legacy_version_component_re = re.compile(r"(\d+ | [a-z]+ | \.| -)", re.VERBOSE) + +_legacy_version_replacement_map = { + "pre": "c", + "preview": "c", + "-": "final-", + "rc": "c", + "dev": "@", +} + + +def _parse_version_parts(s: str) -> Iterator[str]: + for part in _legacy_version_component_re.split(s): + part = _legacy_version_replacement_map.get(part, part) + + if not part or part == ".": + continue + + if part[:1] in "0123456789": + # pad for numeric comparison + yield part.zfill(8) + else: + yield "*" + part + + # ensure that alpha/beta/candidate are before final + yield "*final" + + +def _legacy_cmpkey(version: str) -> LegacyCmpKey: + + # We hardcode an epoch of -1 here. A PEP 440 version can only have a epoch + # greater than or equal to 0. This will effectively put the LegacyVersion, + # which uses the defacto standard originally implemented by setuptools, + # as before all PEP 440 versions. + epoch = -1 + + # This scheme is taken from pkg_resources.parse_version setuptools prior to + # it's adoption of the packaging library. + parts: List[str] = [] + for part in _parse_version_parts(version.lower()): + if part.startswith("*"): + # remove "-" before a prerelease tag + if part < "*final": + while parts and parts[-1] == "*final-": + parts.pop() + + # remove trailing zeros from each series of numeric parts + while parts and parts[-1] == "00000000": + parts.pop() + + parts.append(part) + + return epoch, tuple(parts) + + +# Deliberately not anchored to the start and end of the string, to make it +# easier for 3rd party code to reuse +VERSION_PATTERN = r""" + v? + (?: + (?:(?P[0-9]+)!)? # epoch + (?P[0-9]+(?:\.[0-9]+)*) # release segment + (?P
                                          # pre-release
+            [-_\.]?
+            (?P(a|b|c|rc|alpha|beta|pre|preview))
+            [-_\.]?
+            (?P[0-9]+)?
+        )?
+        (?P                                         # post release
+            (?:-(?P[0-9]+))
+            |
+            (?:
+                [-_\.]?
+                (?Ppost|rev|r)
+                [-_\.]?
+                (?P[0-9]+)?
+            )
+        )?
+        (?P                                          # dev release
+            [-_\.]?
+            (?Pdev)
+            [-_\.]?
+            (?P[0-9]+)?
+        )?
+    )
+    (?:\+(?P[a-z0-9]+(?:[-_\.][a-z0-9]+)*))?       # local version
+"""
+
+
+class Version(_BaseVersion):
+
+    _regex = re.compile(r"^\s*" + VERSION_PATTERN + r"\s*$", re.VERBOSE | re.IGNORECASE)
+
+    def __init__(self, version: str) -> None:
+
+        # Validate the version and parse it into pieces
+        match = self._regex.search(version)
+        if not match:
+            raise InvalidVersion(f"Invalid version: '{version}'")
+
+        # Store the parsed out pieces of the version
+        self._version = _Version(
+            epoch=int(match.group("epoch")) if match.group("epoch") else 0,
+            release=tuple(int(i) for i in match.group("release").split(".")),
+            pre=_parse_letter_version(match.group("pre_l"), match.group("pre_n")),
+            post=_parse_letter_version(
+                match.group("post_l"), match.group("post_n1") or match.group("post_n2")
+            ),
+            dev=_parse_letter_version(match.group("dev_l"), match.group("dev_n")),
+            local=_parse_local_version(match.group("local")),
+        )
+
+        # Generate a key which will be used for sorting
+        self._key = _cmpkey(
+            self._version.epoch,
+            self._version.release,
+            self._version.pre,
+            self._version.post,
+            self._version.dev,
+            self._version.local,
+        )
+
+    def __repr__(self) -> str:
+        return f""
+
+    def __str__(self) -> str:
+        parts = []
+
+        # Epoch
+        if self.epoch != 0:
+            parts.append(f"{self.epoch}!")
+
+        # Release segment
+        parts.append(".".join(str(x) for x in self.release))
+
+        # Pre-release
+        if self.pre is not None:
+            parts.append("".join(str(x) for x in self.pre))
+
+        # Post-release
+        if self.post is not None:
+            parts.append(f".post{self.post}")
+
+        # Development release
+        if self.dev is not None:
+            parts.append(f".dev{self.dev}")
+
+        # Local version segment
+        if self.local is not None:
+            parts.append(f"+{self.local}")
+
+        return "".join(parts)
+
+    @property
+    def epoch(self) -> int:
+        _epoch: int = self._version.epoch
+        return _epoch
+
+    @property
+    def release(self) -> Tuple[int, ...]:
+        _release: Tuple[int, ...] = self._version.release
+        return _release
+
+    @property
+    def pre(self) -> Optional[Tuple[str, int]]:
+        _pre: Optional[Tuple[str, int]] = self._version.pre
+        return _pre
+
+    @property
+    def post(self) -> Optional[int]:
+        return self._version.post[1] if self._version.post else None
+
+    @property
+    def dev(self) -> Optional[int]:
+        return self._version.dev[1] if self._version.dev else None
+
+    @property
+    def local(self) -> Optional[str]:
+        if self._version.local:
+            return ".".join(str(x) for x in self._version.local)
+        else:
+            return None
+
+    @property
+    def public(self) -> str:
+        return str(self).split("+", 1)[0]
+
+    @property
+    def base_version(self) -> str:
+        parts = []
+
+        # Epoch
+        if self.epoch != 0:
+            parts.append(f"{self.epoch}!")
+
+        # Release segment
+        parts.append(".".join(str(x) for x in self.release))
+
+        return "".join(parts)
+
+    @property
+    def is_prerelease(self) -> bool:
+        return self.dev is not None or self.pre is not None
+
+    @property
+    def is_postrelease(self) -> bool:
+        return self.post is not None
+
+    @property
+    def is_devrelease(self) -> bool:
+        return self.dev is not None
+
+    @property
+    def major(self) -> int:
+        return self.release[0] if len(self.release) >= 1 else 0
+
+    @property
+    def minor(self) -> int:
+        return self.release[1] if len(self.release) >= 2 else 0
+
+    @property
+    def micro(self) -> int:
+        return self.release[2] if len(self.release) >= 3 else 0
+
+
+def _parse_letter_version(
+    letter: str, number: Union[str, bytes, SupportsInt]
+) -> Optional[Tuple[str, int]]:
+
+    if letter:
+        # We consider there to be an implicit 0 in a pre-release if there is
+        # not a numeral associated with it.
+        if number is None:
+            number = 0
+
+        # We normalize any letters to their lower case form
+        letter = letter.lower()
+
+        # We consider some words to be alternate spellings of other words and
+        # in those cases we want to normalize the spellings to our preferred
+        # spelling.
+        if letter == "alpha":
+            letter = "a"
+        elif letter == "beta":
+            letter = "b"
+        elif letter in ["c", "pre", "preview"]:
+            letter = "rc"
+        elif letter in ["rev", "r"]:
+            letter = "post"
+
+        return letter, int(number)
+    if not letter and number:
+        # We assume if we are given a number, but we are not given a letter
+        # then this is using the implicit post release syntax (e.g. 1.0-1)
+        letter = "post"
+
+        return letter, int(number)
+
+    return None
+
+
+_local_version_separators = re.compile(r"[\._-]")
+
+
+def _parse_local_version(local: str) -> Optional[LocalType]:
+    """
+    Takes a string like abc.1.twelve and turns it into ("abc", 1, "twelve").
+    """
+    if local is not None:
+        return tuple(
+            part.lower() if not part.isdigit() else int(part)
+            for part in _local_version_separators.split(local)
+        )
+    return None
+
+
+def _cmpkey(
+    epoch: int,
+    release: Tuple[int, ...],
+    pre: Optional[Tuple[str, int]],
+    post: Optional[Tuple[str, int]],
+    dev: Optional[Tuple[str, int]],
+    local: Optional[Tuple[SubLocalType]],
+) -> CmpKey:
+
+    # When we compare a release version, we want to compare it with all of the
+    # trailing zeros removed. So we'll use a reverse the list, drop all the now
+    # leading zeros until we come to something non zero, then take the rest
+    # re-reverse it back into the correct order and make it a tuple and use
+    # that for our sorting key.
+    _release = tuple(
+        reversed(list(itertools.dropwhile(lambda x: x == 0, reversed(release))))
+    )
+
+    # We need to "trick" the sorting algorithm to put 1.0.dev0 before 1.0a0.
+    # We'll do this by abusing the pre segment, but we _only_ want to do this
+    # if there is not a pre or a post segment. If we have one of those then
+    # the normal sorting rules will handle this case correctly.
+    if pre is None and post is None and dev is not None:
+        _pre: PrePostDevType = NegativeInfinity
+    # Versions without a pre-release (except as noted above) should sort after
+    # those with one.
+    elif pre is None:
+        _pre = Infinity
+    else:
+        _pre = pre
+
+    # Versions without a post segment should sort before those with one.
+    if post is None:
+        _post: PrePostDevType = NegativeInfinity
+
+    else:
+        _post = post
+
+    # Versions without a development segment should sort after those with one.
+    if dev is None:
+        _dev: PrePostDevType = Infinity
+
+    else:
+        _dev = dev
+
+    if local is None:
+        # Versions without a local segment should sort before those with one.
+        _local: LocalType = NegativeInfinity
+    else:
+        # Versions with a local segment need that segment parsed to implement
+        # the sorting rules in PEP440.
+        # - Alpha numeric segments sort before numeric segments
+        # - Alpha numeric segments sort lexicographically
+        # - Numeric segments sort numerically
+        # - Shorter versions sort before longer versions when the prefixes
+        #   match exactly
+        _local = tuple(
+            (i, "") if isinstance(i, int) else (NegativeInfinity, i) for i in local
+        )
+
+    return epoch, _release, _pre, _post, _dev, _local
diff --git a/llmeval-env/lib/python3.10/site-packages/pkg_resources/_vendor/pyparsing.py b/llmeval-env/lib/python3.10/site-packages/pkg_resources/_vendor/pyparsing.py
new file mode 100644
index 0000000000000000000000000000000000000000..cf75e1e5fcbfe7eac41d2a9e446c5c980741087b
--- /dev/null
+++ b/llmeval-env/lib/python3.10/site-packages/pkg_resources/_vendor/pyparsing.py
@@ -0,0 +1,5742 @@
+# module pyparsing.py
+#
+# Copyright (c) 2003-2018  Paul T. McGuire
+#
+# Permission is hereby granted, free of charge, to any person obtaining
+# a copy of this software and associated documentation files (the
+# "Software"), to deal in the Software without restriction, including
+# without limitation the rights to use, copy, modify, merge, publish,
+# distribute, sublicense, and/or sell copies of the Software, and to
+# permit persons to whom the Software is furnished to do so, subject to
+# the following conditions:
+#
+# The above copyright notice and this permission notice shall be
+# included in all copies or substantial portions of the Software.
+#
+# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
+# EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
+# MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.
+# IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY
+# CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,
+# TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE
+# SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
+#
+
+__doc__ = \
+"""
+pyparsing module - Classes and methods to define and execute parsing grammars
+=============================================================================
+
+The pyparsing module is an alternative approach to creating and executing simple grammars,
+vs. the traditional lex/yacc approach, or the use of regular expressions.  With pyparsing, you
+don't need to learn a new syntax for defining grammars or matching expressions - the parsing module
+provides a library of classes that you use to construct the grammar directly in Python.
+
+Here is a program to parse "Hello, World!" (or any greeting of the form 
+C{", !"}), built up using L{Word}, L{Literal}, and L{And} elements 
+(L{'+'} operator gives L{And} expressions, strings are auto-converted to
+L{Literal} expressions)::
+
+    from pyparsing import Word, alphas
+
+    # define grammar of a greeting
+    greet = Word(alphas) + "," + Word(alphas) + "!"
+
+    hello = "Hello, World!"
+    print (hello, "->", greet.parseString(hello))
+
+The program outputs the following::
+
+    Hello, World! -> ['Hello', ',', 'World', '!']
+
+The Python representation of the grammar is quite readable, owing to the self-explanatory
+class names, and the use of '+', '|' and '^' operators.
+
+The L{ParseResults} object returned from L{ParserElement.parseString} can be accessed as a nested list, a dictionary, or an
+object with named attributes.
+
+The pyparsing module handles some of the problems that are typically vexing when writing text parsers:
+ - extra or missing whitespace (the above program will also handle "Hello,World!", "Hello  ,  World  !", etc.)
+ - quoted strings
+ - embedded comments
+
+
+Getting Started -
+-----------------
+Visit the classes L{ParserElement} and L{ParseResults} to see the base classes that most other pyparsing
+classes inherit from. Use the docstrings for examples of how to:
+ - construct literal match expressions from L{Literal} and L{CaselessLiteral} classes
+ - construct character word-group expressions using the L{Word} class
+ - see how to create repetitive expressions using L{ZeroOrMore} and L{OneOrMore} classes
+ - use L{'+'}, L{'|'}, L{'^'}, and L{'&'} operators to combine simple expressions into more complex ones
+ - associate names with your parsed results using L{ParserElement.setResultsName}
+ - find some helpful expression short-cuts like L{delimitedList} and L{oneOf}
+ - find more useful common expressions in the L{pyparsing_common} namespace class
+"""
+
+__version__ = "2.2.1"
+__versionTime__ = "18 Sep 2018 00:49 UTC"
+__author__ = "Paul McGuire "
+
+import string
+from weakref import ref as wkref
+import copy
+import sys
+import warnings
+import re
+import sre_constants
+import collections
+import pprint
+import traceback
+import types
+from datetime import datetime
+
+try:
+    from _thread import RLock
+except ImportError:
+    from threading import RLock
+
+try:
+    # Python 3
+    from collections.abc import Iterable
+    from collections.abc import MutableMapping
+except ImportError:
+    # Python 2.7
+    from collections import Iterable
+    from collections import MutableMapping
+
+try:
+    from collections import OrderedDict as _OrderedDict
+except ImportError:
+    try:
+        from ordereddict import OrderedDict as _OrderedDict
+    except ImportError:
+        _OrderedDict = None
+
+#~ sys.stderr.write( "testing pyparsing module, version %s, %s\n" % (__version__,__versionTime__ ) )
+
+__all__ = [
+'And', 'CaselessKeyword', 'CaselessLiteral', 'CharsNotIn', 'Combine', 'Dict', 'Each', 'Empty',
+'FollowedBy', 'Forward', 'GoToColumn', 'Group', 'Keyword', 'LineEnd', 'LineStart', 'Literal',
+'MatchFirst', 'NoMatch', 'NotAny', 'OneOrMore', 'OnlyOnce', 'Optional', 'Or',
+'ParseBaseException', 'ParseElementEnhance', 'ParseException', 'ParseExpression', 'ParseFatalException',
+'ParseResults', 'ParseSyntaxException', 'ParserElement', 'QuotedString', 'RecursiveGrammarException',
+'Regex', 'SkipTo', 'StringEnd', 'StringStart', 'Suppress', 'Token', 'TokenConverter', 
+'White', 'Word', 'WordEnd', 'WordStart', 'ZeroOrMore',
+'alphanums', 'alphas', 'alphas8bit', 'anyCloseTag', 'anyOpenTag', 'cStyleComment', 'col',
+'commaSeparatedList', 'commonHTMLEntity', 'countedArray', 'cppStyleComment', 'dblQuotedString',
+'dblSlashComment', 'delimitedList', 'dictOf', 'downcaseTokens', 'empty', 'hexnums',
+'htmlComment', 'javaStyleComment', 'line', 'lineEnd', 'lineStart', 'lineno',
+'makeHTMLTags', 'makeXMLTags', 'matchOnlyAtCol', 'matchPreviousExpr', 'matchPreviousLiteral',
+'nestedExpr', 'nullDebugAction', 'nums', 'oneOf', 'opAssoc', 'operatorPrecedence', 'printables',
+'punc8bit', 'pythonStyleComment', 'quotedString', 'removeQuotes', 'replaceHTMLEntity', 
+'replaceWith', 'restOfLine', 'sglQuotedString', 'srange', 'stringEnd',
+'stringStart', 'traceParseAction', 'unicodeString', 'upcaseTokens', 'withAttribute',
+'indentedBlock', 'originalTextFor', 'ungroup', 'infixNotation','locatedExpr', 'withClass',
+'CloseMatch', 'tokenMap', 'pyparsing_common',
+]
+
+system_version = tuple(sys.version_info)[:3]
+PY_3 = system_version[0] == 3
+if PY_3:
+    _MAX_INT = sys.maxsize
+    basestring = str
+    unichr = chr
+    _ustr = str
+
+    # build list of single arg builtins, that can be used as parse actions
+    singleArgBuiltins = [sum, len, sorted, reversed, list, tuple, set, any, all, min, max]
+
+else:
+    _MAX_INT = sys.maxint
+    range = xrange
+
+    def _ustr(obj):
+        """Drop-in replacement for str(obj) that tries to be Unicode friendly. It first tries
+           str(obj). If that fails with a UnicodeEncodeError, then it tries unicode(obj). It
+           then < returns the unicode object | encodes it with the default encoding | ... >.
+        """
+        if isinstance(obj,unicode):
+            return obj
+
+        try:
+            # If this works, then _ustr(obj) has the same behaviour as str(obj), so
+            # it won't break any existing code.
+            return str(obj)
+
+        except UnicodeEncodeError:
+            # Else encode it
+            ret = unicode(obj).encode(sys.getdefaultencoding(), 'xmlcharrefreplace')
+            xmlcharref = Regex(r'&#\d+;')
+            xmlcharref.setParseAction(lambda t: '\\u' + hex(int(t[0][2:-1]))[2:])
+            return xmlcharref.transformString(ret)
+
+    # build list of single arg builtins, tolerant of Python version, that can be used as parse actions
+    singleArgBuiltins = []
+    import __builtin__
+    for fname in "sum len sorted reversed list tuple set any all min max".split():
+        try:
+            singleArgBuiltins.append(getattr(__builtin__,fname))
+        except AttributeError:
+            continue
+            
+_generatorType = type((y for y in range(1)))
+ 
+def _xml_escape(data):
+    """Escape &, <, >, ", ', etc. in a string of data."""
+
+    # ampersand must be replaced first
+    from_symbols = '&><"\''
+    to_symbols = ('&'+s+';' for s in "amp gt lt quot apos".split())
+    for from_,to_ in zip(from_symbols, to_symbols):
+        data = data.replace(from_, to_)
+    return data
+
+class _Constants(object):
+    pass
+
+alphas     = string.ascii_uppercase + string.ascii_lowercase
+nums       = "0123456789"
+hexnums    = nums + "ABCDEFabcdef"
+alphanums  = alphas + nums
+_bslash    = chr(92)
+printables = "".join(c for c in string.printable if c not in string.whitespace)
+
+class ParseBaseException(Exception):
+    """base exception class for all parsing runtime exceptions"""
+    # Performance tuning: we construct a *lot* of these, so keep this
+    # constructor as small and fast as possible
+    def __init__( self, pstr, loc=0, msg=None, elem=None ):
+        self.loc = loc
+        if msg is None:
+            self.msg = pstr
+            self.pstr = ""
+        else:
+            self.msg = msg
+            self.pstr = pstr
+        self.parserElement = elem
+        self.args = (pstr, loc, msg)
+
+    @classmethod
+    def _from_exception(cls, pe):
+        """
+        internal factory method to simplify creating one type of ParseException 
+        from another - avoids having __init__ signature conflicts among subclasses
+        """
+        return cls(pe.pstr, pe.loc, pe.msg, pe.parserElement)
+
+    def __getattr__( self, aname ):
+        """supported attributes by name are:
+            - lineno - returns the line number of the exception text
+            - col - returns the column number of the exception text
+            - line - returns the line containing the exception text
+        """
+        if( aname == "lineno" ):
+            return lineno( self.loc, self.pstr )
+        elif( aname in ("col", "column") ):
+            return col( self.loc, self.pstr )
+        elif( aname == "line" ):
+            return line( self.loc, self.pstr )
+        else:
+            raise AttributeError(aname)
+
+    def __str__( self ):
+        return "%s (at char %d), (line:%d, col:%d)" % \
+                ( self.msg, self.loc, self.lineno, self.column )
+    def __repr__( self ):
+        return _ustr(self)
+    def markInputline( self, markerString = ">!<" ):
+        """Extracts the exception line from the input string, and marks
+           the location of the exception with a special symbol.
+        """
+        line_str = self.line
+        line_column = self.column - 1
+        if markerString:
+            line_str = "".join((line_str[:line_column],
+                                markerString, line_str[line_column:]))
+        return line_str.strip()
+    def __dir__(self):
+        return "lineno col line".split() + dir(type(self))
+
+class ParseException(ParseBaseException):
+    """
+    Exception thrown when parse expressions don't match class;
+    supported attributes by name are:
+     - lineno - returns the line number of the exception text
+     - col - returns the column number of the exception text
+     - line - returns the line containing the exception text
+        
+    Example::
+        try:
+            Word(nums).setName("integer").parseString("ABC")
+        except ParseException as pe:
+            print(pe)
+            print("column: {}".format(pe.col))
+            
+    prints::
+       Expected integer (at char 0), (line:1, col:1)
+        column: 1
+    """
+    pass
+
+class ParseFatalException(ParseBaseException):
+    """user-throwable exception thrown when inconsistent parse content
+       is found; stops all parsing immediately"""
+    pass
+
+class ParseSyntaxException(ParseFatalException):
+    """just like L{ParseFatalException}, but thrown internally when an
+       L{ErrorStop} ('-' operator) indicates that parsing is to stop 
+       immediately because an unbacktrackable syntax error has been found"""
+    pass
+
+#~ class ReparseException(ParseBaseException):
+    #~ """Experimental class - parse actions can raise this exception to cause
+       #~ pyparsing to reparse the input string:
+        #~ - with a modified input string, and/or
+        #~ - with a modified start location
+       #~ Set the values of the ReparseException in the constructor, and raise the
+       #~ exception in a parse action to cause pyparsing to use the new string/location.
+       #~ Setting the values as None causes no change to be made.
+       #~ """
+    #~ def __init_( self, newstring, restartLoc ):
+        #~ self.newParseText = newstring
+        #~ self.reparseLoc = restartLoc
+
+class RecursiveGrammarException(Exception):
+    """exception thrown by L{ParserElement.validate} if the grammar could be improperly recursive"""
+    def __init__( self, parseElementList ):
+        self.parseElementTrace = parseElementList
+
+    def __str__( self ):
+        return "RecursiveGrammarException: %s" % self.parseElementTrace
+
+class _ParseResultsWithOffset(object):
+    def __init__(self,p1,p2):
+        self.tup = (p1,p2)
+    def __getitem__(self,i):
+        return self.tup[i]
+    def __repr__(self):
+        return repr(self.tup[0])
+    def setOffset(self,i):
+        self.tup = (self.tup[0],i)
+
+class ParseResults(object):
+    """
+    Structured parse results, to provide multiple means of access to the parsed data:
+       - as a list (C{len(results)})
+       - by list index (C{results[0], results[1]}, etc.)
+       - by attribute (C{results.} - see L{ParserElement.setResultsName})
+
+    Example::
+        integer = Word(nums)
+        date_str = (integer.setResultsName("year") + '/' 
+                        + integer.setResultsName("month") + '/' 
+                        + integer.setResultsName("day"))
+        # equivalent form:
+        # date_str = integer("year") + '/' + integer("month") + '/' + integer("day")
+
+        # parseString returns a ParseResults object
+        result = date_str.parseString("1999/12/31")
+
+        def test(s, fn=repr):
+            print("%s -> %s" % (s, fn(eval(s))))
+        test("list(result)")
+        test("result[0]")
+        test("result['month']")
+        test("result.day")
+        test("'month' in result")
+        test("'minutes' in result")
+        test("result.dump()", str)
+    prints::
+        list(result) -> ['1999', '/', '12', '/', '31']
+        result[0] -> '1999'
+        result['month'] -> '12'
+        result.day -> '31'
+        'month' in result -> True
+        'minutes' in result -> False
+        result.dump() -> ['1999', '/', '12', '/', '31']
+        - day: 31
+        - month: 12
+        - year: 1999
+    """
+    def __new__(cls, toklist=None, name=None, asList=True, modal=True ):
+        if isinstance(toklist, cls):
+            return toklist
+        retobj = object.__new__(cls)
+        retobj.__doinit = True
+        return retobj
+
+    # Performance tuning: we construct a *lot* of these, so keep this
+    # constructor as small and fast as possible
+    def __init__( self, toklist=None, name=None, asList=True, modal=True, isinstance=isinstance ):
+        if self.__doinit:
+            self.__doinit = False
+            self.__name = None
+            self.__parent = None
+            self.__accumNames = {}
+            self.__asList = asList
+            self.__modal = modal
+            if toklist is None:
+                toklist = []
+            if isinstance(toklist, list):
+                self.__toklist = toklist[:]
+            elif isinstance(toklist, _generatorType):
+                self.__toklist = list(toklist)
+            else:
+                self.__toklist = [toklist]
+            self.__tokdict = dict()
+
+        if name is not None and name:
+            if not modal:
+                self.__accumNames[name] = 0
+            if isinstance(name,int):
+                name = _ustr(name) # will always return a str, but use _ustr for consistency
+            self.__name = name
+            if not (isinstance(toklist, (type(None), basestring, list)) and toklist in (None,'',[])):
+                if isinstance(toklist,basestring):
+                    toklist = [ toklist ]
+                if asList:
+                    if isinstance(toklist,ParseResults):
+                        self[name] = _ParseResultsWithOffset(toklist.copy(),0)
+                    else:
+                        self[name] = _ParseResultsWithOffset(ParseResults(toklist[0]),0)
+                    self[name].__name = name
+                else:
+                    try:
+                        self[name] = toklist[0]
+                    except (KeyError,TypeError,IndexError):
+                        self[name] = toklist
+
+    def __getitem__( self, i ):
+        if isinstance( i, (int,slice) ):
+            return self.__toklist[i]
+        else:
+            if i not in self.__accumNames:
+                return self.__tokdict[i][-1][0]
+            else:
+                return ParseResults([ v[0] for v in self.__tokdict[i] ])
+
+    def __setitem__( self, k, v, isinstance=isinstance ):
+        if isinstance(v,_ParseResultsWithOffset):
+            self.__tokdict[k] = self.__tokdict.get(k,list()) + [v]
+            sub = v[0]
+        elif isinstance(k,(int,slice)):
+            self.__toklist[k] = v
+            sub = v
+        else:
+            self.__tokdict[k] = self.__tokdict.get(k,list()) + [_ParseResultsWithOffset(v,0)]
+            sub = v
+        if isinstance(sub,ParseResults):
+            sub.__parent = wkref(self)
+
+    def __delitem__( self, i ):
+        if isinstance(i,(int,slice)):
+            mylen = len( self.__toklist )
+            del self.__toklist[i]
+
+            # convert int to slice
+            if isinstance(i, int):
+                if i < 0:
+                    i += mylen
+                i = slice(i, i+1)
+            # get removed indices
+            removed = list(range(*i.indices(mylen)))
+            removed.reverse()
+            # fixup indices in token dictionary
+            for name,occurrences in self.__tokdict.items():
+                for j in removed:
+                    for k, (value, position) in enumerate(occurrences):
+                        occurrences[k] = _ParseResultsWithOffset(value, position - (position > j))
+        else:
+            del self.__tokdict[i]
+
+    def __contains__( self, k ):
+        return k in self.__tokdict
+
+    def __len__( self ): return len( self.__toklist )
+    def __bool__(self): return ( not not self.__toklist )
+    __nonzero__ = __bool__
+    def __iter__( self ): return iter( self.__toklist )
+    def __reversed__( self ): return iter( self.__toklist[::-1] )
+    def _iterkeys( self ):
+        if hasattr(self.__tokdict, "iterkeys"):
+            return self.__tokdict.iterkeys()
+        else:
+            return iter(self.__tokdict)
+
+    def _itervalues( self ):
+        return (self[k] for k in self._iterkeys())
+            
+    def _iteritems( self ):
+        return ((k, self[k]) for k in self._iterkeys())
+
+    if PY_3:
+        keys = _iterkeys       
+        """Returns an iterator of all named result keys (Python 3.x only)."""
+
+        values = _itervalues
+        """Returns an iterator of all named result values (Python 3.x only)."""
+
+        items = _iteritems
+        """Returns an iterator of all named result key-value tuples (Python 3.x only)."""
+
+    else:
+        iterkeys = _iterkeys
+        """Returns an iterator of all named result keys (Python 2.x only)."""
+
+        itervalues = _itervalues
+        """Returns an iterator of all named result values (Python 2.x only)."""
+
+        iteritems = _iteritems
+        """Returns an iterator of all named result key-value tuples (Python 2.x only)."""
+
+        def keys( self ):
+            """Returns all named result keys (as a list in Python 2.x, as an iterator in Python 3.x)."""
+            return list(self.iterkeys())
+
+        def values( self ):
+            """Returns all named result values (as a list in Python 2.x, as an iterator in Python 3.x)."""
+            return list(self.itervalues())
+                
+        def items( self ):
+            """Returns all named result key-values (as a list of tuples in Python 2.x, as an iterator in Python 3.x)."""
+            return list(self.iteritems())
+
+    def haskeys( self ):
+        """Since keys() returns an iterator, this method is helpful in bypassing
+           code that looks for the existence of any defined results names."""
+        return bool(self.__tokdict)
+        
+    def pop( self, *args, **kwargs):
+        """
+        Removes and returns item at specified index (default=C{last}).
+        Supports both C{list} and C{dict} semantics for C{pop()}. If passed no
+        argument or an integer argument, it will use C{list} semantics
+        and pop tokens from the list of parsed tokens. If passed a 
+        non-integer argument (most likely a string), it will use C{dict}
+        semantics and pop the corresponding value from any defined 
+        results names. A second default return value argument is 
+        supported, just as in C{dict.pop()}.
+
+        Example::
+            def remove_first(tokens):
+                tokens.pop(0)
+            print(OneOrMore(Word(nums)).parseString("0 123 321")) # -> ['0', '123', '321']
+            print(OneOrMore(Word(nums)).addParseAction(remove_first).parseString("0 123 321")) # -> ['123', '321']
+
+            label = Word(alphas)
+            patt = label("LABEL") + OneOrMore(Word(nums))
+            print(patt.parseString("AAB 123 321").dump())
+
+            # Use pop() in a parse action to remove named result (note that corresponding value is not
+            # removed from list form of results)
+            def remove_LABEL(tokens):
+                tokens.pop("LABEL")
+                return tokens
+            patt.addParseAction(remove_LABEL)
+            print(patt.parseString("AAB 123 321").dump())
+        prints::
+            ['AAB', '123', '321']
+            - LABEL: AAB
+
+            ['AAB', '123', '321']
+        """
+        if not args:
+            args = [-1]
+        for k,v in kwargs.items():
+            if k == 'default':
+                args = (args[0], v)
+            else:
+                raise TypeError("pop() got an unexpected keyword argument '%s'" % k)
+        if (isinstance(args[0], int) or 
+                        len(args) == 1 or 
+                        args[0] in self):
+            index = args[0]
+            ret = self[index]
+            del self[index]
+            return ret
+        else:
+            defaultvalue = args[1]
+            return defaultvalue
+
+    def get(self, key, defaultValue=None):
+        """
+        Returns named result matching the given key, or if there is no
+        such name, then returns the given C{defaultValue} or C{None} if no
+        C{defaultValue} is specified.
+
+        Similar to C{dict.get()}.
+        
+        Example::
+            integer = Word(nums)
+            date_str = integer("year") + '/' + integer("month") + '/' + integer("day")           
+
+            result = date_str.parseString("1999/12/31")
+            print(result.get("year")) # -> '1999'
+            print(result.get("hour", "not specified")) # -> 'not specified'
+            print(result.get("hour")) # -> None
+        """
+        if key in self:
+            return self[key]
+        else:
+            return defaultValue
+
+    def insert( self, index, insStr ):
+        """
+        Inserts new element at location index in the list of parsed tokens.
+        
+        Similar to C{list.insert()}.
+
+        Example::
+            print(OneOrMore(Word(nums)).parseString("0 123 321")) # -> ['0', '123', '321']
+
+            # use a parse action to insert the parse location in the front of the parsed results
+            def insert_locn(locn, tokens):
+                tokens.insert(0, locn)
+            print(OneOrMore(Word(nums)).addParseAction(insert_locn).parseString("0 123 321")) # -> [0, '0', '123', '321']
+        """
+        self.__toklist.insert(index, insStr)
+        # fixup indices in token dictionary
+        for name,occurrences in self.__tokdict.items():
+            for k, (value, position) in enumerate(occurrences):
+                occurrences[k] = _ParseResultsWithOffset(value, position + (position > index))
+
+    def append( self, item ):
+        """
+        Add single element to end of ParseResults list of elements.
+
+        Example::
+            print(OneOrMore(Word(nums)).parseString("0 123 321")) # -> ['0', '123', '321']
+            
+            # use a parse action to compute the sum of the parsed integers, and add it to the end
+            def append_sum(tokens):
+                tokens.append(sum(map(int, tokens)))
+            print(OneOrMore(Word(nums)).addParseAction(append_sum).parseString("0 123 321")) # -> ['0', '123', '321', 444]
+        """
+        self.__toklist.append(item)
+
+    def extend( self, itemseq ):
+        """
+        Add sequence of elements to end of ParseResults list of elements.
+
+        Example::
+            patt = OneOrMore(Word(alphas))
+            
+            # use a parse action to append the reverse of the matched strings, to make a palindrome
+            def make_palindrome(tokens):
+                tokens.extend(reversed([t[::-1] for t in tokens]))
+                return ''.join(tokens)
+            print(patt.addParseAction(make_palindrome).parseString("lskdj sdlkjf lksd")) # -> 'lskdjsdlkjflksddsklfjkldsjdksl'
+        """
+        if isinstance(itemseq, ParseResults):
+            self += itemseq
+        else:
+            self.__toklist.extend(itemseq)
+
+    def clear( self ):
+        """
+        Clear all elements and results names.
+        """
+        del self.__toklist[:]
+        self.__tokdict.clear()
+
+    def __getattr__( self, name ):
+        try:
+            return self[name]
+        except KeyError:
+            return ""
+            
+        if name in self.__tokdict:
+            if name not in self.__accumNames:
+                return self.__tokdict[name][-1][0]
+            else:
+                return ParseResults([ v[0] for v in self.__tokdict[name] ])
+        else:
+            return ""
+
+    def __add__( self, other ):
+        ret = self.copy()
+        ret += other
+        return ret
+
+    def __iadd__( self, other ):
+        if other.__tokdict:
+            offset = len(self.__toklist)
+            addoffset = lambda a: offset if a<0 else a+offset
+            otheritems = other.__tokdict.items()
+            otherdictitems = [(k, _ParseResultsWithOffset(v[0],addoffset(v[1])) )
+                                for (k,vlist) in otheritems for v in vlist]
+            for k,v in otherdictitems:
+                self[k] = v
+                if isinstance(v[0],ParseResults):
+                    v[0].__parent = wkref(self)
+            
+        self.__toklist += other.__toklist
+        self.__accumNames.update( other.__accumNames )
+        return self
+
+    def __radd__(self, other):
+        if isinstance(other,int) and other == 0:
+            # useful for merging many ParseResults using sum() builtin
+            return self.copy()
+        else:
+            # this may raise a TypeError - so be it
+            return other + self
+        
+    def __repr__( self ):
+        return "(%s, %s)" % ( repr( self.__toklist ), repr( self.__tokdict ) )
+
+    def __str__( self ):
+        return '[' + ', '.join(_ustr(i) if isinstance(i, ParseResults) else repr(i) for i in self.__toklist) + ']'
+
+    def _asStringList( self, sep='' ):
+        out = []
+        for item in self.__toklist:
+            if out and sep:
+                out.append(sep)
+            if isinstance( item, ParseResults ):
+                out += item._asStringList()
+            else:
+                out.append( _ustr(item) )
+        return out
+
+    def asList( self ):
+        """
+        Returns the parse results as a nested list of matching tokens, all converted to strings.
+
+        Example::
+            patt = OneOrMore(Word(alphas))
+            result = patt.parseString("sldkj lsdkj sldkj")
+            # even though the result prints in string-like form, it is actually a pyparsing ParseResults
+            print(type(result), result) # ->  ['sldkj', 'lsdkj', 'sldkj']
+            
+            # Use asList() to create an actual list
+            result_list = result.asList()
+            print(type(result_list), result_list) # ->  ['sldkj', 'lsdkj', 'sldkj']
+        """
+        return [res.asList() if isinstance(res,ParseResults) else res for res in self.__toklist]
+
+    def asDict( self ):
+        """
+        Returns the named parse results as a nested dictionary.
+
+        Example::
+            integer = Word(nums)
+            date_str = integer("year") + '/' + integer("month") + '/' + integer("day")
+            
+            result = date_str.parseString('12/31/1999')
+            print(type(result), repr(result)) # ->  (['12', '/', '31', '/', '1999'], {'day': [('1999', 4)], 'year': [('12', 0)], 'month': [('31', 2)]})
+            
+            result_dict = result.asDict()
+            print(type(result_dict), repr(result_dict)) # ->  {'day': '1999', 'year': '12', 'month': '31'}
+
+            # even though a ParseResults supports dict-like access, sometime you just need to have a dict
+            import json
+            print(json.dumps(result)) # -> Exception: TypeError: ... is not JSON serializable
+            print(json.dumps(result.asDict())) # -> {"month": "31", "day": "1999", "year": "12"}
+        """
+        if PY_3:
+            item_fn = self.items
+        else:
+            item_fn = self.iteritems
+            
+        def toItem(obj):
+            if isinstance(obj, ParseResults):
+                if obj.haskeys():
+                    return obj.asDict()
+                else:
+                    return [toItem(v) for v in obj]
+            else:
+                return obj
+                
+        return dict((k,toItem(v)) for k,v in item_fn())
+
+    def copy( self ):
+        """
+        Returns a new copy of a C{ParseResults} object.
+        """
+        ret = ParseResults( self.__toklist )
+        ret.__tokdict = self.__tokdict.copy()
+        ret.__parent = self.__parent
+        ret.__accumNames.update( self.__accumNames )
+        ret.__name = self.__name
+        return ret
+
+    def asXML( self, doctag=None, namedItemsOnly=False, indent="", formatted=True ):
+        """
+        (Deprecated) Returns the parse results as XML. Tags are created for tokens and lists that have defined results names.
+        """
+        nl = "\n"
+        out = []
+        namedItems = dict((v[1],k) for (k,vlist) in self.__tokdict.items()
+                                                            for v in vlist)
+        nextLevelIndent = indent + "  "
+
+        # collapse out indents if formatting is not desired
+        if not formatted:
+            indent = ""
+            nextLevelIndent = ""
+            nl = ""
+
+        selfTag = None
+        if doctag is not None:
+            selfTag = doctag
+        else:
+            if self.__name:
+                selfTag = self.__name
+
+        if not selfTag:
+            if namedItemsOnly:
+                return ""
+            else:
+                selfTag = "ITEM"
+
+        out += [ nl, indent, "<", selfTag, ">" ]
+
+        for i,res in enumerate(self.__toklist):
+            if isinstance(res,ParseResults):
+                if i in namedItems:
+                    out += [ res.asXML(namedItems[i],
+                                        namedItemsOnly and doctag is None,
+                                        nextLevelIndent,
+                                        formatted)]
+                else:
+                    out += [ res.asXML(None,
+                                        namedItemsOnly and doctag is None,
+                                        nextLevelIndent,
+                                        formatted)]
+            else:
+                # individual token, see if there is a name for it
+                resTag = None
+                if i in namedItems:
+                    resTag = namedItems[i]
+                if not resTag:
+                    if namedItemsOnly:
+                        continue
+                    else:
+                        resTag = "ITEM"
+                xmlBodyText = _xml_escape(_ustr(res))
+                out += [ nl, nextLevelIndent, "<", resTag, ">",
+                                                xmlBodyText,
+                                                "" ]
+
+        out += [ nl, indent, "" ]
+        return "".join(out)
+
+    def __lookup(self,sub):
+        for k,vlist in self.__tokdict.items():
+            for v,loc in vlist:
+                if sub is v:
+                    return k
+        return None
+
+    def getName(self):
+        r"""
+        Returns the results name for this token expression. Useful when several 
+        different expressions might match at a particular location.
+
+        Example::
+            integer = Word(nums)
+            ssn_expr = Regex(r"\d\d\d-\d\d-\d\d\d\d")
+            house_number_expr = Suppress('#') + Word(nums, alphanums)
+            user_data = (Group(house_number_expr)("house_number") 
+                        | Group(ssn_expr)("ssn")
+                        | Group(integer)("age"))
+            user_info = OneOrMore(user_data)
+            
+            result = user_info.parseString("22 111-22-3333 #221B")
+            for item in result:
+                print(item.getName(), ':', item[0])
+        prints::
+            age : 22
+            ssn : 111-22-3333
+            house_number : 221B
+        """
+        if self.__name:
+            return self.__name
+        elif self.__parent:
+            par = self.__parent()
+            if par:
+                return par.__lookup(self)
+            else:
+                return None
+        elif (len(self) == 1 and
+               len(self.__tokdict) == 1 and
+               next(iter(self.__tokdict.values()))[0][1] in (0,-1)):
+            return next(iter(self.__tokdict.keys()))
+        else:
+            return None
+
+    def dump(self, indent='', depth=0, full=True):
+        """
+        Diagnostic method for listing out the contents of a C{ParseResults}.
+        Accepts an optional C{indent} argument so that this string can be embedded
+        in a nested display of other data.
+
+        Example::
+            integer = Word(nums)
+            date_str = integer("year") + '/' + integer("month") + '/' + integer("day")
+            
+            result = date_str.parseString('12/31/1999')
+            print(result.dump())
+        prints::
+            ['12', '/', '31', '/', '1999']
+            - day: 1999
+            - month: 31
+            - year: 12
+        """
+        out = []
+        NL = '\n'
+        out.append( indent+_ustr(self.asList()) )
+        if full:
+            if self.haskeys():
+                items = sorted((str(k), v) for k,v in self.items())
+                for k,v in items:
+                    if out:
+                        out.append(NL)
+                    out.append( "%s%s- %s: " % (indent,('  '*depth), k) )
+                    if isinstance(v,ParseResults):
+                        if v:
+                            out.append( v.dump(indent,depth+1) )
+                        else:
+                            out.append(_ustr(v))
+                    else:
+                        out.append(repr(v))
+            elif any(isinstance(vv,ParseResults) for vv in self):
+                v = self
+                for i,vv in enumerate(v):
+                    if isinstance(vv,ParseResults):
+                        out.append("\n%s%s[%d]:\n%s%s%s" % (indent,('  '*(depth)),i,indent,('  '*(depth+1)),vv.dump(indent,depth+1) ))
+                    else:
+                        out.append("\n%s%s[%d]:\n%s%s%s" % (indent,('  '*(depth)),i,indent,('  '*(depth+1)),_ustr(vv)))
+            
+        return "".join(out)
+
+    def pprint(self, *args, **kwargs):
+        """
+        Pretty-printer for parsed results as a list, using the C{pprint} module.
+        Accepts additional positional or keyword args as defined for the 
+        C{pprint.pprint} method. (U{http://docs.python.org/3/library/pprint.html#pprint.pprint})
+
+        Example::
+            ident = Word(alphas, alphanums)
+            num = Word(nums)
+            func = Forward()
+            term = ident | num | Group('(' + func + ')')
+            func <<= ident + Group(Optional(delimitedList(term)))
+            result = func.parseString("fna a,b,(fnb c,d,200),100")
+            result.pprint(width=40)
+        prints::
+            ['fna',
+             ['a',
+              'b',
+              ['(', 'fnb', ['c', 'd', '200'], ')'],
+              '100']]
+        """
+        pprint.pprint(self.asList(), *args, **kwargs)
+
+    # add support for pickle protocol
+    def __getstate__(self):
+        return ( self.__toklist,
+                 ( self.__tokdict.copy(),
+                   self.__parent is not None and self.__parent() or None,
+                   self.__accumNames,
+                   self.__name ) )
+
+    def __setstate__(self,state):
+        self.__toklist = state[0]
+        (self.__tokdict,
+         par,
+         inAccumNames,
+         self.__name) = state[1]
+        self.__accumNames = {}
+        self.__accumNames.update(inAccumNames)
+        if par is not None:
+            self.__parent = wkref(par)
+        else:
+            self.__parent = None
+
+    def __getnewargs__(self):
+        return self.__toklist, self.__name, self.__asList, self.__modal
+
+    def __dir__(self):
+        return (dir(type(self)) + list(self.keys()))
+
+MutableMapping.register(ParseResults)
+
+def col (loc,strg):
+    """Returns current column within a string, counting newlines as line separators.
+   The first column is number 1.
+
+   Note: the default parsing behavior is to expand tabs in the input string
+   before starting the parsing process.  See L{I{ParserElement.parseString}} for more information
+   on parsing strings containing C{}s, and suggested methods to maintain a
+   consistent view of the parsed string, the parse location, and line and column
+   positions within the parsed string.
+   """
+    s = strg
+    return 1 if 0} for more information
+   on parsing strings containing C{}s, and suggested methods to maintain a
+   consistent view of the parsed string, the parse location, and line and column
+   positions within the parsed string.
+   """
+    return strg.count("\n",0,loc) + 1
+
+def line( loc, strg ):
+    """Returns the line of text containing loc within a string, counting newlines as line separators.
+       """
+    lastCR = strg.rfind("\n", 0, loc)
+    nextCR = strg.find("\n", loc)
+    if nextCR >= 0:
+        return strg[lastCR+1:nextCR]
+    else:
+        return strg[lastCR+1:]
+
+def _defaultStartDebugAction( instring, loc, expr ):
+    print (("Match " + _ustr(expr) + " at loc " + _ustr(loc) + "(%d,%d)" % ( lineno(loc,instring), col(loc,instring) )))
+
+def _defaultSuccessDebugAction( instring, startloc, endloc, expr, toks ):
+    print ("Matched " + _ustr(expr) + " -> " + str(toks.asList()))
+
+def _defaultExceptionDebugAction( instring, loc, expr, exc ):
+    print ("Exception raised:" + _ustr(exc))
+
+def nullDebugAction(*args):
+    """'Do-nothing' debug action, to suppress debugging output during parsing."""
+    pass
+
+# Only works on Python 3.x - nonlocal is toxic to Python 2 installs
+#~ 'decorator to trim function calls to match the arity of the target'
+#~ def _trim_arity(func, maxargs=3):
+    #~ if func in singleArgBuiltins:
+        #~ return lambda s,l,t: func(t)
+    #~ limit = 0
+    #~ foundArity = False
+    #~ def wrapper(*args):
+        #~ nonlocal limit,foundArity
+        #~ while 1:
+            #~ try:
+                #~ ret = func(*args[limit:])
+                #~ foundArity = True
+                #~ return ret
+            #~ except TypeError:
+                #~ if limit == maxargs or foundArity:
+                    #~ raise
+                #~ limit += 1
+                #~ continue
+    #~ return wrapper
+
+# this version is Python 2.x-3.x cross-compatible
+'decorator to trim function calls to match the arity of the target'
+def _trim_arity(func, maxargs=2):
+    if func in singleArgBuiltins:
+        return lambda s,l,t: func(t)
+    limit = [0]
+    foundArity = [False]
+    
+    # traceback return data structure changed in Py3.5 - normalize back to plain tuples
+    if system_version[:2] >= (3,5):
+        def extract_stack(limit=0):
+            # special handling for Python 3.5.0 - extra deep call stack by 1
+            offset = -3 if system_version == (3,5,0) else -2
+            frame_summary = traceback.extract_stack(limit=-offset+limit-1)[offset]
+            return [frame_summary[:2]]
+        def extract_tb(tb, limit=0):
+            frames = traceback.extract_tb(tb, limit=limit)
+            frame_summary = frames[-1]
+            return [frame_summary[:2]]
+    else:
+        extract_stack = traceback.extract_stack
+        extract_tb = traceback.extract_tb
+    
+    # synthesize what would be returned by traceback.extract_stack at the call to 
+    # user's parse action 'func', so that we don't incur call penalty at parse time
+    
+    LINE_DIFF = 6
+    # IF ANY CODE CHANGES, EVEN JUST COMMENTS OR BLANK LINES, BETWEEN THE NEXT LINE AND 
+    # THE CALL TO FUNC INSIDE WRAPPER, LINE_DIFF MUST BE MODIFIED!!!!
+    this_line = extract_stack(limit=2)[-1]
+    pa_call_line_synth = (this_line[0], this_line[1]+LINE_DIFF)
+
+    def wrapper(*args):
+        while 1:
+            try:
+                ret = func(*args[limit[0]:])
+                foundArity[0] = True
+                return ret
+            except TypeError:
+                # re-raise TypeErrors if they did not come from our arity testing
+                if foundArity[0]:
+                    raise
+                else:
+                    try:
+                        tb = sys.exc_info()[-1]
+                        if not extract_tb(tb, limit=2)[-1][:2] == pa_call_line_synth:
+                            raise
+                    finally:
+                        del tb
+
+                if limit[0] <= maxargs:
+                    limit[0] += 1
+                    continue
+                raise
+
+    # copy func name to wrapper for sensible debug output
+    func_name = ""
+    try:
+        func_name = getattr(func, '__name__', 
+                            getattr(func, '__class__').__name__)
+    except Exception:
+        func_name = str(func)
+    wrapper.__name__ = func_name
+
+    return wrapper
+
+class ParserElement(object):
+    """Abstract base level parser element class."""
+    DEFAULT_WHITE_CHARS = " \n\t\r"
+    verbose_stacktrace = False
+
+    @staticmethod
+    def setDefaultWhitespaceChars( chars ):
+        r"""
+        Overrides the default whitespace chars
+
+        Example::
+            # default whitespace chars are space,  and newline
+            OneOrMore(Word(alphas)).parseString("abc def\nghi jkl")  # -> ['abc', 'def', 'ghi', 'jkl']
+            
+            # change to just treat newline as significant
+            ParserElement.setDefaultWhitespaceChars(" \t")
+            OneOrMore(Word(alphas)).parseString("abc def\nghi jkl")  # -> ['abc', 'def']
+        """
+        ParserElement.DEFAULT_WHITE_CHARS = chars
+
+    @staticmethod
+    def inlineLiteralsUsing(cls):
+        """
+        Set class to be used for inclusion of string literals into a parser.
+        
+        Example::
+            # default literal class used is Literal
+            integer = Word(nums)
+            date_str = integer("year") + '/' + integer("month") + '/' + integer("day")           
+
+            date_str.parseString("1999/12/31")  # -> ['1999', '/', '12', '/', '31']
+
+
+            # change to Suppress
+            ParserElement.inlineLiteralsUsing(Suppress)
+            date_str = integer("year") + '/' + integer("month") + '/' + integer("day")           
+
+            date_str.parseString("1999/12/31")  # -> ['1999', '12', '31']
+        """
+        ParserElement._literalStringClass = cls
+
+    def __init__( self, savelist=False ):
+        self.parseAction = list()
+        self.failAction = None
+        #~ self.name = ""  # don't define self.name, let subclasses try/except upcall
+        self.strRepr = None
+        self.resultsName = None
+        self.saveAsList = savelist
+        self.skipWhitespace = True
+        self.whiteChars = ParserElement.DEFAULT_WHITE_CHARS
+        self.copyDefaultWhiteChars = True
+        self.mayReturnEmpty = False # used when checking for left-recursion
+        self.keepTabs = False
+        self.ignoreExprs = list()
+        self.debug = False
+        self.streamlined = False
+        self.mayIndexError = True # used to optimize exception handling for subclasses that don't advance parse index
+        self.errmsg = ""
+        self.modalResults = True # used to mark results names as modal (report only last) or cumulative (list all)
+        self.debugActions = ( None, None, None ) #custom debug actions
+        self.re = None
+        self.callPreparse = True # used to avoid redundant calls to preParse
+        self.callDuringTry = False
+
+    def copy( self ):
+        """
+        Make a copy of this C{ParserElement}.  Useful for defining different parse actions
+        for the same parsing pattern, using copies of the original parse element.
+        
+        Example::
+            integer = Word(nums).setParseAction(lambda toks: int(toks[0]))
+            integerK = integer.copy().addParseAction(lambda toks: toks[0]*1024) + Suppress("K")
+            integerM = integer.copy().addParseAction(lambda toks: toks[0]*1024*1024) + Suppress("M")
+            
+            print(OneOrMore(integerK | integerM | integer).parseString("5K 100 640K 256M"))
+        prints::
+            [5120, 100, 655360, 268435456]
+        Equivalent form of C{expr.copy()} is just C{expr()}::
+            integerM = integer().addParseAction(lambda toks: toks[0]*1024*1024) + Suppress("M")
+        """
+        cpy = copy.copy( self )
+        cpy.parseAction = self.parseAction[:]
+        cpy.ignoreExprs = self.ignoreExprs[:]
+        if self.copyDefaultWhiteChars:
+            cpy.whiteChars = ParserElement.DEFAULT_WHITE_CHARS
+        return cpy
+
+    def setName( self, name ):
+        """
+        Define name for this expression, makes debugging and exception messages clearer.
+        
+        Example::
+            Word(nums).parseString("ABC")  # -> Exception: Expected W:(0123...) (at char 0), (line:1, col:1)
+            Word(nums).setName("integer").parseString("ABC")  # -> Exception: Expected integer (at char 0), (line:1, col:1)
+        """
+        self.name = name
+        self.errmsg = "Expected " + self.name
+        if hasattr(self,"exception"):
+            self.exception.msg = self.errmsg
+        return self
+
+    def setResultsName( self, name, listAllMatches=False ):
+        """
+        Define name for referencing matching tokens as a nested attribute
+        of the returned parse results.
+        NOTE: this returns a *copy* of the original C{ParserElement} object;
+        this is so that the client can define a basic element, such as an
+        integer, and reference it in multiple places with different names.
+
+        You can also set results names using the abbreviated syntax,
+        C{expr("name")} in place of C{expr.setResultsName("name")} - 
+        see L{I{__call__}<__call__>}.
+
+        Example::
+            date_str = (integer.setResultsName("year") + '/' 
+                        + integer.setResultsName("month") + '/' 
+                        + integer.setResultsName("day"))
+
+            # equivalent form:
+            date_str = integer("year") + '/' + integer("month") + '/' + integer("day")
+        """
+        newself = self.copy()
+        if name.endswith("*"):
+            name = name[:-1]
+            listAllMatches=True
+        newself.resultsName = name
+        newself.modalResults = not listAllMatches
+        return newself
+
+    def setBreak(self,breakFlag = True):
+        """Method to invoke the Python pdb debugger when this element is
+           about to be parsed. Set C{breakFlag} to True to enable, False to
+           disable.
+        """
+        if breakFlag:
+            _parseMethod = self._parse
+            def breaker(instring, loc, doActions=True, callPreParse=True):
+                import pdb
+                pdb.set_trace()
+                return _parseMethod( instring, loc, doActions, callPreParse )
+            breaker._originalParseMethod = _parseMethod
+            self._parse = breaker
+        else:
+            if hasattr(self._parse,"_originalParseMethod"):
+                self._parse = self._parse._originalParseMethod
+        return self
+
+    def setParseAction( self, *fns, **kwargs ):
+        """
+        Define one or more actions to perform when successfully matching parse element definition.
+        Parse action fn is a callable method with 0-3 arguments, called as C{fn(s,loc,toks)},
+        C{fn(loc,toks)}, C{fn(toks)}, or just C{fn()}, where:
+         - s   = the original string being parsed (see note below)
+         - loc = the location of the matching substring
+         - toks = a list of the matched tokens, packaged as a C{L{ParseResults}} object
+        If the functions in fns modify the tokens, they can return them as the return
+        value from fn, and the modified list of tokens will replace the original.
+        Otherwise, fn does not need to return any value.
+
+        Optional keyword arguments:
+         - callDuringTry = (default=C{False}) indicate if parse action should be run during lookaheads and alternate testing
+
+        Note: the default parsing behavior is to expand tabs in the input string
+        before starting the parsing process.  See L{I{parseString}} for more information
+        on parsing strings containing C{}s, and suggested methods to maintain a
+        consistent view of the parsed string, the parse location, and line and column
+        positions within the parsed string.
+        
+        Example::
+            integer = Word(nums)
+            date_str = integer + '/' + integer + '/' + integer
+
+            date_str.parseString("1999/12/31")  # -> ['1999', '/', '12', '/', '31']
+
+            # use parse action to convert to ints at parse time
+            integer = Word(nums).setParseAction(lambda toks: int(toks[0]))
+            date_str = integer + '/' + integer + '/' + integer
+
+            # note that integer fields are now ints, not strings
+            date_str.parseString("1999/12/31")  # -> [1999, '/', 12, '/', 31]
+        """
+        self.parseAction = list(map(_trim_arity, list(fns)))
+        self.callDuringTry = kwargs.get("callDuringTry", False)
+        return self
+
+    def addParseAction( self, *fns, **kwargs ):
+        """
+        Add one or more parse actions to expression's list of parse actions. See L{I{setParseAction}}.
+        
+        See examples in L{I{copy}}.
+        """
+        self.parseAction += list(map(_trim_arity, list(fns)))
+        self.callDuringTry = self.callDuringTry or kwargs.get("callDuringTry", False)
+        return self
+
+    def addCondition(self, *fns, **kwargs):
+        """Add a boolean predicate function to expression's list of parse actions. See 
+        L{I{setParseAction}} for function call signatures. Unlike C{setParseAction}, 
+        functions passed to C{addCondition} need to return boolean success/fail of the condition.
+
+        Optional keyword arguments:
+         - message = define a custom message to be used in the raised exception
+         - fatal   = if True, will raise ParseFatalException to stop parsing immediately; otherwise will raise ParseException
+         
+        Example::
+            integer = Word(nums).setParseAction(lambda toks: int(toks[0]))
+            year_int = integer.copy()
+            year_int.addCondition(lambda toks: toks[0] >= 2000, message="Only support years 2000 and later")
+            date_str = year_int + '/' + integer + '/' + integer
+
+            result = date_str.parseString("1999/12/31")  # -> Exception: Only support years 2000 and later (at char 0), (line:1, col:1)
+        """
+        msg = kwargs.get("message", "failed user-defined condition")
+        exc_type = ParseFatalException if kwargs.get("fatal", False) else ParseException
+        for fn in fns:
+            def pa(s,l,t):
+                if not bool(_trim_arity(fn)(s,l,t)):
+                    raise exc_type(s,l,msg)
+            self.parseAction.append(pa)
+        self.callDuringTry = self.callDuringTry or kwargs.get("callDuringTry", False)
+        return self
+
+    def setFailAction( self, fn ):
+        """Define action to perform if parsing fails at this expression.
+           Fail acton fn is a callable function that takes the arguments
+           C{fn(s,loc,expr,err)} where:
+            - s = string being parsed
+            - loc = location where expression match was attempted and failed
+            - expr = the parse expression that failed
+            - err = the exception thrown
+           The function returns no value.  It may throw C{L{ParseFatalException}}
+           if it is desired to stop parsing immediately."""
+        self.failAction = fn
+        return self
+
+    def _skipIgnorables( self, instring, loc ):
+        exprsFound = True
+        while exprsFound:
+            exprsFound = False
+            for e in self.ignoreExprs:
+                try:
+                    while 1:
+                        loc,dummy = e._parse( instring, loc )
+                        exprsFound = True
+                except ParseException:
+                    pass
+        return loc
+
+    def preParse( self, instring, loc ):
+        if self.ignoreExprs:
+            loc = self._skipIgnorables( instring, loc )
+
+        if self.skipWhitespace:
+            wt = self.whiteChars
+            instrlen = len(instring)
+            while loc < instrlen and instring[loc] in wt:
+                loc += 1
+
+        return loc
+
+    def parseImpl( self, instring, loc, doActions=True ):
+        return loc, []
+
+    def postParse( self, instring, loc, tokenlist ):
+        return tokenlist
+
+    #~ @profile
+    def _parseNoCache( self, instring, loc, doActions=True, callPreParse=True ):
+        debugging = ( self.debug ) #and doActions )
+
+        if debugging or self.failAction:
+            #~ print ("Match",self,"at loc",loc,"(%d,%d)" % ( lineno(loc,instring), col(loc,instring) ))
+            if (self.debugActions[0] ):
+                self.debugActions[0]( instring, loc, self )
+            if callPreParse and self.callPreparse:
+                preloc = self.preParse( instring, loc )
+            else:
+                preloc = loc
+            tokensStart = preloc
+            try:
+                try:
+                    loc,tokens = self.parseImpl( instring, preloc, doActions )
+                except IndexError:
+                    raise ParseException( instring, len(instring), self.errmsg, self )
+            except ParseBaseException as err:
+                #~ print ("Exception raised:", err)
+                if self.debugActions[2]:
+                    self.debugActions[2]( instring, tokensStart, self, err )
+                if self.failAction:
+                    self.failAction( instring, tokensStart, self, err )
+                raise
+        else:
+            if callPreParse and self.callPreparse:
+                preloc = self.preParse( instring, loc )
+            else:
+                preloc = loc
+            tokensStart = preloc
+            if self.mayIndexError or preloc >= len(instring):
+                try:
+                    loc,tokens = self.parseImpl( instring, preloc, doActions )
+                except IndexError:
+                    raise ParseException( instring, len(instring), self.errmsg, self )
+            else:
+                loc,tokens = self.parseImpl( instring, preloc, doActions )
+
+        tokens = self.postParse( instring, loc, tokens )
+
+        retTokens = ParseResults( tokens, self.resultsName, asList=self.saveAsList, modal=self.modalResults )
+        if self.parseAction and (doActions or self.callDuringTry):
+            if debugging:
+                try:
+                    for fn in self.parseAction:
+                        tokens = fn( instring, tokensStart, retTokens )
+                        if tokens is not None:
+                            retTokens = ParseResults( tokens,
+                                                      self.resultsName,
+                                                      asList=self.saveAsList and isinstance(tokens,(ParseResults,list)),
+                                                      modal=self.modalResults )
+                except ParseBaseException as err:
+                    #~ print "Exception raised in user parse action:", err
+                    if (self.debugActions[2] ):
+                        self.debugActions[2]( instring, tokensStart, self, err )
+                    raise
+            else:
+                for fn in self.parseAction:
+                    tokens = fn( instring, tokensStart, retTokens )
+                    if tokens is not None:
+                        retTokens = ParseResults( tokens,
+                                                  self.resultsName,
+                                                  asList=self.saveAsList and isinstance(tokens,(ParseResults,list)),
+                                                  modal=self.modalResults )
+        if debugging:
+            #~ print ("Matched",self,"->",retTokens.asList())
+            if (self.debugActions[1] ):
+                self.debugActions[1]( instring, tokensStart, loc, self, retTokens )
+
+        return loc, retTokens
+
+    def tryParse( self, instring, loc ):
+        try:
+            return self._parse( instring, loc, doActions=False )[0]
+        except ParseFatalException:
+            raise ParseException( instring, loc, self.errmsg, self)
+    
+    def canParseNext(self, instring, loc):
+        try:
+            self.tryParse(instring, loc)
+        except (ParseException, IndexError):
+            return False
+        else:
+            return True
+
+    class _UnboundedCache(object):
+        def __init__(self):
+            cache = {}
+            self.not_in_cache = not_in_cache = object()
+
+            def get(self, key):
+                return cache.get(key, not_in_cache)
+
+            def set(self, key, value):
+                cache[key] = value
+
+            def clear(self):
+                cache.clear()
+                
+            def cache_len(self):
+                return len(cache)
+
+            self.get = types.MethodType(get, self)
+            self.set = types.MethodType(set, self)
+            self.clear = types.MethodType(clear, self)
+            self.__len__ = types.MethodType(cache_len, self)
+
+    if _OrderedDict is not None:
+        class _FifoCache(object):
+            def __init__(self, size):
+                self.not_in_cache = not_in_cache = object()
+
+                cache = _OrderedDict()
+
+                def get(self, key):
+                    return cache.get(key, not_in_cache)
+
+                def set(self, key, value):
+                    cache[key] = value
+                    while len(cache) > size:
+                        try:
+                            cache.popitem(False)
+                        except KeyError:
+                            pass
+
+                def clear(self):
+                    cache.clear()
+
+                def cache_len(self):
+                    return len(cache)
+
+                self.get = types.MethodType(get, self)
+                self.set = types.MethodType(set, self)
+                self.clear = types.MethodType(clear, self)
+                self.__len__ = types.MethodType(cache_len, self)
+
+    else:
+        class _FifoCache(object):
+            def __init__(self, size):
+                self.not_in_cache = not_in_cache = object()
+
+                cache = {}
+                key_fifo = collections.deque([], size)
+
+                def get(self, key):
+                    return cache.get(key, not_in_cache)
+
+                def set(self, key, value):
+                    cache[key] = value
+                    while len(key_fifo) > size:
+                        cache.pop(key_fifo.popleft(), None)
+                    key_fifo.append(key)
+
+                def clear(self):
+                    cache.clear()
+                    key_fifo.clear()
+
+                def cache_len(self):
+                    return len(cache)
+
+                self.get = types.MethodType(get, self)
+                self.set = types.MethodType(set, self)
+                self.clear = types.MethodType(clear, self)
+                self.__len__ = types.MethodType(cache_len, self)
+
+    # argument cache for optimizing repeated calls when backtracking through recursive expressions
+    packrat_cache = {} # this is set later by enabledPackrat(); this is here so that resetCache() doesn't fail
+    packrat_cache_lock = RLock()
+    packrat_cache_stats = [0, 0]
+
+    # this method gets repeatedly called during backtracking with the same arguments -
+    # we can cache these arguments and save ourselves the trouble of re-parsing the contained expression
+    def _parseCache( self, instring, loc, doActions=True, callPreParse=True ):
+        HIT, MISS = 0, 1
+        lookup = (self, instring, loc, callPreParse, doActions)
+        with ParserElement.packrat_cache_lock:
+            cache = ParserElement.packrat_cache
+            value = cache.get(lookup)
+            if value is cache.not_in_cache:
+                ParserElement.packrat_cache_stats[MISS] += 1
+                try:
+                    value = self._parseNoCache(instring, loc, doActions, callPreParse)
+                except ParseBaseException as pe:
+                    # cache a copy of the exception, without the traceback
+                    cache.set(lookup, pe.__class__(*pe.args))
+                    raise
+                else:
+                    cache.set(lookup, (value[0], value[1].copy()))
+                    return value
+            else:
+                ParserElement.packrat_cache_stats[HIT] += 1
+                if isinstance(value, Exception):
+                    raise value
+                return (value[0], value[1].copy())
+
+    _parse = _parseNoCache
+
+    @staticmethod
+    def resetCache():
+        ParserElement.packrat_cache.clear()
+        ParserElement.packrat_cache_stats[:] = [0] * len(ParserElement.packrat_cache_stats)
+
+    _packratEnabled = False
+    @staticmethod
+    def enablePackrat(cache_size_limit=128):
+        """Enables "packrat" parsing, which adds memoizing to the parsing logic.
+           Repeated parse attempts at the same string location (which happens
+           often in many complex grammars) can immediately return a cached value,
+           instead of re-executing parsing/validating code.  Memoizing is done of
+           both valid results and parsing exceptions.
+           
+           Parameters:
+            - cache_size_limit - (default=C{128}) - if an integer value is provided
+              will limit the size of the packrat cache; if None is passed, then
+              the cache size will be unbounded; if 0 is passed, the cache will
+              be effectively disabled.
+            
+           This speedup may break existing programs that use parse actions that
+           have side-effects.  For this reason, packrat parsing is disabled when
+           you first import pyparsing.  To activate the packrat feature, your
+           program must call the class method C{ParserElement.enablePackrat()}.  If
+           your program uses C{psyco} to "compile as you go", you must call
+           C{enablePackrat} before calling C{psyco.full()}.  If you do not do this,
+           Python will crash.  For best results, call C{enablePackrat()} immediately
+           after importing pyparsing.
+           
+           Example::
+               import pyparsing
+               pyparsing.ParserElement.enablePackrat()
+        """
+        if not ParserElement._packratEnabled:
+            ParserElement._packratEnabled = True
+            if cache_size_limit is None:
+                ParserElement.packrat_cache = ParserElement._UnboundedCache()
+            else:
+                ParserElement.packrat_cache = ParserElement._FifoCache(cache_size_limit)
+            ParserElement._parse = ParserElement._parseCache
+
+    def parseString( self, instring, parseAll=False ):
+        """
+        Execute the parse expression with the given string.
+        This is the main interface to the client code, once the complete
+        expression has been built.
+
+        If you want the grammar to require that the entire input string be
+        successfully parsed, then set C{parseAll} to True (equivalent to ending
+        the grammar with C{L{StringEnd()}}).
+
+        Note: C{parseString} implicitly calls C{expandtabs()} on the input string,
+        in order to report proper column numbers in parse actions.
+        If the input string contains tabs and
+        the grammar uses parse actions that use the C{loc} argument to index into the
+        string being parsed, you can ensure you have a consistent view of the input
+        string by:
+         - calling C{parseWithTabs} on your grammar before calling C{parseString}
+           (see L{I{parseWithTabs}})
+         - define your parse action using the full C{(s,loc,toks)} signature, and
+           reference the input string using the parse action's C{s} argument
+         - explictly expand the tabs in your input string before calling
+           C{parseString}
+        
+        Example::
+            Word('a').parseString('aaaaabaaa')  # -> ['aaaaa']
+            Word('a').parseString('aaaaabaaa', parseAll=True)  # -> Exception: Expected end of text
+        """
+        ParserElement.resetCache()
+        if not self.streamlined:
+            self.streamline()
+            #~ self.saveAsList = True
+        for e in self.ignoreExprs:
+            e.streamline()
+        if not self.keepTabs:
+            instring = instring.expandtabs()
+        try:
+            loc, tokens = self._parse( instring, 0 )
+            if parseAll:
+                loc = self.preParse( instring, loc )
+                se = Empty() + StringEnd()
+                se._parse( instring, loc )
+        except ParseBaseException as exc:
+            if ParserElement.verbose_stacktrace:
+                raise
+            else:
+                # catch and re-raise exception from here, clears out pyparsing internal stack trace
+                raise exc
+        else:
+            return tokens
+
+    def scanString( self, instring, maxMatches=_MAX_INT, overlap=False ):
+        """
+        Scan the input string for expression matches.  Each match will return the
+        matching tokens, start location, and end location.  May be called with optional
+        C{maxMatches} argument, to clip scanning after 'n' matches are found.  If
+        C{overlap} is specified, then overlapping matches will be reported.
+
+        Note that the start and end locations are reported relative to the string
+        being parsed.  See L{I{parseString}} for more information on parsing
+        strings with embedded tabs.
+
+        Example::
+            source = "sldjf123lsdjjkf345sldkjf879lkjsfd987"
+            print(source)
+            for tokens,start,end in Word(alphas).scanString(source):
+                print(' '*start + '^'*(end-start))
+                print(' '*start + tokens[0])
+        
+        prints::
+        
+            sldjf123lsdjjkf345sldkjf879lkjsfd987
+            ^^^^^
+            sldjf
+                    ^^^^^^^
+                    lsdjjkf
+                              ^^^^^^
+                              sldkjf
+                                       ^^^^^^
+                                       lkjsfd
+        """
+        if not self.streamlined:
+            self.streamline()
+        for e in self.ignoreExprs:
+            e.streamline()
+
+        if not self.keepTabs:
+            instring = _ustr(instring).expandtabs()
+        instrlen = len(instring)
+        loc = 0
+        preparseFn = self.preParse
+        parseFn = self._parse
+        ParserElement.resetCache()
+        matches = 0
+        try:
+            while loc <= instrlen and matches < maxMatches:
+                try:
+                    preloc = preparseFn( instring, loc )
+                    nextLoc,tokens = parseFn( instring, preloc, callPreParse=False )
+                except ParseException:
+                    loc = preloc+1
+                else:
+                    if nextLoc > loc:
+                        matches += 1
+                        yield tokens, preloc, nextLoc
+                        if overlap:
+                            nextloc = preparseFn( instring, loc )
+                            if nextloc > loc:
+                                loc = nextLoc
+                            else:
+                                loc += 1
+                        else:
+                            loc = nextLoc
+                    else:
+                        loc = preloc+1
+        except ParseBaseException as exc:
+            if ParserElement.verbose_stacktrace:
+                raise
+            else:
+                # catch and re-raise exception from here, clears out pyparsing internal stack trace
+                raise exc
+
+    def transformString( self, instring ):
+        """
+        Extension to C{L{scanString}}, to modify matching text with modified tokens that may
+        be returned from a parse action.  To use C{transformString}, define a grammar and
+        attach a parse action to it that modifies the returned token list.
+        Invoking C{transformString()} on a target string will then scan for matches,
+        and replace the matched text patterns according to the logic in the parse
+        action.  C{transformString()} returns the resulting transformed string.
+        
+        Example::
+            wd = Word(alphas)
+            wd.setParseAction(lambda toks: toks[0].title())
+            
+            print(wd.transformString("now is the winter of our discontent made glorious summer by this sun of york."))
+        Prints::
+            Now Is The Winter Of Our Discontent Made Glorious Summer By This Sun Of York.
+        """
+        out = []
+        lastE = 0
+        # force preservation of s, to minimize unwanted transformation of string, and to
+        # keep string locs straight between transformString and scanString
+        self.keepTabs = True
+        try:
+            for t,s,e in self.scanString( instring ):
+                out.append( instring[lastE:s] )
+                if t:
+                    if isinstance(t,ParseResults):
+                        out += t.asList()
+                    elif isinstance(t,list):
+                        out += t
+                    else:
+                        out.append(t)
+                lastE = e
+            out.append(instring[lastE:])
+            out = [o for o in out if o]
+            return "".join(map(_ustr,_flatten(out)))
+        except ParseBaseException as exc:
+            if ParserElement.verbose_stacktrace:
+                raise
+            else:
+                # catch and re-raise exception from here, clears out pyparsing internal stack trace
+                raise exc
+
+    def searchString( self, instring, maxMatches=_MAX_INT ):
+        """
+        Another extension to C{L{scanString}}, simplifying the access to the tokens found
+        to match the given parse expression.  May be called with optional
+        C{maxMatches} argument, to clip searching after 'n' matches are found.
+        
+        Example::
+            # a capitalized word starts with an uppercase letter, followed by zero or more lowercase letters
+            cap_word = Word(alphas.upper(), alphas.lower())
+            
+            print(cap_word.searchString("More than Iron, more than Lead, more than Gold I need Electricity"))
+
+            # the sum() builtin can be used to merge results into a single ParseResults object
+            print(sum(cap_word.searchString("More than Iron, more than Lead, more than Gold I need Electricity")))
+        prints::
+            [['More'], ['Iron'], ['Lead'], ['Gold'], ['I'], ['Electricity']]
+            ['More', 'Iron', 'Lead', 'Gold', 'I', 'Electricity']
+        """
+        try:
+            return ParseResults([ t for t,s,e in self.scanString( instring, maxMatches ) ])
+        except ParseBaseException as exc:
+            if ParserElement.verbose_stacktrace:
+                raise
+            else:
+                # catch and re-raise exception from here, clears out pyparsing internal stack trace
+                raise exc
+
+    def split(self, instring, maxsplit=_MAX_INT, includeSeparators=False):
+        """
+        Generator method to split a string using the given expression as a separator.
+        May be called with optional C{maxsplit} argument, to limit the number of splits;
+        and the optional C{includeSeparators} argument (default=C{False}), if the separating
+        matching text should be included in the split results.
+        
+        Example::        
+            punc = oneOf(list(".,;:/-!?"))
+            print(list(punc.split("This, this?, this sentence, is badly punctuated!")))
+        prints::
+            ['This', ' this', '', ' this sentence', ' is badly punctuated', '']
+        """
+        splits = 0
+        last = 0
+        for t,s,e in self.scanString(instring, maxMatches=maxsplit):
+            yield instring[last:s]
+            if includeSeparators:
+                yield t[0]
+            last = e
+        yield instring[last:]
+
+    def __add__(self, other ):
+        """
+        Implementation of + operator - returns C{L{And}}. Adding strings to a ParserElement
+        converts them to L{Literal}s by default.
+        
+        Example::
+            greet = Word(alphas) + "," + Word(alphas) + "!"
+            hello = "Hello, World!"
+            print (hello, "->", greet.parseString(hello))
+        Prints::
+            Hello, World! -> ['Hello', ',', 'World', '!']
+        """
+        if isinstance( other, basestring ):
+            other = ParserElement._literalStringClass( other )
+        if not isinstance( other, ParserElement ):
+            warnings.warn("Cannot combine element of type %s with ParserElement" % type(other),
+                    SyntaxWarning, stacklevel=2)
+            return None
+        return And( [ self, other ] )
+
+    def __radd__(self, other ):
+        """
+        Implementation of + operator when left operand is not a C{L{ParserElement}}
+        """
+        if isinstance( other, basestring ):
+            other = ParserElement._literalStringClass( other )
+        if not isinstance( other, ParserElement ):
+            warnings.warn("Cannot combine element of type %s with ParserElement" % type(other),
+                    SyntaxWarning, stacklevel=2)
+            return None
+        return other + self
+
+    def __sub__(self, other):
+        """
+        Implementation of - operator, returns C{L{And}} with error stop
+        """
+        if isinstance( other, basestring ):
+            other = ParserElement._literalStringClass( other )
+        if not isinstance( other, ParserElement ):
+            warnings.warn("Cannot combine element of type %s with ParserElement" % type(other),
+                    SyntaxWarning, stacklevel=2)
+            return None
+        return self + And._ErrorStop() + other
+
+    def __rsub__(self, other ):
+        """
+        Implementation of - operator when left operand is not a C{L{ParserElement}}
+        """
+        if isinstance( other, basestring ):
+            other = ParserElement._literalStringClass( other )
+        if not isinstance( other, ParserElement ):
+            warnings.warn("Cannot combine element of type %s with ParserElement" % type(other),
+                    SyntaxWarning, stacklevel=2)
+            return None
+        return other - self
+
+    def __mul__(self,other):
+        """
+        Implementation of * operator, allows use of C{expr * 3} in place of
+        C{expr + expr + expr}.  Expressions may also me multiplied by a 2-integer
+        tuple, similar to C{{min,max}} multipliers in regular expressions.  Tuples
+        may also include C{None} as in:
+         - C{expr*(n,None)} or C{expr*(n,)} is equivalent
+              to C{expr*n + L{ZeroOrMore}(expr)}
+              (read as "at least n instances of C{expr}")
+         - C{expr*(None,n)} is equivalent to C{expr*(0,n)}
+              (read as "0 to n instances of C{expr}")
+         - C{expr*(None,None)} is equivalent to C{L{ZeroOrMore}(expr)}
+         - C{expr*(1,None)} is equivalent to C{L{OneOrMore}(expr)}
+
+        Note that C{expr*(None,n)} does not raise an exception if
+        more than n exprs exist in the input stream; that is,
+        C{expr*(None,n)} does not enforce a maximum number of expr
+        occurrences.  If this behavior is desired, then write
+        C{expr*(None,n) + ~expr}
+        """
+        if isinstance(other,int):
+            minElements, optElements = other,0
+        elif isinstance(other,tuple):
+            other = (other + (None, None))[:2]
+            if other[0] is None:
+                other = (0, other[1])
+            if isinstance(other[0],int) and other[1] is None:
+                if other[0] == 0:
+                    return ZeroOrMore(self)
+                if other[0] == 1:
+                    return OneOrMore(self)
+                else:
+                    return self*other[0] + ZeroOrMore(self)
+            elif isinstance(other[0],int) and isinstance(other[1],int):
+                minElements, optElements = other
+                optElements -= minElements
+            else:
+                raise TypeError("cannot multiply 'ParserElement' and ('%s','%s') objects", type(other[0]),type(other[1]))
+        else:
+            raise TypeError("cannot multiply 'ParserElement' and '%s' objects", type(other))
+
+        if minElements < 0:
+            raise ValueError("cannot multiply ParserElement by negative value")
+        if optElements < 0:
+            raise ValueError("second tuple value must be greater or equal to first tuple value")
+        if minElements == optElements == 0:
+            raise ValueError("cannot multiply ParserElement by 0 or (0,0)")
+
+        if (optElements):
+            def makeOptionalList(n):
+                if n>1:
+                    return Optional(self + makeOptionalList(n-1))
+                else:
+                    return Optional(self)
+            if minElements:
+                if minElements == 1:
+                    ret = self + makeOptionalList(optElements)
+                else:
+                    ret = And([self]*minElements) + makeOptionalList(optElements)
+            else:
+                ret = makeOptionalList(optElements)
+        else:
+            if minElements == 1:
+                ret = self
+            else:
+                ret = And([self]*minElements)
+        return ret
+
+    def __rmul__(self, other):
+        return self.__mul__(other)
+
+    def __or__(self, other ):
+        """
+        Implementation of | operator - returns C{L{MatchFirst}}
+        """
+        if isinstance( other, basestring ):
+            other = ParserElement._literalStringClass( other )
+        if not isinstance( other, ParserElement ):
+            warnings.warn("Cannot combine element of type %s with ParserElement" % type(other),
+                    SyntaxWarning, stacklevel=2)
+            return None
+        return MatchFirst( [ self, other ] )
+
+    def __ror__(self, other ):
+        """
+        Implementation of | operator when left operand is not a C{L{ParserElement}}
+        """
+        if isinstance( other, basestring ):
+            other = ParserElement._literalStringClass( other )
+        if not isinstance( other, ParserElement ):
+            warnings.warn("Cannot combine element of type %s with ParserElement" % type(other),
+                    SyntaxWarning, stacklevel=2)
+            return None
+        return other | self
+
+    def __xor__(self, other ):
+        """
+        Implementation of ^ operator - returns C{L{Or}}
+        """
+        if isinstance( other, basestring ):
+            other = ParserElement._literalStringClass( other )
+        if not isinstance( other, ParserElement ):
+            warnings.warn("Cannot combine element of type %s with ParserElement" % type(other),
+                    SyntaxWarning, stacklevel=2)
+            return None
+        return Or( [ self, other ] )
+
+    def __rxor__(self, other ):
+        """
+        Implementation of ^ operator when left operand is not a C{L{ParserElement}}
+        """
+        if isinstance( other, basestring ):
+            other = ParserElement._literalStringClass( other )
+        if not isinstance( other, ParserElement ):
+            warnings.warn("Cannot combine element of type %s with ParserElement" % type(other),
+                    SyntaxWarning, stacklevel=2)
+            return None
+        return other ^ self
+
+    def __and__(self, other ):
+        """
+        Implementation of & operator - returns C{L{Each}}
+        """
+        if isinstance( other, basestring ):
+            other = ParserElement._literalStringClass( other )
+        if not isinstance( other, ParserElement ):
+            warnings.warn("Cannot combine element of type %s with ParserElement" % type(other),
+                    SyntaxWarning, stacklevel=2)
+            return None
+        return Each( [ self, other ] )
+
+    def __rand__(self, other ):
+        """
+        Implementation of & operator when left operand is not a C{L{ParserElement}}
+        """
+        if isinstance( other, basestring ):
+            other = ParserElement._literalStringClass( other )
+        if not isinstance( other, ParserElement ):
+            warnings.warn("Cannot combine element of type %s with ParserElement" % type(other),
+                    SyntaxWarning, stacklevel=2)
+            return None
+        return other & self
+
+    def __invert__( self ):
+        """
+        Implementation of ~ operator - returns C{L{NotAny}}
+        """
+        return NotAny( self )
+
+    def __call__(self, name=None):
+        """
+        Shortcut for C{L{setResultsName}}, with C{listAllMatches=False}.
+        
+        If C{name} is given with a trailing C{'*'} character, then C{listAllMatches} will be
+        passed as C{True}.
+           
+        If C{name} is omitted, same as calling C{L{copy}}.
+
+        Example::
+            # these are equivalent
+            userdata = Word(alphas).setResultsName("name") + Word(nums+"-").setResultsName("socsecno")
+            userdata = Word(alphas)("name") + Word(nums+"-")("socsecno")             
+        """
+        if name is not None:
+            return self.setResultsName(name)
+        else:
+            return self.copy()
+
+    def suppress( self ):
+        """
+        Suppresses the output of this C{ParserElement}; useful to keep punctuation from
+        cluttering up returned output.
+        """
+        return Suppress( self )
+
+    def leaveWhitespace( self ):
+        """
+        Disables the skipping of whitespace before matching the characters in the
+        C{ParserElement}'s defined pattern.  This is normally only used internally by
+        the pyparsing module, but may be needed in some whitespace-sensitive grammars.
+        """
+        self.skipWhitespace = False
+        return self
+
+    def setWhitespaceChars( self, chars ):
+        """
+        Overrides the default whitespace chars
+        """
+        self.skipWhitespace = True
+        self.whiteChars = chars
+        self.copyDefaultWhiteChars = False
+        return self
+
+    def parseWithTabs( self ):
+        """
+        Overrides default behavior to expand C{}s to spaces before parsing the input string.
+        Must be called before C{parseString} when the input grammar contains elements that
+        match C{} characters.
+        """
+        self.keepTabs = True
+        return self
+
+    def ignore( self, other ):
+        """
+        Define expression to be ignored (e.g., comments) while doing pattern
+        matching; may be called repeatedly, to define multiple comment or other
+        ignorable patterns.
+        
+        Example::
+            patt = OneOrMore(Word(alphas))
+            patt.parseString('ablaj /* comment */ lskjd') # -> ['ablaj']
+            
+            patt.ignore(cStyleComment)
+            patt.parseString('ablaj /* comment */ lskjd') # -> ['ablaj', 'lskjd']
+        """
+        if isinstance(other, basestring):
+            other = Suppress(other)
+
+        if isinstance( other, Suppress ):
+            if other not in self.ignoreExprs:
+                self.ignoreExprs.append(other)
+        else:
+            self.ignoreExprs.append( Suppress( other.copy() ) )
+        return self
+
+    def setDebugActions( self, startAction, successAction, exceptionAction ):
+        """
+        Enable display of debugging messages while doing pattern matching.
+        """
+        self.debugActions = (startAction or _defaultStartDebugAction,
+                             successAction or _defaultSuccessDebugAction,
+                             exceptionAction or _defaultExceptionDebugAction)
+        self.debug = True
+        return self
+
+    def setDebug( self, flag=True ):
+        """
+        Enable display of debugging messages while doing pattern matching.
+        Set C{flag} to True to enable, False to disable.
+
+        Example::
+            wd = Word(alphas).setName("alphaword")
+            integer = Word(nums).setName("numword")
+            term = wd | integer
+            
+            # turn on debugging for wd
+            wd.setDebug()
+
+            OneOrMore(term).parseString("abc 123 xyz 890")
+        
+        prints::
+            Match alphaword at loc 0(1,1)
+            Matched alphaword -> ['abc']
+            Match alphaword at loc 3(1,4)
+            Exception raised:Expected alphaword (at char 4), (line:1, col:5)
+            Match alphaword at loc 7(1,8)
+            Matched alphaword -> ['xyz']
+            Match alphaword at loc 11(1,12)
+            Exception raised:Expected alphaword (at char 12), (line:1, col:13)
+            Match alphaword at loc 15(1,16)
+            Exception raised:Expected alphaword (at char 15), (line:1, col:16)
+
+        The output shown is that produced by the default debug actions - custom debug actions can be
+        specified using L{setDebugActions}. Prior to attempting
+        to match the C{wd} expression, the debugging message C{"Match  at loc (,)"}
+        is shown. Then if the parse succeeds, a C{"Matched"} message is shown, or an C{"Exception raised"}
+        message is shown. Also note the use of L{setName} to assign a human-readable name to the expression,
+        which makes debugging and exception messages easier to understand - for instance, the default
+        name created for the C{Word} expression without calling C{setName} is C{"W:(ABCD...)"}.
+        """
+        if flag:
+            self.setDebugActions( _defaultStartDebugAction, _defaultSuccessDebugAction, _defaultExceptionDebugAction )
+        else:
+            self.debug = False
+        return self
+
+    def __str__( self ):
+        return self.name
+
+    def __repr__( self ):
+        return _ustr(self)
+
+    def streamline( self ):
+        self.streamlined = True
+        self.strRepr = None
+        return self
+
+    def checkRecursion( self, parseElementList ):
+        pass
+
+    def validate( self, validateTrace=[] ):
+        """
+        Check defined expressions for valid structure, check for infinite recursive definitions.
+        """
+        self.checkRecursion( [] )
+
+    def parseFile( self, file_or_filename, parseAll=False ):
+        """
+        Execute the parse expression on the given file or filename.
+        If a filename is specified (instead of a file object),
+        the entire file is opened, read, and closed before parsing.
+        """
+        try:
+            file_contents = file_or_filename.read()
+        except AttributeError:
+            with open(file_or_filename, "r") as f:
+                file_contents = f.read()
+        try:
+            return self.parseString(file_contents, parseAll)
+        except ParseBaseException as exc:
+            if ParserElement.verbose_stacktrace:
+                raise
+            else:
+                # catch and re-raise exception from here, clears out pyparsing internal stack trace
+                raise exc
+
+    def __eq__(self,other):
+        if isinstance(other, ParserElement):
+            return self is other or vars(self) == vars(other)
+        elif isinstance(other, basestring):
+            return self.matches(other)
+        else:
+            return super(ParserElement,self)==other
+
+    def __ne__(self,other):
+        return not (self == other)
+
+    def __hash__(self):
+        return hash(id(self))
+
+    def __req__(self,other):
+        return self == other
+
+    def __rne__(self,other):
+        return not (self == other)
+
+    def matches(self, testString, parseAll=True):
+        """
+        Method for quick testing of a parser against a test string. Good for simple 
+        inline microtests of sub expressions while building up larger parser.
+           
+        Parameters:
+         - testString - to test against this expression for a match
+         - parseAll - (default=C{True}) - flag to pass to C{L{parseString}} when running tests
+            
+        Example::
+            expr = Word(nums)
+            assert expr.matches("100")
+        """
+        try:
+            self.parseString(_ustr(testString), parseAll=parseAll)
+            return True
+        except ParseBaseException:
+            return False
+                
+    def runTests(self, tests, parseAll=True, comment='#', fullDump=True, printResults=True, failureTests=False):
+        """
+        Execute the parse expression on a series of test strings, showing each
+        test, the parsed results or where the parse failed. Quick and easy way to
+        run a parse expression against a list of sample strings.
+           
+        Parameters:
+         - tests - a list of separate test strings, or a multiline string of test strings
+         - parseAll - (default=C{True}) - flag to pass to C{L{parseString}} when running tests           
+         - comment - (default=C{'#'}) - expression for indicating embedded comments in the test 
+              string; pass None to disable comment filtering
+         - fullDump - (default=C{True}) - dump results as list followed by results names in nested outline;
+              if False, only dump nested list
+         - printResults - (default=C{True}) prints test output to stdout
+         - failureTests - (default=C{False}) indicates if these tests are expected to fail parsing
+
+        Returns: a (success, results) tuple, where success indicates that all tests succeeded
+        (or failed if C{failureTests} is True), and the results contain a list of lines of each 
+        test's output
+        
+        Example::
+            number_expr = pyparsing_common.number.copy()
+
+            result = number_expr.runTests('''
+                # unsigned integer
+                100
+                # negative integer
+                -100
+                # float with scientific notation
+                6.02e23
+                # integer with scientific notation
+                1e-12
+                ''')
+            print("Success" if result[0] else "Failed!")
+
+            result = number_expr.runTests('''
+                # stray character
+                100Z
+                # missing leading digit before '.'
+                -.100
+                # too many '.'
+                3.14.159
+                ''', failureTests=True)
+            print("Success" if result[0] else "Failed!")
+        prints::
+            # unsigned integer
+            100
+            [100]
+
+            # negative integer
+            -100
+            [-100]
+
+            # float with scientific notation
+            6.02e23
+            [6.02e+23]
+
+            # integer with scientific notation
+            1e-12
+            [1e-12]
+
+            Success
+            
+            # stray character
+            100Z
+               ^
+            FAIL: Expected end of text (at char 3), (line:1, col:4)
+
+            # missing leading digit before '.'
+            -.100
+            ^
+            FAIL: Expected {real number with scientific notation | real number | signed integer} (at char 0), (line:1, col:1)
+
+            # too many '.'
+            3.14.159
+                ^
+            FAIL: Expected end of text (at char 4), (line:1, col:5)
+
+            Success
+
+        Each test string must be on a single line. If you want to test a string that spans multiple
+        lines, create a test like this::
+
+            expr.runTest(r"this is a test\\n of strings that spans \\n 3 lines")
+        
+        (Note that this is a raw string literal, you must include the leading 'r'.)
+        """
+        if isinstance(tests, basestring):
+            tests = list(map(str.strip, tests.rstrip().splitlines()))
+        if isinstance(comment, basestring):
+            comment = Literal(comment)
+        allResults = []
+        comments = []
+        success = True
+        for t in tests:
+            if comment is not None and comment.matches(t, False) or comments and not t:
+                comments.append(t)
+                continue
+            if not t:
+                continue
+            out = ['\n'.join(comments), t]
+            comments = []
+            try:
+                t = t.replace(r'\n','\n')
+                result = self.parseString(t, parseAll=parseAll)
+                out.append(result.dump(full=fullDump))
+                success = success and not failureTests
+            except ParseBaseException as pe:
+                fatal = "(FATAL)" if isinstance(pe, ParseFatalException) else ""
+                if '\n' in t:
+                    out.append(line(pe.loc, t))
+                    out.append(' '*(col(pe.loc,t)-1) + '^' + fatal)
+                else:
+                    out.append(' '*pe.loc + '^' + fatal)
+                out.append("FAIL: " + str(pe))
+                success = success and failureTests
+                result = pe
+            except Exception as exc:
+                out.append("FAIL-EXCEPTION: " + str(exc))
+                success = success and failureTests
+                result = exc
+
+            if printResults:
+                if fullDump:
+                    out.append('')
+                print('\n'.join(out))
+
+            allResults.append((t, result))
+        
+        return success, allResults
+
+        
+class Token(ParserElement):
+    """
+    Abstract C{ParserElement} subclass, for defining atomic matching patterns.
+    """
+    def __init__( self ):
+        super(Token,self).__init__( savelist=False )
+
+
+class Empty(Token):
+    """
+    An empty token, will always match.
+    """
+    def __init__( self ):
+        super(Empty,self).__init__()
+        self.name = "Empty"
+        self.mayReturnEmpty = True
+        self.mayIndexError = False
+
+
+class NoMatch(Token):
+    """
+    A token that will never match.
+    """
+    def __init__( self ):
+        super(NoMatch,self).__init__()
+        self.name = "NoMatch"
+        self.mayReturnEmpty = True
+        self.mayIndexError = False
+        self.errmsg = "Unmatchable token"
+
+    def parseImpl( self, instring, loc, doActions=True ):
+        raise ParseException(instring, loc, self.errmsg, self)
+
+
+class Literal(Token):
+    """
+    Token to exactly match a specified string.
+    
+    Example::
+        Literal('blah').parseString('blah')  # -> ['blah']
+        Literal('blah').parseString('blahfooblah')  # -> ['blah']
+        Literal('blah').parseString('bla')  # -> Exception: Expected "blah"
+    
+    For case-insensitive matching, use L{CaselessLiteral}.
+    
+    For keyword matching (force word break before and after the matched string),
+    use L{Keyword} or L{CaselessKeyword}.
+    """
+    def __init__( self, matchString ):
+        super(Literal,self).__init__()
+        self.match = matchString
+        self.matchLen = len(matchString)
+        try:
+            self.firstMatchChar = matchString[0]
+        except IndexError:
+            warnings.warn("null string passed to Literal; use Empty() instead",
+                            SyntaxWarning, stacklevel=2)
+            self.__class__ = Empty
+        self.name = '"%s"' % _ustr(self.match)
+        self.errmsg = "Expected " + self.name
+        self.mayReturnEmpty = False
+        self.mayIndexError = False
+
+    # Performance tuning: this routine gets called a *lot*
+    # if this is a single character match string  and the first character matches,
+    # short-circuit as quickly as possible, and avoid calling startswith
+    #~ @profile
+    def parseImpl( self, instring, loc, doActions=True ):
+        if (instring[loc] == self.firstMatchChar and
+            (self.matchLen==1 or instring.startswith(self.match,loc)) ):
+            return loc+self.matchLen, self.match
+        raise ParseException(instring, loc, self.errmsg, self)
+_L = Literal
+ParserElement._literalStringClass = Literal
+
+class Keyword(Token):
+    """
+    Token to exactly match a specified string as a keyword, that is, it must be
+    immediately followed by a non-keyword character.  Compare with C{L{Literal}}:
+     - C{Literal("if")} will match the leading C{'if'} in C{'ifAndOnlyIf'}.
+     - C{Keyword("if")} will not; it will only match the leading C{'if'} in C{'if x=1'}, or C{'if(y==2)'}
+    Accepts two optional constructor arguments in addition to the keyword string:
+     - C{identChars} is a string of characters that would be valid identifier characters,
+          defaulting to all alphanumerics + "_" and "$"
+     - C{caseless} allows case-insensitive matching, default is C{False}.
+       
+    Example::
+        Keyword("start").parseString("start")  # -> ['start']
+        Keyword("start").parseString("starting")  # -> Exception
+
+    For case-insensitive matching, use L{CaselessKeyword}.
+    """
+    DEFAULT_KEYWORD_CHARS = alphanums+"_$"
+
+    def __init__( self, matchString, identChars=None, caseless=False ):
+        super(Keyword,self).__init__()
+        if identChars is None:
+            identChars = Keyword.DEFAULT_KEYWORD_CHARS
+        self.match = matchString
+        self.matchLen = len(matchString)
+        try:
+            self.firstMatchChar = matchString[0]
+        except IndexError:
+            warnings.warn("null string passed to Keyword; use Empty() instead",
+                            SyntaxWarning, stacklevel=2)
+        self.name = '"%s"' % self.match
+        self.errmsg = "Expected " + self.name
+        self.mayReturnEmpty = False
+        self.mayIndexError = False
+        self.caseless = caseless
+        if caseless:
+            self.caselessmatch = matchString.upper()
+            identChars = identChars.upper()
+        self.identChars = set(identChars)
+
+    def parseImpl( self, instring, loc, doActions=True ):
+        if self.caseless:
+            if ( (instring[ loc:loc+self.matchLen ].upper() == self.caselessmatch) and
+                 (loc >= len(instring)-self.matchLen or instring[loc+self.matchLen].upper() not in self.identChars) and
+                 (loc == 0 or instring[loc-1].upper() not in self.identChars) ):
+                return loc+self.matchLen, self.match
+        else:
+            if (instring[loc] == self.firstMatchChar and
+                (self.matchLen==1 or instring.startswith(self.match,loc)) and
+                (loc >= len(instring)-self.matchLen or instring[loc+self.matchLen] not in self.identChars) and
+                (loc == 0 or instring[loc-1] not in self.identChars) ):
+                return loc+self.matchLen, self.match
+        raise ParseException(instring, loc, self.errmsg, self)
+
+    def copy(self):
+        c = super(Keyword,self).copy()
+        c.identChars = Keyword.DEFAULT_KEYWORD_CHARS
+        return c
+
+    @staticmethod
+    def setDefaultKeywordChars( chars ):
+        """Overrides the default Keyword chars
+        """
+        Keyword.DEFAULT_KEYWORD_CHARS = chars
+
+class CaselessLiteral(Literal):
+    """
+    Token to match a specified string, ignoring case of letters.
+    Note: the matched results will always be in the case of the given
+    match string, NOT the case of the input text.
+
+    Example::
+        OneOrMore(CaselessLiteral("CMD")).parseString("cmd CMD Cmd10") # -> ['CMD', 'CMD', 'CMD']
+        
+    (Contrast with example for L{CaselessKeyword}.)
+    """
+    def __init__( self, matchString ):
+        super(CaselessLiteral,self).__init__( matchString.upper() )
+        # Preserve the defining literal.
+        self.returnString = matchString
+        self.name = "'%s'" % self.returnString
+        self.errmsg = "Expected " + self.name
+
+    def parseImpl( self, instring, loc, doActions=True ):
+        if instring[ loc:loc+self.matchLen ].upper() == self.match:
+            return loc+self.matchLen, self.returnString
+        raise ParseException(instring, loc, self.errmsg, self)
+
+class CaselessKeyword(Keyword):
+    """
+    Caseless version of L{Keyword}.
+
+    Example::
+        OneOrMore(CaselessKeyword("CMD")).parseString("cmd CMD Cmd10") # -> ['CMD', 'CMD']
+        
+    (Contrast with example for L{CaselessLiteral}.)
+    """
+    def __init__( self, matchString, identChars=None ):
+        super(CaselessKeyword,self).__init__( matchString, identChars, caseless=True )
+
+    def parseImpl( self, instring, loc, doActions=True ):
+        if ( (instring[ loc:loc+self.matchLen ].upper() == self.caselessmatch) and
+             (loc >= len(instring)-self.matchLen or instring[loc+self.matchLen].upper() not in self.identChars) ):
+            return loc+self.matchLen, self.match
+        raise ParseException(instring, loc, self.errmsg, self)
+
+class CloseMatch(Token):
+    """
+    A variation on L{Literal} which matches "close" matches, that is, 
+    strings with at most 'n' mismatching characters. C{CloseMatch} takes parameters:
+     - C{match_string} - string to be matched
+     - C{maxMismatches} - (C{default=1}) maximum number of mismatches allowed to count as a match
+    
+    The results from a successful parse will contain the matched text from the input string and the following named results:
+     - C{mismatches} - a list of the positions within the match_string where mismatches were found
+     - C{original} - the original match_string used to compare against the input string
+    
+    If C{mismatches} is an empty list, then the match was an exact match.
+    
+    Example::
+        patt = CloseMatch("ATCATCGAATGGA")
+        patt.parseString("ATCATCGAAXGGA") # -> (['ATCATCGAAXGGA'], {'mismatches': [[9]], 'original': ['ATCATCGAATGGA']})
+        patt.parseString("ATCAXCGAAXGGA") # -> Exception: Expected 'ATCATCGAATGGA' (with up to 1 mismatches) (at char 0), (line:1, col:1)
+
+        # exact match
+        patt.parseString("ATCATCGAATGGA") # -> (['ATCATCGAATGGA'], {'mismatches': [[]], 'original': ['ATCATCGAATGGA']})
+
+        # close match allowing up to 2 mismatches
+        patt = CloseMatch("ATCATCGAATGGA", maxMismatches=2)
+        patt.parseString("ATCAXCGAAXGGA") # -> (['ATCAXCGAAXGGA'], {'mismatches': [[4, 9]], 'original': ['ATCATCGAATGGA']})
+    """
+    def __init__(self, match_string, maxMismatches=1):
+        super(CloseMatch,self).__init__()
+        self.name = match_string
+        self.match_string = match_string
+        self.maxMismatches = maxMismatches
+        self.errmsg = "Expected %r (with up to %d mismatches)" % (self.match_string, self.maxMismatches)
+        self.mayIndexError = False
+        self.mayReturnEmpty = False
+
+    def parseImpl( self, instring, loc, doActions=True ):
+        start = loc
+        instrlen = len(instring)
+        maxloc = start + len(self.match_string)
+
+        if maxloc <= instrlen:
+            match_string = self.match_string
+            match_stringloc = 0
+            mismatches = []
+            maxMismatches = self.maxMismatches
+
+            for match_stringloc,s_m in enumerate(zip(instring[loc:maxloc], self.match_string)):
+                src,mat = s_m
+                if src != mat:
+                    mismatches.append(match_stringloc)
+                    if len(mismatches) > maxMismatches:
+                        break
+            else:
+                loc = match_stringloc + 1
+                results = ParseResults([instring[start:loc]])
+                results['original'] = self.match_string
+                results['mismatches'] = mismatches
+                return loc, results
+
+        raise ParseException(instring, loc, self.errmsg, self)
+
+
+class Word(Token):
+    """
+    Token for matching words composed of allowed character sets.
+    Defined with string containing all allowed initial characters,
+    an optional string containing allowed body characters (if omitted,
+    defaults to the initial character set), and an optional minimum,
+    maximum, and/or exact length.  The default value for C{min} is 1 (a
+    minimum value < 1 is not valid); the default values for C{max} and C{exact}
+    are 0, meaning no maximum or exact length restriction. An optional
+    C{excludeChars} parameter can list characters that might be found in 
+    the input C{bodyChars} string; useful to define a word of all printables
+    except for one or two characters, for instance.
+    
+    L{srange} is useful for defining custom character set strings for defining 
+    C{Word} expressions, using range notation from regular expression character sets.
+    
+    A common mistake is to use C{Word} to match a specific literal string, as in 
+    C{Word("Address")}. Remember that C{Word} uses the string argument to define
+    I{sets} of matchable characters. This expression would match "Add", "AAA",
+    "dAred", or any other word made up of the characters 'A', 'd', 'r', 'e', and 's'.
+    To match an exact literal string, use L{Literal} or L{Keyword}.
+
+    pyparsing includes helper strings for building Words:
+     - L{alphas}
+     - L{nums}
+     - L{alphanums}
+     - L{hexnums}
+     - L{alphas8bit} (alphabetic characters in ASCII range 128-255 - accented, tilded, umlauted, etc.)
+     - L{punc8bit} (non-alphabetic characters in ASCII range 128-255 - currency, symbols, superscripts, diacriticals, etc.)
+     - L{printables} (any non-whitespace character)
+
+    Example::
+        # a word composed of digits
+        integer = Word(nums) # equivalent to Word("0123456789") or Word(srange("0-9"))
+        
+        # a word with a leading capital, and zero or more lowercase
+        capital_word = Word(alphas.upper(), alphas.lower())
+
+        # hostnames are alphanumeric, with leading alpha, and '-'
+        hostname = Word(alphas, alphanums+'-')
+        
+        # roman numeral (not a strict parser, accepts invalid mix of characters)
+        roman = Word("IVXLCDM")
+        
+        # any string of non-whitespace characters, except for ','
+        csv_value = Word(printables, excludeChars=",")
+    """
+    def __init__( self, initChars, bodyChars=None, min=1, max=0, exact=0, asKeyword=False, excludeChars=None ):
+        super(Word,self).__init__()
+        if excludeChars:
+            initChars = ''.join(c for c in initChars if c not in excludeChars)
+            if bodyChars:
+                bodyChars = ''.join(c for c in bodyChars if c not in excludeChars)
+        self.initCharsOrig = initChars
+        self.initChars = set(initChars)
+        if bodyChars :
+            self.bodyCharsOrig = bodyChars
+            self.bodyChars = set(bodyChars)
+        else:
+            self.bodyCharsOrig = initChars
+            self.bodyChars = set(initChars)
+
+        self.maxSpecified = max > 0
+
+        if min < 1:
+            raise ValueError("cannot specify a minimum length < 1; use Optional(Word()) if zero-length word is permitted")
+
+        self.minLen = min
+
+        if max > 0:
+            self.maxLen = max
+        else:
+            self.maxLen = _MAX_INT
+
+        if exact > 0:
+            self.maxLen = exact
+            self.minLen = exact
+
+        self.name = _ustr(self)
+        self.errmsg = "Expected " + self.name
+        self.mayIndexError = False
+        self.asKeyword = asKeyword
+
+        if ' ' not in self.initCharsOrig+self.bodyCharsOrig and (min==1 and max==0 and exact==0):
+            if self.bodyCharsOrig == self.initCharsOrig:
+                self.reString = "[%s]+" % _escapeRegexRangeChars(self.initCharsOrig)
+            elif len(self.initCharsOrig) == 1:
+                self.reString = "%s[%s]*" % \
+                                      (re.escape(self.initCharsOrig),
+                                      _escapeRegexRangeChars(self.bodyCharsOrig),)
+            else:
+                self.reString = "[%s][%s]*" % \
+                                      (_escapeRegexRangeChars(self.initCharsOrig),
+                                      _escapeRegexRangeChars(self.bodyCharsOrig),)
+            if self.asKeyword:
+                self.reString = r"\b"+self.reString+r"\b"
+            try:
+                self.re = re.compile( self.reString )
+            except Exception:
+                self.re = None
+
+    def parseImpl( self, instring, loc, doActions=True ):
+        if self.re:
+            result = self.re.match(instring,loc)
+            if not result:
+                raise ParseException(instring, loc, self.errmsg, self)
+
+            loc = result.end()
+            return loc, result.group()
+
+        if not(instring[ loc ] in self.initChars):
+            raise ParseException(instring, loc, self.errmsg, self)
+
+        start = loc
+        loc += 1
+        instrlen = len(instring)
+        bodychars = self.bodyChars
+        maxloc = start + self.maxLen
+        maxloc = min( maxloc, instrlen )
+        while loc < maxloc and instring[loc] in bodychars:
+            loc += 1
+
+        throwException = False
+        if loc - start < self.minLen:
+            throwException = True
+        if self.maxSpecified and loc < instrlen and instring[loc] in bodychars:
+            throwException = True
+        if self.asKeyword:
+            if (start>0 and instring[start-1] in bodychars) or (loc4:
+                    return s[:4]+"..."
+                else:
+                    return s
+
+            if ( self.initCharsOrig != self.bodyCharsOrig ):
+                self.strRepr = "W:(%s,%s)" % ( charsAsStr(self.initCharsOrig), charsAsStr(self.bodyCharsOrig) )
+            else:
+                self.strRepr = "W:(%s)" % charsAsStr(self.initCharsOrig)
+
+        return self.strRepr
+
+
+class Regex(Token):
+    r"""
+    Token for matching strings that match a given regular expression.
+    Defined with string specifying the regular expression in a form recognized by the inbuilt Python re module.
+    If the given regex contains named groups (defined using C{(?P...)}), these will be preserved as 
+    named parse results.
+
+    Example::
+        realnum = Regex(r"[+-]?\d+\.\d*")
+        date = Regex(r'(?P\d{4})-(?P\d\d?)-(?P\d\d?)')
+        # ref: http://stackoverflow.com/questions/267399/how-do-you-match-only-valid-roman-numerals-with-a-regular-expression
+        roman = Regex(r"M{0,4}(CM|CD|D?C{0,3})(XC|XL|L?X{0,3})(IX|IV|V?I{0,3})")
+    """
+    compiledREtype = type(re.compile("[A-Z]"))
+    def __init__( self, pattern, flags=0):
+        """The parameters C{pattern} and C{flags} are passed to the C{re.compile()} function as-is. See the Python C{re} module for an explanation of the acceptable patterns and flags."""
+        super(Regex,self).__init__()
+
+        if isinstance(pattern, basestring):
+            if not pattern:
+                warnings.warn("null string passed to Regex; use Empty() instead",
+                        SyntaxWarning, stacklevel=2)
+
+            self.pattern = pattern
+            self.flags = flags
+
+            try:
+                self.re = re.compile(self.pattern, self.flags)
+                self.reString = self.pattern
+            except sre_constants.error:
+                warnings.warn("invalid pattern (%s) passed to Regex" % pattern,
+                    SyntaxWarning, stacklevel=2)
+                raise
+
+        elif isinstance(pattern, Regex.compiledREtype):
+            self.re = pattern
+            self.pattern = \
+            self.reString = str(pattern)
+            self.flags = flags
+            
+        else:
+            raise ValueError("Regex may only be constructed with a string or a compiled RE object")
+
+        self.name = _ustr(self)
+        self.errmsg = "Expected " + self.name
+        self.mayIndexError = False
+        self.mayReturnEmpty = True
+
+    def parseImpl( self, instring, loc, doActions=True ):
+        result = self.re.match(instring,loc)
+        if not result:
+            raise ParseException(instring, loc, self.errmsg, self)
+
+        loc = result.end()
+        d = result.groupdict()
+        ret = ParseResults(result.group())
+        if d:
+            for k in d:
+                ret[k] = d[k]
+        return loc,ret
+
+    def __str__( self ):
+        try:
+            return super(Regex,self).__str__()
+        except Exception:
+            pass
+
+        if self.strRepr is None:
+            self.strRepr = "Re:(%s)" % repr(self.pattern)
+
+        return self.strRepr
+
+
+class QuotedString(Token):
+    r"""
+    Token for matching strings that are delimited by quoting characters.
+    
+    Defined with the following parameters:
+        - quoteChar - string of one or more characters defining the quote delimiting string
+        - escChar - character to escape quotes, typically backslash (default=C{None})
+        - escQuote - special quote sequence to escape an embedded quote string (such as SQL's "" to escape an embedded ") (default=C{None})
+        - multiline - boolean indicating whether quotes can span multiple lines (default=C{False})
+        - unquoteResults - boolean indicating whether the matched text should be unquoted (default=C{True})
+        - endQuoteChar - string of one or more characters defining the end of the quote delimited string (default=C{None} => same as quoteChar)
+        - convertWhitespaceEscapes - convert escaped whitespace (C{'\t'}, C{'\n'}, etc.) to actual whitespace (default=C{True})
+
+    Example::
+        qs = QuotedString('"')
+        print(qs.searchString('lsjdf "This is the quote" sldjf'))
+        complex_qs = QuotedString('{{', endQuoteChar='}}')
+        print(complex_qs.searchString('lsjdf {{This is the "quote"}} sldjf'))
+        sql_qs = QuotedString('"', escQuote='""')
+        print(sql_qs.searchString('lsjdf "This is the quote with ""embedded"" quotes" sldjf'))
+    prints::
+        [['This is the quote']]
+        [['This is the "quote"']]
+        [['This is the quote with "embedded" quotes']]
+    """
+    def __init__( self, quoteChar, escChar=None, escQuote=None, multiline=False, unquoteResults=True, endQuoteChar=None, convertWhitespaceEscapes=True):
+        super(QuotedString,self).__init__()
+
+        # remove white space from quote chars - wont work anyway
+        quoteChar = quoteChar.strip()
+        if not quoteChar:
+            warnings.warn("quoteChar cannot be the empty string",SyntaxWarning,stacklevel=2)
+            raise SyntaxError()
+
+        if endQuoteChar is None:
+            endQuoteChar = quoteChar
+        else:
+            endQuoteChar = endQuoteChar.strip()
+            if not endQuoteChar:
+                warnings.warn("endQuoteChar cannot be the empty string",SyntaxWarning,stacklevel=2)
+                raise SyntaxError()
+
+        self.quoteChar = quoteChar
+        self.quoteCharLen = len(quoteChar)
+        self.firstQuoteChar = quoteChar[0]
+        self.endQuoteChar = endQuoteChar
+        self.endQuoteCharLen = len(endQuoteChar)
+        self.escChar = escChar
+        self.escQuote = escQuote
+        self.unquoteResults = unquoteResults
+        self.convertWhitespaceEscapes = convertWhitespaceEscapes
+
+        if multiline:
+            self.flags = re.MULTILINE | re.DOTALL
+            self.pattern = r'%s(?:[^%s%s]' % \
+                ( re.escape(self.quoteChar),
+                  _escapeRegexRangeChars(self.endQuoteChar[0]),
+                  (escChar is not None and _escapeRegexRangeChars(escChar) or '') )
+        else:
+            self.flags = 0
+            self.pattern = r'%s(?:[^%s\n\r%s]' % \
+                ( re.escape(self.quoteChar),
+                  _escapeRegexRangeChars(self.endQuoteChar[0]),
+                  (escChar is not None and _escapeRegexRangeChars(escChar) or '') )
+        if len(self.endQuoteChar) > 1:
+            self.pattern += (
+                '|(?:' + ')|(?:'.join("%s[^%s]" % (re.escape(self.endQuoteChar[:i]),
+                                               _escapeRegexRangeChars(self.endQuoteChar[i]))
+                                    for i in range(len(self.endQuoteChar)-1,0,-1)) + ')'
+                )
+        if escQuote:
+            self.pattern += (r'|(?:%s)' % re.escape(escQuote))
+        if escChar:
+            self.pattern += (r'|(?:%s.)' % re.escape(escChar))
+            self.escCharReplacePattern = re.escape(self.escChar)+"(.)"
+        self.pattern += (r')*%s' % re.escape(self.endQuoteChar))
+
+        try:
+            self.re = re.compile(self.pattern, self.flags)
+            self.reString = self.pattern
+        except sre_constants.error:
+            warnings.warn("invalid pattern (%s) passed to Regex" % self.pattern,
+                SyntaxWarning, stacklevel=2)
+            raise
+
+        self.name = _ustr(self)
+        self.errmsg = "Expected " + self.name
+        self.mayIndexError = False
+        self.mayReturnEmpty = True
+
+    def parseImpl( self, instring, loc, doActions=True ):
+        result = instring[loc] == self.firstQuoteChar and self.re.match(instring,loc) or None
+        if not result:
+            raise ParseException(instring, loc, self.errmsg, self)
+
+        loc = result.end()
+        ret = result.group()
+
+        if self.unquoteResults:
+
+            # strip off quotes
+            ret = ret[self.quoteCharLen:-self.endQuoteCharLen]
+
+            if isinstance(ret,basestring):
+                # replace escaped whitespace
+                if '\\' in ret and self.convertWhitespaceEscapes:
+                    ws_map = {
+                        r'\t' : '\t',
+                        r'\n' : '\n',
+                        r'\f' : '\f',
+                        r'\r' : '\r',
+                    }
+                    for wslit,wschar in ws_map.items():
+                        ret = ret.replace(wslit, wschar)
+
+                # replace escaped characters
+                if self.escChar:
+                    ret = re.sub(self.escCharReplacePattern, r"\g<1>", ret)
+
+                # replace escaped quotes
+                if self.escQuote:
+                    ret = ret.replace(self.escQuote, self.endQuoteChar)
+
+        return loc, ret
+
+    def __str__( self ):
+        try:
+            return super(QuotedString,self).__str__()
+        except Exception:
+            pass
+
+        if self.strRepr is None:
+            self.strRepr = "quoted string, starting with %s ending with %s" % (self.quoteChar, self.endQuoteChar)
+
+        return self.strRepr
+
+
+class CharsNotIn(Token):
+    """
+    Token for matching words composed of characters I{not} in a given set (will
+    include whitespace in matched characters if not listed in the provided exclusion set - see example).
+    Defined with string containing all disallowed characters, and an optional
+    minimum, maximum, and/or exact length.  The default value for C{min} is 1 (a
+    minimum value < 1 is not valid); the default values for C{max} and C{exact}
+    are 0, meaning no maximum or exact length restriction.
+
+    Example::
+        # define a comma-separated-value as anything that is not a ','
+        csv_value = CharsNotIn(',')
+        print(delimitedList(csv_value).parseString("dkls,lsdkjf,s12 34,@!#,213"))
+    prints::
+        ['dkls', 'lsdkjf', 's12 34', '@!#', '213']
+    """
+    def __init__( self, notChars, min=1, max=0, exact=0 ):
+        super(CharsNotIn,self).__init__()
+        self.skipWhitespace = False
+        self.notChars = notChars
+
+        if min < 1:
+            raise ValueError("cannot specify a minimum length < 1; use Optional(CharsNotIn()) if zero-length char group is permitted")
+
+        self.minLen = min
+
+        if max > 0:
+            self.maxLen = max
+        else:
+            self.maxLen = _MAX_INT
+
+        if exact > 0:
+            self.maxLen = exact
+            self.minLen = exact
+
+        self.name = _ustr(self)
+        self.errmsg = "Expected " + self.name
+        self.mayReturnEmpty = ( self.minLen == 0 )
+        self.mayIndexError = False
+
+    def parseImpl( self, instring, loc, doActions=True ):
+        if instring[loc] in self.notChars:
+            raise ParseException(instring, loc, self.errmsg, self)
+
+        start = loc
+        loc += 1
+        notchars = self.notChars
+        maxlen = min( start+self.maxLen, len(instring) )
+        while loc < maxlen and \
+              (instring[loc] not in notchars):
+            loc += 1
+
+        if loc - start < self.minLen:
+            raise ParseException(instring, loc, self.errmsg, self)
+
+        return loc, instring[start:loc]
+
+    def __str__( self ):
+        try:
+            return super(CharsNotIn, self).__str__()
+        except Exception:
+            pass
+
+        if self.strRepr is None:
+            if len(self.notChars) > 4:
+                self.strRepr = "!W:(%s...)" % self.notChars[:4]
+            else:
+                self.strRepr = "!W:(%s)" % self.notChars
+
+        return self.strRepr
+
+class White(Token):
+    """
+    Special matching class for matching whitespace.  Normally, whitespace is ignored
+    by pyparsing grammars.  This class is included when some whitespace structures
+    are significant.  Define with a string containing the whitespace characters to be
+    matched; default is C{" \\t\\r\\n"}.  Also takes optional C{min}, C{max}, and C{exact} arguments,
+    as defined for the C{L{Word}} class.
+    """
+    whiteStrs = {
+        " " : "",
+        "\t": "",
+        "\n": "",
+        "\r": "",
+        "\f": "",
+        }
+    def __init__(self, ws=" \t\r\n", min=1, max=0, exact=0):
+        super(White,self).__init__()
+        self.matchWhite = ws
+        self.setWhitespaceChars( "".join(c for c in self.whiteChars if c not in self.matchWhite) )
+        #~ self.leaveWhitespace()
+        self.name = ("".join(White.whiteStrs[c] for c in self.matchWhite))
+        self.mayReturnEmpty = True
+        self.errmsg = "Expected " + self.name
+
+        self.minLen = min
+
+        if max > 0:
+            self.maxLen = max
+        else:
+            self.maxLen = _MAX_INT
+
+        if exact > 0:
+            self.maxLen = exact
+            self.minLen = exact
+
+    def parseImpl( self, instring, loc, doActions=True ):
+        if not(instring[ loc ] in self.matchWhite):
+            raise ParseException(instring, loc, self.errmsg, self)
+        start = loc
+        loc += 1
+        maxloc = start + self.maxLen
+        maxloc = min( maxloc, len(instring) )
+        while loc < maxloc and instring[loc] in self.matchWhite:
+            loc += 1
+
+        if loc - start < self.minLen:
+            raise ParseException(instring, loc, self.errmsg, self)
+
+        return loc, instring[start:loc]
+
+
+class _PositionToken(Token):
+    def __init__( self ):
+        super(_PositionToken,self).__init__()
+        self.name=self.__class__.__name__
+        self.mayReturnEmpty = True
+        self.mayIndexError = False
+
+class GoToColumn(_PositionToken):
+    """
+    Token to advance to a specific column of input text; useful for tabular report scraping.
+    """
+    def __init__( self, colno ):
+        super(GoToColumn,self).__init__()
+        self.col = colno
+
+    def preParse( self, instring, loc ):
+        if col(loc,instring) != self.col:
+            instrlen = len(instring)
+            if self.ignoreExprs:
+                loc = self._skipIgnorables( instring, loc )
+            while loc < instrlen and instring[loc].isspace() and col( loc, instring ) != self.col :
+                loc += 1
+        return loc
+
+    def parseImpl( self, instring, loc, doActions=True ):
+        thiscol = col( loc, instring )
+        if thiscol > self.col:
+            raise ParseException( instring, loc, "Text not in expected column", self )
+        newloc = loc + self.col - thiscol
+        ret = instring[ loc: newloc ]
+        return newloc, ret
+
+
+class LineStart(_PositionToken):
+    """
+    Matches if current position is at the beginning of a line within the parse string
+    
+    Example::
+    
+        test = '''\
+        AAA this line
+        AAA and this line
+          AAA but not this one
+        B AAA and definitely not this one
+        '''
+
+        for t in (LineStart() + 'AAA' + restOfLine).searchString(test):
+            print(t)
+    
+    Prints::
+        ['AAA', ' this line']
+        ['AAA', ' and this line']    
+
+    """
+    def __init__( self ):
+        super(LineStart,self).__init__()
+        self.errmsg = "Expected start of line"
+
+    def parseImpl( self, instring, loc, doActions=True ):
+        if col(loc, instring) == 1:
+            return loc, []
+        raise ParseException(instring, loc, self.errmsg, self)
+
+class LineEnd(_PositionToken):
+    """
+    Matches if current position is at the end of a line within the parse string
+    """
+    def __init__( self ):
+        super(LineEnd,self).__init__()
+        self.setWhitespaceChars( ParserElement.DEFAULT_WHITE_CHARS.replace("\n","") )
+        self.errmsg = "Expected end of line"
+
+    def parseImpl( self, instring, loc, doActions=True ):
+        if loc len(instring):
+            return loc, []
+        else:
+            raise ParseException(instring, loc, self.errmsg, self)
+
+class WordStart(_PositionToken):
+    """
+    Matches if the current position is at the beginning of a Word, and
+    is not preceded by any character in a given set of C{wordChars}
+    (default=C{printables}). To emulate the C{\b} behavior of regular expressions,
+    use C{WordStart(alphanums)}. C{WordStart} will also match at the beginning of
+    the string being parsed, or at the beginning of a line.
+    """
+    def __init__(self, wordChars = printables):
+        super(WordStart,self).__init__()
+        self.wordChars = set(wordChars)
+        self.errmsg = "Not at the start of a word"
+
+    def parseImpl(self, instring, loc, doActions=True ):
+        if loc != 0:
+            if (instring[loc-1] in self.wordChars or
+                instring[loc] not in self.wordChars):
+                raise ParseException(instring, loc, self.errmsg, self)
+        return loc, []
+
+class WordEnd(_PositionToken):
+    """
+    Matches if the current position is at the end of a Word, and
+    is not followed by any character in a given set of C{wordChars}
+    (default=C{printables}). To emulate the C{\b} behavior of regular expressions,
+    use C{WordEnd(alphanums)}. C{WordEnd} will also match at the end of
+    the string being parsed, or at the end of a line.
+    """
+    def __init__(self, wordChars = printables):
+        super(WordEnd,self).__init__()
+        self.wordChars = set(wordChars)
+        self.skipWhitespace = False
+        self.errmsg = "Not at the end of a word"
+
+    def parseImpl(self, instring, loc, doActions=True ):
+        instrlen = len(instring)
+        if instrlen>0 and loc maxExcLoc:
+                    maxException = err
+                    maxExcLoc = err.loc
+            except IndexError:
+                if len(instring) > maxExcLoc:
+                    maxException = ParseException(instring,len(instring),e.errmsg,self)
+                    maxExcLoc = len(instring)
+            else:
+                # save match among all matches, to retry longest to shortest
+                matches.append((loc2, e))
+
+        if matches:
+            matches.sort(key=lambda x: -x[0])
+            for _,e in matches:
+                try:
+                    return e._parse( instring, loc, doActions )
+                except ParseException as err:
+                    err.__traceback__ = None
+                    if err.loc > maxExcLoc:
+                        maxException = err
+                        maxExcLoc = err.loc
+
+        if maxException is not None:
+            maxException.msg = self.errmsg
+            raise maxException
+        else:
+            raise ParseException(instring, loc, "no defined alternatives to match", self)
+
+
+    def __ixor__(self, other ):
+        if isinstance( other, basestring ):
+            other = ParserElement._literalStringClass( other )
+        return self.append( other ) #Or( [ self, other ] )
+
+    def __str__( self ):
+        if hasattr(self,"name"):
+            return self.name
+
+        if self.strRepr is None:
+            self.strRepr = "{" + " ^ ".join(_ustr(e) for e in self.exprs) + "}"
+
+        return self.strRepr
+
+    def checkRecursion( self, parseElementList ):
+        subRecCheckList = parseElementList[:] + [ self ]
+        for e in self.exprs:
+            e.checkRecursion( subRecCheckList )
+
+
+class MatchFirst(ParseExpression):
+    """
+    Requires that at least one C{ParseExpression} is found.
+    If two expressions match, the first one listed is the one that will match.
+    May be constructed using the C{'|'} operator.
+
+    Example::
+        # construct MatchFirst using '|' operator
+        
+        # watch the order of expressions to match
+        number = Word(nums) | Combine(Word(nums) + '.' + Word(nums))
+        print(number.searchString("123 3.1416 789")) #  Fail! -> [['123'], ['3'], ['1416'], ['789']]
+
+        # put more selective expression first
+        number = Combine(Word(nums) + '.' + Word(nums)) | Word(nums)
+        print(number.searchString("123 3.1416 789")) #  Better -> [['123'], ['3.1416'], ['789']]
+    """
+    def __init__( self, exprs, savelist = False ):
+        super(MatchFirst,self).__init__(exprs, savelist)
+        if self.exprs:
+            self.mayReturnEmpty = any(e.mayReturnEmpty for e in self.exprs)
+        else:
+            self.mayReturnEmpty = True
+
+    def parseImpl( self, instring, loc, doActions=True ):
+        maxExcLoc = -1
+        maxException = None
+        for e in self.exprs:
+            try:
+                ret = e._parse( instring, loc, doActions )
+                return ret
+            except ParseException as err:
+                if err.loc > maxExcLoc:
+                    maxException = err
+                    maxExcLoc = err.loc
+            except IndexError:
+                if len(instring) > maxExcLoc:
+                    maxException = ParseException(instring,len(instring),e.errmsg,self)
+                    maxExcLoc = len(instring)
+
+        # only got here if no expression matched, raise exception for match that made it the furthest
+        else:
+            if maxException is not None:
+                maxException.msg = self.errmsg
+                raise maxException
+            else:
+                raise ParseException(instring, loc, "no defined alternatives to match", self)
+
+    def __ior__(self, other ):
+        if isinstance( other, basestring ):
+            other = ParserElement._literalStringClass( other )
+        return self.append( other ) #MatchFirst( [ self, other ] )
+
+    def __str__( self ):
+        if hasattr(self,"name"):
+            return self.name
+
+        if self.strRepr is None:
+            self.strRepr = "{" + " | ".join(_ustr(e) for e in self.exprs) + "}"
+
+        return self.strRepr
+
+    def checkRecursion( self, parseElementList ):
+        subRecCheckList = parseElementList[:] + [ self ]
+        for e in self.exprs:
+            e.checkRecursion( subRecCheckList )
+
+
+class Each(ParseExpression):
+    """
+    Requires all given C{ParseExpression}s to be found, but in any order.
+    Expressions may be separated by whitespace.
+    May be constructed using the C{'&'} operator.
+
+    Example::
+        color = oneOf("RED ORANGE YELLOW GREEN BLUE PURPLE BLACK WHITE BROWN")
+        shape_type = oneOf("SQUARE CIRCLE TRIANGLE STAR HEXAGON OCTAGON")
+        integer = Word(nums)
+        shape_attr = "shape:" + shape_type("shape")
+        posn_attr = "posn:" + Group(integer("x") + ',' + integer("y"))("posn")
+        color_attr = "color:" + color("color")
+        size_attr = "size:" + integer("size")
+
+        # use Each (using operator '&') to accept attributes in any order 
+        # (shape and posn are required, color and size are optional)
+        shape_spec = shape_attr & posn_attr & Optional(color_attr) & Optional(size_attr)
+
+        shape_spec.runTests('''
+            shape: SQUARE color: BLACK posn: 100, 120
+            shape: CIRCLE size: 50 color: BLUE posn: 50,80
+            color:GREEN size:20 shape:TRIANGLE posn:20,40
+            '''
+            )
+    prints::
+        shape: SQUARE color: BLACK posn: 100, 120
+        ['shape:', 'SQUARE', 'color:', 'BLACK', 'posn:', ['100', ',', '120']]
+        - color: BLACK
+        - posn: ['100', ',', '120']
+          - x: 100
+          - y: 120
+        - shape: SQUARE
+
+
+        shape: CIRCLE size: 50 color: BLUE posn: 50,80
+        ['shape:', 'CIRCLE', 'size:', '50', 'color:', 'BLUE', 'posn:', ['50', ',', '80']]
+        - color: BLUE
+        - posn: ['50', ',', '80']
+          - x: 50
+          - y: 80
+        - shape: CIRCLE
+        - size: 50
+
+
+        color: GREEN size: 20 shape: TRIANGLE posn: 20,40
+        ['color:', 'GREEN', 'size:', '20', 'shape:', 'TRIANGLE', 'posn:', ['20', ',', '40']]
+        - color: GREEN
+        - posn: ['20', ',', '40']
+          - x: 20
+          - y: 40
+        - shape: TRIANGLE
+        - size: 20
+    """
+    def __init__( self, exprs, savelist = True ):
+        super(Each,self).__init__(exprs, savelist)
+        self.mayReturnEmpty = all(e.mayReturnEmpty for e in self.exprs)
+        self.skipWhitespace = True
+        self.initExprGroups = True
+
+    def parseImpl( self, instring, loc, doActions=True ):
+        if self.initExprGroups:
+            self.opt1map = dict((id(e.expr),e) for e in self.exprs if isinstance(e,Optional))
+            opt1 = [ e.expr for e in self.exprs if isinstance(e,Optional) ]
+            opt2 = [ e for e in self.exprs if e.mayReturnEmpty and not isinstance(e,Optional)]
+            self.optionals = opt1 + opt2
+            self.multioptionals = [ e.expr for e in self.exprs if isinstance(e,ZeroOrMore) ]
+            self.multirequired = [ e.expr for e in self.exprs if isinstance(e,OneOrMore) ]
+            self.required = [ e for e in self.exprs if not isinstance(e,(Optional,ZeroOrMore,OneOrMore)) ]
+            self.required += self.multirequired
+            self.initExprGroups = False
+        tmpLoc = loc
+        tmpReqd = self.required[:]
+        tmpOpt  = self.optionals[:]
+        matchOrder = []
+
+        keepMatching = True
+        while keepMatching:
+            tmpExprs = tmpReqd + tmpOpt + self.multioptionals + self.multirequired
+            failed = []
+            for e in tmpExprs:
+                try:
+                    tmpLoc = e.tryParse( instring, tmpLoc )
+                except ParseException:
+                    failed.append(e)
+                else:
+                    matchOrder.append(self.opt1map.get(id(e),e))
+                    if e in tmpReqd:
+                        tmpReqd.remove(e)
+                    elif e in tmpOpt:
+                        tmpOpt.remove(e)
+            if len(failed) == len(tmpExprs):
+                keepMatching = False
+
+        if tmpReqd:
+            missing = ", ".join(_ustr(e) for e in tmpReqd)
+            raise ParseException(instring,loc,"Missing one or more required elements (%s)" % missing )
+
+        # add any unmatched Optionals, in case they have default values defined
+        matchOrder += [e for e in self.exprs if isinstance(e,Optional) and e.expr in tmpOpt]
+
+        resultlist = []
+        for e in matchOrder:
+            loc,results = e._parse(instring,loc,doActions)
+            resultlist.append(results)
+
+        finalResults = sum(resultlist, ParseResults([]))
+        return loc, finalResults
+
+    def __str__( self ):
+        if hasattr(self,"name"):
+            return self.name
+
+        if self.strRepr is None:
+            self.strRepr = "{" + " & ".join(_ustr(e) for e in self.exprs) + "}"
+
+        return self.strRepr
+
+    def checkRecursion( self, parseElementList ):
+        subRecCheckList = parseElementList[:] + [ self ]
+        for e in self.exprs:
+            e.checkRecursion( subRecCheckList )
+
+
+class ParseElementEnhance(ParserElement):
+    """
+    Abstract subclass of C{ParserElement}, for combining and post-processing parsed tokens.
+    """
+    def __init__( self, expr, savelist=False ):
+        super(ParseElementEnhance,self).__init__(savelist)
+        if isinstance( expr, basestring ):
+            if issubclass(ParserElement._literalStringClass, Token):
+                expr = ParserElement._literalStringClass(expr)
+            else:
+                expr = ParserElement._literalStringClass(Literal(expr))
+        self.expr = expr
+        self.strRepr = None
+        if expr is not None:
+            self.mayIndexError = expr.mayIndexError
+            self.mayReturnEmpty = expr.mayReturnEmpty
+            self.setWhitespaceChars( expr.whiteChars )
+            self.skipWhitespace = expr.skipWhitespace
+            self.saveAsList = expr.saveAsList
+            self.callPreparse = expr.callPreparse
+            self.ignoreExprs.extend(expr.ignoreExprs)
+
+    def parseImpl( self, instring, loc, doActions=True ):
+        if self.expr is not None:
+            return self.expr._parse( instring, loc, doActions, callPreParse=False )
+        else:
+            raise ParseException("",loc,self.errmsg,self)
+
+    def leaveWhitespace( self ):
+        self.skipWhitespace = False
+        self.expr = self.expr.copy()
+        if self.expr is not None:
+            self.expr.leaveWhitespace()
+        return self
+
+    def ignore( self, other ):
+        if isinstance( other, Suppress ):
+            if other not in self.ignoreExprs:
+                super( ParseElementEnhance, self).ignore( other )
+                if self.expr is not None:
+                    self.expr.ignore( self.ignoreExprs[-1] )
+        else:
+            super( ParseElementEnhance, self).ignore( other )
+            if self.expr is not None:
+                self.expr.ignore( self.ignoreExprs[-1] )
+        return self
+
+    def streamline( self ):
+        super(ParseElementEnhance,self).streamline()
+        if self.expr is not None:
+            self.expr.streamline()
+        return self
+
+    def checkRecursion( self, parseElementList ):
+        if self in parseElementList:
+            raise RecursiveGrammarException( parseElementList+[self] )
+        subRecCheckList = parseElementList[:] + [ self ]
+        if self.expr is not None:
+            self.expr.checkRecursion( subRecCheckList )
+
+    def validate( self, validateTrace=[] ):
+        tmp = validateTrace[:]+[self]
+        if self.expr is not None:
+            self.expr.validate(tmp)
+        self.checkRecursion( [] )
+
+    def __str__( self ):
+        try:
+            return super(ParseElementEnhance,self).__str__()
+        except Exception:
+            pass
+
+        if self.strRepr is None and self.expr is not None:
+            self.strRepr = "%s:(%s)" % ( self.__class__.__name__, _ustr(self.expr) )
+        return self.strRepr
+
+
+class FollowedBy(ParseElementEnhance):
+    """
+    Lookahead matching of the given parse expression.  C{FollowedBy}
+    does I{not} advance the parsing position within the input string, it only
+    verifies that the specified parse expression matches at the current
+    position.  C{FollowedBy} always returns a null token list.
+
+    Example::
+        # use FollowedBy to match a label only if it is followed by a ':'
+        data_word = Word(alphas)
+        label = data_word + FollowedBy(':')
+        attr_expr = Group(label + Suppress(':') + OneOrMore(data_word, stopOn=label).setParseAction(' '.join))
+        
+        OneOrMore(attr_expr).parseString("shape: SQUARE color: BLACK posn: upper left").pprint()
+    prints::
+        [['shape', 'SQUARE'], ['color', 'BLACK'], ['posn', 'upper left']]
+    """
+    def __init__( self, expr ):
+        super(FollowedBy,self).__init__(expr)
+        self.mayReturnEmpty = True
+
+    def parseImpl( self, instring, loc, doActions=True ):
+        self.expr.tryParse( instring, loc )
+        return loc, []
+
+
+class NotAny(ParseElementEnhance):
+    """
+    Lookahead to disallow matching with the given parse expression.  C{NotAny}
+    does I{not} advance the parsing position within the input string, it only
+    verifies that the specified parse expression does I{not} match at the current
+    position.  Also, C{NotAny} does I{not} skip over leading whitespace. C{NotAny}
+    always returns a null token list.  May be constructed using the '~' operator.
+
+    Example::
+        
+    """
+    def __init__( self, expr ):
+        super(NotAny,self).__init__(expr)
+        #~ self.leaveWhitespace()
+        self.skipWhitespace = False  # do NOT use self.leaveWhitespace(), don't want to propagate to exprs
+        self.mayReturnEmpty = True
+        self.errmsg = "Found unwanted token, "+_ustr(self.expr)
+
+    def parseImpl( self, instring, loc, doActions=True ):
+        if self.expr.canParseNext(instring, loc):
+            raise ParseException(instring, loc, self.errmsg, self)
+        return loc, []
+
+    def __str__( self ):
+        if hasattr(self,"name"):
+            return self.name
+
+        if self.strRepr is None:
+            self.strRepr = "~{" + _ustr(self.expr) + "}"
+
+        return self.strRepr
+
+class _MultipleMatch(ParseElementEnhance):
+    def __init__( self, expr, stopOn=None):
+        super(_MultipleMatch, self).__init__(expr)
+        self.saveAsList = True
+        ender = stopOn
+        if isinstance(ender, basestring):
+            ender = ParserElement._literalStringClass(ender)
+        self.not_ender = ~ender if ender is not None else None
+
+    def parseImpl( self, instring, loc, doActions=True ):
+        self_expr_parse = self.expr._parse
+        self_skip_ignorables = self._skipIgnorables
+        check_ender = self.not_ender is not None
+        if check_ender:
+            try_not_ender = self.not_ender.tryParse
+        
+        # must be at least one (but first see if we are the stopOn sentinel;
+        # if so, fail)
+        if check_ender:
+            try_not_ender(instring, loc)
+        loc, tokens = self_expr_parse( instring, loc, doActions, callPreParse=False )
+        try:
+            hasIgnoreExprs = (not not self.ignoreExprs)
+            while 1:
+                if check_ender:
+                    try_not_ender(instring, loc)
+                if hasIgnoreExprs:
+                    preloc = self_skip_ignorables( instring, loc )
+                else:
+                    preloc = loc
+                loc, tmptokens = self_expr_parse( instring, preloc, doActions )
+                if tmptokens or tmptokens.haskeys():
+                    tokens += tmptokens
+        except (ParseException,IndexError):
+            pass
+
+        return loc, tokens
+        
+class OneOrMore(_MultipleMatch):
+    """
+    Repetition of one or more of the given expression.
+    
+    Parameters:
+     - expr - expression that must match one or more times
+     - stopOn - (default=C{None}) - expression for a terminating sentinel
+          (only required if the sentinel would ordinarily match the repetition 
+          expression)          
+
+    Example::
+        data_word = Word(alphas)
+        label = data_word + FollowedBy(':')
+        attr_expr = Group(label + Suppress(':') + OneOrMore(data_word).setParseAction(' '.join))
+
+        text = "shape: SQUARE posn: upper left color: BLACK"
+        OneOrMore(attr_expr).parseString(text).pprint()  # Fail! read 'color' as data instead of next label -> [['shape', 'SQUARE color']]
+
+        # use stopOn attribute for OneOrMore to avoid reading label string as part of the data
+        attr_expr = Group(label + Suppress(':') + OneOrMore(data_word, stopOn=label).setParseAction(' '.join))
+        OneOrMore(attr_expr).parseString(text).pprint() # Better -> [['shape', 'SQUARE'], ['posn', 'upper left'], ['color', 'BLACK']]
+        
+        # could also be written as
+        (attr_expr * (1,)).parseString(text).pprint()
+    """
+
+    def __str__( self ):
+        if hasattr(self,"name"):
+            return self.name
+
+        if self.strRepr is None:
+            self.strRepr = "{" + _ustr(self.expr) + "}..."
+
+        return self.strRepr
+
+class ZeroOrMore(_MultipleMatch):
+    """
+    Optional repetition of zero or more of the given expression.
+    
+    Parameters:
+     - expr - expression that must match zero or more times
+     - stopOn - (default=C{None}) - expression for a terminating sentinel
+          (only required if the sentinel would ordinarily match the repetition 
+          expression)          
+
+    Example: similar to L{OneOrMore}
+    """
+    def __init__( self, expr, stopOn=None):
+        super(ZeroOrMore,self).__init__(expr, stopOn=stopOn)
+        self.mayReturnEmpty = True
+        
+    def parseImpl( self, instring, loc, doActions=True ):
+        try:
+            return super(ZeroOrMore, self).parseImpl(instring, loc, doActions)
+        except (ParseException,IndexError):
+            return loc, []
+
+    def __str__( self ):
+        if hasattr(self,"name"):
+            return self.name
+
+        if self.strRepr is None:
+            self.strRepr = "[" + _ustr(self.expr) + "]..."
+
+        return self.strRepr
+
+class _NullToken(object):
+    def __bool__(self):
+        return False
+    __nonzero__ = __bool__
+    def __str__(self):
+        return ""
+
+_optionalNotMatched = _NullToken()
+class Optional(ParseElementEnhance):
+    """
+    Optional matching of the given expression.
+
+    Parameters:
+     - expr - expression that must match zero or more times
+     - default (optional) - value to be returned if the optional expression is not found.
+
+    Example::
+        # US postal code can be a 5-digit zip, plus optional 4-digit qualifier
+        zip = Combine(Word(nums, exact=5) + Optional('-' + Word(nums, exact=4)))
+        zip.runTests('''
+            # traditional ZIP code
+            12345
+            
+            # ZIP+4 form
+            12101-0001
+            
+            # invalid ZIP
+            98765-
+            ''')
+    prints::
+        # traditional ZIP code
+        12345
+        ['12345']
+
+        # ZIP+4 form
+        12101-0001
+        ['12101-0001']
+
+        # invalid ZIP
+        98765-
+             ^
+        FAIL: Expected end of text (at char 5), (line:1, col:6)
+    """
+    def __init__( self, expr, default=_optionalNotMatched ):
+        super(Optional,self).__init__( expr, savelist=False )
+        self.saveAsList = self.expr.saveAsList
+        self.defaultValue = default
+        self.mayReturnEmpty = True
+
+    def parseImpl( self, instring, loc, doActions=True ):
+        try:
+            loc, tokens = self.expr._parse( instring, loc, doActions, callPreParse=False )
+        except (ParseException,IndexError):
+            if self.defaultValue is not _optionalNotMatched:
+                if self.expr.resultsName:
+                    tokens = ParseResults([ self.defaultValue ])
+                    tokens[self.expr.resultsName] = self.defaultValue
+                else:
+                    tokens = [ self.defaultValue ]
+            else:
+                tokens = []
+        return loc, tokens
+
+    def __str__( self ):
+        if hasattr(self,"name"):
+            return self.name
+
+        if self.strRepr is None:
+            self.strRepr = "[" + _ustr(self.expr) + "]"
+
+        return self.strRepr
+
+class SkipTo(ParseElementEnhance):
+    """
+    Token for skipping over all undefined text until the matched expression is found.
+
+    Parameters:
+     - expr - target expression marking the end of the data to be skipped
+     - include - (default=C{False}) if True, the target expression is also parsed 
+          (the skipped text and target expression are returned as a 2-element list).
+     - ignore - (default=C{None}) used to define grammars (typically quoted strings and 
+          comments) that might contain false matches to the target expression
+     - failOn - (default=C{None}) define expressions that are not allowed to be 
+          included in the skipped test; if found before the target expression is found, 
+          the SkipTo is not a match
+
+    Example::
+        report = '''
+            Outstanding Issues Report - 1 Jan 2000
+
+               # | Severity | Description                               |  Days Open
+            -----+----------+-------------------------------------------+-----------
+             101 | Critical | Intermittent system crash                 |          6
+              94 | Cosmetic | Spelling error on Login ('log|n')         |         14
+              79 | Minor    | System slow when running too many reports |         47
+            '''
+        integer = Word(nums)
+        SEP = Suppress('|')
+        # use SkipTo to simply match everything up until the next SEP
+        # - ignore quoted strings, so that a '|' character inside a quoted string does not match
+        # - parse action will call token.strip() for each matched token, i.e., the description body
+        string_data = SkipTo(SEP, ignore=quotedString)
+        string_data.setParseAction(tokenMap(str.strip))
+        ticket_expr = (integer("issue_num") + SEP 
+                      + string_data("sev") + SEP 
+                      + string_data("desc") + SEP 
+                      + integer("days_open"))
+        
+        for tkt in ticket_expr.searchString(report):
+            print tkt.dump()
+    prints::
+        ['101', 'Critical', 'Intermittent system crash', '6']
+        - days_open: 6
+        - desc: Intermittent system crash
+        - issue_num: 101
+        - sev: Critical
+        ['94', 'Cosmetic', "Spelling error on Login ('log|n')", '14']
+        - days_open: 14
+        - desc: Spelling error on Login ('log|n')
+        - issue_num: 94
+        - sev: Cosmetic
+        ['79', 'Minor', 'System slow when running too many reports', '47']
+        - days_open: 47
+        - desc: System slow when running too many reports
+        - issue_num: 79
+        - sev: Minor
+    """
+    def __init__( self, other, include=False, ignore=None, failOn=None ):
+        super( SkipTo, self ).__init__( other )
+        self.ignoreExpr = ignore
+        self.mayReturnEmpty = True
+        self.mayIndexError = False
+        self.includeMatch = include
+        self.asList = False
+        if isinstance(failOn, basestring):
+            self.failOn = ParserElement._literalStringClass(failOn)
+        else:
+            self.failOn = failOn
+        self.errmsg = "No match found for "+_ustr(self.expr)
+
+    def parseImpl( self, instring, loc, doActions=True ):
+        startloc = loc
+        instrlen = len(instring)
+        expr = self.expr
+        expr_parse = self.expr._parse
+        self_failOn_canParseNext = self.failOn.canParseNext if self.failOn is not None else None
+        self_ignoreExpr_tryParse = self.ignoreExpr.tryParse if self.ignoreExpr is not None else None
+        
+        tmploc = loc
+        while tmploc <= instrlen:
+            if self_failOn_canParseNext is not None:
+                # break if failOn expression matches
+                if self_failOn_canParseNext(instring, tmploc):
+                    break
+                    
+            if self_ignoreExpr_tryParse is not None:
+                # advance past ignore expressions
+                while 1:
+                    try:
+                        tmploc = self_ignoreExpr_tryParse(instring, tmploc)
+                    except ParseBaseException:
+                        break
+            
+            try:
+                expr_parse(instring, tmploc, doActions=False, callPreParse=False)
+            except (ParseException, IndexError):
+                # no match, advance loc in string
+                tmploc += 1
+            else:
+                # matched skipto expr, done
+                break
+
+        else:
+            # ran off the end of the input string without matching skipto expr, fail
+            raise ParseException(instring, loc, self.errmsg, self)
+
+        # build up return values
+        loc = tmploc
+        skiptext = instring[startloc:loc]
+        skipresult = ParseResults(skiptext)
+        
+        if self.includeMatch:
+            loc, mat = expr_parse(instring,loc,doActions,callPreParse=False)
+            skipresult += mat
+
+        return loc, skipresult
+
+class Forward(ParseElementEnhance):
+    """
+    Forward declaration of an expression to be defined later -
+    used for recursive grammars, such as algebraic infix notation.
+    When the expression is known, it is assigned to the C{Forward} variable using the '<<' operator.
+
+    Note: take care when assigning to C{Forward} not to overlook precedence of operators.
+    Specifically, '|' has a lower precedence than '<<', so that::
+        fwdExpr << a | b | c
+    will actually be evaluated as::
+        (fwdExpr << a) | b | c
+    thereby leaving b and c out as parseable alternatives.  It is recommended that you
+    explicitly group the values inserted into the C{Forward}::
+        fwdExpr << (a | b | c)
+    Converting to use the '<<=' operator instead will avoid this problem.
+
+    See L{ParseResults.pprint} for an example of a recursive parser created using
+    C{Forward}.
+    """
+    def __init__( self, other=None ):
+        super(Forward,self).__init__( other, savelist=False )
+
+    def __lshift__( self, other ):
+        if isinstance( other, basestring ):
+            other = ParserElement._literalStringClass(other)
+        self.expr = other
+        self.strRepr = None
+        self.mayIndexError = self.expr.mayIndexError
+        self.mayReturnEmpty = self.expr.mayReturnEmpty
+        self.setWhitespaceChars( self.expr.whiteChars )
+        self.skipWhitespace = self.expr.skipWhitespace
+        self.saveAsList = self.expr.saveAsList
+        self.ignoreExprs.extend(self.expr.ignoreExprs)
+        return self
+        
+    def __ilshift__(self, other):
+        return self << other
+    
+    def leaveWhitespace( self ):
+        self.skipWhitespace = False
+        return self
+
+    def streamline( self ):
+        if not self.streamlined:
+            self.streamlined = True
+            if self.expr is not None:
+                self.expr.streamline()
+        return self
+
+    def validate( self, validateTrace=[] ):
+        if self not in validateTrace:
+            tmp = validateTrace[:]+[self]
+            if self.expr is not None:
+                self.expr.validate(tmp)
+        self.checkRecursion([])
+
+    def __str__( self ):
+        if hasattr(self,"name"):
+            return self.name
+        return self.__class__.__name__ + ": ..."
+
+        # stubbed out for now - creates awful memory and perf issues
+        self._revertClass = self.__class__
+        self.__class__ = _ForwardNoRecurse
+        try:
+            if self.expr is not None:
+                retString = _ustr(self.expr)
+            else:
+                retString = "None"
+        finally:
+            self.__class__ = self._revertClass
+        return self.__class__.__name__ + ": " + retString
+
+    def copy(self):
+        if self.expr is not None:
+            return super(Forward,self).copy()
+        else:
+            ret = Forward()
+            ret <<= self
+            return ret
+
+class _ForwardNoRecurse(Forward):
+    def __str__( self ):
+        return "..."
+
+class TokenConverter(ParseElementEnhance):
+    """
+    Abstract subclass of C{ParseExpression}, for converting parsed results.
+    """
+    def __init__( self, expr, savelist=False ):
+        super(TokenConverter,self).__init__( expr )#, savelist )
+        self.saveAsList = False
+
+class Combine(TokenConverter):
+    """
+    Converter to concatenate all matching tokens to a single string.
+    By default, the matching patterns must also be contiguous in the input string;
+    this can be disabled by specifying C{'adjacent=False'} in the constructor.
+
+    Example::
+        real = Word(nums) + '.' + Word(nums)
+        print(real.parseString('3.1416')) # -> ['3', '.', '1416']
+        # will also erroneously match the following
+        print(real.parseString('3. 1416')) # -> ['3', '.', '1416']
+
+        real = Combine(Word(nums) + '.' + Word(nums))
+        print(real.parseString('3.1416')) # -> ['3.1416']
+        # no match when there are internal spaces
+        print(real.parseString('3. 1416')) # -> Exception: Expected W:(0123...)
+    """
+    def __init__( self, expr, joinString="", adjacent=True ):
+        super(Combine,self).__init__( expr )
+        # suppress whitespace-stripping in contained parse expressions, but re-enable it on the Combine itself
+        if adjacent:
+            self.leaveWhitespace()
+        self.adjacent = adjacent
+        self.skipWhitespace = True
+        self.joinString = joinString
+        self.callPreparse = True
+
+    def ignore( self, other ):
+        if self.adjacent:
+            ParserElement.ignore(self, other)
+        else:
+            super( Combine, self).ignore( other )
+        return self
+
+    def postParse( self, instring, loc, tokenlist ):
+        retToks = tokenlist.copy()
+        del retToks[:]
+        retToks += ParseResults([ "".join(tokenlist._asStringList(self.joinString)) ], modal=self.modalResults)
+
+        if self.resultsName and retToks.haskeys():
+            return [ retToks ]
+        else:
+            return retToks
+
+class Group(TokenConverter):
+    """
+    Converter to return the matched tokens as a list - useful for returning tokens of C{L{ZeroOrMore}} and C{L{OneOrMore}} expressions.
+
+    Example::
+        ident = Word(alphas)
+        num = Word(nums)
+        term = ident | num
+        func = ident + Optional(delimitedList(term))
+        print(func.parseString("fn a,b,100"))  # -> ['fn', 'a', 'b', '100']
+
+        func = ident + Group(Optional(delimitedList(term)))
+        print(func.parseString("fn a,b,100"))  # -> ['fn', ['a', 'b', '100']]
+    """
+    def __init__( self, expr ):
+        super(Group,self).__init__( expr )
+        self.saveAsList = True
+
+    def postParse( self, instring, loc, tokenlist ):
+        return [ tokenlist ]
+
+class Dict(TokenConverter):
+    """
+    Converter to return a repetitive expression as a list, but also as a dictionary.
+    Each element can also be referenced using the first token in the expression as its key.
+    Useful for tabular report scraping when the first column can be used as a item key.
+
+    Example::
+        data_word = Word(alphas)
+        label = data_word + FollowedBy(':')
+        attr_expr = Group(label + Suppress(':') + OneOrMore(data_word).setParseAction(' '.join))
+
+        text = "shape: SQUARE posn: upper left color: light blue texture: burlap"
+        attr_expr = (label + Suppress(':') + OneOrMore(data_word, stopOn=label).setParseAction(' '.join))
+        
+        # print attributes as plain groups
+        print(OneOrMore(attr_expr).parseString(text).dump())
+        
+        # instead of OneOrMore(expr), parse using Dict(OneOrMore(Group(expr))) - Dict will auto-assign names
+        result = Dict(OneOrMore(Group(attr_expr))).parseString(text)
+        print(result.dump())
+        
+        # access named fields as dict entries, or output as dict
+        print(result['shape'])        
+        print(result.asDict())
+    prints::
+        ['shape', 'SQUARE', 'posn', 'upper left', 'color', 'light blue', 'texture', 'burlap']
+
+        [['shape', 'SQUARE'], ['posn', 'upper left'], ['color', 'light blue'], ['texture', 'burlap']]
+        - color: light blue
+        - posn: upper left
+        - shape: SQUARE
+        - texture: burlap
+        SQUARE
+        {'color': 'light blue', 'posn': 'upper left', 'texture': 'burlap', 'shape': 'SQUARE'}
+    See more examples at L{ParseResults} of accessing fields by results name.
+    """
+    def __init__( self, expr ):
+        super(Dict,self).__init__( expr )
+        self.saveAsList = True
+
+    def postParse( self, instring, loc, tokenlist ):
+        for i,tok in enumerate(tokenlist):
+            if len(tok) == 0:
+                continue
+            ikey = tok[0]
+            if isinstance(ikey,int):
+                ikey = _ustr(tok[0]).strip()
+            if len(tok)==1:
+                tokenlist[ikey] = _ParseResultsWithOffset("",i)
+            elif len(tok)==2 and not isinstance(tok[1],ParseResults):
+                tokenlist[ikey] = _ParseResultsWithOffset(tok[1],i)
+            else:
+                dictvalue = tok.copy() #ParseResults(i)
+                del dictvalue[0]
+                if len(dictvalue)!= 1 or (isinstance(dictvalue,ParseResults) and dictvalue.haskeys()):
+                    tokenlist[ikey] = _ParseResultsWithOffset(dictvalue,i)
+                else:
+                    tokenlist[ikey] = _ParseResultsWithOffset(dictvalue[0],i)
+
+        if self.resultsName:
+            return [ tokenlist ]
+        else:
+            return tokenlist
+
+
+class Suppress(TokenConverter):
+    """
+    Converter for ignoring the results of a parsed expression.
+
+    Example::
+        source = "a, b, c,d"
+        wd = Word(alphas)
+        wd_list1 = wd + ZeroOrMore(',' + wd)
+        print(wd_list1.parseString(source))
+
+        # often, delimiters that are useful during parsing are just in the
+        # way afterward - use Suppress to keep them out of the parsed output
+        wd_list2 = wd + ZeroOrMore(Suppress(',') + wd)
+        print(wd_list2.parseString(source))
+    prints::
+        ['a', ',', 'b', ',', 'c', ',', 'd']
+        ['a', 'b', 'c', 'd']
+    (See also L{delimitedList}.)
+    """
+    def postParse( self, instring, loc, tokenlist ):
+        return []
+
+    def suppress( self ):
+        return self
+
+
+class OnlyOnce(object):
+    """
+    Wrapper for parse actions, to ensure they are only called once.
+    """
+    def __init__(self, methodCall):
+        self.callable = _trim_arity(methodCall)
+        self.called = False
+    def __call__(self,s,l,t):
+        if not self.called:
+            results = self.callable(s,l,t)
+            self.called = True
+            return results
+        raise ParseException(s,l,"")
+    def reset(self):
+        self.called = False
+
+def traceParseAction(f):
+    """
+    Decorator for debugging parse actions. 
+    
+    When the parse action is called, this decorator will print C{">> entering I{method-name}(line:I{current_source_line}, I{parse_location}, I{matched_tokens})".}
+    When the parse action completes, the decorator will print C{"<<"} followed by the returned value, or any exception that the parse action raised.
+
+    Example::
+        wd = Word(alphas)
+
+        @traceParseAction
+        def remove_duplicate_chars(tokens):
+            return ''.join(sorted(set(''.join(tokens))))
+
+        wds = OneOrMore(wd).setParseAction(remove_duplicate_chars)
+        print(wds.parseString("slkdjs sld sldd sdlf sdljf"))
+    prints::
+        >>entering remove_duplicate_chars(line: 'slkdjs sld sldd sdlf sdljf', 0, (['slkdjs', 'sld', 'sldd', 'sdlf', 'sdljf'], {}))
+        <3:
+            thisFunc = paArgs[0].__class__.__name__ + '.' + thisFunc
+        sys.stderr.write( ">>entering %s(line: '%s', %d, %r)\n" % (thisFunc,line(l,s),l,t) )
+        try:
+            ret = f(*paArgs)
+        except Exception as exc:
+            sys.stderr.write( "< ['aa', 'bb', 'cc']
+        delimitedList(Word(hexnums), delim=':', combine=True).parseString("AA:BB:CC:DD:EE") # -> ['AA:BB:CC:DD:EE']
+    """
+    dlName = _ustr(expr)+" ["+_ustr(delim)+" "+_ustr(expr)+"]..."
+    if combine:
+        return Combine( expr + ZeroOrMore( delim + expr ) ).setName(dlName)
+    else:
+        return ( expr + ZeroOrMore( Suppress( delim ) + expr ) ).setName(dlName)
+
+def countedArray( expr, intExpr=None ):
+    """
+    Helper to define a counted list of expressions.
+    This helper defines a pattern of the form::
+        integer expr expr expr...
+    where the leading integer tells how many expr expressions follow.
+    The matched tokens returns the array of expr tokens as a list - the leading count token is suppressed.
+    
+    If C{intExpr} is specified, it should be a pyparsing expression that produces an integer value.
+
+    Example::
+        countedArray(Word(alphas)).parseString('2 ab cd ef')  # -> ['ab', 'cd']
+
+        # in this parser, the leading integer value is given in binary,
+        # '10' indicating that 2 values are in the array
+        binaryConstant = Word('01').setParseAction(lambda t: int(t[0], 2))
+        countedArray(Word(alphas), intExpr=binaryConstant).parseString('10 ab cd ef')  # -> ['ab', 'cd']
+    """
+    arrayExpr = Forward()
+    def countFieldParseAction(s,l,t):
+        n = t[0]
+        arrayExpr << (n and Group(And([expr]*n)) or Group(empty))
+        return []
+    if intExpr is None:
+        intExpr = Word(nums).setParseAction(lambda t:int(t[0]))
+    else:
+        intExpr = intExpr.copy()
+    intExpr.setName("arrayLen")
+    intExpr.addParseAction(countFieldParseAction, callDuringTry=True)
+    return ( intExpr + arrayExpr ).setName('(len) ' + _ustr(expr) + '...')
+
+def _flatten(L):
+    ret = []
+    for i in L:
+        if isinstance(i,list):
+            ret.extend(_flatten(i))
+        else:
+            ret.append(i)
+    return ret
+
+def matchPreviousLiteral(expr):
+    """
+    Helper to define an expression that is indirectly defined from
+    the tokens matched in a previous expression, that is, it looks
+    for a 'repeat' of a previous expression.  For example::
+        first = Word(nums)
+        second = matchPreviousLiteral(first)
+        matchExpr = first + ":" + second
+    will match C{"1:1"}, but not C{"1:2"}.  Because this matches a
+    previous literal, will also match the leading C{"1:1"} in C{"1:10"}.
+    If this is not desired, use C{matchPreviousExpr}.
+    Do I{not} use with packrat parsing enabled.
+    """
+    rep = Forward()
+    def copyTokenToRepeater(s,l,t):
+        if t:
+            if len(t) == 1:
+                rep << t[0]
+            else:
+                # flatten t tokens
+                tflat = _flatten(t.asList())
+                rep << And(Literal(tt) for tt in tflat)
+        else:
+            rep << Empty()
+    expr.addParseAction(copyTokenToRepeater, callDuringTry=True)
+    rep.setName('(prev) ' + _ustr(expr))
+    return rep
+
+def matchPreviousExpr(expr):
+    """
+    Helper to define an expression that is indirectly defined from
+    the tokens matched in a previous expression, that is, it looks
+    for a 'repeat' of a previous expression.  For example::
+        first = Word(nums)
+        second = matchPreviousExpr(first)
+        matchExpr = first + ":" + second
+    will match C{"1:1"}, but not C{"1:2"}.  Because this matches by
+    expressions, will I{not} match the leading C{"1:1"} in C{"1:10"};
+    the expressions are evaluated first, and then compared, so
+    C{"1"} is compared with C{"10"}.
+    Do I{not} use with packrat parsing enabled.
+    """
+    rep = Forward()
+    e2 = expr.copy()
+    rep <<= e2
+    def copyTokenToRepeater(s,l,t):
+        matchTokens = _flatten(t.asList())
+        def mustMatchTheseTokens(s,l,t):
+            theseTokens = _flatten(t.asList())
+            if  theseTokens != matchTokens:
+                raise ParseException("",0,"")
+        rep.setParseAction( mustMatchTheseTokens, callDuringTry=True )
+    expr.addParseAction(copyTokenToRepeater, callDuringTry=True)
+    rep.setName('(prev) ' + _ustr(expr))
+    return rep
+
+def _escapeRegexRangeChars(s):
+    #~  escape these chars: ^-]
+    for c in r"\^-]":
+        s = s.replace(c,_bslash+c)
+    s = s.replace("\n",r"\n")
+    s = s.replace("\t",r"\t")
+    return _ustr(s)
+
+def oneOf( strs, caseless=False, useRegex=True ):
+    """
+    Helper to quickly define a set of alternative Literals, and makes sure to do
+    longest-first testing when there is a conflict, regardless of the input order,
+    but returns a C{L{MatchFirst}} for best performance.
+
+    Parameters:
+     - strs - a string of space-delimited literals, or a collection of string literals
+     - caseless - (default=C{False}) - treat all literals as caseless
+     - useRegex - (default=C{True}) - as an optimization, will generate a Regex
+          object; otherwise, will generate a C{MatchFirst} object (if C{caseless=True}, or
+          if creating a C{Regex} raises an exception)
+
+    Example::
+        comp_oper = oneOf("< = > <= >= !=")
+        var = Word(alphas)
+        number = Word(nums)
+        term = var | number
+        comparison_expr = term + comp_oper + term
+        print(comparison_expr.searchString("B = 12  AA=23 B<=AA AA>12"))
+    prints::
+        [['B', '=', '12'], ['AA', '=', '23'], ['B', '<=', 'AA'], ['AA', '>', '12']]
+    """
+    if caseless:
+        isequal = ( lambda a,b: a.upper() == b.upper() )
+        masks = ( lambda a,b: b.upper().startswith(a.upper()) )
+        parseElementClass = CaselessLiteral
+    else:
+        isequal = ( lambda a,b: a == b )
+        masks = ( lambda a,b: b.startswith(a) )
+        parseElementClass = Literal
+
+    symbols = []
+    if isinstance(strs,basestring):
+        symbols = strs.split()
+    elif isinstance(strs, Iterable):
+        symbols = list(strs)
+    else:
+        warnings.warn("Invalid argument to oneOf, expected string or iterable",
+                SyntaxWarning, stacklevel=2)
+    if not symbols:
+        return NoMatch()
+
+    i = 0
+    while i < len(symbols)-1:
+        cur = symbols[i]
+        for j,other in enumerate(symbols[i+1:]):
+            if ( isequal(other, cur) ):
+                del symbols[i+j+1]
+                break
+            elif ( masks(cur, other) ):
+                del symbols[i+j+1]
+                symbols.insert(i,other)
+                cur = other
+                break
+        else:
+            i += 1
+
+    if not caseless and useRegex:
+        #~ print (strs,"->", "|".join( [ _escapeRegexChars(sym) for sym in symbols] ))
+        try:
+            if len(symbols)==len("".join(symbols)):
+                return Regex( "[%s]" % "".join(_escapeRegexRangeChars(sym) for sym in symbols) ).setName(' | '.join(symbols))
+            else:
+                return Regex( "|".join(re.escape(sym) for sym in symbols) ).setName(' | '.join(symbols))
+        except Exception:
+            warnings.warn("Exception creating Regex for oneOf, building MatchFirst",
+                    SyntaxWarning, stacklevel=2)
+
+
+    # last resort, just use MatchFirst
+    return MatchFirst(parseElementClass(sym) for sym in symbols).setName(' | '.join(symbols))
+
+def dictOf( key, value ):
+    """
+    Helper to easily and clearly define a dictionary by specifying the respective patterns
+    for the key and value.  Takes care of defining the C{L{Dict}}, C{L{ZeroOrMore}}, and C{L{Group}} tokens
+    in the proper order.  The key pattern can include delimiting markers or punctuation,
+    as long as they are suppressed, thereby leaving the significant key text.  The value
+    pattern can include named results, so that the C{Dict} results can include named token
+    fields.
+
+    Example::
+        text = "shape: SQUARE posn: upper left color: light blue texture: burlap"
+        attr_expr = (label + Suppress(':') + OneOrMore(data_word, stopOn=label).setParseAction(' '.join))
+        print(OneOrMore(attr_expr).parseString(text).dump())
+        
+        attr_label = label
+        attr_value = Suppress(':') + OneOrMore(data_word, stopOn=label).setParseAction(' '.join)
+
+        # similar to Dict, but simpler call format
+        result = dictOf(attr_label, attr_value).parseString(text)
+        print(result.dump())
+        print(result['shape'])
+        print(result.shape)  # object attribute access works too
+        print(result.asDict())
+    prints::
+        [['shape', 'SQUARE'], ['posn', 'upper left'], ['color', 'light blue'], ['texture', 'burlap']]
+        - color: light blue
+        - posn: upper left
+        - shape: SQUARE
+        - texture: burlap
+        SQUARE
+        SQUARE
+        {'color': 'light blue', 'shape': 'SQUARE', 'posn': 'upper left', 'texture': 'burlap'}
+    """
+    return Dict( ZeroOrMore( Group ( key + value ) ) )
+
+def originalTextFor(expr, asString=True):
+    """
+    Helper to return the original, untokenized text for a given expression.  Useful to
+    restore the parsed fields of an HTML start tag into the raw tag text itself, or to
+    revert separate tokens with intervening whitespace back to the original matching
+    input text. By default, returns astring containing the original parsed text.  
+       
+    If the optional C{asString} argument is passed as C{False}, then the return value is a 
+    C{L{ParseResults}} containing any results names that were originally matched, and a 
+    single token containing the original matched text from the input string.  So if 
+    the expression passed to C{L{originalTextFor}} contains expressions with defined
+    results names, you must set C{asString} to C{False} if you want to preserve those
+    results name values.
+
+    Example::
+        src = "this is test  bold text  normal text "
+        for tag in ("b","i"):
+            opener,closer = makeHTMLTags(tag)
+            patt = originalTextFor(opener + SkipTo(closer) + closer)
+            print(patt.searchString(src)[0])
+    prints::
+        [' bold text ']
+        ['text']
+    """
+    locMarker = Empty().setParseAction(lambda s,loc,t: loc)
+    endlocMarker = locMarker.copy()
+    endlocMarker.callPreparse = False
+    matchExpr = locMarker("_original_start") + expr + endlocMarker("_original_end")
+    if asString:
+        extractText = lambda s,l,t: s[t._original_start:t._original_end]
+    else:
+        def extractText(s,l,t):
+            t[:] = [s[t.pop('_original_start'):t.pop('_original_end')]]
+    matchExpr.setParseAction(extractText)
+    matchExpr.ignoreExprs = expr.ignoreExprs
+    return matchExpr
+
+def ungroup(expr): 
+    """
+    Helper to undo pyparsing's default grouping of And expressions, even
+    if all but one are non-empty.
+    """
+    return TokenConverter(expr).setParseAction(lambda t:t[0])
+
+def locatedExpr(expr):
+    """
+    Helper to decorate a returned token with its starting and ending locations in the input string.
+    This helper adds the following results names:
+     - locn_start = location where matched expression begins
+     - locn_end = location where matched expression ends
+     - value = the actual parsed results
+
+    Be careful if the input text contains C{} characters, you may want to call
+    C{L{ParserElement.parseWithTabs}}
+
+    Example::
+        wd = Word(alphas)
+        for match in locatedExpr(wd).searchString("ljsdf123lksdjjf123lkkjj1222"):
+            print(match)
+    prints::
+        [[0, 'ljsdf', 5]]
+        [[8, 'lksdjjf', 15]]
+        [[18, 'lkkjj', 23]]
+    """
+    locator = Empty().setParseAction(lambda s,l,t: l)
+    return Group(locator("locn_start") + expr("value") + locator.copy().leaveWhitespace()("locn_end"))
+
+
+# convenience constants for positional expressions
+empty       = Empty().setName("empty")
+lineStart   = LineStart().setName("lineStart")
+lineEnd     = LineEnd().setName("lineEnd")
+stringStart = StringStart().setName("stringStart")
+stringEnd   = StringEnd().setName("stringEnd")
+
+_escapedPunc = Word( _bslash, r"\[]-*.$+^?()~ ", exact=2 ).setParseAction(lambda s,l,t:t[0][1])
+_escapedHexChar = Regex(r"\\0?[xX][0-9a-fA-F]+").setParseAction(lambda s,l,t:unichr(int(t[0].lstrip(r'\0x'),16)))
+_escapedOctChar = Regex(r"\\0[0-7]+").setParseAction(lambda s,l,t:unichr(int(t[0][1:],8)))
+_singleChar = _escapedPunc | _escapedHexChar | _escapedOctChar | CharsNotIn(r'\]', exact=1)
+_charRange = Group(_singleChar + Suppress("-") + _singleChar)
+_reBracketExpr = Literal("[") + Optional("^").setResultsName("negate") + Group( OneOrMore( _charRange | _singleChar ) ).setResultsName("body") + "]"
+
+def srange(s):
+    r"""
+    Helper to easily define string ranges for use in Word construction.  Borrows
+    syntax from regexp '[]' string range definitions::
+        srange("[0-9]")   -> "0123456789"
+        srange("[a-z]")   -> "abcdefghijklmnopqrstuvwxyz"
+        srange("[a-z$_]") -> "abcdefghijklmnopqrstuvwxyz$_"
+    The input string must be enclosed in []'s, and the returned string is the expanded
+    character set joined into a single string.
+    The values enclosed in the []'s may be:
+     - a single character
+     - an escaped character with a leading backslash (such as C{\-} or C{\]})
+     - an escaped hex character with a leading C{'\x'} (C{\x21}, which is a C{'!'} character) 
+         (C{\0x##} is also supported for backwards compatibility) 
+     - an escaped octal character with a leading C{'\0'} (C{\041}, which is a C{'!'} character)
+     - a range of any of the above, separated by a dash (C{'a-z'}, etc.)
+     - any combination of the above (C{'aeiouy'}, C{'a-zA-Z0-9_$'}, etc.)
+    """
+    _expanded = lambda p: p if not isinstance(p,ParseResults) else ''.join(unichr(c) for c in range(ord(p[0]),ord(p[1])+1))
+    try:
+        return "".join(_expanded(part) for part in _reBracketExpr.parseString(s).body)
+    except Exception:
+        return ""
+
+def matchOnlyAtCol(n):
+    """
+    Helper method for defining parse actions that require matching at a specific
+    column in the input text.
+    """
+    def verifyCol(strg,locn,toks):
+        if col(locn,strg) != n:
+            raise ParseException(strg,locn,"matched token not at column %d" % n)
+    return verifyCol
+
+def replaceWith(replStr):
+    """
+    Helper method for common parse actions that simply return a literal value.  Especially
+    useful when used with C{L{transformString}()}.
+
+    Example::
+        num = Word(nums).setParseAction(lambda toks: int(toks[0]))
+        na = oneOf("N/A NA").setParseAction(replaceWith(math.nan))
+        term = na | num
+        
+        OneOrMore(term).parseString("324 234 N/A 234") # -> [324, 234, nan, 234]
+    """
+    return lambda s,l,t: [replStr]
+
+def removeQuotes(s,l,t):
+    """
+    Helper parse action for removing quotation marks from parsed quoted strings.
+
+    Example::
+        # by default, quotation marks are included in parsed results
+        quotedString.parseString("'Now is the Winter of our Discontent'") # -> ["'Now is the Winter of our Discontent'"]
+
+        # use removeQuotes to strip quotation marks from parsed results
+        quotedString.setParseAction(removeQuotes)
+        quotedString.parseString("'Now is the Winter of our Discontent'") # -> ["Now is the Winter of our Discontent"]
+    """
+    return t[0][1:-1]
+
+def tokenMap(func, *args):
+    """
+    Helper to define a parse action by mapping a function to all elements of a ParseResults list.If any additional 
+    args are passed, they are forwarded to the given function as additional arguments after
+    the token, as in C{hex_integer = Word(hexnums).setParseAction(tokenMap(int, 16))}, which will convert the
+    parsed data to an integer using base 16.
+
+    Example (compare the last to example in L{ParserElement.transformString}::
+        hex_ints = OneOrMore(Word(hexnums)).setParseAction(tokenMap(int, 16))
+        hex_ints.runTests('''
+            00 11 22 aa FF 0a 0d 1a
+            ''')
+        
+        upperword = Word(alphas).setParseAction(tokenMap(str.upper))
+        OneOrMore(upperword).runTests('''
+            my kingdom for a horse
+            ''')
+
+        wd = Word(alphas).setParseAction(tokenMap(str.title))
+        OneOrMore(wd).setParseAction(' '.join).runTests('''
+            now is the winter of our discontent made glorious summer by this sun of york
+            ''')
+    prints::
+        00 11 22 aa FF 0a 0d 1a
+        [0, 17, 34, 170, 255, 10, 13, 26]
+
+        my kingdom for a horse
+        ['MY', 'KINGDOM', 'FOR', 'A', 'HORSE']
+
+        now is the winter of our discontent made glorious summer by this sun of york
+        ['Now Is The Winter Of Our Discontent Made Glorious Summer By This Sun Of York']
+    """
+    def pa(s,l,t):
+        return [func(tokn, *args) for tokn in t]
+
+    try:
+        func_name = getattr(func, '__name__', 
+                            getattr(func, '__class__').__name__)
+    except Exception:
+        func_name = str(func)
+    pa.__name__ = func_name
+
+    return pa
+
+upcaseTokens = tokenMap(lambda t: _ustr(t).upper())
+"""(Deprecated) Helper parse action to convert tokens to upper case. Deprecated in favor of L{pyparsing_common.upcaseTokens}"""
+
+downcaseTokens = tokenMap(lambda t: _ustr(t).lower())
+"""(Deprecated) Helper parse action to convert tokens to lower case. Deprecated in favor of L{pyparsing_common.downcaseTokens}"""
+    
+def _makeTags(tagStr, xml):
+    """Internal helper to construct opening and closing tag expressions, given a tag name"""
+    if isinstance(tagStr,basestring):
+        resname = tagStr
+        tagStr = Keyword(tagStr, caseless=not xml)
+    else:
+        resname = tagStr.name
+
+    tagAttrName = Word(alphas,alphanums+"_-:")
+    if (xml):
+        tagAttrValue = dblQuotedString.copy().setParseAction( removeQuotes )
+        openTag = Suppress("<") + tagStr("tag") + \
+                Dict(ZeroOrMore(Group( tagAttrName + Suppress("=") + tagAttrValue ))) + \
+                Optional("/",default=[False]).setResultsName("empty").setParseAction(lambda s,l,t:t[0]=='/') + Suppress(">")
+    else:
+        printablesLessRAbrack = "".join(c for c in printables if c not in ">")
+        tagAttrValue = quotedString.copy().setParseAction( removeQuotes ) | Word(printablesLessRAbrack)
+        openTag = Suppress("<") + tagStr("tag") + \
+                Dict(ZeroOrMore(Group( tagAttrName.setParseAction(downcaseTokens) + \
+                Optional( Suppress("=") + tagAttrValue ) ))) + \
+                Optional("/",default=[False]).setResultsName("empty").setParseAction(lambda s,l,t:t[0]=='/') + Suppress(">")
+    closeTag = Combine(_L("")
+
+    openTag = openTag.setResultsName("start"+"".join(resname.replace(":"," ").title().split())).setName("<%s>" % resname)
+    closeTag = closeTag.setResultsName("end"+"".join(resname.replace(":"," ").title().split())).setName("" % resname)
+    openTag.tag = resname
+    closeTag.tag = resname
+    return openTag, closeTag
+
+def makeHTMLTags(tagStr):
+    """
+    Helper to construct opening and closing tag expressions for HTML, given a tag name. Matches
+    tags in either upper or lower case, attributes with namespaces and with quoted or unquoted values.
+
+    Example::
+        text = 'More info at the pyparsing wiki page'
+        # makeHTMLTags returns pyparsing expressions for the opening and closing tags as a 2-tuple
+        a,a_end = makeHTMLTags("A")
+        link_expr = a + SkipTo(a_end)("link_text") + a_end
+        
+        for link in link_expr.searchString(text):
+            # attributes in the  tag (like "href" shown here) are also accessible as named results
+            print(link.link_text, '->', link.href)
+    prints::
+        pyparsing -> http://pyparsing.wikispaces.com
+    """
+    return _makeTags( tagStr, False )
+
+def makeXMLTags(tagStr):
+    """
+    Helper to construct opening and closing tag expressions for XML, given a tag name. Matches
+    tags only in the given upper/lower case.
+
+    Example: similar to L{makeHTMLTags}
+    """
+    return _makeTags( tagStr, True )
+
+def withAttribute(*args,**attrDict):
+    """
+    Helper to create a validating parse action to be used with start tags created
+    with C{L{makeXMLTags}} or C{L{makeHTMLTags}}. Use C{withAttribute} to qualify a starting tag
+    with a required attribute value, to avoid false matches on common tags such as
+    C{} or C{
}.
+
+    Call C{withAttribute} with a series of attribute names and values. Specify the list
+    of filter attributes names and values as:
+     - keyword arguments, as in C{(align="right")}, or
+     - as an explicit dict with C{**} operator, when an attribute name is also a Python
+          reserved word, as in C{**{"class":"Customer", "align":"right"}}
+     - a list of name-value tuples, as in ( ("ns1:class", "Customer"), ("ns2:align","right") )
+    For attribute names with a namespace prefix, you must use the second form.  Attribute
+    names are matched insensitive to upper/lower case.
+       
+    If just testing for C{class} (with or without a namespace), use C{L{withClass}}.
+
+    To verify that the attribute exists, but without specifying a value, pass
+    C{withAttribute.ANY_VALUE} as the value.
+
+    Example::
+        html = '''
+            

+            Some text
+            
1 4 0 1 0

+            
1,3 2,3 1,1

+            
this has no type

+            

+                
+        '''
+        div,div_end = makeHTMLTags("div")
+
+        # only match div tag having a type attribute with value "grid"
+        div_grid = div().setParseAction(withAttribute(type="grid"))
+        grid_expr = div_grid + SkipTo(div | div_end)("body")
+        for grid_header in grid_expr.searchString(html):
+            print(grid_header.body)
+        
+        # construct a match with any div tag having a type attribute, regardless of the value
+        div_any_type = div().setParseAction(withAttribute(type=withAttribute.ANY_VALUE))
+        div_expr = div_any_type + SkipTo(div | div_end)("body")
+        for div_header in div_expr.searchString(html):
+            print(div_header.body)
+    prints::
+        1 4 0 1 0
+
+        1 4 0 1 0
+        1,3 2,3 1,1
+    """
+    if args:
+        attrs = args[:]
+    else:
+        attrs = attrDict.items()
+    attrs = [(k,v) for k,v in attrs]
+    def pa(s,l,tokens):
+        for attrName,attrValue in attrs:
+            if attrName not in tokens:
+                raise ParseException(s,l,"no matching attribute " + attrName)
+            if attrValue != withAttribute.ANY_VALUE and tokens[attrName] != attrValue:
+                raise ParseException(s,l,"attribute '%s' has value '%s', must be '%s'" %
+                                            (attrName, tokens[attrName], attrValue))
+    return pa
+withAttribute.ANY_VALUE = object()
+
+def withClass(classname, namespace=''):
+    """
+    Simplified version of C{L{withAttribute}} when matching on a div class - made
+    difficult because C{class} is a reserved word in Python.
+
+    Example::
+        html = '''
+            

+            Some text
+            
1 4 0 1 0

+            
1,3 2,3 1,1

+            
this <div> has no class

+            

+                
+        '''
+        div,div_end = makeHTMLTags("div")
+        div_grid = div().setParseAction(withClass("grid"))
+        
+        grid_expr = div_grid + SkipTo(div | div_end)("body")
+        for grid_header in grid_expr.searchString(html):
+            print(grid_header.body)
+        
+        div_any_type = div().setParseAction(withClass(withAttribute.ANY_VALUE))
+        div_expr = div_any_type + SkipTo(div | div_end)("body")
+        for div_header in div_expr.searchString(html):
+            print(div_header.body)
+    prints::
+        1 4 0 1 0
+
+        1 4 0 1 0
+        1,3 2,3 1,1
+    """
+    classattr = "%s:class" % namespace if namespace else "class"
+    return withAttribute(**{classattr : classname})        
+
+opAssoc = _Constants()
+opAssoc.LEFT = object()
+opAssoc.RIGHT = object()
+
+def infixNotation( baseExpr, opList, lpar=Suppress('('), rpar=Suppress(')') ):
+    """
+    Helper method for constructing grammars of expressions made up of
+    operators working in a precedence hierarchy.  Operators may be unary or
+    binary, left- or right-associative.  Parse actions can also be attached
+    to operator expressions. The generated parser will also recognize the use 
+    of parentheses to override operator precedences (see example below).
+    
+    Note: if you define a deep operator list, you may see performance issues
+    when using infixNotation. See L{ParserElement.enablePackrat} for a
+    mechanism to potentially improve your parser performance.
+
+    Parameters:
+     - baseExpr - expression representing the most basic element for the nested
+     - opList - list of tuples, one for each operator precedence level in the
+      expression grammar; each tuple is of the form
+      (opExpr, numTerms, rightLeftAssoc, parseAction), where:
+       - opExpr is the pyparsing expression for the operator;
+          may also be a string, which will be converted to a Literal;
+          if numTerms is 3, opExpr is a tuple of two expressions, for the
+          two operators separating the 3 terms
+       - numTerms is the number of terms for this operator (must
+          be 1, 2, or 3)
+       - rightLeftAssoc is the indicator whether the operator is
+          right or left associative, using the pyparsing-defined
+          constants C{opAssoc.RIGHT} and C{opAssoc.LEFT}.
+       - parseAction is the parse action to be associated with
+          expressions matching this operator expression (the
+          parse action tuple member may be omitted); if the parse action
+          is passed a tuple or list of functions, this is equivalent to
+          calling C{setParseAction(*fn)} (L{ParserElement.setParseAction})
+     - lpar - expression for matching left-parentheses (default=C{Suppress('(')})
+     - rpar - expression for matching right-parentheses (default=C{Suppress(')')})
+
+    Example::
+        # simple example of four-function arithmetic with ints and variable names
+        integer = pyparsing_common.signed_integer
+        varname = pyparsing_common.identifier 
+        
+        arith_expr = infixNotation(integer | varname,
+            [
+            ('-', 1, opAssoc.RIGHT),
+            (oneOf('* /'), 2, opAssoc.LEFT),
+            (oneOf('+ -'), 2, opAssoc.LEFT),
+            ])
+        
+        arith_expr.runTests('''
+            5+3*6
+            (5+3)*6
+            -2--11
+            ''', fullDump=False)
+    prints::
+        5+3*6
+        [[5, '+', [3, '*', 6]]]
+
+        (5+3)*6
+        [[[5, '+', 3], '*', 6]]
+
+        -2--11
+        [[['-', 2], '-', ['-', 11]]]
+    """
+    ret = Forward()
+    lastExpr = baseExpr | ( lpar + ret + rpar )
+    for i,operDef in enumerate(opList):
+        opExpr,arity,rightLeftAssoc,pa = (operDef + (None,))[:4]
+        termName = "%s term" % opExpr if arity < 3 else "%s%s term" % opExpr
+        if arity == 3:
+            if opExpr is None or len(opExpr) != 2:
+                raise ValueError("if numterms=3, opExpr must be a tuple or list of two expressions")
+            opExpr1, opExpr2 = opExpr
+        thisExpr = Forward().setName(termName)
+        if rightLeftAssoc == opAssoc.LEFT:
+            if arity == 1:
+                matchExpr = FollowedBy(lastExpr + opExpr) + Group( lastExpr + OneOrMore( opExpr ) )
+            elif arity == 2:
+                if opExpr is not None:
+                    matchExpr = FollowedBy(lastExpr + opExpr + lastExpr) + Group( lastExpr + OneOrMore( opExpr + lastExpr ) )
+                else:
+                    matchExpr = FollowedBy(lastExpr+lastExpr) + Group( lastExpr + OneOrMore(lastExpr) )
+            elif arity == 3:
+                matchExpr = FollowedBy(lastExpr + opExpr1 + lastExpr + opExpr2 + lastExpr) + \
+                            Group( lastExpr + opExpr1 + lastExpr + opExpr2 + lastExpr )
+            else:
+                raise ValueError("operator must be unary (1), binary (2), or ternary (3)")
+        elif rightLeftAssoc == opAssoc.RIGHT:
+            if arity == 1:
+                # try to avoid LR with this extra test
+                if not isinstance(opExpr, Optional):
+                    opExpr = Optional(opExpr)
+                matchExpr = FollowedBy(opExpr.expr + thisExpr) + Group( opExpr + thisExpr )
+            elif arity == 2:
+                if opExpr is not None:
+                    matchExpr = FollowedBy(lastExpr + opExpr + thisExpr) + Group( lastExpr + OneOrMore( opExpr + thisExpr ) )
+                else:
+                    matchExpr = FollowedBy(lastExpr + thisExpr) + Group( lastExpr + OneOrMore( thisExpr ) )
+            elif arity == 3:
+                matchExpr = FollowedBy(lastExpr + opExpr1 + thisExpr + opExpr2 + thisExpr) + \
+                            Group( lastExpr + opExpr1 + thisExpr + opExpr2 + thisExpr )
+            else:
+                raise ValueError("operator must be unary (1), binary (2), or ternary (3)")
+        else:
+            raise ValueError("operator must indicate right or left associativity")
+        if pa:
+            if isinstance(pa, (tuple, list)):
+                matchExpr.setParseAction(*pa)
+            else:
+                matchExpr.setParseAction(pa)
+        thisExpr <<= ( matchExpr.setName(termName) | lastExpr )
+        lastExpr = thisExpr
+    ret <<= lastExpr
+    return ret
+
+operatorPrecedence = infixNotation
+"""(Deprecated) Former name of C{L{infixNotation}}, will be dropped in a future release."""
+
+dblQuotedString = Combine(Regex(r'"(?:[^"\n\r\\]|(?:"")|(?:\\(?:[^x]|x[0-9a-fA-F]+)))*')+'"').setName("string enclosed in double quotes")
+sglQuotedString = Combine(Regex(r"'(?:[^'\n\r\\]|(?:'')|(?:\\(?:[^x]|x[0-9a-fA-F]+)))*")+"'").setName("string enclosed in single quotes")
+quotedString = Combine(Regex(r'"(?:[^"\n\r\\]|(?:"")|(?:\\(?:[^x]|x[0-9a-fA-F]+)))*')+'"'|
+                       Regex(r"'(?:[^'\n\r\\]|(?:'')|(?:\\(?:[^x]|x[0-9a-fA-F]+)))*")+"'").setName("quotedString using single or double quotes")
+unicodeString = Combine(_L('u') + quotedString.copy()).setName("unicode string literal")
+
+def nestedExpr(opener="(", closer=")", content=None, ignoreExpr=quotedString.copy()):
+    """
+    Helper method for defining nested lists enclosed in opening and closing
+    delimiters ("(" and ")" are the default).
+
+    Parameters:
+     - opener - opening character for a nested list (default=C{"("}); can also be a pyparsing expression
+     - closer - closing character for a nested list (default=C{")"}); can also be a pyparsing expression
+     - content - expression for items within the nested lists (default=C{None})
+     - ignoreExpr - expression for ignoring opening and closing delimiters (default=C{quotedString})
+
+    If an expression is not provided for the content argument, the nested
+    expression will capture all whitespace-delimited content between delimiters
+    as a list of separate values.
+
+    Use the C{ignoreExpr} argument to define expressions that may contain
+    opening or closing characters that should not be treated as opening
+    or closing characters for nesting, such as quotedString or a comment
+    expression.  Specify multiple expressions using an C{L{Or}} or C{L{MatchFirst}}.
+    The default is L{quotedString}, but if no expressions are to be ignored,
+    then pass C{None} for this argument.
+
+    Example::
+        data_type = oneOf("void int short long char float double")
+        decl_data_type = Combine(data_type + Optional(Word('*')))
+        ident = Word(alphas+'_', alphanums+'_')
+        number = pyparsing_common.number
+        arg = Group(decl_data_type + ident)
+        LPAR,RPAR = map(Suppress, "()")
+
+        code_body = nestedExpr('{', '}', ignoreExpr=(quotedString | cStyleComment))
+
+        c_function = (decl_data_type("type") 
+                      + ident("name")
+                      + LPAR + Optional(delimitedList(arg), [])("args") + RPAR 
+                      + code_body("body"))
+        c_function.ignore(cStyleComment)
+        
+        source_code = '''
+            int is_odd(int x) { 
+                return (x%2); 
+            }
+                
+            int dec_to_hex(char hchar) { 
+                if (hchar >= '0' && hchar <= '9') { 
+                    return (ord(hchar)-ord('0')); 
+                } else { 
+                    return (10+ord(hchar)-ord('A'));
+                } 
+            }
+        '''
+        for func in c_function.searchString(source_code):
+            print("%(name)s (%(type)s) args: %(args)s" % func)
+
+    prints::
+        is_odd (int) args: [['int', 'x']]
+        dec_to_hex (int) args: [['char', 'hchar']]
+    """
+    if opener == closer:
+        raise ValueError("opening and closing strings cannot be the same")
+    if content is None:
+        if isinstance(opener,basestring) and isinstance(closer,basestring):
+            if len(opener) == 1 and len(closer)==1:
+                if ignoreExpr is not None:
+                    content = (Combine(OneOrMore(~ignoreExpr +
+                                    CharsNotIn(opener+closer+ParserElement.DEFAULT_WHITE_CHARS,exact=1))
+                                ).setParseAction(lambda t:t[0].strip()))
+                else:
+                    content = (empty.copy()+CharsNotIn(opener+closer+ParserElement.DEFAULT_WHITE_CHARS
+                                ).setParseAction(lambda t:t[0].strip()))
+            else:
+                if ignoreExpr is not None:
+                    content = (Combine(OneOrMore(~ignoreExpr + 
+                                    ~Literal(opener) + ~Literal(closer) +
+                                    CharsNotIn(ParserElement.DEFAULT_WHITE_CHARS,exact=1))
+                                ).setParseAction(lambda t:t[0].strip()))
+                else:
+                    content = (Combine(OneOrMore(~Literal(opener) + ~Literal(closer) +
+                                    CharsNotIn(ParserElement.DEFAULT_WHITE_CHARS,exact=1))
+                                ).setParseAction(lambda t:t[0].strip()))
+        else:
+            raise ValueError("opening and closing arguments must be strings if no content expression is given")
+    ret = Forward()
+    if ignoreExpr is not None:
+        ret <<= Group( Suppress(opener) + ZeroOrMore( ignoreExpr | ret | content ) + Suppress(closer) )
+    else:
+        ret <<= Group( Suppress(opener) + ZeroOrMore( ret | content )  + Suppress(closer) )
+    ret.setName('nested %s%s expression' % (opener,closer))
+    return ret
+
+def indentedBlock(blockStatementExpr, indentStack, indent=True):
+    """
+    Helper method for defining space-delimited indentation blocks, such as
+    those used to define block statements in Python source code.
+
+    Parameters:
+     - blockStatementExpr - expression defining syntax of statement that
+            is repeated within the indented block
+     - indentStack - list created by caller to manage indentation stack
+            (multiple statementWithIndentedBlock expressions within a single grammar
+            should share a common indentStack)
+     - indent - boolean indicating whether block must be indented beyond the
+            the current level; set to False for block of left-most statements
+            (default=C{True})
+
+    A valid block must contain at least one C{blockStatement}.
+
+    Example::
+        data = '''
+        def A(z):
+          A1
+          B = 100
+          G = A2
+          A2
+          A3
+        B
+        def BB(a,b,c):
+          BB1
+          def BBA():
+            bba1
+            bba2
+            bba3
+        C
+        D
+        def spam(x,y):
+             def eggs(z):
+                 pass
+        '''
+
+
+        indentStack = [1]
+        stmt = Forward()
+
+        identifier = Word(alphas, alphanums)
+        funcDecl = ("def" + identifier + Group( "(" + Optional( delimitedList(identifier) ) + ")" ) + ":")
+        func_body = indentedBlock(stmt, indentStack)
+        funcDef = Group( funcDecl + func_body )
+
+        rvalue = Forward()
+        funcCall = Group(identifier + "(" + Optional(delimitedList(rvalue)) + ")")
+        rvalue << (funcCall | identifier | Word(nums))
+        assignment = Group(identifier + "=" + rvalue)
+        stmt << ( funcDef | assignment | identifier )
+
+        module_body = OneOrMore(stmt)
+
+        parseTree = module_body.parseString(data)
+        parseTree.pprint()
+    prints::
+        [['def',
+          'A',
+          ['(', 'z', ')'],
+          ':',
+          [['A1'], [['B', '=', '100']], [['G', '=', 'A2']], ['A2'], ['A3']]],
+         'B',
+         ['def',
+          'BB',
+          ['(', 'a', 'b', 'c', ')'],
+          ':',
+          [['BB1'], [['def', 'BBA', ['(', ')'], ':', [['bba1'], ['bba2'], ['bba3']]]]]],
+         'C',
+         'D',
+         ['def',
+          'spam',
+          ['(', 'x', 'y', ')'],
+          ':',
+          [[['def', 'eggs', ['(', 'z', ')'], ':', [['pass']]]]]]] 
+    """
+    def checkPeerIndent(s,l,t):
+        if l >= len(s): return
+        curCol = col(l,s)
+        if curCol != indentStack[-1]:
+            if curCol > indentStack[-1]:
+                raise ParseFatalException(s,l,"illegal nesting")
+            raise ParseException(s,l,"not a peer entry")
+
+    def checkSubIndent(s,l,t):
+        curCol = col(l,s)
+        if curCol > indentStack[-1]:
+            indentStack.append( curCol )
+        else:
+            raise ParseException(s,l,"not a subentry")
+
+    def checkUnindent(s,l,t):
+        if l >= len(s): return
+        curCol = col(l,s)
+        if not(indentStack and curCol < indentStack[-1] and curCol <= indentStack[-2]):
+            raise ParseException(s,l,"not an unindent")
+        indentStack.pop()
+
+    NL = OneOrMore(LineEnd().setWhitespaceChars("\t ").suppress())
+    INDENT = (Empty() + Empty().setParseAction(checkSubIndent)).setName('INDENT')
+    PEER   = Empty().setParseAction(checkPeerIndent).setName('')
+    UNDENT = Empty().setParseAction(checkUnindent).setName('UNINDENT')
+    if indent:
+        smExpr = Group( Optional(NL) +
+            #~ FollowedBy(blockStatementExpr) +
+            INDENT + (OneOrMore( PEER + Group(blockStatementExpr) + Optional(NL) )) + UNDENT)
+    else:
+        smExpr = Group( Optional(NL) +
+            (OneOrMore( PEER + Group(blockStatementExpr) + Optional(NL) )) )
+    blockStatementExpr.ignore(_bslash + LineEnd())
+    return smExpr.setName('indented block')
+
+alphas8bit = srange(r"[\0xc0-\0xd6\0xd8-\0xf6\0xf8-\0xff]")
+punc8bit = srange(r"[\0xa1-\0xbf\0xd7\0xf7]")
+
+anyOpenTag,anyCloseTag = makeHTMLTags(Word(alphas,alphanums+"_:").setName('any tag'))
+_htmlEntityMap = dict(zip("gt lt amp nbsp quot apos".split(),'><& "\''))
+commonHTMLEntity = Regex('&(?P' + '|'.join(_htmlEntityMap.keys()) +");").setName("common HTML entity")
+def replaceHTMLEntity(t):
+    """Helper parser action to replace common HTML entities with their special characters"""
+    return _htmlEntityMap.get(t.entity)
+
+# it's easy to get these comment structures wrong - they're very common, so may as well make them available
+cStyleComment = Combine(Regex(r"/\*(?:[^*]|\*(?!/))*") + '*/').setName("C style comment")
+"Comment of the form C{/* ... */}"
+
+htmlComment = Regex(r"").setName("HTML comment")
+"Comment of the form C{}"
+
+restOfLine = Regex(r".*").leaveWhitespace().setName("rest of line")
+dblSlashComment = Regex(r"//(?:\\\n|[^\n])*").setName("// comment")
+"Comment of the form C{// ... (to end of line)}"
+
+cppStyleComment = Combine(Regex(r"/\*(?:[^*]|\*(?!/))*") + '*/'| dblSlashComment).setName("C++ style comment")
+"Comment of either form C{L{cStyleComment}} or C{L{dblSlashComment}}"
+
+javaStyleComment = cppStyleComment
+"Same as C{L{cppStyleComment}}"
+
+pythonStyleComment = Regex(r"#.*").setName("Python style comment")
+"Comment of the form C{# ... (to end of line)}"
+
+_commasepitem = Combine(OneOrMore(Word(printables, excludeChars=',') +
+                                  Optional( Word(" \t") +
+                                            ~Literal(",") + ~LineEnd() ) ) ).streamline().setName("commaItem")
+commaSeparatedList = delimitedList( Optional( quotedString.copy() | _commasepitem, default="") ).setName("commaSeparatedList")
+"""(Deprecated) Predefined expression of 1 or more printable words or quoted strings, separated by commas.
+   This expression is deprecated in favor of L{pyparsing_common.comma_separated_list}."""
+
+# some other useful expressions - using lower-case class name since we are really using this as a namespace
+class pyparsing_common:
+    """
+    Here are some common low-level expressions that may be useful in jump-starting parser development:
+     - numeric forms (L{integers}, L{reals}, L{scientific notation})
+     - common L{programming identifiers}
+     - network addresses (L{MAC}, L{IPv4}, L{IPv6})
+     - ISO8601 L{dates} and L{datetime}
+     - L{UUID}
+     - L{comma-separated list}
+    Parse actions:
+     - C{L{convertToInteger}}
+     - C{L{convertToFloat}}
+     - C{L{convertToDate}}
+     - C{L{convertToDatetime}}
+     - C{L{stripHTMLTags}}
+     - C{L{upcaseTokens}}
+     - C{L{downcaseTokens}}
+
+    Example::
+        pyparsing_common.number.runTests('''
+            # any int or real number, returned as the appropriate type
+            100
+            -100
+            +100
+            3.14159
+            6.02e23
+            1e-12
+            ''')
+
+        pyparsing_common.fnumber.runTests('''
+            # any int or real number, returned as float
+            100
+            -100
+            +100
+            3.14159
+            6.02e23
+            1e-12
+            ''')
+
+        pyparsing_common.hex_integer.runTests('''
+            # hex numbers
+            100
+            FF
+            ''')
+
+        pyparsing_common.fraction.runTests('''
+            # fractions
+            1/2
+            -3/4
+            ''')
+
+        pyparsing_common.mixed_integer.runTests('''
+            # mixed fractions
+            1
+            1/2
+            -3/4
+            1-3/4
+            ''')
+
+        import uuid
+        pyparsing_common.uuid.setParseAction(tokenMap(uuid.UUID))
+        pyparsing_common.uuid.runTests('''
+            # uuid
+            12345678-1234-5678-1234-567812345678
+            ''')
+    prints::
+        # any int or real number, returned as the appropriate type
+        100
+        [100]
+
+        -100
+        [-100]
+
+        +100
+        [100]
+
+        3.14159
+        [3.14159]
+
+        6.02e23
+        [6.02e+23]
+
+        1e-12
+        [1e-12]
+
+        # any int or real number, returned as float
+        100
+        [100.0]
+
+        -100
+        [-100.0]
+
+        +100
+        [100.0]
+
+        3.14159
+        [3.14159]
+
+        6.02e23
+        [6.02e+23]
+
+        1e-12
+        [1e-12]
+
+        # hex numbers
+        100
+        [256]
+
+        FF
+        [255]
+
+        # fractions
+        1/2
+        [0.5]
+
+        -3/4
+        [-0.75]
+
+        # mixed fractions
+        1
+        [1]
+
+        1/2
+        [0.5]
+
+        -3/4
+        [-0.75]
+
+        1-3/4
+        [1.75]
+
+        # uuid
+        12345678-1234-5678-1234-567812345678
+        [UUID('12345678-1234-5678-1234-567812345678')]
+    """
+
+    convertToInteger = tokenMap(int)
+    """
+    Parse action for converting parsed integers to Python int
+    """
+
+    convertToFloat = tokenMap(float)
+    """
+    Parse action for converting parsed numbers to Python float
+    """
+
+    integer = Word(nums).setName("integer").setParseAction(convertToInteger)
+    """expression that parses an unsigned integer, returns an int"""
+
+    hex_integer = Word(hexnums).setName("hex integer").setParseAction(tokenMap(int,16))
+    """expression that parses a hexadecimal integer, returns an int"""
+
+    signed_integer = Regex(r'[+-]?\d+').setName("signed integer").setParseAction(convertToInteger)
+    """expression that parses an integer with optional leading sign, returns an int"""
+
+    fraction = (signed_integer().setParseAction(convertToFloat) + '/' + signed_integer().setParseAction(convertToFloat)).setName("fraction")
+    """fractional expression of an integer divided by an integer, returns a float"""
+    fraction.addParseAction(lambda t: t[0]/t[-1])
+
+    mixed_integer = (fraction | signed_integer + Optional(Optional('-').suppress() + fraction)).setName("fraction or mixed integer-fraction")
+    """mixed integer of the form 'integer - fraction', with optional leading integer, returns float"""
+    mixed_integer.addParseAction(sum)
+
+    real = Regex(r'[+-]?\d+\.\d*').setName("real number").setParseAction(convertToFloat)
+    """expression that parses a floating point number and returns a float"""
+
+    sci_real = Regex(r'[+-]?\d+([eE][+-]?\d+|\.\d*([eE][+-]?\d+)?)').setName("real number with scientific notation").setParseAction(convertToFloat)
+    """expression that parses a floating point number with optional scientific notation and returns a float"""
+
+    # streamlining this expression makes the docs nicer-looking
+    number = (sci_real | real | signed_integer).streamline()
+    """any numeric expression, returns the corresponding Python type"""
+
+    fnumber = Regex(r'[+-]?\d+\.?\d*([eE][+-]?\d+)?').setName("fnumber").setParseAction(convertToFloat)
+    """any int or real number, returned as float"""
+    
+    identifier = Word(alphas+'_', alphanums+'_').setName("identifier")
+    """typical code identifier (leading alpha or '_', followed by 0 or more alphas, nums, or '_')"""
+    
+    ipv4_address = Regex(r'(25[0-5]|2[0-4][0-9]|1?[0-9]{1,2})(\.(25[0-5]|2[0-4][0-9]|1?[0-9]{1,2})){3}').setName("IPv4 address")
+    "IPv4 address (C{0.0.0.0 - 255.255.255.255})"
+
+    _ipv6_part = Regex(r'[0-9a-fA-F]{1,4}').setName("hex_integer")
+    _full_ipv6_address = (_ipv6_part + (':' + _ipv6_part)*7).setName("full IPv6 address")
+    _short_ipv6_address = (Optional(_ipv6_part + (':' + _ipv6_part)*(0,6)) + "::" + Optional(_ipv6_part + (':' + _ipv6_part)*(0,6))).setName("short IPv6 address")
+    _short_ipv6_address.addCondition(lambda t: sum(1 for tt in t if pyparsing_common._ipv6_part.matches(tt)) < 8)
+    _mixed_ipv6_address = ("::ffff:" + ipv4_address).setName("mixed IPv6 address")
+    ipv6_address = Combine((_full_ipv6_address | _mixed_ipv6_address | _short_ipv6_address).setName("IPv6 address")).setName("IPv6 address")
+    "IPv6 address (long, short, or mixed form)"
+    
+    mac_address = Regex(r'[0-9a-fA-F]{2}([:.-])[0-9a-fA-F]{2}(?:\1[0-9a-fA-F]{2}){4}').setName("MAC address")
+    "MAC address xx:xx:xx:xx:xx (may also have '-' or '.' delimiters)"
+
+    @staticmethod
+    def convertToDate(fmt="%Y-%m-%d"):
+        """
+        Helper to create a parse action for converting parsed date string to Python datetime.date
+
+        Params -
+         - fmt - format to be passed to datetime.strptime (default=C{"%Y-%m-%d"})
+
+        Example::
+            date_expr = pyparsing_common.iso8601_date.copy()
+            date_expr.setParseAction(pyparsing_common.convertToDate())
+            print(date_expr.parseString("1999-12-31"))
+        prints::
+            [datetime.date(1999, 12, 31)]
+        """
+        def cvt_fn(s,l,t):
+            try:
+                return datetime.strptime(t[0], fmt).date()
+            except ValueError as ve:
+                raise ParseException(s, l, str(ve))
+        return cvt_fn
+
+    @staticmethod
+    def convertToDatetime(fmt="%Y-%m-%dT%H:%M:%S.%f"):
+        """
+        Helper to create a parse action for converting parsed datetime string to Python datetime.datetime
+
+        Params -
+         - fmt - format to be passed to datetime.strptime (default=C{"%Y-%m-%dT%H:%M:%S.%f"})
+
+        Example::
+            dt_expr = pyparsing_common.iso8601_datetime.copy()
+            dt_expr.setParseAction(pyparsing_common.convertToDatetime())
+            print(dt_expr.parseString("1999-12-31T23:59:59.999"))
+        prints::
+            [datetime.datetime(1999, 12, 31, 23, 59, 59, 999000)]
+        """
+        def cvt_fn(s,l,t):
+            try:
+                return datetime.strptime(t[0], fmt)
+            except ValueError as ve:
+                raise ParseException(s, l, str(ve))
+        return cvt_fn
+
+    iso8601_date = Regex(r'(?P\d{4})(?:-(?P\d\d)(?:-(?P\d\d))?)?').setName("ISO8601 date")
+    "ISO8601 date (C{yyyy-mm-dd})"
+
+    iso8601_datetime = Regex(r'(?P\d{4})-(?P\d\d)-(?P\d\d)[T ](?P\d\d):(?P\d\d)(:(?P\d\d(\.\d*)?)?)?(?PZ|[+-]\d\d:?\d\d)?').setName("ISO8601 datetime")
+    "ISO8601 datetime (C{yyyy-mm-ddThh:mm:ss.s(Z|+-00:00)}) - trailing seconds, milliseconds, and timezone optional; accepts separating C{'T'} or C{' '}"
+
+    uuid = Regex(r'[0-9a-fA-F]{8}(-[0-9a-fA-F]{4}){3}-[0-9a-fA-F]{12}').setName("UUID")
+    "UUID (C{xxxxxxxx-xxxx-xxxx-xxxx-xxxxxxxxxxxx})"
+
+    _html_stripper = anyOpenTag.suppress() | anyCloseTag.suppress()
+    @staticmethod
+    def stripHTMLTags(s, l, tokens):
+        """
+        Parse action to remove HTML tags from web page HTML source
+
+        Example::
+            # strip HTML links from normal text 
+            text = 'More info at the pyparsing wiki page'
+            td,td_end = makeHTMLTags("TD")
+            table_text = td + SkipTo(td_end).setParseAction(pyparsing_common.stripHTMLTags)("body") + td_end
+            
+            print(table_text.parseString(text).body) # -> 'More info at the pyparsing wiki page'
+        """
+        return pyparsing_common._html_stripper.transformString(tokens[0])
+
+    _commasepitem = Combine(OneOrMore(~Literal(",") + ~LineEnd() + Word(printables, excludeChars=',') 
+                                        + Optional( White(" \t") ) ) ).streamline().setName("commaItem")
+    comma_separated_list = delimitedList( Optional( quotedString.copy() | _commasepitem, default="") ).setName("comma separated list")
+    """Predefined expression of 1 or more printable words or quoted strings, separated by commas."""
+
+    upcaseTokens = staticmethod(tokenMap(lambda t: _ustr(t).upper()))
+    """Parse action to convert tokens to upper case."""
+
+    downcaseTokens = staticmethod(tokenMap(lambda t: _ustr(t).lower()))
+    """Parse action to convert tokens to lower case."""
+
+
+if __name__ == "__main__":
+
+    selectToken    = CaselessLiteral("select")
+    fromToken      = CaselessLiteral("from")
+
+    ident          = Word(alphas, alphanums + "_$")
+
+    columnName     = delimitedList(ident, ".", combine=True).setParseAction(upcaseTokens)
+    columnNameList = Group(delimitedList(columnName)).setName("columns")
+    columnSpec     = ('*' | columnNameList)
+
+    tableName      = delimitedList(ident, ".", combine=True).setParseAction(upcaseTokens)
+    tableNameList  = Group(delimitedList(tableName)).setName("tables")
+    
+    simpleSQL      = selectToken("command") + columnSpec("columns") + fromToken + tableNameList("tables")
+
+    # demo runTests method, including embedded comments in test string
+    simpleSQL.runTests("""
+        # '*' as column list and dotted table name
+        select * from SYS.XYZZY
+
+        # caseless match on "SELECT", and casts back to "select"
+        SELECT * from XYZZY, ABC
+
+        # list of column names, and mixed case SELECT keyword
+        Select AA,BB,CC from Sys.dual
+
+        # multiple tables
+        Select A, B, C from Sys.dual, Table2
+
+        # invalid SELECT keyword - should fail
+        Xelect A, B, C from Sys.dual
+
+        # incomplete command - should fail
+        Select
+
+        # invalid column name - should fail
+        Select ^^^ frox Sys.dual
+
+        """)
+
+    pyparsing_common.number.runTests("""
+        100
+        -100
+        +100
+        3.14159
+        6.02e23
+        1e-12
+        """)
+
+    # any int or real number, returned as float
+    pyparsing_common.fnumber.runTests("""
+        100
+        -100
+        +100
+        3.14159
+        6.02e23
+        1e-12
+        """)
+
+    pyparsing_common.hex_integer.runTests("""
+        100
+        FF
+        """)
+
+    import uuid
+    pyparsing_common.uuid.setParseAction(tokenMap(uuid.UUID))
+    pyparsing_common.uuid.runTests("""
+        12345678-1234-5678-1234-567812345678
+        """)
diff --git a/llmeval-env/lib/python3.10/site-packages/pkg_resources/extern/__init__.py b/llmeval-env/lib/python3.10/site-packages/pkg_resources/extern/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..fed59295403b80b1711d0d189ff97dde22808690
--- /dev/null
+++ b/llmeval-env/lib/python3.10/site-packages/pkg_resources/extern/__init__.py
@@ -0,0 +1,73 @@
+import importlib.util
+import sys
+
+
+class VendorImporter:
+    """
+    A PEP 302 meta path importer for finding optionally-vendored
+    or otherwise naturally-installed packages from root_name.
+    """
+
+    def __init__(self, root_name, vendored_names=(), vendor_pkg=None):
+        self.root_name = root_name
+        self.vendored_names = set(vendored_names)
+        self.vendor_pkg = vendor_pkg or root_name.replace('extern', '_vendor')
+
+    @property
+    def search_path(self):
+        """
+        Search first the vendor package then as a natural package.
+        """
+        yield self.vendor_pkg + '.'
+        yield ''
+
+    def _module_matches_namespace(self, fullname):
+        """Figure out if the target module is vendored."""
+        root, base, target = fullname.partition(self.root_name + '.')
+        return not root and any(map(target.startswith, self.vendored_names))
+
+    def load_module(self, fullname):
+        """
+        Iterate over the search path to locate and load fullname.
+        """
+        root, base, target = fullname.partition(self.root_name + '.')
+        for prefix in self.search_path:
+            try:
+                extant = prefix + target
+                __import__(extant)
+                mod = sys.modules[extant]
+                sys.modules[fullname] = mod
+                return mod
+            except ImportError:
+                pass
+        else:
+            raise ImportError(
+                "The '{target}' package is required; "
+                "normally this is bundled with this package so if you get "
+                "this warning, consult the packager of your "
+                "distribution.".format(**locals())
+            )
+
+    def create_module(self, spec):
+        return self.load_module(spec.name)
+
+    def exec_module(self, module):
+        pass
+
+    def find_spec(self, fullname, path=None, target=None):
+        """Return a module spec for vendored names."""
+        return (
+            importlib.util.spec_from_loader(fullname, self)
+            if self._module_matches_namespace(fullname) else None
+        )
+
+    def install(self):
+        """
+        Install this importer into sys.meta_path if not already present.
+        """
+        if self not in sys.meta_path:
+            sys.meta_path.append(self)
+
+
+names = 'packaging', 'pyparsing', 'appdirs'
+VendorImporter(__name__, names).install()
diff --git a/llmeval-env/lib/python3.10/site-packages/pkg_resources/extern/__pycache__/__init__.cpython-310.pyc b/llmeval-env/lib/python3.10/site-packages/pkg_resources/extern/__pycache__/__init__.cpython-310.pyc
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diff --git a/llmeval-env/lib/python3.10/site-packages/pkg_resources/tests/data/my-test-package-source/__pycache__/setup.cpython-310.pyc b/llmeval-env/lib/python3.10/site-packages/pkg_resources/tests/data/my-test-package-source/__pycache__/setup.cpython-310.pyc
new file mode 100644
index 0000000000000000000000000000000000000000..89ebe07a7f29940d0987cadc4b6522b69698c78a
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diff --git a/llmeval-env/lib/python3.10/site-packages/pkg_resources/tests/data/my-test-package-source/setup.py b/llmeval-env/lib/python3.10/site-packages/pkg_resources/tests/data/my-test-package-source/setup.py
new file mode 100644
index 0000000000000000000000000000000000000000..fe80d28f4658fdabdc1ec17b830fef00d20d41b3
--- /dev/null
+++ b/llmeval-env/lib/python3.10/site-packages/pkg_resources/tests/data/my-test-package-source/setup.py
@@ -0,0 +1,6 @@
+import setuptools
+setuptools.setup(
+    name="my-test-package",
+    version="1.0",
+    zip_safe=True,
+)
diff --git a/llmeval-env/lib/python3.10/site-packages/sympy/physics/__init__.py b/llmeval-env/lib/python3.10/site-packages/sympy/physics/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..60989896ae8b3f69efc7d2350add8f6f19d85669
--- /dev/null
+++ b/llmeval-env/lib/python3.10/site-packages/sympy/physics/__init__.py
@@ -0,0 +1,12 @@
+"""
+A module that helps solving problems in physics.
+"""
+
+from . import units
+from .matrices import mgamma, msigma, minkowski_tensor, mdft
+
+__all__ = [
+    'units',
+
+    'mgamma', 'msigma', 'minkowski_tensor', 'mdft',
+]
diff --git a/llmeval-env/lib/python3.10/site-packages/sympy/physics/hep/__init__.py b/llmeval-env/lib/python3.10/site-packages/sympy/physics/hep/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..e69de29bb2d1d6434b8b29ae775ad8c2e48c5391
diff --git a/llmeval-env/lib/python3.10/site-packages/sympy/physics/hep/__pycache__/__init__.cpython-310.pyc b/llmeval-env/lib/python3.10/site-packages/sympy/physics/hep/__pycache__/__init__.cpython-310.pyc
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@@ -0,0 +1,716 @@
+"""
+    Module to handle gamma matrices expressed as tensor objects.
+
+    Examples
+    ========
+
+    >>> from sympy.physics.hep.gamma_matrices import GammaMatrix as G, LorentzIndex
+    >>> from sympy.tensor.tensor import tensor_indices
+    >>> i = tensor_indices('i', LorentzIndex)
+    >>> G(i)
+    GammaMatrix(i)
+
+    Note that there is already an instance of GammaMatrixHead in four dimensions:
+    GammaMatrix, which is simply declare as
+
+    >>> from sympy.physics.hep.gamma_matrices import GammaMatrix
+    >>> from sympy.tensor.tensor import tensor_indices
+    >>> i = tensor_indices('i', LorentzIndex)
+    >>> GammaMatrix(i)
+    GammaMatrix(i)
+
+    To access the metric tensor
+
+    >>> LorentzIndex.metric
+    metric(LorentzIndex,LorentzIndex)
+
+"""
+from sympy.core.mul import Mul
+from sympy.core.singleton import S
+from sympy.matrices.dense import eye
+from sympy.matrices.expressions.trace import trace
+from sympy.tensor.tensor import TensorIndexType, TensorIndex,\
+    TensMul, TensAdd, tensor_mul, Tensor, TensorHead, TensorSymmetry
+
+
+# DiracSpinorIndex = TensorIndexType('DiracSpinorIndex', dim=4, dummy_name="S")
+
+
+LorentzIndex = TensorIndexType('LorentzIndex', dim=4, dummy_name="L")
+
+
+GammaMatrix = TensorHead("GammaMatrix", [LorentzIndex],
+                         TensorSymmetry.no_symmetry(1), comm=None)
+
+
+def extract_type_tens(expression, component):
+    """
+    Extract from a ``TensExpr`` all tensors with `component`.
+
+    Returns two tensor expressions:
+
+    * the first contains all ``Tensor`` of having `component`.
+    * the second contains all remaining.
+
+
+    """
+    if isinstance(expression, Tensor):
+        sp = [expression]
+    elif isinstance(expression, TensMul):
+        sp = expression.args
+    else:
+        raise ValueError('wrong type')
+
+    # Collect all gamma matrices of the same dimension
+    new_expr = S.One
+    residual_expr = S.One
+    for i in sp:
+        if isinstance(i, Tensor) and i.component == component:
+            new_expr *= i
+        else:
+            residual_expr *= i
+    return new_expr, residual_expr
+
+
+def simplify_gamma_expression(expression):
+    extracted_expr, residual_expr = extract_type_tens(expression, GammaMatrix)
+    res_expr = _simplify_single_line(extracted_expr)
+    return res_expr * residual_expr
+
+
+def simplify_gpgp(ex, sort=True):
+    """
+    simplify products ``G(i)*p(-i)*G(j)*p(-j) -> p(i)*p(-i)``
+
+    Examples
+    ========
+
+    >>> from sympy.physics.hep.gamma_matrices import GammaMatrix as G, \
+        LorentzIndex, simplify_gpgp
+    >>> from sympy.tensor.tensor import tensor_indices, tensor_heads
+    >>> p, q = tensor_heads('p, q', [LorentzIndex])
+    >>> i0,i1,i2,i3,i4,i5 = tensor_indices('i0:6', LorentzIndex)
+    >>> ps = p(i0)*G(-i0)
+    >>> qs = q(i0)*G(-i0)
+    >>> simplify_gpgp(ps*qs*qs)
+    GammaMatrix(-L_0)*p(L_0)*q(L_1)*q(-L_1)
+    """
+    def _simplify_gpgp(ex):
+        components = ex.components
+        a = []
+        comp_map = []
+        for i, comp in enumerate(components):
+            comp_map.extend([i]*comp.rank)
+        dum = [(i[0], i[1], comp_map[i[0]], comp_map[i[1]]) for i in ex.dum]
+        for i in range(len(components)):
+            if components[i] != GammaMatrix:
+                continue
+            for dx in dum:
+                if dx[2] == i:
+                    p_pos1 = dx[3]
+                elif dx[3] == i:
+                    p_pos1 = dx[2]
+                else:
+                    continue
+                comp1 = components[p_pos1]
+                if comp1.comm == 0 and comp1.rank == 1:
+                    a.append((i, p_pos1))
+        if not a:
+            return ex
+        elim = set()
+        tv = []
+        hit = True
+        coeff = S.One
+        ta = None
+        while hit:
+            hit = False
+            for i, ai in enumerate(a[:-1]):
+                if ai[0] in elim:
+                    continue
+                if ai[0] != a[i + 1][0] - 1:
+                    continue
+                if components[ai[1]] != components[a[i + 1][1]]:
+                    continue
+                elim.add(ai[0])
+                elim.add(ai[1])
+                elim.add(a[i + 1][0])
+                elim.add(a[i + 1][1])
+                if not ta:
+                    ta = ex.split()
+                    mu = TensorIndex('mu', LorentzIndex)
+                hit = True
+                if i == 0:
+                    coeff = ex.coeff
+                tx = components[ai[1]](mu)*components[ai[1]](-mu)
+                if len(a) == 2:
+                    tx *= 4  # eye(4)
+                tv.append(tx)
+                break
+
+        if tv:
+            a = [x for j, x in enumerate(ta) if j not in elim]
+            a.extend(tv)
+            t = tensor_mul(*a)*coeff
+            # t = t.replace(lambda x: x.is_Matrix, lambda x: 1)
+            return t
+        else:
+            return ex
+
+    if sort:
+        ex = ex.sorted_components()
+    # this would be better off with pattern matching
+    while 1:
+        t = _simplify_gpgp(ex)
+        if t != ex:
+            ex = t
+        else:
+            return t
+
+
+def gamma_trace(t):
+    """
+    trace of a single line of gamma matrices
+
+    Examples
+    ========
+
+    >>> from sympy.physics.hep.gamma_matrices import GammaMatrix as G, \
+        gamma_trace, LorentzIndex
+    >>> from sympy.tensor.tensor import tensor_indices, tensor_heads
+    >>> p, q = tensor_heads('p, q', [LorentzIndex])
+    >>> i0,i1,i2,i3,i4,i5 = tensor_indices('i0:6', LorentzIndex)
+    >>> ps = p(i0)*G(-i0)
+    >>> qs = q(i0)*G(-i0)
+    >>> gamma_trace(G(i0)*G(i1))
+    4*metric(i0, i1)
+    >>> gamma_trace(ps*ps) - 4*p(i0)*p(-i0)
+    0
+    >>> gamma_trace(ps*qs + ps*ps) - 4*p(i0)*p(-i0) - 4*p(i0)*q(-i0)
+    0
+
+    """
+    if isinstance(t, TensAdd):
+        res = TensAdd(*[gamma_trace(x) for x in t.args])
+        return res
+    t = _simplify_single_line(t)
+    res = _trace_single_line(t)
+    return res
+
+
+def _simplify_single_line(expression):
+    """
+    Simplify single-line product of gamma matrices.
+
+    Examples
+    ========
+
+    >>> from sympy.physics.hep.gamma_matrices import GammaMatrix as G, \
+        LorentzIndex, _simplify_single_line
+    >>> from sympy.tensor.tensor import tensor_indices, TensorHead
+    >>> p = TensorHead('p', [LorentzIndex])
+    >>> i0,i1 = tensor_indices('i0:2', LorentzIndex)
+    >>> _simplify_single_line(G(i0)*G(i1)*p(-i1)*G(-i0)) + 2*G(i0)*p(-i0)
+    0
+
+    """
+    t1, t2 = extract_type_tens(expression, GammaMatrix)
+    if t1 != 1:
+        t1 = kahane_simplify(t1)
+    res = t1*t2
+    return res
+
+
+def _trace_single_line(t):
+    """
+    Evaluate the trace of a single gamma matrix line inside a ``TensExpr``.
+
+    Notes
+    =====
+
+    If there are ``DiracSpinorIndex.auto_left`` and ``DiracSpinorIndex.auto_right``
+    indices trace over them; otherwise traces are not implied (explain)
+
+
+    Examples
+    ========
+
+    >>> from sympy.physics.hep.gamma_matrices import GammaMatrix as G, \
+        LorentzIndex, _trace_single_line
+    >>> from sympy.tensor.tensor import tensor_indices, TensorHead
+    >>> p = TensorHead('p', [LorentzIndex])
+    >>> i0,i1,i2,i3,i4,i5 = tensor_indices('i0:6', LorentzIndex)
+    >>> _trace_single_line(G(i0)*G(i1))
+    4*metric(i0, i1)
+    >>> _trace_single_line(G(i0)*p(-i0)*G(i1)*p(-i1)) - 4*p(i0)*p(-i0)
+    0
+
+    """
+    def _trace_single_line1(t):
+        t = t.sorted_components()
+        components = t.components
+        ncomps = len(components)
+        g = LorentzIndex.metric
+        # gamma matirices are in a[i:j]
+        hit = 0
+        for i in range(ncomps):
+            if components[i] == GammaMatrix:
+                hit = 1
+                break
+
+        for j in range(i + hit, ncomps):
+            if components[j] != GammaMatrix:
+                break
+        else:
+            j = ncomps
+        numG = j - i
+        if numG == 0:
+            tcoeff = t.coeff
+            return t.nocoeff if tcoeff else t
+        if numG % 2 == 1:
+            return TensMul.from_data(S.Zero, [], [], [])
+        elif numG > 4:
+            # find the open matrix indices and connect them:
+            a = t.split()
+            ind1 = a[i].get_indices()[0]
+            ind2 = a[i + 1].get_indices()[0]
+            aa = a[:i] + a[i + 2:]
+            t1 = tensor_mul(*aa)*g(ind1, ind2)
+            t1 = t1.contract_metric(g)
+            args = [t1]
+            sign = 1
+            for k in range(i + 2, j):
+                sign = -sign
+                ind2 = a[k].get_indices()[0]
+                aa = a[:i] + a[i + 1:k] + a[k + 1:]
+                t2 = sign*tensor_mul(*aa)*g(ind1, ind2)
+                t2 = t2.contract_metric(g)
+                t2 = simplify_gpgp(t2, False)
+                args.append(t2)
+            t3 = TensAdd(*args)
+            t3 = _trace_single_line(t3)
+            return t3
+        else:
+            a = t.split()
+            t1 = _gamma_trace1(*a[i:j])
+            a2 = a[:i] + a[j:]
+            t2 = tensor_mul(*a2)
+            t3 = t1*t2
+            if not t3:
+                return t3
+            t3 = t3.contract_metric(g)
+            return t3
+
+    t = t.expand()
+    if isinstance(t, TensAdd):
+        a = [_trace_single_line1(x)*x.coeff for x in t.args]
+        return TensAdd(*a)
+    elif isinstance(t, (Tensor, TensMul)):
+        r = t.coeff*_trace_single_line1(t)
+        return r
+    else:
+        return trace(t)
+
+
+def _gamma_trace1(*a):
+    gctr = 4  # FIXME specific for d=4
+    g = LorentzIndex.metric
+    if not a:
+        return gctr
+    n = len(a)
+    if n%2 == 1:
+        #return TensMul.from_data(S.Zero, [], [], [])
+        return S.Zero
+    if n == 2:
+        ind0 = a[0].get_indices()[0]
+        ind1 = a[1].get_indices()[0]
+        return gctr*g(ind0, ind1)
+    if n == 4:
+        ind0 = a[0].get_indices()[0]
+        ind1 = a[1].get_indices()[0]
+        ind2 = a[2].get_indices()[0]
+        ind3 = a[3].get_indices()[0]
+
+        return gctr*(g(ind0, ind1)*g(ind2, ind3) - \
+           g(ind0, ind2)*g(ind1, ind3) + g(ind0, ind3)*g(ind1, ind2))
+
+
+def kahane_simplify(expression):
+    r"""
+    This function cancels contracted elements in a product of four
+    dimensional gamma matrices, resulting in an expression equal to the given
+    one, without the contracted gamma matrices.
+
+    Parameters
+    ==========
+
+    `expression`    the tensor expression containing the gamma matrices to simplify.
+
+    Notes
+    =====
+
+    If spinor indices are given, the matrices must be given in
+    the order given in the product.
+
+    Algorithm
+    =========
+
+    The idea behind the algorithm is to use some well-known identities,
+    i.e., for contractions enclosing an even number of `\gamma` matrices
+
+    `\gamma^\mu \gamma_{a_1} \cdots \gamma_{a_{2N}} \gamma_\mu = 2 (\gamma_{a_{2N}} \gamma_{a_1} \cdots \gamma_{a_{2N-1}} + \gamma_{a_{2N-1}} \cdots \gamma_{a_1} \gamma_{a_{2N}} )`
+
+    for an odd number of `\gamma` matrices
+
+    `\gamma^\mu \gamma_{a_1} \cdots \gamma_{a_{2N+1}} \gamma_\mu = -2 \gamma_{a_{2N+1}} \gamma_{a_{2N}} \cdots \gamma_{a_{1}}`
+
+    Instead of repeatedly applying these identities to cancel out all contracted indices,
+    it is possible to recognize the links that would result from such an operation,
+    the problem is thus reduced to a simple rearrangement of free gamma matrices.
+
+    Examples
+    ========
+
+    When using, always remember that the original expression coefficient
+    has to be handled separately
+
+    >>> from sympy.physics.hep.gamma_matrices import GammaMatrix as G, LorentzIndex
+    >>> from sympy.physics.hep.gamma_matrices import kahane_simplify
+    >>> from sympy.tensor.tensor import tensor_indices
+    >>> i0, i1, i2 = tensor_indices('i0:3', LorentzIndex)
+    >>> ta = G(i0)*G(-i0)
+    >>> kahane_simplify(ta)
+    Matrix([
+    [4, 0, 0, 0],
+    [0, 4, 0, 0],
+    [0, 0, 4, 0],
+    [0, 0, 0, 4]])
+    >>> tb = G(i0)*G(i1)*G(-i0)
+    >>> kahane_simplify(tb)
+    -2*GammaMatrix(i1)
+    >>> t = G(i0)*G(-i0)
+    >>> kahane_simplify(t)
+    Matrix([
+    [4, 0, 0, 0],
+    [0, 4, 0, 0],
+    [0, 0, 4, 0],
+    [0, 0, 0, 4]])
+    >>> t = G(i0)*G(-i0)
+    >>> kahane_simplify(t)
+    Matrix([
+    [4, 0, 0, 0],
+    [0, 4, 0, 0],
+    [0, 0, 4, 0],
+    [0, 0, 0, 4]])
+
+    If there are no contractions, the same expression is returned
+
+    >>> tc = G(i0)*G(i1)
+    >>> kahane_simplify(tc)
+    GammaMatrix(i0)*GammaMatrix(i1)
+
+    References
+    ==========
+
+    [1] Algorithm for Reducing Contracted Products of gamma Matrices,
+    Joseph Kahane, Journal of Mathematical Physics, Vol. 9, No. 10, October 1968.
+    """
+
+    if isinstance(expression, Mul):
+        return expression
+    if isinstance(expression, TensAdd):
+        return TensAdd(*[kahane_simplify(arg) for arg in expression.args])
+
+    if isinstance(expression, Tensor):
+        return expression
+
+    assert isinstance(expression, TensMul)
+
+    gammas = expression.args
+
+    for gamma in gammas:
+        assert gamma.component == GammaMatrix
+
+    free = expression.free
+    # spinor_free = [_ for _ in expression.free_in_args if _[1] != 0]
+
+    # if len(spinor_free) == 2:
+    #     spinor_free.sort(key=lambda x: x[2])
+    #     assert spinor_free[0][1] == 1 and spinor_free[-1][1] == 2
+    #     assert spinor_free[0][2] == 0
+    # elif spinor_free:
+    #     raise ValueError('spinor indices do not match')
+
+    dum = []
+    for dum_pair in expression.dum:
+        if expression.index_types[dum_pair[0]] == LorentzIndex:
+            dum.append((dum_pair[0], dum_pair[1]))
+
+    dum = sorted(dum)
+
+    if len(dum) == 0:  # or GammaMatrixHead:
+        # no contractions in `expression`, just return it.
+        return expression
+
+    # find the `first_dum_pos`, i.e. the position of the first contracted
+    # gamma matrix, Kahane's algorithm as described in his paper requires the
+    # gamma matrix expression to start with a contracted gamma matrix, this is
+    # a workaround which ignores possible initial free indices, and re-adds
+    # them later.
+
+    first_dum_pos = min(map(min, dum))
+
+    # for p1, p2, a1, a2 in expression.dum_in_args:
+    #     if p1 != 0 or p2 != 0:
+    #         # only Lorentz indices, skip Dirac indices:
+    #         continue
+    #     first_dum_pos = min(p1, p2)
+    #     break
+
+    total_number = len(free) + len(dum)*2
+    number_of_contractions = len(dum)
+
+    free_pos = [None]*total_number
+    for i in free:
+        free_pos[i[1]] = i[0]
+
+    # `index_is_free` is a list of booleans, to identify index position
+    # and whether that index is free or dummy.
+    index_is_free = [False]*total_number
+
+    for i, indx in enumerate(free):
+        index_is_free[indx[1]] = True
+
+    # `links` is a dictionary containing the graph described in Kahane's paper,
+    # to every key correspond one or two values, representing the linked indices.
+    # All values in `links` are integers, negative numbers are used in the case
+    # where it is necessary to insert gamma matrices between free indices, in
+    # order to make Kahane's algorithm work (see paper).
+    links = {i: [] for i in range(first_dum_pos, total_number)}
+
+    # `cum_sign` is a step variable to mark the sign of every index, see paper.
+    cum_sign = -1
+    # `cum_sign_list` keeps storage for all `cum_sign` (every index).
+    cum_sign_list = [None]*total_number
+    block_free_count = 0
+
+    # multiply `resulting_coeff` by the coefficient parameter, the rest
+    # of the algorithm ignores a scalar coefficient.
+    resulting_coeff = S.One
+
+    # initialize a list of lists of indices. The outer list will contain all
+    # additive tensor expressions, while the inner list will contain the
+    # free indices (rearranged according to the algorithm).
+    resulting_indices = [[]]
+
+    # start to count the `connected_components`, which together with the number
+    # of contractions, determines a -1 or +1 factor to be multiplied.
+    connected_components = 1
+
+    # First loop: here we fill `cum_sign_list`, and draw the links
+    # among consecutive indices (they are stored in `links`). Links among
+    # non-consecutive indices will be drawn later.
+    for i, is_free in enumerate(index_is_free):
+        # if `expression` starts with free indices, they are ignored here;
+        # they are later added as they are to the beginning of all
+        # `resulting_indices` list of lists of indices.
+        if i < first_dum_pos:
+            continue
+
+        if is_free:
+            block_free_count += 1
+            # if previous index was free as well, draw an arch in `links`.
+            if block_free_count > 1:
+                links[i - 1].append(i)
+                links[i].append(i - 1)
+        else:
+            # Change the sign of the index (`cum_sign`) if the number of free
+            # indices preceding it is even.
+            cum_sign *= 1 if (block_free_count % 2) else -1
+            if block_free_count == 0 and i != first_dum_pos:
+                # check if there are two consecutive dummy indices:
+                # in this case create virtual indices with negative position,
+                # these "virtual" indices represent the insertion of two
+                # gamma^0 matrices to separate consecutive dummy indices, as
+                # Kahane's algorithm requires dummy indices to be separated by
+                # free indices. The product of two gamma^0 matrices is unity,
+                # so the new expression being examined is the same as the
+                # original one.
+                if cum_sign == -1:
+                    links[-1-i] = [-1-i+1]
+                    links[-1-i+1] = [-1-i]
+            if (i - cum_sign) in links:
+                if i != first_dum_pos:
+                    links[i].append(i - cum_sign)
+                if block_free_count != 0:
+                    if i - cum_sign < len(index_is_free):
+                        if index_is_free[i - cum_sign]:
+                            links[i - cum_sign].append(i)
+            block_free_count = 0
+
+        cum_sign_list[i] = cum_sign
+
+    # The previous loop has only created links between consecutive free indices,
+    # it is necessary to properly create links among dummy (contracted) indices,
+    # according to the rules described in Kahane's paper. There is only one exception
+    # to Kahane's rules: the negative indices, which handle the case of some
+    # consecutive free indices (Kahane's paper just describes dummy indices
+    # separated by free indices, hinting that free indices can be added without
+    # altering the expression result).
+    for i in dum:
+        # get the positions of the two contracted indices:
+        pos1 = i[0]
+        pos2 = i[1]
+
+        # create Kahane's upper links, i.e. the upper arcs between dummy
+        # (i.e. contracted) indices:
+        links[pos1].append(pos2)
+        links[pos2].append(pos1)
+
+        # create Kahane's lower links, this corresponds to the arcs below
+        # the line described in the paper:
+
+        # first we move `pos1` and `pos2` according to the sign of the indices:
+        linkpos1 = pos1 + cum_sign_list[pos1]
+        linkpos2 = pos2 + cum_sign_list[pos2]
+
+        # otherwise, perform some checks before creating the lower arcs:
+
+        # make sure we are not exceeding the total number of indices:
+        if linkpos1 >= total_number:
+            continue
+        if linkpos2 >= total_number:
+            continue
+
+        # make sure we are not below the first dummy index in `expression`:
+        if linkpos1 < first_dum_pos:
+            continue
+        if linkpos2 < first_dum_pos:
+            continue
+
+        # check if the previous loop created "virtual" indices between dummy
+        # indices, in such a case relink `linkpos1` and `linkpos2`:
+        if (-1-linkpos1) in links:
+            linkpos1 = -1-linkpos1
+        if (-1-linkpos2) in links:
+            linkpos2 = -1-linkpos2
+
+        # move only if not next to free index:
+        if linkpos1 >= 0 and not index_is_free[linkpos1]:
+            linkpos1 = pos1
+
+        if linkpos2 >=0 and not index_is_free[linkpos2]:
+            linkpos2 = pos2
+
+        # create the lower arcs:
+        if linkpos2 not in links[linkpos1]:
+            links[linkpos1].append(linkpos2)
+        if linkpos1 not in links[linkpos2]:
+            links[linkpos2].append(linkpos1)
+
+    # This loop starts from the `first_dum_pos` index (first dummy index)
+    # walks through the graph deleting the visited indices from `links`,
+    # it adds a gamma matrix for every free index in encounters, while it
+    # completely ignores dummy indices and virtual indices.
+    pointer = first_dum_pos
+    previous_pointer = 0
+    while True:
+        if pointer in links:
+            next_ones = links.pop(pointer)
+        else:
+            break
+
+        if previous_pointer in next_ones:
+            next_ones.remove(previous_pointer)
+
+        previous_pointer = pointer
+
+        if next_ones:
+            pointer = next_ones[0]
+        else:
+            break
+
+        if pointer == previous_pointer:
+            break
+        if pointer >=0 and free_pos[pointer] is not None:
+            for ri in resulting_indices:
+                ri.append(free_pos[pointer])
+
+    # The following loop removes the remaining connected components in `links`.
+    # If there are free indices inside a connected component, it gives a
+    # contribution to the resulting expression given by the factor
+    # `gamma_a gamma_b ... gamma_z + gamma_z ... gamma_b gamma_a`, in Kahanes's
+    # paper represented as  {gamma_a, gamma_b, ... , gamma_z},
+    # virtual indices are ignored. The variable `connected_components` is
+    # increased by one for every connected component this loop encounters.
+
+    # If the connected component has virtual and dummy indices only
+    # (no free indices), it contributes to `resulting_indices` by a factor of two.
+    # The multiplication by two is a result of the
+    # factor {gamma^0, gamma^0} = 2 I, as it appears in Kahane's paper.
+    # Note: curly brackets are meant as in the paper, as a generalized
+    # multi-element anticommutator!
+
+    while links:
+        connected_components += 1
+        pointer = min(links.keys())
+        previous_pointer = pointer
+        # the inner loop erases the visited indices from `links`, and it adds
+        # all free indices to `prepend_indices` list, virtual indices are
+        # ignored.
+        prepend_indices = []
+        while True:
+            if pointer in links:
+                next_ones = links.pop(pointer)
+            else:
+                break
+
+            if previous_pointer in next_ones:
+                if len(next_ones) > 1:
+                    next_ones.remove(previous_pointer)
+
+            previous_pointer = pointer
+
+            if next_ones:
+                pointer = next_ones[0]
+
+            if pointer >= first_dum_pos and free_pos[pointer] is not None:
+                prepend_indices.insert(0, free_pos[pointer])
+        # if `prepend_indices` is void, it means there are no free indices
+        # in the loop (and it can be shown that there must be a virtual index),
+        # loops of virtual indices only contribute by a factor of two:
+        if len(prepend_indices) == 0:
+            resulting_coeff *= 2
+        # otherwise, add the free indices in `prepend_indices` to
+        # the `resulting_indices`:
+        else:
+            expr1 = prepend_indices
+            expr2 = list(reversed(prepend_indices))
+            resulting_indices = [expri + ri for ri in resulting_indices for expri in (expr1, expr2)]
+
+    # sign correction, as described in Kahane's paper:
+    resulting_coeff *= -1 if (number_of_contractions - connected_components + 1) % 2 else 1
+    # power of two factor, as described in Kahane's paper:
+    resulting_coeff *= 2**(number_of_contractions)
+
+    # If `first_dum_pos` is not zero, it means that there are trailing free gamma
+    # matrices in front of `expression`, so multiply by them:
+    resulting_indices = [ free_pos[0:first_dum_pos] + ri for ri in resulting_indices ]
+
+    resulting_expr = S.Zero
+    for i in resulting_indices:
+        temp_expr = S.One
+        for j in i:
+            temp_expr *= GammaMatrix(j)
+        resulting_expr += temp_expr
+
+    t = resulting_coeff * resulting_expr
+    t1 = None
+    if isinstance(t, TensAdd):
+        t1 = t.args[0]
+    elif isinstance(t, TensMul):
+        t1 = t
+    if t1:
+        pass
+    else:
+        t = eye(4)*t
+    return t
diff --git a/llmeval-env/lib/python3.10/site-packages/sympy/physics/matrices.py b/llmeval-env/lib/python3.10/site-packages/sympy/physics/matrices.py
new file mode 100644
index 0000000000000000000000000000000000000000..d91466220d63956053b91bd76b948ee677e7c191
--- /dev/null
+++ b/llmeval-env/lib/python3.10/site-packages/sympy/physics/matrices.py
@@ -0,0 +1,176 @@
+"""Known matrices related to physics"""
+
+from sympy.core.numbers import I
+from sympy.matrices.dense import MutableDenseMatrix as Matrix
+from sympy.utilities.decorator import deprecated
+
+
+def msigma(i):
+    r"""Returns a Pauli matrix `\sigma_i` with `i=1,2,3`.
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Pauli_matrices
+
+    Examples
+    ========
+
+    >>> from sympy.physics.matrices import msigma
+    >>> msigma(1)
+    Matrix([
+    [0, 1],
+    [1, 0]])
+    """
+    if i == 1:
+        mat = (
+            (0, 1),
+            (1, 0)
+        )
+    elif i == 2:
+        mat = (
+            (0, -I),
+            (I, 0)
+        )
+    elif i == 3:
+        mat = (
+            (1, 0),
+            (0, -1)
+        )
+    else:
+        raise IndexError("Invalid Pauli index")
+    return Matrix(mat)
+
+
+def pat_matrix(m, dx, dy, dz):
+    """Returns the Parallel Axis Theorem matrix to translate the inertia
+    matrix a distance of `(dx, dy, dz)` for a body of mass m.
+
+    Examples
+    ========
+
+    To translate a body having a mass of 2 units a distance of 1 unit along
+    the `x`-axis we get:
+
+    >>> from sympy.physics.matrices import pat_matrix
+    >>> pat_matrix(2, 1, 0, 0)
+    Matrix([
+    [0, 0, 0],
+    [0, 2, 0],
+    [0, 0, 2]])
+
+    """
+    dxdy = -dx*dy
+    dydz = -dy*dz
+    dzdx = -dz*dx
+    dxdx = dx**2
+    dydy = dy**2
+    dzdz = dz**2
+    mat = ((dydy + dzdz, dxdy, dzdx),
+           (dxdy, dxdx + dzdz, dydz),
+           (dzdx, dydz, dydy + dxdx))
+    return m*Matrix(mat)
+
+
+def mgamma(mu, lower=False):
+    r"""Returns a Dirac gamma matrix `\gamma^\mu` in the standard
+    (Dirac) representation.
+
+    Explanation
+    ===========
+
+    If you want `\gamma_\mu`, use ``gamma(mu, True)``.
+
+    We use a convention:
+
+    `\gamma^5 = i \cdot \gamma^0 \cdot \gamma^1 \cdot \gamma^2 \cdot \gamma^3`
+
+    `\gamma_5 = i \cdot \gamma_0 \cdot \gamma_1 \cdot \gamma_2 \cdot \gamma_3 = - \gamma^5`
+
+    References
+    ==========
+
+    .. [1] https://en.wikipedia.org/wiki/Gamma_matrices
+
+    Examples
+    ========
+
+    >>> from sympy.physics.matrices import mgamma
+    >>> mgamma(1)
+    Matrix([
+    [ 0,  0, 0, 1],
+    [ 0,  0, 1, 0],
+    [ 0, -1, 0, 0],
+    [-1,  0, 0, 0]])
+    """
+    if mu not in (0, 1, 2, 3, 5):
+        raise IndexError("Invalid Dirac index")
+    if mu == 0:
+        mat = (
+            (1, 0, 0, 0),
+            (0, 1, 0, 0),
+            (0, 0, -1, 0),
+            (0, 0, 0, -1)
+        )
+    elif mu == 1:
+        mat = (
+            (0, 0, 0, 1),
+            (0, 0, 1, 0),
+            (0, -1, 0, 0),
+            (-1, 0, 0, 0)
+        )
+    elif mu == 2:
+        mat = (
+            (0, 0, 0, -I),
+            (0, 0, I, 0),
+            (0, I, 0, 0),
+            (-I, 0, 0, 0)
+        )
+    elif mu == 3:
+        mat = (
+            (0, 0, 1, 0),
+            (0, 0, 0, -1),
+            (-1, 0, 0, 0),
+            (0, 1, 0, 0)
+        )
+    elif mu == 5:
+        mat = (
+            (0, 0, 1, 0),
+            (0, 0, 0, 1),
+            (1, 0, 0, 0),
+            (0, 1, 0, 0)
+        )
+    m = Matrix(mat)
+    if lower:
+        if mu in (1, 2, 3, 5):
+            m = -m
+    return m
+
+#Minkowski tensor using the convention (+,-,-,-) used in the Quantum Field
+#Theory
+minkowski_tensor = Matrix( (
+    (1, 0, 0, 0),
+    (0, -1, 0, 0),
+    (0, 0, -1, 0),
+    (0, 0, 0, -1)
+))
+
+
+@deprecated(
+    """
+    The sympy.physics.matrices.mdft method is deprecated. Use
+    sympy.DFT(n).as_explicit() instead.
+    """,
+    deprecated_since_version="1.9",
+    active_deprecations_target="deprecated-physics-mdft",
+)
+def mdft(n):
+    r"""
+    .. deprecated:: 1.9
+
+       Use DFT from sympy.matrices.expressions.fourier instead.
+
+       To get identical behavior to ``mdft(n)``, use ``DFT(n).as_explicit()``.
+    """
+    from sympy.matrices.expressions.fourier import DFT
+    return DFT(n).as_mutable()
diff --git a/llmeval-env/lib/python3.10/site-packages/sympy/physics/paulialgebra.py b/llmeval-env/lib/python3.10/site-packages/sympy/physics/paulialgebra.py
new file mode 100644
index 0000000000000000000000000000000000000000..300957354ff34907035aa1d1a48b00276230a1e5
--- /dev/null
+++ b/llmeval-env/lib/python3.10/site-packages/sympy/physics/paulialgebra.py
@@ -0,0 +1,231 @@
+"""
+This module implements Pauli algebra by subclassing Symbol. Only algebraic
+properties of Pauli matrices are used (we do not use the Matrix class).
+
+See the documentation to the class Pauli for examples.
+
+References
+==========
+
+.. [1] https://en.wikipedia.org/wiki/Pauli_matrices
+"""
+
+from sympy.core.add import Add
+from sympy.core.mul import Mul
+from sympy.core.numbers import I
+from sympy.core.power import Pow
+from sympy.core.symbol import Symbol
+from sympy.physics.quantum import TensorProduct
+
+__all__ = ['evaluate_pauli_product']
+
+
+def delta(i, j):
+    """
+    Returns 1 if ``i == j``, else 0.
+
+    This is used in the multiplication of Pauli matrices.
+
+    Examples
+    ========
+
+    >>> from sympy.physics.paulialgebra import delta
+    >>> delta(1, 1)
+    1
+    >>> delta(2, 3)
+    0
+    """
+    if i == j:
+        return 1
+    else:
+        return 0
+
+
+def epsilon(i, j, k):
+    """
+    Return 1 if i,j,k is equal to (1,2,3), (2,3,1), or (3,1,2);
+    -1 if ``i``,``j``,``k`` is equal to (1,3,2), (3,2,1), or (2,1,3);
+    else return 0.
+
+    This is used in the multiplication of Pauli matrices.
+
+    Examples
+    ========
+
+    >>> from sympy.physics.paulialgebra import epsilon
+    >>> epsilon(1, 2, 3)
+    1
+    >>> epsilon(1, 3, 2)
+    -1
+    """
+    if (i, j, k) in ((1, 2, 3), (2, 3, 1), (3, 1, 2)):
+        return 1
+    elif (i, j, k) in ((1, 3, 2), (3, 2, 1), (2, 1, 3)):
+        return -1
+    else:
+        return 0
+
+
+class Pauli(Symbol):
+    """
+    The class representing algebraic properties of Pauli matrices.
+
+    Explanation
+    ===========
+
+    The symbol used to display the Pauli matrices can be changed with an
+    optional parameter ``label="sigma"``. Pauli matrices with different
+    ``label`` attributes cannot multiply together.
+
+    If the left multiplication of symbol or number with Pauli matrix is needed,
+    please use parentheses  to separate Pauli and symbolic multiplication
+    (for example: 2*I*(Pauli(3)*Pauli(2))).
+
+    Another variant is to use evaluate_pauli_product function to evaluate
+    the product of Pauli matrices and other symbols (with commutative
+    multiply rules).
+
+    See Also
+    ========
+
+    evaluate_pauli_product
+
+    Examples
+    ========
+
+    >>> from sympy.physics.paulialgebra import Pauli
+    >>> Pauli(1)
+    sigma1
+    >>> Pauli(1)*Pauli(2)
+    I*sigma3
+    >>> Pauli(1)*Pauli(1)
+    1
+    >>> Pauli(3)**4
+    1
+    >>> Pauli(1)*Pauli(2)*Pauli(3)
+    I
+
+    >>> from sympy.physics.paulialgebra import Pauli
+    >>> Pauli(1, label="tau")
+    tau1
+    >>> Pauli(1)*Pauli(2, label="tau")
+    sigma1*tau2
+    >>> Pauli(1, label="tau")*Pauli(2, label="tau")
+    I*tau3
+
+    >>> from sympy import I
+    >>> I*(Pauli(2)*Pauli(3))
+    -sigma1
+
+    >>> from sympy.physics.paulialgebra import evaluate_pauli_product
+    >>> f = I*Pauli(2)*Pauli(3)
+    >>> f
+    I*sigma2*sigma3
+    >>> evaluate_pauli_product(f)
+    -sigma1
+    """
+
+    __slots__ = ("i", "label")
+
+    def __new__(cls, i, label="sigma"):
+        if i not in [1, 2, 3]:
+            raise IndexError("Invalid Pauli index")
+        obj = Symbol.__new__(cls, "%s%d" %(label,i), commutative=False, hermitian=True)
+        obj.i = i
+        obj.label = label
+        return obj
+
+    def __getnewargs_ex__(self):
+        return (self.i, self.label), {}
+
+    def _hashable_content(self):
+        return (self.i, self.label)
+
+    # FIXME don't work for -I*Pauli(2)*Pauli(3)
+    def __mul__(self, other):
+        if isinstance(other, Pauli):
+            j = self.i
+            k = other.i
+            jlab = self.label
+            klab = other.label
+
+            if jlab == klab:
+                return delta(j, k) \
+                    + I*epsilon(j, k, 1)*Pauli(1,jlab) \
+                    + I*epsilon(j, k, 2)*Pauli(2,jlab) \
+                    + I*epsilon(j, k, 3)*Pauli(3,jlab)
+        return super().__mul__(other)
+
+    def _eval_power(b, e):
+        if e.is_Integer and e.is_positive:
+            return super().__pow__(int(e) % 2)
+
+
+def evaluate_pauli_product(arg):
+    '''Help function to evaluate Pauli matrices product
+    with symbolic objects.
+
+    Parameters
+    ==========
+
+    arg: symbolic expression that contains Paulimatrices
+
+    Examples
+    ========
+
+    >>> from sympy.physics.paulialgebra import Pauli, evaluate_pauli_product
+    >>> from sympy import I
+    >>> evaluate_pauli_product(I*Pauli(1)*Pauli(2))
+    -sigma3
+
+    >>> from sympy.abc import x
+    >>> evaluate_pauli_product(x**2*Pauli(2)*Pauli(1))
+    -I*x**2*sigma3
+    '''
+    start = arg
+    end = arg
+
+    if isinstance(arg, Pow) and isinstance(arg.args[0], Pauli):
+        if arg.args[1].is_odd:
+            return arg.args[0]
+        else:
+            return 1
+
+    if isinstance(arg, Add):
+        return Add(*[evaluate_pauli_product(part) for part in arg.args])
+
+    if isinstance(arg, TensorProduct):
+        return TensorProduct(*[evaluate_pauli_product(part) for part in arg.args])
+
+    elif not(isinstance(arg, Mul)):
+        return arg
+
+    while not start == end or start == arg and end == arg:
+        start = end
+
+        tmp = start.as_coeff_mul()
+        sigma_product = 1
+        com_product = 1
+        keeper = 1
+
+        for el in tmp[1]:
+            if isinstance(el, Pauli):
+                sigma_product *= el
+            elif not el.is_commutative:
+                if isinstance(el, Pow) and isinstance(el.args[0], Pauli):
+                    if el.args[1].is_odd:
+                        sigma_product *= el.args[0]
+                elif isinstance(el, TensorProduct):
+                    keeper = keeper*sigma_product*\
+                        TensorProduct(
+                            *[evaluate_pauli_product(part) for part in el.args]
+                        )
+                    sigma_product = 1
+                else:
+                    keeper = keeper*sigma_product*el
+                    sigma_product = 1
+            else:
+                com_product *= el
+        end = tmp[0]*keeper*sigma_product*com_product
+        if end == arg: break
+    return end
diff --git a/llmeval-env/lib/python3.10/site-packages/sympy/physics/pring.py b/llmeval-env/lib/python3.10/site-packages/sympy/physics/pring.py
new file mode 100644
index 0000000000000000000000000000000000000000..325f4ff98a8c9fc428b4e332153af533f4d199ca
--- /dev/null
+++ b/llmeval-env/lib/python3.10/site-packages/sympy/physics/pring.py
@@ -0,0 +1,94 @@
+from sympy.core.numbers import (I, pi)
+from sympy.core.singleton import S
+from sympy.functions.elementary.exponential import exp
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.physics.quantum.constants import hbar
+
+
+def wavefunction(n, x):
+    """
+    Returns the wavefunction for particle on ring.
+
+    Parameters
+    ==========
+
+    n : The quantum number.
+        Here ``n`` can be positive as well as negative
+        which can be used to describe the direction of motion of particle.
+    x :
+        The angle.
+
+    Examples
+    ========
+
+    >>> from sympy.physics.pring import wavefunction
+    >>> from sympy import Symbol, integrate, pi
+    >>> x=Symbol("x")
+    >>> wavefunction(1, x)
+    sqrt(2)*exp(I*x)/(2*sqrt(pi))
+    >>> wavefunction(2, x)
+    sqrt(2)*exp(2*I*x)/(2*sqrt(pi))
+    >>> wavefunction(3, x)
+    sqrt(2)*exp(3*I*x)/(2*sqrt(pi))
+
+    The normalization of the wavefunction is:
+
+    >>> integrate(wavefunction(2, x)*wavefunction(-2, x), (x, 0, 2*pi))
+    1
+    >>> integrate(wavefunction(4, x)*wavefunction(-4, x), (x, 0, 2*pi))
+    1
+
+    References
+    ==========
+
+    .. [1] Atkins, Peter W.; Friedman, Ronald (2005). Molecular Quantum
+           Mechanics (4th ed.).  Pages 71-73.
+
+    """
+    # sympify arguments
+    n, x = S(n), S(x)
+    return exp(n * I * x) / sqrt(2 * pi)
+
+
+def energy(n, m, r):
+    """
+    Returns the energy of the state corresponding to quantum number ``n``.
+
+    E=(n**2 * (hcross)**2) / (2 * m * r**2)
+
+    Parameters
+    ==========
+
+    n :
+        The quantum number.
+    m :
+        Mass of the particle.
+    r :
+        Radius of circle.
+
+    Examples
+    ========
+
+    >>> from sympy.physics.pring import energy
+    >>> from sympy import Symbol
+    >>> m=Symbol("m")
+    >>> r=Symbol("r")
+    >>> energy(1, m, r)
+    hbar**2/(2*m*r**2)
+    >>> energy(2, m, r)
+    2*hbar**2/(m*r**2)
+    >>> energy(-2, 2.0, 3.0)
+    0.111111111111111*hbar**2
+
+    References
+    ==========
+
+    .. [1] Atkins, Peter W.; Friedman, Ronald (2005). Molecular Quantum
+           Mechanics (4th ed.).  Pages 71-73.
+
+    """
+    n, m, r = S(n), S(m), S(r)
+    if n.is_integer:
+        return (n**2 * hbar**2) / (2 * m * r**2)
+    else:
+        raise ValueError("'n' must be integer")
diff --git a/llmeval-env/lib/python3.10/site-packages/sympy/physics/qho_1d.py b/llmeval-env/lib/python3.10/site-packages/sympy/physics/qho_1d.py
new file mode 100644
index 0000000000000000000000000000000000000000..f418e0e954656923fbfa64cea2145581ddf65aea
--- /dev/null
+++ b/llmeval-env/lib/python3.10/site-packages/sympy/physics/qho_1d.py
@@ -0,0 +1,88 @@
+from sympy.core import S, pi, Rational
+from sympy.functions import hermite, sqrt, exp, factorial, Abs
+from sympy.physics.quantum.constants import hbar
+
+
+def psi_n(n, x, m, omega):
+    """
+    Returns the wavefunction psi_{n} for the One-dimensional harmonic oscillator.
+
+    Parameters
+    ==========
+
+    n :
+        the "nodal" quantum number.  Corresponds to the number of nodes in the
+        wavefunction.  ``n >= 0``
+    x :
+        x coordinate.
+    m :
+        Mass of the particle.
+    omega :
+        Angular frequency of the oscillator.
+
+    Examples
+    ========
+
+    >>> from sympy.physics.qho_1d import psi_n
+    >>> from sympy.abc import m, x, omega
+    >>> psi_n(0, x, m, omega)
+    (m*omega)**(1/4)*exp(-m*omega*x**2/(2*hbar))/(hbar**(1/4)*pi**(1/4))
+
+    """
+
+    # sympify arguments
+    n, x, m, omega = map(S, [n, x, m, omega])
+    nu = m * omega / hbar
+    # normalization coefficient
+    C = (nu/pi)**Rational(1, 4) * sqrt(1/(2**n*factorial(n)))
+
+    return C * exp(-nu* x**2 /2) * hermite(n, sqrt(nu)*x)
+
+
+def E_n(n, omega):
+    """
+    Returns the Energy of the One-dimensional harmonic oscillator.
+
+    Parameters
+    ==========
+
+    n :
+        The "nodal" quantum number.
+    omega :
+        The harmonic oscillator angular frequency.
+
+    Notes
+    =====
+
+    The unit of the returned value matches the unit of hw, since the energy is
+    calculated as:
+
+        E_n = hbar * omega*(n + 1/2)
+
+    Examples
+    ========
+
+    >>> from sympy.physics.qho_1d import E_n
+    >>> from sympy.abc import x, omega
+    >>> E_n(x, omega)
+    hbar*omega*(x + 1/2)
+    """
+
+    return hbar * omega * (n + S.Half)
+
+
+def coherent_state(n, alpha):
+    """
+    Returns  for the coherent states of 1D harmonic oscillator.
+    See https://en.wikipedia.org/wiki/Coherent_states
+
+    Parameters
+    ==========
+
+    n :
+        The "nodal" quantum number.
+    alpha :
+        The eigen value of annihilation operator.
+    """
+
+    return exp(- Abs(alpha)**2/2)*(alpha**n)/sqrt(factorial(n))
diff --git a/llmeval-env/lib/python3.10/site-packages/sympy/physics/secondquant.py b/llmeval-env/lib/python3.10/site-packages/sympy/physics/secondquant.py
new file mode 100644
index 0000000000000000000000000000000000000000..464fae9acee368b4f68f1436ffd3bc419b0a72d4
--- /dev/null
+++ b/llmeval-env/lib/python3.10/site-packages/sympy/physics/secondquant.py
@@ -0,0 +1,3114 @@
+"""
+Second quantization operators and states for bosons.
+
+This follow the formulation of Fetter and Welecka, "Quantum Theory
+of Many-Particle Systems."
+"""
+from collections import defaultdict
+
+from sympy.core.add import Add
+from sympy.core.basic import Basic
+from sympy.core.cache import cacheit
+from sympy.core.containers import Tuple
+from sympy.core.expr import Expr
+from sympy.core.function import Function
+from sympy.core.mul import Mul
+from sympy.core.numbers import I
+from sympy.core.power import Pow
+from sympy.core.singleton import S
+from sympy.core.sorting import default_sort_key
+from sympy.core.symbol import Dummy, Symbol
+from sympy.core.sympify import sympify
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.functions.special.tensor_functions import KroneckerDelta
+from sympy.matrices.dense import zeros
+from sympy.printing.str import StrPrinter
+from sympy.utilities.iterables import has_dups
+
+__all__ = [
+    'Dagger',
+    'KroneckerDelta',
+    'BosonicOperator',
+    'AnnihilateBoson',
+    'CreateBoson',
+    'AnnihilateFermion',
+    'CreateFermion',
+    'FockState',
+    'FockStateBra',
+    'FockStateKet',
+    'FockStateBosonKet',
+    'FockStateBosonBra',
+    'FockStateFermionKet',
+    'FockStateFermionBra',
+    'BBra',
+    'BKet',
+    'FBra',
+    'FKet',
+    'F',
+    'Fd',
+    'B',
+    'Bd',
+    'apply_operators',
+    'InnerProduct',
+    'BosonicBasis',
+    'VarBosonicBasis',
+    'FixedBosonicBasis',
+    'Commutator',
+    'matrix_rep',
+    'contraction',
+    'wicks',
+    'NO',
+    'evaluate_deltas',
+    'AntiSymmetricTensor',
+    'substitute_dummies',
+    'PermutationOperator',
+    'simplify_index_permutations',
+]
+
+
+class SecondQuantizationError(Exception):
+    pass
+
+
+class AppliesOnlyToSymbolicIndex(SecondQuantizationError):
+    pass
+
+
+class ContractionAppliesOnlyToFermions(SecondQuantizationError):
+    pass
+
+
+class ViolationOfPauliPrinciple(SecondQuantizationError):
+    pass
+
+
+class SubstitutionOfAmbigousOperatorFailed(SecondQuantizationError):
+    pass
+
+
+class WicksTheoremDoesNotApply(SecondQuantizationError):
+    pass
+
+
+class Dagger(Expr):
+    """
+    Hermitian conjugate of creation/annihilation operators.
+
+    Examples
+    ========
+
+    >>> from sympy import I
+    >>> from sympy.physics.secondquant import Dagger, B, Bd
+    >>> Dagger(2*I)
+    -2*I
+    >>> Dagger(B(0))
+    CreateBoson(0)
+    >>> Dagger(Bd(0))
+    AnnihilateBoson(0)
+
+    """
+
+    def __new__(cls, arg):
+        arg = sympify(arg)
+        r = cls.eval(arg)
+        if isinstance(r, Basic):
+            return r
+        obj = Basic.__new__(cls, arg)
+        return obj
+
+    @classmethod
+    def eval(cls, arg):
+        """
+        Evaluates the Dagger instance.
+
+        Examples
+        ========
+
+        >>> from sympy import I
+        >>> from sympy.physics.secondquant import Dagger, B, Bd
+        >>> Dagger(2*I)
+        -2*I
+        >>> Dagger(B(0))
+        CreateBoson(0)
+        >>> Dagger(Bd(0))
+        AnnihilateBoson(0)
+
+        The eval() method is called automatically.
+
+        """
+        dagger = getattr(arg, '_dagger_', None)
+        if dagger is not None:
+            return dagger()
+        if isinstance(arg, Basic):
+            if arg.is_Add:
+                return Add(*tuple(map(Dagger, arg.args)))
+            if arg.is_Mul:
+                return Mul(*tuple(map(Dagger, reversed(arg.args))))
+            if arg.is_Number:
+                return arg
+            if arg.is_Pow:
+                return Pow(Dagger(arg.args[0]), arg.args[1])
+            if arg == I:
+                return -arg
+        else:
+            return None
+
+    def _dagger_(self):
+        return self.args[0]
+
+
+class TensorSymbol(Expr):
+
+    is_commutative = True
+
+
+class AntiSymmetricTensor(TensorSymbol):
+    """Stores upper and lower indices in separate Tuple's.
+
+    Each group of indices is assumed to be antisymmetric.
+
+    Examples
+    ========
+
+    >>> from sympy import symbols
+    >>> from sympy.physics.secondquant import AntiSymmetricTensor
+    >>> i, j = symbols('i j', below_fermi=True)
+    >>> a, b = symbols('a b', above_fermi=True)
+    >>> AntiSymmetricTensor('v', (a, i), (b, j))
+    AntiSymmetricTensor(v, (a, i), (b, j))
+    >>> AntiSymmetricTensor('v', (i, a), (b, j))
+    -AntiSymmetricTensor(v, (a, i), (b, j))
+
+    As you can see, the indices are automatically sorted to a canonical form.
+
+    """
+
+    def __new__(cls, symbol, upper, lower):
+
+        try:
+            upper, signu = _sort_anticommuting_fermions(
+                upper, key=cls._sortkey)
+            lower, signl = _sort_anticommuting_fermions(
+                lower, key=cls._sortkey)
+
+        except ViolationOfPauliPrinciple:
+            return S.Zero
+
+        symbol = sympify(symbol)
+        upper = Tuple(*upper)
+        lower = Tuple(*lower)
+
+        if (signu + signl) % 2:
+            return -TensorSymbol.__new__(cls, symbol, upper, lower)
+        else:
+
+            return TensorSymbol.__new__(cls, symbol, upper, lower)
+
+    @classmethod
+    def _sortkey(cls, index):
+        """Key for sorting of indices.
+
+        particle < hole < general
+
+        FIXME: This is a bottle-neck, can we do it faster?
+        """
+        h = hash(index)
+        label = str(index)
+        if isinstance(index, Dummy):
+            if index.assumptions0.get('above_fermi'):
+                return (20, label, h)
+            elif index.assumptions0.get('below_fermi'):
+                return (21, label, h)
+            else:
+                return (22, label, h)
+
+        if index.assumptions0.get('above_fermi'):
+            return (10, label, h)
+        elif index.assumptions0.get('below_fermi'):
+            return (11, label, h)
+        else:
+            return (12, label, h)
+
+    def _latex(self, printer):
+        return "{%s^{%s}_{%s}}" % (
+            self.symbol,
+            "".join([ i.name for i in self.args[1]]),
+            "".join([ i.name for i in self.args[2]])
+        )
+
+    @property
+    def symbol(self):
+        """
+        Returns the symbol of the tensor.
+
+        Examples
+        ========
+
+        >>> from sympy import symbols
+        >>> from sympy.physics.secondquant import AntiSymmetricTensor
+        >>> i, j = symbols('i,j', below_fermi=True)
+        >>> a, b = symbols('a,b', above_fermi=True)
+        >>> AntiSymmetricTensor('v', (a, i), (b, j))
+        AntiSymmetricTensor(v, (a, i), (b, j))
+        >>> AntiSymmetricTensor('v', (a, i), (b, j)).symbol
+        v
+
+        """
+        return self.args[0]
+
+    @property
+    def upper(self):
+        """
+        Returns the upper indices.
+
+        Examples
+        ========
+
+        >>> from sympy import symbols
+        >>> from sympy.physics.secondquant import AntiSymmetricTensor
+        >>> i, j = symbols('i,j', below_fermi=True)
+        >>> a, b = symbols('a,b', above_fermi=True)
+        >>> AntiSymmetricTensor('v', (a, i), (b, j))
+        AntiSymmetricTensor(v, (a, i), (b, j))
+        >>> AntiSymmetricTensor('v', (a, i), (b, j)).upper
+        (a, i)
+
+
+        """
+        return self.args[1]
+
+    @property
+    def lower(self):
+        """
+        Returns the lower indices.
+
+        Examples
+        ========
+
+        >>> from sympy import symbols
+        >>> from sympy.physics.secondquant import AntiSymmetricTensor
+        >>> i, j = symbols('i,j', below_fermi=True)
+        >>> a, b = symbols('a,b', above_fermi=True)
+        >>> AntiSymmetricTensor('v', (a, i), (b, j))
+        AntiSymmetricTensor(v, (a, i), (b, j))
+        >>> AntiSymmetricTensor('v', (a, i), (b, j)).lower
+        (b, j)
+
+        """
+        return self.args[2]
+
+    def __str__(self):
+        return "%s(%s,%s)" % self.args
+
+
+class SqOperator(Expr):
+    """
+    Base class for Second Quantization operators.
+    """
+
+    op_symbol = 'sq'
+
+    is_commutative = False
+
+    def __new__(cls, k):
+        obj = Basic.__new__(cls, sympify(k))
+        return obj
+
+    @property
+    def state(self):
+        """
+        Returns the state index related to this operator.
+
+        Examples
+        ========
+
+        >>> from sympy import Symbol
+        >>> from sympy.physics.secondquant import F, Fd, B, Bd
+        >>> p = Symbol('p')
+        >>> F(p).state
+        p
+        >>> Fd(p).state
+        p
+        >>> B(p).state
+        p
+        >>> Bd(p).state
+        p
+
+        """
+        return self.args[0]
+
+    @property
+    def is_symbolic(self):
+        """
+        Returns True if the state is a symbol (as opposed to a number).
+
+        Examples
+        ========
+
+        >>> from sympy import Symbol
+        >>> from sympy.physics.secondquant import F
+        >>> p = Symbol('p')
+        >>> F(p).is_symbolic
+        True
+        >>> F(1).is_symbolic
+        False
+
+        """
+        if self.state.is_Integer:
+            return False
+        else:
+            return True
+
+    def __repr__(self):
+        return NotImplemented
+
+    def __str__(self):
+        return "%s(%r)" % (self.op_symbol, self.state)
+
+    def apply_operator(self, state):
+        """
+        Applies an operator to itself.
+        """
+        raise NotImplementedError('implement apply_operator in a subclass')
+
+
+class BosonicOperator(SqOperator):
+    pass
+
+
+class Annihilator(SqOperator):
+    pass
+
+
+class Creator(SqOperator):
+    pass
+
+
+class AnnihilateBoson(BosonicOperator, Annihilator):
+    """
+    Bosonic annihilation operator.
+
+    Examples
+    ========
+
+    >>> from sympy.physics.secondquant import B
+    >>> from sympy.abc import x
+    >>> B(x)
+    AnnihilateBoson(x)
+    """
+
+    op_symbol = 'b'
+
+    def _dagger_(self):
+        return CreateBoson(self.state)
+
+    def apply_operator(self, state):
+        """
+        Apply state to self if self is not symbolic and state is a FockStateKet, else
+        multiply self by state.
+
+        Examples
+        ========
+
+        >>> from sympy.physics.secondquant import B, BKet
+        >>> from sympy.abc import x, y, n
+        >>> B(x).apply_operator(y)
+        y*AnnihilateBoson(x)
+        >>> B(0).apply_operator(BKet((n,)))
+        sqrt(n)*FockStateBosonKet((n - 1,))
+
+        """
+        if not self.is_symbolic and isinstance(state, FockStateKet):
+            element = self.state
+            amp = sqrt(state[element])
+            return amp*state.down(element)
+        else:
+            return Mul(self, state)
+
+    def __repr__(self):
+        return "AnnihilateBoson(%s)" % self.state
+
+    def _latex(self, printer):
+        if self.state is S.Zero:
+            return "b_{0}"
+        else:
+            return "b_{%s}" % self.state.name
+
+class CreateBoson(BosonicOperator, Creator):
+    """
+    Bosonic creation operator.
+    """
+
+    op_symbol = 'b+'
+
+    def _dagger_(self):
+        return AnnihilateBoson(self.state)
+
+    def apply_operator(self, state):
+        """
+        Apply state to self if self is not symbolic and state is a FockStateKet, else
+        multiply self by state.
+
+        Examples
+        ========
+
+        >>> from sympy.physics.secondquant import B, Dagger, BKet
+        >>> from sympy.abc import x, y, n
+        >>> Dagger(B(x)).apply_operator(y)
+        y*CreateBoson(x)
+        >>> B(0).apply_operator(BKet((n,)))
+        sqrt(n)*FockStateBosonKet((n - 1,))
+        """
+        if not self.is_symbolic and isinstance(state, FockStateKet):
+            element = self.state
+            amp = sqrt(state[element] + 1)
+            return amp*state.up(element)
+        else:
+            return Mul(self, state)
+
+    def __repr__(self):
+        return "CreateBoson(%s)" % self.state
+
+    def _latex(self, printer):
+        if self.state is S.Zero:
+            return "{b^\\dagger_{0}}"
+        else:
+            return "{b^\\dagger_{%s}}" % self.state.name
+
+B = AnnihilateBoson
+Bd = CreateBoson
+
+
+class FermionicOperator(SqOperator):
+
+    @property
+    def is_restricted(self):
+        """
+        Is this FermionicOperator restricted with respect to fermi level?
+
+        Returns
+        =======
+
+        1  : restricted to orbits above fermi
+        0  : no restriction
+        -1 : restricted to orbits below fermi
+
+        Examples
+        ========
+
+        >>> from sympy import Symbol
+        >>> from sympy.physics.secondquant import F, Fd
+        >>> a = Symbol('a', above_fermi=True)
+        >>> i = Symbol('i', below_fermi=True)
+        >>> p = Symbol('p')
+
+        >>> F(a).is_restricted
+        1
+        >>> Fd(a).is_restricted
+        1
+        >>> F(i).is_restricted
+        -1
+        >>> Fd(i).is_restricted
+        -1
+        >>> F(p).is_restricted
+        0
+        >>> Fd(p).is_restricted
+        0
+
+        """
+        ass = self.args[0].assumptions0
+        if ass.get("below_fermi"):
+            return -1
+        if ass.get("above_fermi"):
+            return 1
+        return 0
+
+    @property
+    def is_above_fermi(self):
+        """
+        Does the index of this FermionicOperator allow values above fermi?
+
+        Examples
+        ========
+
+        >>> from sympy import Symbol
+        >>> from sympy.physics.secondquant import F
+        >>> a = Symbol('a', above_fermi=True)
+        >>> i = Symbol('i', below_fermi=True)
+        >>> p = Symbol('p')
+
+        >>> F(a).is_above_fermi
+        True
+        >>> F(i).is_above_fermi
+        False
+        >>> F(p).is_above_fermi
+        True
+
+        Note
+        ====
+
+        The same applies to creation operators Fd
+
+        """
+        return not self.args[0].assumptions0.get("below_fermi")
+
+    @property
+    def is_below_fermi(self):
+        """
+        Does the index of this FermionicOperator allow values below fermi?
+
+        Examples
+        ========
+
+        >>> from sympy import Symbol
+        >>> from sympy.physics.secondquant import F
+        >>> a = Symbol('a', above_fermi=True)
+        >>> i = Symbol('i', below_fermi=True)
+        >>> p = Symbol('p')
+
+        >>> F(a).is_below_fermi
+        False
+        >>> F(i).is_below_fermi
+        True
+        >>> F(p).is_below_fermi
+        True
+
+        The same applies to creation operators Fd
+
+        """
+        return not self.args[0].assumptions0.get("above_fermi")
+
+    @property
+    def is_only_below_fermi(self):
+        """
+        Is the index of this FermionicOperator restricted to values below fermi?
+
+        Examples
+        ========
+
+        >>> from sympy import Symbol
+        >>> from sympy.physics.secondquant import F
+        >>> a = Symbol('a', above_fermi=True)
+        >>> i = Symbol('i', below_fermi=True)
+        >>> p = Symbol('p')
+
+        >>> F(a).is_only_below_fermi
+        False
+        >>> F(i).is_only_below_fermi
+        True
+        >>> F(p).is_only_below_fermi
+        False
+
+        The same applies to creation operators Fd
+        """
+        return self.is_below_fermi and not self.is_above_fermi
+
+    @property
+    def is_only_above_fermi(self):
+        """
+        Is the index of this FermionicOperator restricted to values above fermi?
+
+        Examples
+        ========
+
+        >>> from sympy import Symbol
+        >>> from sympy.physics.secondquant import F
+        >>> a = Symbol('a', above_fermi=True)
+        >>> i = Symbol('i', below_fermi=True)
+        >>> p = Symbol('p')
+
+        >>> F(a).is_only_above_fermi
+        True
+        >>> F(i).is_only_above_fermi
+        False
+        >>> F(p).is_only_above_fermi
+        False
+
+        The same applies to creation operators Fd
+        """
+        return self.is_above_fermi and not self.is_below_fermi
+
+    def _sortkey(self):
+        h = hash(self)
+        label = str(self.args[0])
+
+        if self.is_only_q_creator:
+            return 1, label, h
+        if self.is_only_q_annihilator:
+            return 4, label, h
+        if isinstance(self, Annihilator):
+            return 3, label, h
+        if isinstance(self, Creator):
+            return 2, label, h
+
+
+class AnnihilateFermion(FermionicOperator, Annihilator):
+    """
+    Fermionic annihilation operator.
+    """
+
+    op_symbol = 'f'
+
+    def _dagger_(self):
+        return CreateFermion(self.state)
+
+    def apply_operator(self, state):
+        """
+        Apply state to self if self is not symbolic and state is a FockStateKet, else
+        multiply self by state.
+
+        Examples
+        ========
+
+        >>> from sympy.physics.secondquant import B, Dagger, BKet
+        >>> from sympy.abc import x, y, n
+        >>> Dagger(B(x)).apply_operator(y)
+        y*CreateBoson(x)
+        >>> B(0).apply_operator(BKet((n,)))
+        sqrt(n)*FockStateBosonKet((n - 1,))
+        """
+        if isinstance(state, FockStateFermionKet):
+            element = self.state
+            return state.down(element)
+
+        elif isinstance(state, Mul):
+            c_part, nc_part = state.args_cnc()
+            if isinstance(nc_part[0], FockStateFermionKet):
+                element = self.state
+                return Mul(*(c_part + [nc_part[0].down(element)] + nc_part[1:]))
+            else:
+                return Mul(self, state)
+
+        else:
+            return Mul(self, state)
+
+    @property
+    def is_q_creator(self):
+        """
+        Can we create a quasi-particle?  (create hole or create particle)
+        If so, would that be above or below the fermi surface?
+
+        Examples
+        ========
+
+        >>> from sympy import Symbol
+        >>> from sympy.physics.secondquant import F
+        >>> a = Symbol('a', above_fermi=True)
+        >>> i = Symbol('i', below_fermi=True)
+        >>> p = Symbol('p')
+
+        >>> F(a).is_q_creator
+        0
+        >>> F(i).is_q_creator
+        -1
+        >>> F(p).is_q_creator
+        -1
+
+        """
+        if self.is_below_fermi:
+            return -1
+        return 0
+
+    @property
+    def is_q_annihilator(self):
+        """
+        Can we destroy a quasi-particle?  (annihilate hole or annihilate particle)
+        If so, would that be above or below the fermi surface?
+
+        Examples
+        ========
+
+        >>> from sympy import Symbol
+        >>> from sympy.physics.secondquant import F
+        >>> a = Symbol('a', above_fermi=1)
+        >>> i = Symbol('i', below_fermi=1)
+        >>> p = Symbol('p')
+
+        >>> F(a).is_q_annihilator
+        1
+        >>> F(i).is_q_annihilator
+        0
+        >>> F(p).is_q_annihilator
+        1
+
+        """
+        if self.is_above_fermi:
+            return 1
+        return 0
+
+    @property
+    def is_only_q_creator(self):
+        """
+        Always create a quasi-particle?  (create hole or create particle)
+
+        Examples
+        ========
+
+        >>> from sympy import Symbol
+        >>> from sympy.physics.secondquant import F
+        >>> a = Symbol('a', above_fermi=True)
+        >>> i = Symbol('i', below_fermi=True)
+        >>> p = Symbol('p')
+
+        >>> F(a).is_only_q_creator
+        False
+        >>> F(i).is_only_q_creator
+        True
+        >>> F(p).is_only_q_creator
+        False
+
+        """
+        return self.is_only_below_fermi
+
+    @property
+    def is_only_q_annihilator(self):
+        """
+        Always destroy a quasi-particle?  (annihilate hole or annihilate particle)
+
+        Examples
+        ========
+
+        >>> from sympy import Symbol
+        >>> from sympy.physics.secondquant import F
+        >>> a = Symbol('a', above_fermi=True)
+        >>> i = Symbol('i', below_fermi=True)
+        >>> p = Symbol('p')
+
+        >>> F(a).is_only_q_annihilator
+        True
+        >>> F(i).is_only_q_annihilator
+        False
+        >>> F(p).is_only_q_annihilator
+        False
+
+        """
+        return self.is_only_above_fermi
+
+    def __repr__(self):
+        return "AnnihilateFermion(%s)" % self.state
+
+    def _latex(self, printer):
+        if self.state is S.Zero:
+            return "a_{0}"
+        else:
+            return "a_{%s}" % self.state.name
+
+
+class CreateFermion(FermionicOperator, Creator):
+    """
+    Fermionic creation operator.
+    """
+
+    op_symbol = 'f+'
+
+    def _dagger_(self):
+        return AnnihilateFermion(self.state)
+
+    def apply_operator(self, state):
+        """
+        Apply state to self if self is not symbolic and state is a FockStateKet, else
+        multiply self by state.
+
+        Examples
+        ========
+
+        >>> from sympy.physics.secondquant import B, Dagger, BKet
+        >>> from sympy.abc import x, y, n
+        >>> Dagger(B(x)).apply_operator(y)
+        y*CreateBoson(x)
+        >>> B(0).apply_operator(BKet((n,)))
+        sqrt(n)*FockStateBosonKet((n - 1,))
+        """
+        if isinstance(state, FockStateFermionKet):
+            element = self.state
+            return state.up(element)
+
+        elif isinstance(state, Mul):
+            c_part, nc_part = state.args_cnc()
+            if isinstance(nc_part[0], FockStateFermionKet):
+                element = self.state
+                return Mul(*(c_part + [nc_part[0].up(element)] + nc_part[1:]))
+
+        return Mul(self, state)
+
+    @property
+    def is_q_creator(self):
+        """
+        Can we create a quasi-particle?  (create hole or create particle)
+        If so, would that be above or below the fermi surface?
+
+        Examples
+        ========
+
+        >>> from sympy import Symbol
+        >>> from sympy.physics.secondquant import Fd
+        >>> a = Symbol('a', above_fermi=True)
+        >>> i = Symbol('i', below_fermi=True)
+        >>> p = Symbol('p')
+
+        >>> Fd(a).is_q_creator
+        1
+        >>> Fd(i).is_q_creator
+        0
+        >>> Fd(p).is_q_creator
+        1
+
+        """
+        if self.is_above_fermi:
+            return 1
+        return 0
+
+    @property
+    def is_q_annihilator(self):
+        """
+        Can we destroy a quasi-particle?  (annihilate hole or annihilate particle)
+        If so, would that be above or below the fermi surface?
+
+        Examples
+        ========
+
+        >>> from sympy import Symbol
+        >>> from sympy.physics.secondquant import Fd
+        >>> a = Symbol('a', above_fermi=1)
+        >>> i = Symbol('i', below_fermi=1)
+        >>> p = Symbol('p')
+
+        >>> Fd(a).is_q_annihilator
+        0
+        >>> Fd(i).is_q_annihilator
+        -1
+        >>> Fd(p).is_q_annihilator
+        -1
+
+        """
+        if self.is_below_fermi:
+            return -1
+        return 0
+
+    @property
+    def is_only_q_creator(self):
+        """
+        Always create a quasi-particle?  (create hole or create particle)
+
+        Examples
+        ========
+
+        >>> from sympy import Symbol
+        >>> from sympy.physics.secondquant import Fd
+        >>> a = Symbol('a', above_fermi=True)
+        >>> i = Symbol('i', below_fermi=True)
+        >>> p = Symbol('p')
+
+        >>> Fd(a).is_only_q_creator
+        True
+        >>> Fd(i).is_only_q_creator
+        False
+        >>> Fd(p).is_only_q_creator
+        False
+
+        """
+        return self.is_only_above_fermi
+
+    @property
+    def is_only_q_annihilator(self):
+        """
+        Always destroy a quasi-particle?  (annihilate hole or annihilate particle)
+
+        Examples
+        ========
+
+        >>> from sympy import Symbol
+        >>> from sympy.physics.secondquant import Fd
+        >>> a = Symbol('a', above_fermi=True)
+        >>> i = Symbol('i', below_fermi=True)
+        >>> p = Symbol('p')
+
+        >>> Fd(a).is_only_q_annihilator
+        False
+        >>> Fd(i).is_only_q_annihilator
+        True
+        >>> Fd(p).is_only_q_annihilator
+        False
+
+        """
+        return self.is_only_below_fermi
+
+    def __repr__(self):
+        return "CreateFermion(%s)" % self.state
+
+    def _latex(self, printer):
+        if self.state is S.Zero:
+            return "{a^\\dagger_{0}}"
+        else:
+            return "{a^\\dagger_{%s}}" % self.state.name
+
+Fd = CreateFermion
+F = AnnihilateFermion
+
+
+class FockState(Expr):
+    """
+    Many particle Fock state with a sequence of occupation numbers.
+
+    Anywhere you can have a FockState, you can also have S.Zero.
+    All code must check for this!
+
+    Base class to represent FockStates.
+    """
+    is_commutative = False
+
+    def __new__(cls, occupations):
+        """
+        occupations is a list with two possible meanings:
+
+        - For bosons it is a list of occupation numbers.
+          Element i is the number of particles in state i.
+
+        - For fermions it is a list of occupied orbits.
+          Element 0 is the state that was occupied first, element i
+          is the i'th occupied state.
+        """
+        occupations = list(map(sympify, occupations))
+        obj = Basic.__new__(cls, Tuple(*occupations))
+        return obj
+
+    def __getitem__(self, i):
+        i = int(i)
+        return self.args[0][i]
+
+    def __repr__(self):
+        return ("FockState(%r)") % (self.args)
+
+    def __str__(self):
+        return "%s%r%s" % (getattr(self, 'lbracket', ""), self._labels(), getattr(self, 'rbracket', ""))
+
+    def _labels(self):
+        return self.args[0]
+
+    def __len__(self):
+        return len(self.args[0])
+
+    def _latex(self, printer):
+        return "%s%s%s" % (getattr(self, 'lbracket_latex', ""), printer._print(self._labels()), getattr(self, 'rbracket_latex', ""))
+
+
+class BosonState(FockState):
+    """
+    Base class for FockStateBoson(Ket/Bra).
+    """
+
+    def up(self, i):
+        """
+        Performs the action of a creation operator.
+
+        Examples
+        ========
+
+        >>> from sympy.physics.secondquant import BBra
+        >>> b = BBra([1, 2])
+        >>> b
+        FockStateBosonBra((1, 2))
+        >>> b.up(1)
+        FockStateBosonBra((1, 3))
+        """
+        i = int(i)
+        new_occs = list(self.args[0])
+        new_occs[i] = new_occs[i] + S.One
+        return self.__class__(new_occs)
+
+    def down(self, i):
+        """
+        Performs the action of an annihilation operator.
+
+        Examples
+        ========
+
+        >>> from sympy.physics.secondquant import BBra
+        >>> b = BBra([1, 2])
+        >>> b
+        FockStateBosonBra((1, 2))
+        >>> b.down(1)
+        FockStateBosonBra((1, 1))
+        """
+        i = int(i)
+        new_occs = list(self.args[0])
+        if new_occs[i] == S.Zero:
+            return S.Zero
+        else:
+            new_occs[i] = new_occs[i] - S.One
+            return self.__class__(new_occs)
+
+
+class FermionState(FockState):
+    """
+    Base class for FockStateFermion(Ket/Bra).
+    """
+
+    fermi_level = 0
+
+    def __new__(cls, occupations, fermi_level=0):
+        occupations = list(map(sympify, occupations))
+        if len(occupations) > 1:
+            try:
+                (occupations, sign) = _sort_anticommuting_fermions(
+                    occupations, key=hash)
+            except ViolationOfPauliPrinciple:
+                return S.Zero
+        else:
+            sign = 0
+
+        cls.fermi_level = fermi_level
+
+        if cls._count_holes(occupations) > fermi_level:
+            return S.Zero
+
+        if sign % 2:
+            return S.NegativeOne*FockState.__new__(cls, occupations)
+        else:
+            return FockState.__new__(cls, occupations)
+
+    def up(self, i):
+        """
+        Performs the action of a creation operator.
+
+        Explanation
+        ===========
+
+        If below fermi we try to remove a hole,
+        if above fermi we try to create a particle.
+
+        If general index p we return ``Kronecker(p,i)*self``
+        where ``i`` is a new symbol with restriction above or below.
+
+        Examples
+        ========
+
+        >>> from sympy import Symbol
+        >>> from sympy.physics.secondquant import FKet
+        >>> a = Symbol('a', above_fermi=True)
+        >>> i = Symbol('i', below_fermi=True)
+        >>> p = Symbol('p')
+
+        >>> FKet([]).up(a)
+        FockStateFermionKet((a,))
+
+        A creator acting on vacuum below fermi vanishes
+
+        >>> FKet([]).up(i)
+        0
+
+
+        """
+        present = i in self.args[0]
+
+        if self._only_above_fermi(i):
+            if present:
+                return S.Zero
+            else:
+                return self._add_orbit(i)
+        elif self._only_below_fermi(i):
+            if present:
+                return self._remove_orbit(i)
+            else:
+                return S.Zero
+        else:
+            if present:
+                hole = Dummy("i", below_fermi=True)
+                return KroneckerDelta(i, hole)*self._remove_orbit(i)
+            else:
+                particle = Dummy("a", above_fermi=True)
+                return KroneckerDelta(i, particle)*self._add_orbit(i)
+
+    def down(self, i):
+        """
+        Performs the action of an annihilation operator.
+
+        Explanation
+        ===========
+
+        If below fermi we try to create a hole,
+        If above fermi we try to remove a particle.
+
+        If general index p we return ``Kronecker(p,i)*self``
+        where ``i`` is a new symbol with restriction above or below.
+
+        Examples
+        ========
+
+        >>> from sympy import Symbol
+        >>> from sympy.physics.secondquant import FKet
+        >>> a = Symbol('a', above_fermi=True)
+        >>> i = Symbol('i', below_fermi=True)
+        >>> p = Symbol('p')
+
+        An annihilator acting on vacuum above fermi vanishes
+
+        >>> FKet([]).down(a)
+        0
+
+        Also below fermi, it vanishes, unless we specify a fermi level > 0
+
+        >>> FKet([]).down(i)
+        0
+        >>> FKet([],4).down(i)
+        FockStateFermionKet((i,))
+
+        """
+        present = i in self.args[0]
+
+        if self._only_above_fermi(i):
+            if present:
+                return self._remove_orbit(i)
+            else:
+                return S.Zero
+
+        elif self._only_below_fermi(i):
+            if present:
+                return S.Zero
+            else:
+                return self._add_orbit(i)
+        else:
+            if present:
+                hole = Dummy("i", below_fermi=True)
+                return KroneckerDelta(i, hole)*self._add_orbit(i)
+            else:
+                particle = Dummy("a", above_fermi=True)
+                return KroneckerDelta(i, particle)*self._remove_orbit(i)
+
+    @classmethod
+    def _only_below_fermi(cls, i):
+        """
+        Tests if given orbit is only below fermi surface.
+
+        If nothing can be concluded we return a conservative False.
+        """
+        if i.is_number:
+            return i <= cls.fermi_level
+        if i.assumptions0.get('below_fermi'):
+            return True
+        return False
+
+    @classmethod
+    def _only_above_fermi(cls, i):
+        """
+        Tests if given orbit is only above fermi surface.
+
+        If fermi level has not been set we return True.
+        If nothing can be concluded we return a conservative False.
+        """
+        if i.is_number:
+            return i > cls.fermi_level
+        if i.assumptions0.get('above_fermi'):
+            return True
+        return not cls.fermi_level
+
+    def _remove_orbit(self, i):
+        """
+        Removes particle/fills hole in orbit i. No input tests performed here.
+        """
+        new_occs = list(self.args[0])
+        pos = new_occs.index(i)
+        del new_occs[pos]
+        if (pos) % 2:
+            return S.NegativeOne*self.__class__(new_occs, self.fermi_level)
+        else:
+            return self.__class__(new_occs, self.fermi_level)
+
+    def _add_orbit(self, i):
+        """
+        Adds particle/creates hole in orbit i. No input tests performed here.
+        """
+        return self.__class__((i,) + self.args[0], self.fermi_level)
+
+    @classmethod
+    def _count_holes(cls, list):
+        """
+        Returns the number of identified hole states in list.
+        """
+        return len([i for i in list if cls._only_below_fermi(i)])
+
+    def _negate_holes(self, list):
+        return tuple([-i if i <= self.fermi_level else i for i in list])
+
+    def __repr__(self):
+        if self.fermi_level:
+            return "FockStateKet(%r, fermi_level=%s)" % (self.args[0], self.fermi_level)
+        else:
+            return "FockStateKet(%r)" % (self.args[0],)
+
+    def _labels(self):
+        return self._negate_holes(self.args[0])
+
+
+class FockStateKet(FockState):
+    """
+    Representation of a ket.
+    """
+    lbracket = '|'
+    rbracket = '>'
+    lbracket_latex = r'\left|'
+    rbracket_latex = r'\right\rangle'
+
+
+class FockStateBra(FockState):
+    """
+    Representation of a bra.
+    """
+    lbracket = '<'
+    rbracket = '|'
+    lbracket_latex = r'\left\langle'
+    rbracket_latex = r'\right|'
+
+    def __mul__(self, other):
+        if isinstance(other, FockStateKet):
+            return InnerProduct(self, other)
+        else:
+            return Expr.__mul__(self, other)
+
+
+class FockStateBosonKet(BosonState, FockStateKet):
+    """
+    Many particle Fock state with a sequence of occupation numbers.
+
+    Occupation numbers can be any integer >= 0.
+
+    Examples
+    ========
+
+    >>> from sympy.physics.secondquant import BKet
+    >>> BKet([1, 2])
+    FockStateBosonKet((1, 2))
+    """
+    def _dagger_(self):
+        return FockStateBosonBra(*self.args)
+
+
+class FockStateBosonBra(BosonState, FockStateBra):
+    """
+    Describes a collection of BosonBra particles.
+
+    Examples
+    ========
+
+    >>> from sympy.physics.secondquant import BBra
+    >>> BBra([1, 2])
+    FockStateBosonBra((1, 2))
+    """
+    def _dagger_(self):
+        return FockStateBosonKet(*self.args)
+
+
+class FockStateFermionKet(FermionState, FockStateKet):
+    """
+    Many-particle Fock state with a sequence of occupied orbits.
+
+    Explanation
+    ===========
+
+    Each state can only have one particle, so we choose to store a list of
+    occupied orbits rather than a tuple with occupation numbers (zeros and ones).
+
+    states below fermi level are holes, and are represented by negative labels
+    in the occupation list.
+
+    For symbolic state labels, the fermi_level caps the number of allowed hole-
+    states.
+
+    Examples
+    ========
+
+    >>> from sympy.physics.secondquant import FKet
+    >>> FKet([1, 2])
+    FockStateFermionKet((1, 2))
+    """
+    def _dagger_(self):
+        return FockStateFermionBra(*self.args)
+
+
+class FockStateFermionBra(FermionState, FockStateBra):
+    """
+    See Also
+    ========
+
+    FockStateFermionKet
+
+    Examples
+    ========
+
+    >>> from sympy.physics.secondquant import FBra
+    >>> FBra([1, 2])
+    FockStateFermionBra((1, 2))
+    """
+    def _dagger_(self):
+        return FockStateFermionKet(*self.args)
+
+BBra = FockStateBosonBra
+BKet = FockStateBosonKet
+FBra = FockStateFermionBra
+FKet = FockStateFermionKet
+
+
+def _apply_Mul(m):
+    """
+    Take a Mul instance with operators and apply them to states.
+
+    Explanation
+    ===========
+
+    This method applies all operators with integer state labels
+    to the actual states.  For symbolic state labels, nothing is done.
+    When inner products of FockStates are encountered (like ),
+    they are converted to instances of InnerProduct.
+
+    This does not currently work on double inner products like,
+    .
+
+    If the argument is not a Mul, it is simply returned as is.
+    """
+    if not isinstance(m, Mul):
+        return m
+    c_part, nc_part = m.args_cnc()
+    n_nc = len(nc_part)
+    if n_nc in (0, 1):
+        return m
+    else:
+        last = nc_part[-1]
+        next_to_last = nc_part[-2]
+        if isinstance(last, FockStateKet):
+            if isinstance(next_to_last, SqOperator):
+                if next_to_last.is_symbolic:
+                    return m
+                else:
+                    result = next_to_last.apply_operator(last)
+                    if result == 0:
+                        return S.Zero
+                    else:
+                        return _apply_Mul(Mul(*(c_part + nc_part[:-2] + [result])))
+            elif isinstance(next_to_last, Pow):
+                if isinstance(next_to_last.base, SqOperator) and \
+                        next_to_last.exp.is_Integer:
+                    if next_to_last.base.is_symbolic:
+                        return m
+                    else:
+                        result = last
+                        for i in range(next_to_last.exp):
+                            result = next_to_last.base.apply_operator(result)
+                            if result == 0:
+                                break
+                        if result == 0:
+                            return S.Zero
+                        else:
+                            return _apply_Mul(Mul(*(c_part + nc_part[:-2] + [result])))
+                else:
+                    return m
+            elif isinstance(next_to_last, FockStateBra):
+                result = InnerProduct(next_to_last, last)
+                if result == 0:
+                    return S.Zero
+                else:
+                    return _apply_Mul(Mul(*(c_part + nc_part[:-2] + [result])))
+            else:
+                return m
+        else:
+            return m
+
+
+def apply_operators(e):
+    """
+    Take a SymPy expression with operators and states and apply the operators.
+
+    Examples
+    ========
+
+    >>> from sympy.physics.secondquant import apply_operators
+    >>> from sympy import sympify
+    >>> apply_operators(sympify(3)+4)
+    7
+    """
+    e = e.expand()
+    muls = e.atoms(Mul)
+    subs_list = [(m, _apply_Mul(m)) for m in iter(muls)]
+    return e.subs(subs_list)
+
+
+class InnerProduct(Basic):
+    """
+    An unevaluated inner product between a bra and ket.
+
+    Explanation
+    ===========
+
+    Currently this class just reduces things to a product of
+    Kronecker Deltas.  In the future, we could introduce abstract
+    states like ``|a>`` and ``|b>``, and leave the inner product unevaluated as
+    ````.
+
+    """
+    is_commutative = True
+
+    def __new__(cls, bra, ket):
+        if not isinstance(bra, FockStateBra):
+            raise TypeError("must be a bra")
+        if not isinstance(ket, FockStateKet):
+            raise TypeError("must be a ket")
+        return cls.eval(bra, ket)
+
+    @classmethod
+    def eval(cls, bra, ket):
+        result = S.One
+        for i, j in zip(bra.args[0], ket.args[0]):
+            result *= KroneckerDelta(i, j)
+            if result == 0:
+                break
+        return result
+
+    @property
+    def bra(self):
+        """Returns the bra part of the state"""
+        return self.args[0]
+
+    @property
+    def ket(self):
+        """Returns the ket part of the state"""
+        return self.args[1]
+
+    def __repr__(self):
+        sbra = repr(self.bra)
+        sket = repr(self.ket)
+        return "%s|%s" % (sbra[:-1], sket[1:])
+
+    def __str__(self):
+        return self.__repr__()
+
+
+def matrix_rep(op, basis):
+    """
+    Find the representation of an operator in a basis.
+
+    Examples
+    ========
+
+    >>> from sympy.physics.secondquant import VarBosonicBasis, B, matrix_rep
+    >>> b = VarBosonicBasis(5)
+    >>> o = B(0)
+    >>> matrix_rep(o, b)
+    Matrix([
+    [0, 1,       0,       0, 0],
+    [0, 0, sqrt(2),       0, 0],
+    [0, 0,       0, sqrt(3), 0],
+    [0, 0,       0,       0, 2],
+    [0, 0,       0,       0, 0]])
+    """
+    a = zeros(len(basis))
+    for i in range(len(basis)):
+        for j in range(len(basis)):
+            a[i, j] = apply_operators(Dagger(basis[i])*op*basis[j])
+    return a
+
+
+class BosonicBasis:
+    """
+    Base class for a basis set of bosonic Fock states.
+    """
+    pass
+
+
+class VarBosonicBasis:
+    """
+    A single state, variable particle number basis set.
+
+    Examples
+    ========
+
+    >>> from sympy.physics.secondquant import VarBosonicBasis
+    >>> b = VarBosonicBasis(5)
+    >>> b
+    [FockState((0,)), FockState((1,)), FockState((2,)),
+     FockState((3,)), FockState((4,))]
+    """
+
+    def __init__(self, n_max):
+        self.n_max = n_max
+        self._build_states()
+
+    def _build_states(self):
+        self.basis = []
+        for i in range(self.n_max):
+            self.basis.append(FockStateBosonKet([i]))
+        self.n_basis = len(self.basis)
+
+    def index(self, state):
+        """
+        Returns the index of state in basis.
+
+        Examples
+        ========
+
+        >>> from sympy.physics.secondquant import VarBosonicBasis
+        >>> b = VarBosonicBasis(3)
+        >>> state = b.state(1)
+        >>> b
+        [FockState((0,)), FockState((1,)), FockState((2,))]
+        >>> state
+        FockStateBosonKet((1,))
+        >>> b.index(state)
+        1
+        """
+        return self.basis.index(state)
+
+    def state(self, i):
+        """
+        The state of a single basis.
+
+        Examples
+        ========
+
+        >>> from sympy.physics.secondquant import VarBosonicBasis
+        >>> b = VarBosonicBasis(5)
+        >>> b.state(3)
+        FockStateBosonKet((3,))
+        """
+        return self.basis[i]
+
+    def __getitem__(self, i):
+        return self.state(i)
+
+    def __len__(self):
+        return len(self.basis)
+
+    def __repr__(self):
+        return repr(self.basis)
+
+
+class FixedBosonicBasis(BosonicBasis):
+    """
+    Fixed particle number basis set.
+
+    Examples
+    ========
+
+    >>> from sympy.physics.secondquant import FixedBosonicBasis
+    >>> b = FixedBosonicBasis(2, 2)
+    >>> state = b.state(1)
+    >>> b
+    [FockState((2, 0)), FockState((1, 1)), FockState((0, 2))]
+    >>> state
+    FockStateBosonKet((1, 1))
+    >>> b.index(state)
+    1
+    """
+    def __init__(self, n_particles, n_levels):
+        self.n_particles = n_particles
+        self.n_levels = n_levels
+        self._build_particle_locations()
+        self._build_states()
+
+    def _build_particle_locations(self):
+        tup = ["i%i" % i for i in range(self.n_particles)]
+        first_loop = "for i0 in range(%i)" % self.n_levels
+        other_loops = ''
+        for cur, prev in zip(tup[1:], tup):
+            temp = "for %s in range(%s + 1) " % (cur, prev)
+            other_loops = other_loops + temp
+        tup_string = "(%s)" % ", ".join(tup)
+        list_comp = "[%s %s %s]" % (tup_string, first_loop, other_loops)
+        result = eval(list_comp)
+        if self.n_particles == 1:
+            result = [(item,) for item in result]
+        self.particle_locations = result
+
+    def _build_states(self):
+        self.basis = []
+        for tuple_of_indices in self.particle_locations:
+            occ_numbers = self.n_levels*[0]
+            for level in tuple_of_indices:
+                occ_numbers[level] += 1
+            self.basis.append(FockStateBosonKet(occ_numbers))
+        self.n_basis = len(self.basis)
+
+    def index(self, state):
+        """Returns the index of state in basis.
+
+        Examples
+        ========
+
+        >>> from sympy.physics.secondquant import FixedBosonicBasis
+        >>> b = FixedBosonicBasis(2, 3)
+        >>> b.index(b.state(3))
+        3
+        """
+        return self.basis.index(state)
+
+    def state(self, i):
+        """Returns the state that lies at index i of the basis
+
+        Examples
+        ========
+
+        >>> from sympy.physics.secondquant import FixedBosonicBasis
+        >>> b = FixedBosonicBasis(2, 3)
+        >>> b.state(3)
+        FockStateBosonKet((1, 0, 1))
+        """
+        return self.basis[i]
+
+    def __getitem__(self, i):
+        return self.state(i)
+
+    def __len__(self):
+        return len(self.basis)
+
+    def __repr__(self):
+        return repr(self.basis)
+
+
+class Commutator(Function):
+    """
+    The Commutator:  [A, B] = A*B - B*A
+
+    The arguments are ordered according to .__cmp__()
+
+    Examples
+    ========
+
+    >>> from sympy import symbols
+    >>> from sympy.physics.secondquant import Commutator
+    >>> A, B = symbols('A,B', commutative=False)
+    >>> Commutator(B, A)
+    -Commutator(A, B)
+
+    Evaluate the commutator with .doit()
+
+    >>> comm = Commutator(A,B); comm
+    Commutator(A, B)
+    >>> comm.doit()
+    A*B - B*A
+
+
+    For two second quantization operators the commutator is evaluated
+    immediately:
+
+    >>> from sympy.physics.secondquant import Fd, F
+    >>> a = symbols('a', above_fermi=True)
+    >>> i = symbols('i', below_fermi=True)
+    >>> p,q = symbols('p,q')
+
+    >>> Commutator(Fd(a),Fd(i))
+    2*NO(CreateFermion(a)*CreateFermion(i))
+
+    But for more complicated expressions, the evaluation is triggered by
+    a call to .doit()
+
+    >>> comm = Commutator(Fd(p)*Fd(q),F(i)); comm
+    Commutator(CreateFermion(p)*CreateFermion(q), AnnihilateFermion(i))
+    >>> comm.doit(wicks=True)
+    -KroneckerDelta(i, p)*CreateFermion(q) +
+     KroneckerDelta(i, q)*CreateFermion(p)
+
+    """
+
+    is_commutative = False
+
+    @classmethod
+    def eval(cls, a, b):
+        """
+        The Commutator [A,B] is on canonical form if A < B.
+
+        Examples
+        ========
+
+        >>> from sympy.physics.secondquant import Commutator, F, Fd
+        >>> from sympy.abc import x
+        >>> c1 = Commutator(F(x), Fd(x))
+        >>> c2 = Commutator(Fd(x), F(x))
+        >>> Commutator.eval(c1, c2)
+        0
+        """
+        if not (a and b):
+            return S.Zero
+        if a == b:
+            return S.Zero
+        if a.is_commutative or b.is_commutative:
+            return S.Zero
+
+        #
+        # [A+B,C]  ->  [A,C] + [B,C]
+        #
+        a = a.expand()
+        if isinstance(a, Add):
+            return Add(*[cls(term, b) for term in a.args])
+        b = b.expand()
+        if isinstance(b, Add):
+            return Add(*[cls(a, term) for term in b.args])
+
+        #
+        # [xA,yB]  ->  xy*[A,B]
+        #
+        ca, nca = a.args_cnc()
+        cb, ncb = b.args_cnc()
+        c_part = list(ca) + list(cb)
+        if c_part:
+            return Mul(Mul(*c_part), cls(Mul._from_args(nca), Mul._from_args(ncb)))
+
+        #
+        # single second quantization operators
+        #
+        if isinstance(a, BosonicOperator) and isinstance(b, BosonicOperator):
+            if isinstance(b, CreateBoson) and isinstance(a, AnnihilateBoson):
+                return KroneckerDelta(a.state, b.state)
+            if isinstance(a, CreateBoson) and isinstance(b, AnnihilateBoson):
+                return S.NegativeOne*KroneckerDelta(a.state, b.state)
+            else:
+                return S.Zero
+        if isinstance(a, FermionicOperator) and isinstance(b, FermionicOperator):
+            return wicks(a*b) - wicks(b*a)
+
+        #
+        # Canonical ordering of arguments
+        #
+        if a.sort_key() > b.sort_key():
+            return S.NegativeOne*cls(b, a)
+
+    def doit(self, **hints):
+        """
+        Enables the computation of complex expressions.
+
+        Examples
+        ========
+
+        >>> from sympy.physics.secondquant import Commutator, F, Fd
+        >>> from sympy import symbols
+        >>> i, j = symbols('i,j', below_fermi=True)
+        >>> a, b = symbols('a,b', above_fermi=True)
+        >>> c = Commutator(Fd(a)*F(i),Fd(b)*F(j))
+        >>> c.doit(wicks=True)
+        0
+        """
+        a = self.args[0]
+        b = self.args[1]
+
+        if hints.get("wicks"):
+            a = a.doit(**hints)
+            b = b.doit(**hints)
+            try:
+                return wicks(a*b) - wicks(b*a)
+            except ContractionAppliesOnlyToFermions:
+                pass
+            except WicksTheoremDoesNotApply:
+                pass
+
+        return (a*b - b*a).doit(**hints)
+
+    def __repr__(self):
+        return "Commutator(%s,%s)" % (self.args[0], self.args[1])
+
+    def __str__(self):
+        return "[%s,%s]" % (self.args[0], self.args[1])
+
+    def _latex(self, printer):
+        return "\\left[%s,%s\\right]" % tuple([
+            printer._print(arg) for arg in self.args])
+
+
+class NO(Expr):
+    """
+    This Object is used to represent normal ordering brackets.
+
+    i.e.  {abcd}  sometimes written  :abcd:
+
+    Explanation
+    ===========
+
+    Applying the function NO(arg) to an argument means that all operators in
+    the argument will be assumed to anticommute, and have vanishing
+    contractions.  This allows an immediate reordering to canonical form
+    upon object creation.
+
+    Examples
+    ========
+
+    >>> from sympy import symbols
+    >>> from sympy.physics.secondquant import NO, F, Fd
+    >>> p,q = symbols('p,q')
+    >>> NO(Fd(p)*F(q))
+    NO(CreateFermion(p)*AnnihilateFermion(q))
+    >>> NO(F(q)*Fd(p))
+    -NO(CreateFermion(p)*AnnihilateFermion(q))
+
+
+    Note
+    ====
+
+    If you want to generate a normal ordered equivalent of an expression, you
+    should use the function wicks().  This class only indicates that all
+    operators inside the brackets anticommute, and have vanishing contractions.
+    Nothing more, nothing less.
+
+    """
+    is_commutative = False
+
+    def __new__(cls, arg):
+        """
+        Use anticommutation to get canonical form of operators.
+
+        Explanation
+        ===========
+
+        Employ associativity of normal ordered product: {ab{cd}} = {abcd}
+        but note that {ab}{cd} /= {abcd}.
+
+        We also employ distributivity: {ab + cd} = {ab} + {cd}.
+
+        Canonical form also implies expand() {ab(c+d)} = {abc} + {abd}.
+
+        """
+
+        # {ab + cd} = {ab} + {cd}
+        arg = sympify(arg)
+        arg = arg.expand()
+        if arg.is_Add:
+            return Add(*[ cls(term) for term in arg.args])
+
+        if arg.is_Mul:
+
+            # take coefficient outside of normal ordering brackets
+            c_part, seq = arg.args_cnc()
+            if c_part:
+                coeff = Mul(*c_part)
+                if not seq:
+                    return coeff
+            else:
+                coeff = S.One
+
+            # {ab{cd}} = {abcd}
+            newseq = []
+            foundit = False
+            for fac in seq:
+                if isinstance(fac, NO):
+                    newseq.extend(fac.args)
+                    foundit = True
+                else:
+                    newseq.append(fac)
+            if foundit:
+                return coeff*cls(Mul(*newseq))
+
+            # We assume that the user don't mix B and F operators
+            if isinstance(seq[0], BosonicOperator):
+                raise NotImplementedError
+
+            try:
+                newseq, sign = _sort_anticommuting_fermions(seq)
+            except ViolationOfPauliPrinciple:
+                return S.Zero
+
+            if sign % 2:
+                return (S.NegativeOne*coeff)*cls(Mul(*newseq))
+            elif sign:
+                return coeff*cls(Mul(*newseq))
+            else:
+                pass  # since sign==0, no permutations was necessary
+
+            # if we couldn't do anything with Mul object, we just
+            # mark it as normal ordered
+            if coeff != S.One:
+                return coeff*cls(Mul(*newseq))
+            return Expr.__new__(cls, Mul(*newseq))
+
+        if isinstance(arg, NO):
+            return arg
+
+        # if object was not Mul or Add, normal ordering does not apply
+        return arg
+
+    @property
+    def has_q_creators(self):
+        """
+        Return 0 if the leftmost argument of the first argument is a not a
+        q_creator, else 1 if it is above fermi or -1 if it is below fermi.
+
+        Examples
+        ========
+
+        >>> from sympy import symbols
+        >>> from sympy.physics.secondquant import NO, F, Fd
+
+        >>> a = symbols('a', above_fermi=True)
+        >>> i = symbols('i', below_fermi=True)
+        >>> NO(Fd(a)*Fd(i)).has_q_creators
+        1
+        >>> NO(F(i)*F(a)).has_q_creators
+        -1
+        >>> NO(Fd(i)*F(a)).has_q_creators           #doctest: +SKIP
+        0
+
+        """
+        return self.args[0].args[0].is_q_creator
+
+    @property
+    def has_q_annihilators(self):
+        """
+        Return 0 if the rightmost argument of the first argument is a not a
+        q_annihilator, else 1 if it is above fermi or -1 if it is below fermi.
+
+        Examples
+        ========
+
+        >>> from sympy import symbols
+        >>> from sympy.physics.secondquant import NO, F, Fd
+
+        >>> a = symbols('a', above_fermi=True)
+        >>> i = symbols('i', below_fermi=True)
+        >>> NO(Fd(a)*Fd(i)).has_q_annihilators
+        -1
+        >>> NO(F(i)*F(a)).has_q_annihilators
+        1
+        >>> NO(Fd(a)*F(i)).has_q_annihilators
+        0
+
+        """
+        return self.args[0].args[-1].is_q_annihilator
+
+    def doit(self, **hints):
+        """
+        Either removes the brackets or enables complex computations
+        in its arguments.
+
+        Examples
+        ========
+
+        >>> from sympy.physics.secondquant import NO, Fd, F
+        >>> from textwrap import fill
+        >>> from sympy import symbols, Dummy
+        >>> p,q = symbols('p,q', cls=Dummy)
+        >>> print(fill(str(NO(Fd(p)*F(q)).doit())))
+        KroneckerDelta(_a, _p)*KroneckerDelta(_a,
+        _q)*CreateFermion(_a)*AnnihilateFermion(_a) + KroneckerDelta(_a,
+        _p)*KroneckerDelta(_i, _q)*CreateFermion(_a)*AnnihilateFermion(_i) -
+        KroneckerDelta(_a, _q)*KroneckerDelta(_i,
+        _p)*AnnihilateFermion(_a)*CreateFermion(_i) - KroneckerDelta(_i,
+        _p)*KroneckerDelta(_i, _q)*AnnihilateFermion(_i)*CreateFermion(_i)
+        """
+        if hints.get("remove_brackets", True):
+            return self._remove_brackets()
+        else:
+            return self.__new__(type(self), self.args[0].doit(**hints))
+
+    def _remove_brackets(self):
+        """
+        Returns the sorted string without normal order brackets.
+
+        The returned string have the property that no nonzero
+        contractions exist.
+        """
+
+        # check if any creator is also an annihilator
+        subslist = []
+        for i in self.iter_q_creators():
+            if self[i].is_q_annihilator:
+                assume = self[i].state.assumptions0
+
+                # only operators with a dummy index can be split in two terms
+                if isinstance(self[i].state, Dummy):
+
+                    # create indices with fermi restriction
+                    assume.pop("above_fermi", None)
+                    assume["below_fermi"] = True
+                    below = Dummy('i', **assume)
+                    assume.pop("below_fermi", None)
+                    assume["above_fermi"] = True
+                    above = Dummy('a', **assume)
+
+                    cls = type(self[i])
+                    split = (
+                        self[i].__new__(cls, below)
+                        * KroneckerDelta(below, self[i].state)
+                        + self[i].__new__(cls, above)
+                        * KroneckerDelta(above, self[i].state)
+                    )
+                    subslist.append((self[i], split))
+                else:
+                    raise SubstitutionOfAmbigousOperatorFailed(self[i])
+        if subslist:
+            result = NO(self.subs(subslist))
+            if isinstance(result, Add):
+                return Add(*[term.doit() for term in result.args])
+        else:
+            return self.args[0]
+
+    def _expand_operators(self):
+        """
+        Returns a sum of NO objects that contain no ambiguous q-operators.
+
+        Explanation
+        ===========
+
+        If an index q has range both above and below fermi, the operator F(q)
+        is ambiguous in the sense that it can be both a q-creator and a q-annihilator.
+        If q is dummy, it is assumed to be a summation variable and this method
+        rewrites it into a sum of NO terms with unambiguous operators:
+
+        {Fd(p)*F(q)} = {Fd(a)*F(b)} + {Fd(a)*F(i)} + {Fd(j)*F(b)} -{F(i)*Fd(j)}
+
+        where a,b are above and i,j are below fermi level.
+        """
+        return NO(self._remove_brackets)
+
+    def __getitem__(self, i):
+        if isinstance(i, slice):
+            indices = i.indices(len(self))
+            return [self.args[0].args[i] for i in range(*indices)]
+        else:
+            return self.args[0].args[i]
+
+    def __len__(self):
+        return len(self.args[0].args)
+
+    def iter_q_annihilators(self):
+        """
+        Iterates over the annihilation operators.
+
+        Examples
+        ========
+
+        >>> from sympy import symbols
+        >>> i, j = symbols('i j', below_fermi=True)
+        >>> a, b = symbols('a b', above_fermi=True)
+        >>> from sympy.physics.secondquant import NO, F, Fd
+        >>> no = NO(Fd(a)*F(i)*F(b)*Fd(j))
+
+        >>> no.iter_q_creators()
+        
+        >>> list(no.iter_q_creators())
+        [0, 1]
+        >>> list(no.iter_q_annihilators())
+        [3, 2]
+
+        """
+        ops = self.args[0].args
+        iter = range(len(ops) - 1, -1, -1)
+        for i in iter:
+            if ops[i].is_q_annihilator:
+                yield i
+            else:
+                break
+
+    def iter_q_creators(self):
+        """
+        Iterates over the creation operators.
+
+        Examples
+        ========
+
+        >>> from sympy import symbols
+        >>> i, j = symbols('i j', below_fermi=True)
+        >>> a, b = symbols('a b', above_fermi=True)
+        >>> from sympy.physics.secondquant import NO, F, Fd
+        >>> no = NO(Fd(a)*F(i)*F(b)*Fd(j))
+
+        >>> no.iter_q_creators()
+        
+        >>> list(no.iter_q_creators())
+        [0, 1]
+        >>> list(no.iter_q_annihilators())
+        [3, 2]
+
+        """
+
+        ops = self.args[0].args
+        iter = range(0, len(ops))
+        for i in iter:
+            if ops[i].is_q_creator:
+                yield i
+            else:
+                break
+
+    def get_subNO(self, i):
+        """
+        Returns a NO() without FermionicOperator at index i.
+
+        Examples
+        ========
+
+        >>> from sympy import symbols
+        >>> from sympy.physics.secondquant import F, NO
+        >>> p, q, r = symbols('p,q,r')
+
+        >>> NO(F(p)*F(q)*F(r)).get_subNO(1)
+        NO(AnnihilateFermion(p)*AnnihilateFermion(r))
+
+        """
+        arg0 = self.args[0]  # it's a Mul by definition of how it's created
+        mul = arg0._new_rawargs(*(arg0.args[:i] + arg0.args[i + 1:]))
+        return NO(mul)
+
+    def _latex(self, printer):
+        return "\\left\\{%s\\right\\}" % printer._print(self.args[0])
+
+    def __repr__(self):
+        return "NO(%s)" % self.args[0]
+
+    def __str__(self):
+        return ":%s:" % self.args[0]
+
+
+def contraction(a, b):
+    """
+    Calculates contraction of Fermionic operators a and b.
+
+    Examples
+    ========
+
+    >>> from sympy import symbols
+    >>> from sympy.physics.secondquant import F, Fd, contraction
+    >>> p, q = symbols('p,q')
+    >>> a, b = symbols('a,b', above_fermi=True)
+    >>> i, j = symbols('i,j', below_fermi=True)
+
+    A contraction is non-zero only if a quasi-creator is to the right of a
+    quasi-annihilator:
+
+    >>> contraction(F(a),Fd(b))
+    KroneckerDelta(a, b)
+    >>> contraction(Fd(i),F(j))
+    KroneckerDelta(i, j)
+
+    For general indices a non-zero result restricts the indices to below/above
+    the fermi surface:
+
+    >>> contraction(Fd(p),F(q))
+    KroneckerDelta(_i, q)*KroneckerDelta(p, q)
+    >>> contraction(F(p),Fd(q))
+    KroneckerDelta(_a, q)*KroneckerDelta(p, q)
+
+    Two creators or two annihilators always vanishes:
+
+    >>> contraction(F(p),F(q))
+    0
+    >>> contraction(Fd(p),Fd(q))
+    0
+
+    """
+    if isinstance(b, FermionicOperator) and isinstance(a, FermionicOperator):
+        if isinstance(a, AnnihilateFermion) and isinstance(b, CreateFermion):
+            if b.state.assumptions0.get("below_fermi"):
+                return S.Zero
+            if a.state.assumptions0.get("below_fermi"):
+                return S.Zero
+            if b.state.assumptions0.get("above_fermi"):
+                return KroneckerDelta(a.state, b.state)
+            if a.state.assumptions0.get("above_fermi"):
+                return KroneckerDelta(a.state, b.state)
+
+            return (KroneckerDelta(a.state, b.state)*
+                    KroneckerDelta(b.state, Dummy('a', above_fermi=True)))
+        if isinstance(b, AnnihilateFermion) and isinstance(a, CreateFermion):
+            if b.state.assumptions0.get("above_fermi"):
+                return S.Zero
+            if a.state.assumptions0.get("above_fermi"):
+                return S.Zero
+            if b.state.assumptions0.get("below_fermi"):
+                return KroneckerDelta(a.state, b.state)
+            if a.state.assumptions0.get("below_fermi"):
+                return KroneckerDelta(a.state, b.state)
+
+            return (KroneckerDelta(a.state, b.state)*
+                    KroneckerDelta(b.state, Dummy('i', below_fermi=True)))
+
+        # vanish if 2xAnnihilator or 2xCreator
+        return S.Zero
+
+    else:
+        #not fermion operators
+        t = ( isinstance(i, FermionicOperator) for i in (a, b) )
+        raise ContractionAppliesOnlyToFermions(*t)
+
+
+def _sqkey(sq_operator):
+    """Generates key for canonical sorting of SQ operators."""
+    return sq_operator._sortkey()
+
+
+def _sort_anticommuting_fermions(string1, key=_sqkey):
+    """Sort fermionic operators to canonical order, assuming all pairs anticommute.
+
+    Explanation
+    ===========
+
+    Uses a bidirectional bubble sort.  Items in string1 are not referenced
+    so in principle they may be any comparable objects.   The sorting depends on the
+    operators '>' and '=='.
+
+    If the Pauli principle is violated, an exception is raised.
+
+    Returns
+    =======
+
+    tuple (sorted_str, sign)
+
+    sorted_str: list containing the sorted operators
+    sign: int telling how many times the sign should be changed
+          (if sign==0 the string was already sorted)
+    """
+
+    verified = False
+    sign = 0
+    rng = list(range(len(string1) - 1))
+    rev = list(range(len(string1) - 3, -1, -1))
+
+    keys = list(map(key, string1))
+    key_val = dict(list(zip(keys, string1)))
+
+    while not verified:
+        verified = True
+        for i in rng:
+            left = keys[i]
+            right = keys[i + 1]
+            if left == right:
+                raise ViolationOfPauliPrinciple([left, right])
+            if left > right:
+                verified = False
+                keys[i:i + 2] = [right, left]
+                sign = sign + 1
+        if verified:
+            break
+        for i in rev:
+            left = keys[i]
+            right = keys[i + 1]
+            if left == right:
+                raise ViolationOfPauliPrinciple([left, right])
+            if left > right:
+                verified = False
+                keys[i:i + 2] = [right, left]
+                sign = sign + 1
+    string1 = [ key_val[k] for k in keys ]
+    return (string1, sign)
+
+
+def evaluate_deltas(e):
+    """
+    We evaluate KroneckerDelta symbols in the expression assuming Einstein summation.
+
+    Explanation
+    ===========
+
+    If one index is repeated it is summed over and in effect substituted with
+    the other one. If both indices are repeated we substitute according to what
+    is the preferred index.  this is determined by
+    KroneckerDelta.preferred_index and KroneckerDelta.killable_index.
+
+    In case there are no possible substitutions or if a substitution would
+    imply a loss of information, nothing is done.
+
+    In case an index appears in more than one KroneckerDelta, the resulting
+    substitution depends on the order of the factors.  Since the ordering is platform
+    dependent, the literal expression resulting from this function may be hard to
+    predict.
+
+    Examples
+    ========
+
+    We assume the following:
+
+    >>> from sympy import symbols, Function, Dummy, KroneckerDelta
+    >>> from sympy.physics.secondquant import evaluate_deltas
+    >>> i,j = symbols('i j', below_fermi=True, cls=Dummy)
+    >>> a,b = symbols('a b', above_fermi=True, cls=Dummy)
+    >>> p,q = symbols('p q', cls=Dummy)
+    >>> f = Function('f')
+    >>> t = Function('t')
+
+    The order of preference for these indices according to KroneckerDelta is
+    (a, b, i, j, p, q).
+
+    Trivial cases:
+
+    >>> evaluate_deltas(KroneckerDelta(i,j)*f(i))       # d_ij f(i) -> f(j)
+    f(_j)
+    >>> evaluate_deltas(KroneckerDelta(i,j)*f(j))       # d_ij f(j) -> f(i)
+    f(_i)
+    >>> evaluate_deltas(KroneckerDelta(i,p)*f(p))       # d_ip f(p) -> f(i)
+    f(_i)
+    >>> evaluate_deltas(KroneckerDelta(q,p)*f(p))       # d_qp f(p) -> f(q)
+    f(_q)
+    >>> evaluate_deltas(KroneckerDelta(q,p)*f(q))       # d_qp f(q) -> f(p)
+    f(_p)
+
+    More interesting cases:
+
+    >>> evaluate_deltas(KroneckerDelta(i,p)*t(a,i)*f(p,q))
+    f(_i, _q)*t(_a, _i)
+    >>> evaluate_deltas(KroneckerDelta(a,p)*t(a,i)*f(p,q))
+    f(_a, _q)*t(_a, _i)
+    >>> evaluate_deltas(KroneckerDelta(p,q)*f(p,q))
+    f(_p, _p)
+
+    Finally, here are some cases where nothing is done, because that would
+    imply a loss of information:
+
+    >>> evaluate_deltas(KroneckerDelta(i,p)*f(q))
+    f(_q)*KroneckerDelta(_i, _p)
+    >>> evaluate_deltas(KroneckerDelta(i,p)*f(i))
+    f(_i)*KroneckerDelta(_i, _p)
+    """
+
+    # We treat Deltas only in mul objects
+    # for general function objects we don't evaluate KroneckerDeltas in arguments,
+    # but here we hard code exceptions to this rule
+    accepted_functions = (
+        Add,
+    )
+    if isinstance(e, accepted_functions):
+        return e.func(*[evaluate_deltas(arg) for arg in e.args])
+
+    elif isinstance(e, Mul):
+        # find all occurrences of delta function and count each index present in
+        # expression.
+        deltas = []
+        indices = {}
+        for i in e.args:
+            for s in i.free_symbols:
+                if s in indices:
+                    indices[s] += 1
+                else:
+                    indices[s] = 0  # geek counting simplifies logic below
+            if isinstance(i, KroneckerDelta):
+                deltas.append(i)
+
+        for d in deltas:
+            # If we do something, and there are more deltas, we should recurse
+            # to treat the resulting expression properly
+            if d.killable_index.is_Symbol and indices[d.killable_index]:
+                e = e.subs(d.killable_index, d.preferred_index)
+                if len(deltas) > 1:
+                    return evaluate_deltas(e)
+            elif (d.preferred_index.is_Symbol and indices[d.preferred_index]
+                  and d.indices_contain_equal_information):
+                e = e.subs(d.preferred_index, d.killable_index)
+                if len(deltas) > 1:
+                    return evaluate_deltas(e)
+            else:
+                pass
+
+        return e
+    # nothing to do, maybe we hit a Symbol or a number
+    else:
+        return e
+
+
+def substitute_dummies(expr, new_indices=False, pretty_indices={}):
+    """
+    Collect terms by substitution of dummy variables.
+
+    Explanation
+    ===========
+
+    This routine allows simplification of Add expressions containing terms
+    which differ only due to dummy variables.
+
+    The idea is to substitute all dummy variables consistently depending on
+    the structure of the term.  For each term, we obtain a sequence of all
+    dummy variables, where the order is determined by the index range, what
+    factors the index belongs to and its position in each factor.  See
+    _get_ordered_dummies() for more information about the sorting of dummies.
+    The index sequence is then substituted consistently in each term.
+
+    Examples
+    ========
+
+    >>> from sympy import symbols, Function, Dummy
+    >>> from sympy.physics.secondquant import substitute_dummies
+    >>> a,b,c,d = symbols('a b c d', above_fermi=True, cls=Dummy)
+    >>> i,j = symbols('i j', below_fermi=True, cls=Dummy)
+    >>> f = Function('f')
+
+    >>> expr = f(a,b) + f(c,d); expr
+    f(_a, _b) + f(_c, _d)
+
+    Since a, b, c and d are equivalent summation indices, the expression can be
+    simplified to a single term (for which the dummy indices are still summed over)
+
+    >>> substitute_dummies(expr)
+    2*f(_a, _b)
+
+
+    Controlling output:
+
+    By default the dummy symbols that are already present in the expression
+    will be reused in a different permutation.  However, if new_indices=True,
+    new dummies will be generated and inserted.  The keyword 'pretty_indices'
+    can be used to control this generation of new symbols.
+
+    By default the new dummies will be generated on the form i_1, i_2, a_1,
+    etc.  If you supply a dictionary with key:value pairs in the form:
+
+        { index_group: string_of_letters }
+
+    The letters will be used as labels for the new dummy symbols.  The
+    index_groups must be one of 'above', 'below' or 'general'.
+
+    >>> expr = f(a,b,i,j)
+    >>> my_dummies = { 'above':'st', 'below':'uv' }
+    >>> substitute_dummies(expr, new_indices=True, pretty_indices=my_dummies)
+    f(_s, _t, _u, _v)
+
+    If we run out of letters, or if there is no keyword for some index_group
+    the default dummy generator will be used as a fallback:
+
+    >>> p,q = symbols('p q', cls=Dummy)  # general indices
+    >>> expr = f(p,q)
+    >>> substitute_dummies(expr, new_indices=True, pretty_indices=my_dummies)
+    f(_p_0, _p_1)
+
+    """
+
+    # setup the replacing dummies
+    if new_indices:
+        letters_above = pretty_indices.get('above', "")
+        letters_below = pretty_indices.get('below', "")
+        letters_general = pretty_indices.get('general', "")
+        len_above = len(letters_above)
+        len_below = len(letters_below)
+        len_general = len(letters_general)
+
+        def _i(number):
+            try:
+                return letters_below[number]
+            except IndexError:
+                return 'i_' + str(number - len_below)
+
+        def _a(number):
+            try:
+                return letters_above[number]
+            except IndexError:
+                return 'a_' + str(number - len_above)
+
+        def _p(number):
+            try:
+                return letters_general[number]
+            except IndexError:
+                return 'p_' + str(number - len_general)
+
+    aboves = []
+    belows = []
+    generals = []
+
+    dummies = expr.atoms(Dummy)
+    if not new_indices:
+        dummies = sorted(dummies, key=default_sort_key)
+
+    # generate lists with the dummies we will insert
+    a = i = p = 0
+    for d in dummies:
+        assum = d.assumptions0
+
+        if assum.get("above_fermi"):
+            if new_indices:
+                sym = _a(a)
+                a += 1
+            l1 = aboves
+        elif assum.get("below_fermi"):
+            if new_indices:
+                sym = _i(i)
+                i += 1
+            l1 = belows
+        else:
+            if new_indices:
+                sym = _p(p)
+                p += 1
+            l1 = generals
+
+        if new_indices:
+            l1.append(Dummy(sym, **assum))
+        else:
+            l1.append(d)
+
+    expr = expr.expand()
+    terms = Add.make_args(expr)
+    new_terms = []
+    for term in terms:
+        i = iter(belows)
+        a = iter(aboves)
+        p = iter(generals)
+        ordered = _get_ordered_dummies(term)
+        subsdict = {}
+        for d in ordered:
+            if d.assumptions0.get('below_fermi'):
+                subsdict[d] = next(i)
+            elif d.assumptions0.get('above_fermi'):
+                subsdict[d] = next(a)
+            else:
+                subsdict[d] = next(p)
+        subslist = []
+        final_subs = []
+        for k, v in subsdict.items():
+            if k == v:
+                continue
+            if v in subsdict:
+                # We check if the sequence of substitutions end quickly.  In
+                # that case, we can avoid temporary symbols if we ensure the
+                # correct substitution order.
+                if subsdict[v] in subsdict:
+                    # (x, y) -> (y, x),  we need a temporary variable
+                    x = Dummy('x')
+                    subslist.append((k, x))
+                    final_subs.append((x, v))
+                else:
+                    # (x, y) -> (y, a),  x->y must be done last
+                    # but before temporary variables are resolved
+                    final_subs.insert(0, (k, v))
+            else:
+                subslist.append((k, v))
+        subslist.extend(final_subs)
+        new_terms.append(term.subs(subslist))
+    return Add(*new_terms)
+
+
+class KeyPrinter(StrPrinter):
+    """Printer for which only equal objects are equal in print"""
+    def _print_Dummy(self, expr):
+        return "(%s_%i)" % (expr.name, expr.dummy_index)
+
+
+def __kprint(expr):
+    p = KeyPrinter()
+    return p.doprint(expr)
+
+
+def _get_ordered_dummies(mul, verbose=False):
+    """Returns all dummies in the mul sorted in canonical order.
+
+    Explanation
+    ===========
+
+    The purpose of the canonical ordering is that dummies can be substituted
+    consistently across terms with the result that equivalent terms can be
+    simplified.
+
+    It is not possible to determine if two terms are equivalent based solely on
+    the dummy order.  However, a consistent substitution guided by the ordered
+    dummies should lead to trivially (non-)equivalent terms, thereby revealing
+    the equivalence.  This also means that if two terms have identical sequences of
+    dummies, the (non-)equivalence should already be apparent.
+
+    Strategy
+    --------
+
+    The canonical order is given by an arbitrary sorting rule.  A sort key
+    is determined for each dummy as a tuple that depends on all factors where
+    the index is present.  The dummies are thereby sorted according to the
+    contraction structure of the term, instead of sorting based solely on the
+    dummy symbol itself.
+
+    After all dummies in the term has been assigned a key, we check for identical
+    keys, i.e. unorderable dummies.  If any are found, we call a specialized
+    method, _determine_ambiguous(), that will determine a unique order based
+    on recursive calls to _get_ordered_dummies().
+
+    Key description
+    ---------------
+
+    A high level description of the sort key:
+
+        1. Range of the dummy index
+        2. Relation to external (non-dummy) indices
+        3. Position of the index in the first factor
+        4. Position of the index in the second factor
+
+    The sort key is a tuple with the following components:
+
+        1. A single character indicating the range of the dummy (above, below
+           or general.)
+        2. A list of strings with fully masked string representations of all
+           factors where the dummy is present.  By masked, we mean that dummies
+           are represented by a symbol to indicate either below fermi, above or
+           general.  No other information is displayed about the dummies at
+           this point.  The list is sorted stringwise.
+        3. An integer number indicating the position of the index, in the first
+           factor as sorted in 2.
+        4. An integer number indicating the position of the index, in the second
+           factor as sorted in 2.
+
+    If a factor is either of type AntiSymmetricTensor or SqOperator, the index
+    position in items 3 and 4 is indicated as 'upper' or 'lower' only.
+    (Creation operators are considered upper and annihilation operators lower.)
+
+    If the masked factors are identical, the two factors cannot be ordered
+    unambiguously in item 2.  In this case, items 3, 4 are left out.  If several
+    indices are contracted between the unorderable factors, it will be handled by
+    _determine_ambiguous()
+
+
+    """
+    # setup dicts to avoid repeated calculations in key()
+    args = Mul.make_args(mul)
+    fac_dum = { fac: fac.atoms(Dummy) for fac in args }
+    fac_repr = { fac: __kprint(fac) for fac in args }
+    all_dums = set().union(*fac_dum.values())
+    mask = {}
+    for d in all_dums:
+        if d.assumptions0.get('below_fermi'):
+            mask[d] = '0'
+        elif d.assumptions0.get('above_fermi'):
+            mask[d] = '1'
+        else:
+            mask[d] = '2'
+    dum_repr = {d: __kprint(d) for d in all_dums}
+
+    def _key(d):
+        dumstruct = [ fac for fac in fac_dum if d in fac_dum[fac] ]
+        other_dums = set().union(*[fac_dum[fac] for fac in dumstruct])
+        fac = dumstruct[-1]
+        if other_dums is fac_dum[fac]:
+            other_dums = fac_dum[fac].copy()
+        other_dums.remove(d)
+        masked_facs = [ fac_repr[fac] for fac in dumstruct ]
+        for d2 in other_dums:
+            masked_facs = [ fac.replace(dum_repr[d2], mask[d2])
+                    for fac in masked_facs ]
+        all_masked = [ fac.replace(dum_repr[d], mask[d])
+                       for fac in masked_facs ]
+        masked_facs = dict(list(zip(dumstruct, masked_facs)))
+
+        # dummies for which the ordering cannot be determined
+        if has_dups(all_masked):
+            all_masked.sort()
+            return mask[d], tuple(all_masked)  # positions are ambiguous
+
+        # sort factors according to fully masked strings
+        keydict = dict(list(zip(dumstruct, all_masked)))
+        dumstruct.sort(key=lambda x: keydict[x])
+        all_masked.sort()
+
+        pos_val = []
+        for fac in dumstruct:
+            if isinstance(fac, AntiSymmetricTensor):
+                if d in fac.upper:
+                    pos_val.append('u')
+                if d in fac.lower:
+                    pos_val.append('l')
+            elif isinstance(fac, Creator):
+                pos_val.append('u')
+            elif isinstance(fac, Annihilator):
+                pos_val.append('l')
+            elif isinstance(fac, NO):
+                ops = [ op for op in fac if op.has(d) ]
+                for op in ops:
+                    if isinstance(op, Creator):
+                        pos_val.append('u')
+                    else:
+                        pos_val.append('l')
+            else:
+                # fallback to position in string representation
+                facpos = -1
+                while 1:
+                    facpos = masked_facs[fac].find(dum_repr[d], facpos + 1)
+                    if facpos == -1:
+                        break
+                    pos_val.append(facpos)
+        return (mask[d], tuple(all_masked), pos_val[0], pos_val[-1])
+    dumkey = dict(list(zip(all_dums, list(map(_key, all_dums)))))
+    result = sorted(all_dums, key=lambda x: dumkey[x])
+    if has_dups(iter(dumkey.values())):
+        # We have ambiguities
+        unordered = defaultdict(set)
+        for d, k in dumkey.items():
+            unordered[k].add(d)
+        for k in [ k for k in unordered if len(unordered[k]) < 2 ]:
+            del unordered[k]
+
+        unordered = [ unordered[k] for k in sorted(unordered) ]
+        result = _determine_ambiguous(mul, result, unordered)
+    return result
+
+
+def _determine_ambiguous(term, ordered, ambiguous_groups):
+    # We encountered a term for which the dummy substitution is ambiguous.
+    # This happens for terms with 2 or more contractions between factors that
+    # cannot be uniquely ordered independent of summation indices.  For
+    # example:
+    #
+    # Sum(p, q) v^{p, .}_{q, .}v^{q, .}_{p, .}
+    #
+    # Assuming that the indices represented by . are dummies with the
+    # same range, the factors cannot be ordered, and there is no
+    # way to determine a consistent ordering of p and q.
+    #
+    # The strategy employed here, is to relabel all unambiguous dummies with
+    # non-dummy symbols and call _get_ordered_dummies again.  This procedure is
+    # applied to the entire term so there is a possibility that
+    # _determine_ambiguous() is called again from a deeper recursion level.
+
+    # break recursion if there are no ordered dummies
+    all_ambiguous = set()
+    for dummies in ambiguous_groups:
+        all_ambiguous |= dummies
+    all_ordered = set(ordered) - all_ambiguous
+    if not all_ordered:
+        # FIXME: If we arrive here, there are no ordered dummies. A method to
+        # handle this needs to be implemented.  In order to return something
+        # useful nevertheless, we choose arbitrarily the first dummy and
+        # determine the rest from this one.  This method is dependent on the
+        # actual dummy labels which violates an assumption for the
+        # canonicalization procedure.  A better implementation is needed.
+        group = [ d for d in ordered if d in ambiguous_groups[0] ]
+        d = group[0]
+        all_ordered.add(d)
+        ambiguous_groups[0].remove(d)
+
+    stored_counter = _symbol_factory._counter
+    subslist = []
+    for d in [ d for d in ordered if d in all_ordered ]:
+        nondum = _symbol_factory._next()
+        subslist.append((d, nondum))
+    newterm = term.subs(subslist)
+    neworder = _get_ordered_dummies(newterm)
+    _symbol_factory._set_counter(stored_counter)
+
+    # update ordered list with new information
+    for group in ambiguous_groups:
+        ordered_group = [ d for d in neworder if d in group ]
+        ordered_group.reverse()
+        result = []
+        for d in ordered:
+            if d in group:
+                result.append(ordered_group.pop())
+            else:
+                result.append(d)
+        ordered = result
+    return ordered
+
+
+class _SymbolFactory:
+    def __init__(self, label):
+        self._counterVar = 0
+        self._label = label
+
+    def _set_counter(self, value):
+        """
+        Sets counter to value.
+        """
+        self._counterVar = value
+
+    @property
+    def _counter(self):
+        """
+        What counter is currently at.
+        """
+        return self._counterVar
+
+    def _next(self):
+        """
+        Generates the next symbols and increments counter by 1.
+        """
+        s = Symbol("%s%i" % (self._label, self._counterVar))
+        self._counterVar += 1
+        return s
+_symbol_factory = _SymbolFactory('_]"]_')  # most certainly a unique label
+
+
+@cacheit
+def _get_contractions(string1, keep_only_fully_contracted=False):
+    """
+    Returns Add-object with contracted terms.
+
+    Uses recursion to find all contractions. -- Internal helper function --
+
+    Will find nonzero contractions in string1 between indices given in
+    leftrange and rightrange.
+
+    """
+
+    # Should we store current level of contraction?
+    if keep_only_fully_contracted and string1:
+        result = []
+    else:
+        result = [NO(Mul(*string1))]
+
+    for i in range(len(string1) - 1):
+        for j in range(i + 1, len(string1)):
+
+            c = contraction(string1[i], string1[j])
+
+            if c:
+                sign = (j - i + 1) % 2
+                if sign:
+                    coeff = S.NegativeOne*c
+                else:
+                    coeff = c
+
+                #
+                #  Call next level of recursion
+                #  ============================
+                #
+                # We now need to find more contractions among operators
+                #
+                # oplist = string1[:i]+ string1[i+1:j] + string1[j+1:]
+                #
+                # To prevent overcounting, we don't allow contractions
+                # we have already encountered. i.e. contractions between
+                #       string1[:i] <---> string1[i+1:j]
+                # and   string1[:i] <---> string1[j+1:].
+                #
+                # This leaves the case:
+                oplist = string1[i + 1:j] + string1[j + 1:]
+
+                if oplist:
+
+                    result.append(coeff*NO(
+                        Mul(*string1[:i])*_get_contractions( oplist,
+                            keep_only_fully_contracted=keep_only_fully_contracted)))
+
+                else:
+                    result.append(coeff*NO( Mul(*string1[:i])))
+
+        if keep_only_fully_contracted:
+            break   # next iteration over i leaves leftmost operator string1[0] uncontracted
+
+    return Add(*result)
+
+
+def wicks(e, **kw_args):
+    """
+    Returns the normal ordered equivalent of an expression using Wicks Theorem.
+
+    Examples
+    ========
+
+    >>> from sympy import symbols, Dummy
+    >>> from sympy.physics.secondquant import wicks, F, Fd
+    >>> p, q, r = symbols('p,q,r')
+    >>> wicks(Fd(p)*F(q))
+    KroneckerDelta(_i, q)*KroneckerDelta(p, q) + NO(CreateFermion(p)*AnnihilateFermion(q))
+
+    By default, the expression is expanded:
+
+    >>> wicks(F(p)*(F(q)+F(r)))
+    NO(AnnihilateFermion(p)*AnnihilateFermion(q)) + NO(AnnihilateFermion(p)*AnnihilateFermion(r))
+
+    With the keyword 'keep_only_fully_contracted=True', only fully contracted
+    terms are returned.
+
+    By request, the result can be simplified in the following order:
+     -- KroneckerDelta functions are evaluated
+     -- Dummy variables are substituted consistently across terms
+
+    >>> p, q, r = symbols('p q r', cls=Dummy)
+    >>> wicks(Fd(p)*(F(q)+F(r)), keep_only_fully_contracted=True)
+    KroneckerDelta(_i, _q)*KroneckerDelta(_p, _q) + KroneckerDelta(_i, _r)*KroneckerDelta(_p, _r)
+
+    """
+
+    if not e:
+        return S.Zero
+
+    opts = {
+        'simplify_kronecker_deltas': False,
+        'expand': True,
+        'simplify_dummies': False,
+        'keep_only_fully_contracted': False
+    }
+    opts.update(kw_args)
+
+    # check if we are already normally ordered
+    if isinstance(e, NO):
+        if opts['keep_only_fully_contracted']:
+            return S.Zero
+        else:
+            return e
+    elif isinstance(e, FermionicOperator):
+        if opts['keep_only_fully_contracted']:
+            return S.Zero
+        else:
+            return e
+
+    # break up any NO-objects, and evaluate commutators
+    e = e.doit(wicks=True)
+
+    # make sure we have only one term to consider
+    e = e.expand()
+    if isinstance(e, Add):
+        if opts['simplify_dummies']:
+            return substitute_dummies(Add(*[ wicks(term, **kw_args) for term in e.args]))
+        else:
+            return Add(*[ wicks(term, **kw_args) for term in e.args])
+
+    # For Mul-objects we can actually do something
+    if isinstance(e, Mul):
+
+        # we don't want to mess around with commuting part of Mul
+        # so we factorize it out before starting recursion
+        c_part = []
+        string1 = []
+        for factor in e.args:
+            if factor.is_commutative:
+                c_part.append(factor)
+            else:
+                string1.append(factor)
+        n = len(string1)
+
+        # catch trivial cases
+        if n == 0:
+            result = e
+        elif n == 1:
+            if opts['keep_only_fully_contracted']:
+                return S.Zero
+            else:
+                result = e
+
+        else:  # non-trivial
+
+            if isinstance(string1[0], BosonicOperator):
+                raise NotImplementedError
+
+            string1 = tuple(string1)
+
+            # recursion over higher order contractions
+            result = _get_contractions(string1,
+                keep_only_fully_contracted=opts['keep_only_fully_contracted'] )
+            result = Mul(*c_part)*result
+
+        if opts['expand']:
+            result = result.expand()
+        if opts['simplify_kronecker_deltas']:
+            result = evaluate_deltas(result)
+
+        return result
+
+    # there was nothing to do
+    return e
+
+
+class PermutationOperator(Expr):
+    """
+    Represents the index permutation operator P(ij).
+
+    P(ij)*f(i)*g(j) = f(i)*g(j) - f(j)*g(i)
+    """
+    is_commutative = True
+
+    def __new__(cls, i, j):
+        i, j = sorted(map(sympify, (i, j)), key=default_sort_key)
+        obj = Basic.__new__(cls, i, j)
+        return obj
+
+    def get_permuted(self, expr):
+        """
+        Returns -expr with permuted indices.
+
+        Explanation
+        ===========
+
+        >>> from sympy import symbols, Function
+        >>> from sympy.physics.secondquant import PermutationOperator
+        >>> p,q = symbols('p,q')
+        >>> f = Function('f')
+        >>> PermutationOperator(p,q).get_permuted(f(p,q))
+        -f(q, p)
+
+        """
+        i = self.args[0]
+        j = self.args[1]
+        if expr.has(i) and expr.has(j):
+            tmp = Dummy()
+            expr = expr.subs(i, tmp)
+            expr = expr.subs(j, i)
+            expr = expr.subs(tmp, j)
+            return S.NegativeOne*expr
+        else:
+            return expr
+
+    def _latex(self, printer):
+        return "P(%s%s)" % self.args
+
+
+def simplify_index_permutations(expr, permutation_operators):
+    """
+    Performs simplification by introducing PermutationOperators where appropriate.
+
+    Explanation
+    ===========
+
+    Schematically:
+        [abij] - [abji] - [baij] + [baji] ->  P(ab)*P(ij)*[abij]
+
+    permutation_operators is a list of PermutationOperators to consider.
+
+    If permutation_operators=[P(ab),P(ij)] we will try to introduce the
+    permutation operators P(ij) and P(ab) in the expression.  If there are other
+    possible simplifications, we ignore them.
+
+    >>> from sympy import symbols, Function
+    >>> from sympy.physics.secondquant import simplify_index_permutations
+    >>> from sympy.physics.secondquant import PermutationOperator
+    >>> p,q,r,s = symbols('p,q,r,s')
+    >>> f = Function('f')
+    >>> g = Function('g')
+
+    >>> expr = f(p)*g(q) - f(q)*g(p); expr
+    f(p)*g(q) - f(q)*g(p)
+    >>> simplify_index_permutations(expr,[PermutationOperator(p,q)])
+    f(p)*g(q)*PermutationOperator(p, q)
+
+    >>> PermutList = [PermutationOperator(p,q),PermutationOperator(r,s)]
+    >>> expr = f(p,r)*g(q,s) - f(q,r)*g(p,s) + f(q,s)*g(p,r) - f(p,s)*g(q,r)
+    >>> simplify_index_permutations(expr,PermutList)
+    f(p, r)*g(q, s)*PermutationOperator(p, q)*PermutationOperator(r, s)
+
+    """
+
+    def _get_indices(expr, ind):
+        """
+        Collects indices recursively in predictable order.
+        """
+        result = []
+        for arg in expr.args:
+            if arg in ind:
+                result.append(arg)
+            else:
+                if arg.args:
+                    result.extend(_get_indices(arg, ind))
+        return result
+
+    def _choose_one_to_keep(a, b, ind):
+        # we keep the one where indices in ind are in order ind[0] < ind[1]
+        return min(a, b, key=lambda x: default_sort_key(_get_indices(x, ind)))
+
+    expr = expr.expand()
+    if isinstance(expr, Add):
+        terms = set(expr.args)
+
+        for P in permutation_operators:
+            new_terms = set()
+            on_hold = set()
+            while terms:
+                term = terms.pop()
+                permuted = P.get_permuted(term)
+                if permuted in terms | on_hold:
+                    try:
+                        terms.remove(permuted)
+                    except KeyError:
+                        on_hold.remove(permuted)
+                    keep = _choose_one_to_keep(term, permuted, P.args)
+                    new_terms.add(P*keep)
+                else:
+
+                    # Some terms must get a second chance because the permuted
+                    # term may already have canonical dummy ordering.  Then
+                    # substitute_dummies() does nothing.  However, the other
+                    # term, if it exists, will be able to match with us.
+                    permuted1 = permuted
+                    permuted = substitute_dummies(permuted)
+                    if permuted1 == permuted:
+                        on_hold.add(term)
+                    elif permuted in terms | on_hold:
+                        try:
+                            terms.remove(permuted)
+                        except KeyError:
+                            on_hold.remove(permuted)
+                        keep = _choose_one_to_keep(term, permuted, P.args)
+                        new_terms.add(P*keep)
+                    else:
+                        new_terms.add(term)
+            terms = new_terms | on_hold
+        return Add(*terms)
+    return expr
diff --git a/llmeval-env/lib/python3.10/site-packages/sympy/physics/vector/__init__.py b/llmeval-env/lib/python3.10/site-packages/sympy/physics/vector/__init__.py
new file mode 100644
index 0000000000000000000000000000000000000000..e714852064c0b940ebda2e5fe7a08faf13f07ed0
--- /dev/null
+++ b/llmeval-env/lib/python3.10/site-packages/sympy/physics/vector/__init__.py
@@ -0,0 +1,36 @@
+__all__ = [
+    'CoordinateSym', 'ReferenceFrame',
+
+    'Dyadic',
+
+    'Vector',
+
+    'Point',
+
+    'cross', 'dot', 'express', 'time_derivative', 'outer',
+    'kinematic_equations', 'get_motion_params', 'partial_velocity',
+    'dynamicsymbols',
+
+    'vprint', 'vsstrrepr', 'vsprint', 'vpprint', 'vlatex', 'init_vprinting',
+
+    'curl', 'divergence', 'gradient', 'is_conservative', 'is_solenoidal',
+    'scalar_potential', 'scalar_potential_difference',
+
+]
+from .frame import CoordinateSym, ReferenceFrame
+
+from .dyadic import Dyadic
+
+from .vector import Vector
+
+from .point import Point
+
+from .functions import (cross, dot, express, time_derivative, outer,
+        kinematic_equations, get_motion_params, partial_velocity,
+        dynamicsymbols)
+
+from .printing import (vprint, vsstrrepr, vsprint, vpprint, vlatex,
+        init_vprinting)
+
+from .fieldfunctions import (curl, divergence, gradient, is_conservative,
+        is_solenoidal, scalar_potential, scalar_potential_difference)
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diff --git a/llmeval-env/lib/python3.10/site-packages/sympy/physics/vector/dyadic.py b/llmeval-env/lib/python3.10/site-packages/sympy/physics/vector/dyadic.py
new file mode 100644
index 0000000000000000000000000000000000000000..93d3e49b6c9c382953faeda8566b6438b13681f4
--- /dev/null
+++ b/llmeval-env/lib/python3.10/site-packages/sympy/physics/vector/dyadic.py
@@ -0,0 +1,601 @@
+from sympy.core.backend import sympify, Add, ImmutableMatrix as Matrix
+from sympy.core.evalf import EvalfMixin
+from sympy.printing.defaults import Printable
+
+from mpmath.libmp.libmpf import prec_to_dps
+
+
+__all__ = ['Dyadic']
+
+
+class Dyadic(Printable, EvalfMixin):
+    """A Dyadic object.
+
+    See:
+    https://en.wikipedia.org/wiki/Dyadic_tensor
+    Kane, T., Levinson, D. Dynamics Theory and Applications. 1985 McGraw-Hill
+
+    A more powerful way to represent a rigid body's inertia. While it is more
+    complex, by choosing Dyadic components to be in body fixed basis vectors,
+    the resulting matrix is equivalent to the inertia tensor.
+
+    """
+
+    is_number = False
+
+    def __init__(self, inlist):
+        """
+        Just like Vector's init, you should not call this unless creating a
+        zero dyadic.
+
+        zd = Dyadic(0)
+
+        Stores a Dyadic as a list of lists; the inner list has the measure
+        number and the two unit vectors; the outerlist holds each unique
+        unit vector pair.
+
+        """
+
+        self.args = []
+        if inlist == 0:
+            inlist = []
+        while len(inlist) != 0:
+            added = 0
+            for i, v in enumerate(self.args):
+                if ((str(inlist[0][1]) == str(self.args[i][1])) and
+                        (str(inlist[0][2]) == str(self.args[i][2]))):
+                    self.args[i] = (self.args[i][0] + inlist[0][0],
+                                    inlist[0][1], inlist[0][2])
+                    inlist.remove(inlist[0])
+                    added = 1
+                    break
+            if added != 1:
+                self.args.append(inlist[0])
+                inlist.remove(inlist[0])
+        i = 0
+        # This code is to remove empty parts from the list
+        while i < len(self.args):
+            if ((self.args[i][0] == 0) | (self.args[i][1] == 0) |
+                    (self.args[i][2] == 0)):
+                self.args.remove(self.args[i])
+                i -= 1
+            i += 1
+
+    @property
+    def func(self):
+        """Returns the class Dyadic. """
+        return Dyadic
+
+    def __add__(self, other):
+        """The add operator for Dyadic. """
+        other = _check_dyadic(other)
+        return Dyadic(self.args + other.args)
+
+    def __and__(self, other):
+        """The inner product operator for a Dyadic and a Dyadic or Vector.
+
+        Parameters
+        ==========
+
+        other : Dyadic or Vector
+            The other Dyadic or Vector to take the inner product with
+
+        Examples
+        ========
+
+        >>> from sympy.physics.vector import ReferenceFrame, outer
+        >>> N = ReferenceFrame('N')
+        >>> D1 = outer(N.x, N.y)
+        >>> D2 = outer(N.y, N.y)
+        >>> D1.dot(D2)
+        (N.x|N.y)
+        >>> D1.dot(N.y)
+        N.x
+
+        """
+        from sympy.physics.vector.vector import Vector, _check_vector
+        if isinstance(other, Dyadic):
+            other = _check_dyadic(other)
+            ol = Dyadic(0)
+            for i, v in enumerate(self.args):
+                for i2, v2 in enumerate(other.args):
+                    ol += v[0] * v2[0] * (v[2] & v2[1]) * (v[1] | v2[2])
+        else:
+            other = _check_vector(other)
+            ol = Vector(0)
+            for i, v in enumerate(self.args):
+                ol += v[0] * v[1] * (v[2] & other)
+        return ol
+
+    def __truediv__(self, other):
+        """Divides the Dyadic by a sympifyable expression. """
+        return self.__mul__(1 / other)
+
+    def __eq__(self, other):
+        """Tests for equality.
+
+        Is currently weak; needs stronger comparison testing
+
+        """
+
+        if other == 0:
+            other = Dyadic(0)
+        other = _check_dyadic(other)
+        if (self.args == []) and (other.args == []):
+            return True
+        elif (self.args == []) or (other.args == []):
+            return False
+        return set(self.args) == set(other.args)
+
+    def __mul__(self, other):
+        """Multiplies the Dyadic by a sympifyable expression.
+
+        Parameters
+        ==========
+
+        other : Sympafiable
+            The scalar to multiply this Dyadic with
+
+        Examples
+        ========
+
+        >>> from sympy.physics.vector import ReferenceFrame, outer
+        >>> N = ReferenceFrame('N')
+        >>> d = outer(N.x, N.x)
+        >>> 5 * d
+        5*(N.x|N.x)
+
+        """
+
+        newlist = list(self.args)
+        other = sympify(other)
+        for i, v in enumerate(newlist):
+            newlist[i] = (other * newlist[i][0], newlist[i][1],
+                          newlist[i][2])
+        return Dyadic(newlist)
+
+    def __ne__(self, other):
+        return not self == other
+
+    def __neg__(self):
+        return self * -1
+
+    def _latex(self, printer):
+        ar = self.args  # just to shorten things
+        if len(ar) == 0:
+            return str(0)
+        ol = []  # output list, to be concatenated to a string
+        for i, v in enumerate(ar):
+            # if the coef of the dyadic is 1, we skip the 1
+            if ar[i][0] == 1:
+                ol.append(' + ' + printer._print(ar[i][1]) + r"\otimes " +
+                          printer._print(ar[i][2]))
+            # if the coef of the dyadic is -1, we skip the 1
+            elif ar[i][0] == -1:
+                ol.append(' - ' +
+                          printer._print(ar[i][1]) +
+                          r"\otimes " +
+                          printer._print(ar[i][2]))
+            # If the coefficient of the dyadic is not 1 or -1,
+            # we might wrap it in parentheses, for readability.
+            elif ar[i][0] != 0:
+                arg_str = printer._print(ar[i][0])
+                if isinstance(ar[i][0], Add):
+                    arg_str = '(%s)' % arg_str
+                if arg_str.startswith('-'):
+                    arg_str = arg_str[1:]
+                    str_start = ' - '
+                else:
+                    str_start = ' + '
+                ol.append(str_start + arg_str + printer._print(ar[i][1]) +
+                          r"\otimes " + printer._print(ar[i][2]))
+        outstr = ''.join(ol)
+        if outstr.startswith(' + '):
+            outstr = outstr[3:]
+        elif outstr.startswith(' '):
+            outstr = outstr[1:]
+        return outstr
+
+    def _pretty(self, printer):
+        e = self
+
+        class Fake:
+            baseline = 0
+
+            def render(self, *args, **kwargs):
+                ar = e.args  # just to shorten things
+                mpp = printer
+                if len(ar) == 0:
+                    return str(0)
+                bar = "\N{CIRCLED TIMES}" if printer._use_unicode else "|"
+                ol = []  # output list, to be concatenated to a string
+                for i, v in enumerate(ar):
+                    # if the coef of the dyadic is 1, we skip the 1
+                    if ar[i][0] == 1:
+                        ol.extend([" + ",
+                                  mpp.doprint(ar[i][1]),
+                                  bar,
+                                  mpp.doprint(ar[i][2])])
+
+                    # if the coef of the dyadic is -1, we skip the 1
+                    elif ar[i][0] == -1:
+                        ol.extend([" - ",
+                                  mpp.doprint(ar[i][1]),
+                                  bar,
+                                  mpp.doprint(ar[i][2])])
+
+                    # If the coefficient of the dyadic is not 1 or -1,
+                    # we might wrap it in parentheses, for readability.
+                    elif ar[i][0] != 0:
+                        if isinstance(ar[i][0], Add):
+                            arg_str = mpp._print(
+                                ar[i][0]).parens()[0]
+                        else:
+                            arg_str = mpp.doprint(ar[i][0])
+                        if arg_str.startswith("-"):
+                            arg_str = arg_str[1:]
+                            str_start = " - "
+                        else:
+                            str_start = " + "
+                        ol.extend([str_start, arg_str, " ",
+                                  mpp.doprint(ar[i][1]),
+                                  bar,
+                                  mpp.doprint(ar[i][2])])
+
+                outstr = "".join(ol)
+                if outstr.startswith(" + "):
+                    outstr = outstr[3:]
+                elif outstr.startswith(" "):
+                    outstr = outstr[1:]
+                return outstr
+        return Fake()
+
+    def __rand__(self, other):
+        """The inner product operator for a Vector or Dyadic, and a Dyadic
+
+        This is for: Vector dot Dyadic
+
+        Parameters
+        ==========
+
+        other : Vector
+            The vector we are dotting with
+
+        Examples
+        ========
+
+        >>> from sympy.physics.vector import ReferenceFrame, dot, outer
+        >>> N = ReferenceFrame('N')
+        >>> d = outer(N.x, N.x)
+        >>> dot(N.x, d)
+        N.x
+
+        """
+
+        from sympy.physics.vector.vector import Vector, _check_vector
+        other = _check_vector(other)
+        ol = Vector(0)
+        for i, v in enumerate(self.args):
+            ol += v[0] * v[2] * (v[1] & other)
+        return ol
+
+    def __rsub__(self, other):
+        return (-1 * self) + other
+
+    def __rxor__(self, other):
+        """For a cross product in the form: Vector x Dyadic
+
+        Parameters
+        ==========
+
+        other : Vector
+            The Vector that we are crossing this Dyadic with
+
+        Examples
+        ========
+
+        >>> from sympy.physics.vector import ReferenceFrame, outer, cross
+        >>> N = ReferenceFrame('N')
+        >>> d = outer(N.x, N.x)
+        >>> cross(N.y, d)
+        - (N.z|N.x)
+
+        """
+
+        from sympy.physics.vector.vector import _check_vector
+        other = _check_vector(other)
+        ol = Dyadic(0)
+        for i, v in enumerate(self.args):
+            ol += v[0] * ((other ^ v[1]) | v[2])
+        return ol
+
+    def _sympystr(self, printer):
+        """Printing method. """
+        ar = self.args  # just to shorten things
+        if len(ar) == 0:
+            return printer._print(0)
+        ol = []  # output list, to be concatenated to a string
+        for i, v in enumerate(ar):
+            # if the coef of the dyadic is 1, we skip the 1
+            if ar[i][0] == 1:
+                ol.append(' + (' + printer._print(ar[i][1]) + '|' +
+                          printer._print(ar[i][2]) + ')')
+            # if the coef of the dyadic is -1, we skip the 1
+            elif ar[i][0] == -1:
+                ol.append(' - (' + printer._print(ar[i][1]) + '|' +
+                          printer._print(ar[i][2]) + ')')
+            # If the coefficient of the dyadic is not 1 or -1,
+            # we might wrap it in parentheses, for readability.
+            elif ar[i][0] != 0:
+                arg_str = printer._print(ar[i][0])
+                if isinstance(ar[i][0], Add):
+                    arg_str = "(%s)" % arg_str
+                if arg_str[0] == '-':
+                    arg_str = arg_str[1:]
+                    str_start = ' - '
+                else:
+                    str_start = ' + '
+                ol.append(str_start + arg_str + '*(' +
+                          printer._print(ar[i][1]) +
+                          '|' + printer._print(ar[i][2]) + ')')
+        outstr = ''.join(ol)
+        if outstr.startswith(' + '):
+            outstr = outstr[3:]
+        elif outstr.startswith(' '):
+            outstr = outstr[1:]
+        return outstr
+
+    def __sub__(self, other):
+        """The subtraction operator. """
+        return self.__add__(other * -1)
+
+    def __xor__(self, other):
+        """For a cross product in the form: Dyadic x Vector.
+
+        Parameters
+        ==========
+
+        other : Vector
+            The Vector that we are crossing this Dyadic with
+
+        Examples
+        ========
+
+        >>> from sympy.physics.vector import ReferenceFrame, outer, cross
+        >>> N = ReferenceFrame('N')
+        >>> d = outer(N.x, N.x)
+        >>> cross(d, N.y)
+        (N.x|N.z)
+
+        """
+
+        from sympy.physics.vector.vector import _check_vector
+        other = _check_vector(other)
+        ol = Dyadic(0)
+        for i, v in enumerate(self.args):
+            ol += v[0] * (v[1] | (v[2] ^ other))
+        return ol
+
+    __radd__ = __add__
+    __rmul__ = __mul__
+
+    def express(self, frame1, frame2=None):
+        """Expresses this Dyadic in alternate frame(s)
+
+        The first frame is the list side expression, the second frame is the
+        right side; if Dyadic is in form A.x|B.y, you can express it in two
+        different frames. If no second frame is given, the Dyadic is
+        expressed in only one frame.
+
+        Calls the global express function
+
+        Parameters
+        ==========
+
+        frame1 : ReferenceFrame
+            The frame to express the left side of the Dyadic in
+        frame2 : ReferenceFrame
+            If provided, the frame to express the right side of the Dyadic in
+
+        Examples
+        ========
+
+        >>> from sympy.physics.vector import ReferenceFrame, outer, dynamicsymbols
+        >>> from sympy.physics.vector import init_vprinting
+        >>> init_vprinting(pretty_print=False)
+        >>> N = ReferenceFrame('N')
+        >>> q = dynamicsymbols('q')
+        >>> B = N.orientnew('B', 'Axis', [q, N.z])
+        >>> d = outer(N.x, N.x)
+        >>> d.express(B, N)
+        cos(q)*(B.x|N.x) - sin(q)*(B.y|N.x)
+
+        """
+        from sympy.physics.vector.functions import express
+        return express(self, frame1, frame2)
+
+    def to_matrix(self, reference_frame, second_reference_frame=None):
+        """Returns the matrix form of the dyadic with respect to one or two
+        reference frames.
+
+        Parameters
+        ----------
+        reference_frame : ReferenceFrame
+            The reference frame that the rows and columns of the matrix
+            correspond to. If a second reference frame is provided, this
+            only corresponds to the rows of the matrix.
+        second_reference_frame : ReferenceFrame, optional, default=None
+            The reference frame that the columns of the matrix correspond
+            to.
+
+        Returns
+        -------
+        matrix : ImmutableMatrix, shape(3,3)
+            The matrix that gives the 2D tensor form.
+
+        Examples
+        ========
+
+        >>> from sympy import symbols
+        >>> from sympy.physics.vector import ReferenceFrame, Vector
+        >>> Vector.simp = True
+        >>> from sympy.physics.mechanics import inertia
+        >>> Ixx, Iyy, Izz, Ixy, Iyz, Ixz = symbols('Ixx, Iyy, Izz, Ixy, Iyz, Ixz')
+        >>> N = ReferenceFrame('N')
+        >>> inertia_dyadic = inertia(N, Ixx, Iyy, Izz, Ixy, Iyz, Ixz)
+        >>> inertia_dyadic.to_matrix(N)
+        Matrix([
+        [Ixx, Ixy, Ixz],
+        [Ixy, Iyy, Iyz],
+        [Ixz, Iyz, Izz]])
+        >>> beta = symbols('beta')
+        >>> A = N.orientnew('A', 'Axis', (beta, N.x))
+        >>> inertia_dyadic.to_matrix(A)
+        Matrix([
+        [                           Ixx,                                           Ixy*cos(beta) + Ixz*sin(beta),                                           -Ixy*sin(beta) + Ixz*cos(beta)],
+        [ Ixy*cos(beta) + Ixz*sin(beta), Iyy*cos(2*beta)/2 + Iyy/2 + Iyz*sin(2*beta) - Izz*cos(2*beta)/2 + Izz/2,                 -Iyy*sin(2*beta)/2 + Iyz*cos(2*beta) + Izz*sin(2*beta)/2],
+        [-Ixy*sin(beta) + Ixz*cos(beta),                -Iyy*sin(2*beta)/2 + Iyz*cos(2*beta) + Izz*sin(2*beta)/2, -Iyy*cos(2*beta)/2 + Iyy/2 - Iyz*sin(2*beta) + Izz*cos(2*beta)/2 + Izz/2]])
+
+        """
+
+        if second_reference_frame is None:
+            second_reference_frame = reference_frame
+
+        return Matrix([i.dot(self).dot(j) for i in reference_frame for j in
+                      second_reference_frame]).reshape(3, 3)
+
+    def doit(self, **hints):
+        """Calls .doit() on each term in the Dyadic"""
+        return sum([Dyadic([(v[0].doit(**hints), v[1], v[2])])
+                    for v in self.args], Dyadic(0))
+
+    def dt(self, frame):
+        """Take the time derivative of this Dyadic in a frame.
+
+        This function calls the global time_derivative method
+
+        Parameters
+        ==========
+
+        frame : ReferenceFrame
+            The frame to take the time derivative in
+
+        Examples
+        ========
+
+        >>> from sympy.physics.vector import ReferenceFrame, outer, dynamicsymbols
+        >>> from sympy.physics.vector import init_vprinting
+        >>> init_vprinting(pretty_print=False)
+        >>> N = ReferenceFrame('N')
+        >>> q = dynamicsymbols('q')
+        >>> B = N.orientnew('B', 'Axis', [q, N.z])
+        >>> d = outer(N.x, N.x)
+        >>> d.dt(B)
+        - q'*(N.y|N.x) - q'*(N.x|N.y)
+
+        """
+        from sympy.physics.vector.functions import time_derivative
+        return time_derivative(self, frame)
+
+    def simplify(self):
+        """Returns a simplified Dyadic."""
+        out = Dyadic(0)
+        for v in self.args:
+            out += Dyadic([(v[0].simplify(), v[1], v[2])])
+        return out
+
+    def subs(self, *args, **kwargs):
+        """Substitution on the Dyadic.
+
+        Examples
+        ========
+
+        >>> from sympy.physics.vector import ReferenceFrame
+        >>> from sympy import Symbol
+        >>> N = ReferenceFrame('N')
+        >>> s = Symbol('s')
+        >>> a = s*(N.x|N.x)
+        >>> a.subs({s: 2})
+        2*(N.x|N.x)
+
+        """
+
+        return sum([Dyadic([(v[0].subs(*args, **kwargs), v[1], v[2])])
+                    for v in self.args], Dyadic(0))
+
+    def applyfunc(self, f):
+        """Apply a function to each component of a Dyadic."""
+        if not callable(f):
+            raise TypeError("`f` must be callable.")
+
+        out = Dyadic(0)
+        for a, b, c in self.args:
+            out += f(a) * (b | c)
+        return out
+
+    dot = __and__
+    cross = __xor__
+
+    def _eval_evalf(self, prec):
+        if not self.args:
+            return self
+        new_args = []
+        dps = prec_to_dps(prec)
+        for inlist in self.args:
+            new_inlist = list(inlist)
+            new_inlist[0] = inlist[0].evalf(n=dps)
+            new_args.append(tuple(new_inlist))
+        return Dyadic(new_args)
+
+    def xreplace(self, rule):
+        """
+        Replace occurrences of objects within the measure numbers of the
+        Dyadic.
+
+        Parameters
+        ==========
+
+        rule : dict-like
+            Expresses a replacement rule.
+
+        Returns
+        =======
+
+        Dyadic
+            Result of the replacement.
+
+        Examples
+        ========
+
+        >>> from sympy import symbols, pi
+        >>> from sympy.physics.vector import ReferenceFrame, outer
+        >>> N = ReferenceFrame('N')
+        >>> D = outer(N.x, N.x)
+        >>> x, y, z = symbols('x y z')
+        >>> ((1 + x*y) * D).xreplace({x: pi})
+        (pi*y + 1)*(N.x|N.x)
+        >>> ((1 + x*y) * D).xreplace({x: pi, y: 2})
+        (1 + 2*pi)*(N.x|N.x)
+
+        Replacements occur only if an entire node in the expression tree is
+        matched:
+
+        >>> ((x*y + z) * D).xreplace({x*y: pi})
+        (z + pi)*(N.x|N.x)
+        >>> ((x*y*z) * D).xreplace({x*y: pi})
+        x*y*z*(N.x|N.x)
+
+        """
+
+        new_args = []
+        for inlist in self.args:
+            new_inlist = list(inlist)
+            new_inlist[0] = new_inlist[0].xreplace(rule)
+            new_args.append(tuple(new_inlist))
+        return Dyadic(new_args)
+
+
+def _check_dyadic(other):
+    if not isinstance(other, Dyadic):
+        raise TypeError('A Dyadic must be supplied')
+    return other
diff --git a/llmeval-env/lib/python3.10/site-packages/sympy/physics/vector/fieldfunctions.py b/llmeval-env/lib/python3.10/site-packages/sympy/physics/vector/fieldfunctions.py
new file mode 100644
index 0000000000000000000000000000000000000000..74169921c587385323b9080709999c65c6ca0843
--- /dev/null
+++ b/llmeval-env/lib/python3.10/site-packages/sympy/physics/vector/fieldfunctions.py
@@ -0,0 +1,313 @@
+from sympy.core.function import diff
+from sympy.core.singleton import S
+from sympy.integrals.integrals import integrate
+from sympy.physics.vector import Vector, express
+from sympy.physics.vector.frame import _check_frame
+from sympy.physics.vector.vector import _check_vector
+
+
+__all__ = ['curl', 'divergence', 'gradient', 'is_conservative',
+           'is_solenoidal', 'scalar_potential',
+           'scalar_potential_difference']
+
+
+def curl(vect, frame):
+    """
+    Returns the curl of a vector field computed wrt the coordinate
+    symbols of the given frame.
+
+    Parameters
+    ==========
+
+    vect : Vector
+        The vector operand
+
+    frame : ReferenceFrame
+        The reference frame to calculate the curl in
+
+    Examples
+    ========
+
+    >>> from sympy.physics.vector import ReferenceFrame
+    >>> from sympy.physics.vector import curl
+    >>> R = ReferenceFrame('R')
+    >>> v1 = R[1]*R[2]*R.x + R[0]*R[2]*R.y + R[0]*R[1]*R.z
+    >>> curl(v1, R)
+    0
+    >>> v2 = R[0]*R[1]*R[2]*R.x
+    >>> curl(v2, R)
+    R_x*R_y*R.y - R_x*R_z*R.z
+
+    """
+
+    _check_vector(vect)
+    if vect == 0:
+        return Vector(0)
+    vect = express(vect, frame, variables=True)
+    # A mechanical approach to avoid looping overheads
+    vectx = vect.dot(frame.x)
+    vecty = vect.dot(frame.y)
+    vectz = vect.dot(frame.z)
+    outvec = Vector(0)
+    outvec += (diff(vectz, frame[1]) - diff(vecty, frame[2])) * frame.x
+    outvec += (diff(vectx, frame[2]) - diff(vectz, frame[0])) * frame.y
+    outvec += (diff(vecty, frame[0]) - diff(vectx, frame[1])) * frame.z
+    return outvec
+
+
+def divergence(vect, frame):
+    """
+    Returns the divergence of a vector field computed wrt the coordinate
+    symbols of the given frame.
+
+    Parameters
+    ==========
+
+    vect : Vector
+        The vector operand
+
+    frame : ReferenceFrame
+        The reference frame to calculate the divergence in
+
+    Examples
+    ========
+
+    >>> from sympy.physics.vector import ReferenceFrame
+    >>> from sympy.physics.vector import divergence
+    >>> R = ReferenceFrame('R')
+    >>> v1 = R[0]*R[1]*R[2] * (R.x+R.y+R.z)
+    >>> divergence(v1, R)
+    R_x*R_y + R_x*R_z + R_y*R_z
+    >>> v2 = 2*R[1]*R[2]*R.y
+    >>> divergence(v2, R)
+    2*R_z
+
+    """
+
+    _check_vector(vect)
+    if vect == 0:
+        return S.Zero
+    vect = express(vect, frame, variables=True)
+    vectx = vect.dot(frame.x)
+    vecty = vect.dot(frame.y)
+    vectz = vect.dot(frame.z)
+    out = S.Zero
+    out += diff(vectx, frame[0])
+    out += diff(vecty, frame[1])
+    out += diff(vectz, frame[2])
+    return out
+
+
+def gradient(scalar, frame):
+    """
+    Returns the vector gradient of a scalar field computed wrt the
+    coordinate symbols of the given frame.
+
+    Parameters
+    ==========
+
+    scalar : sympifiable
+        The scalar field to take the gradient of
+
+    frame : ReferenceFrame
+        The frame to calculate the gradient in
+
+    Examples
+    ========
+
+    >>> from sympy.physics.vector import ReferenceFrame
+    >>> from sympy.physics.vector import gradient
+    >>> R = ReferenceFrame('R')
+    >>> s1 = R[0]*R[1]*R[2]
+    >>> gradient(s1, R)
+    R_y*R_z*R.x + R_x*R_z*R.y + R_x*R_y*R.z
+    >>> s2 = 5*R[0]**2*R[2]
+    >>> gradient(s2, R)
+    10*R_x*R_z*R.x + 5*R_x**2*R.z
+
+    """
+
+    _check_frame(frame)
+    outvec = Vector(0)
+    scalar = express(scalar, frame, variables=True)
+    for i, x in enumerate(frame):
+        outvec += diff(scalar, frame[i]) * x
+    return outvec
+
+
+def is_conservative(field):
+    """
+    Checks if a field is conservative.
+
+    Parameters
+    ==========
+
+    field : Vector
+        The field to check for conservative property
+
+    Examples
+    ========
+
+    >>> from sympy.physics.vector import ReferenceFrame
+    >>> from sympy.physics.vector import is_conservative
+    >>> R = ReferenceFrame('R')
+    >>> is_conservative(R[1]*R[2]*R.x + R[0]*R[2]*R.y + R[0]*R[1]*R.z)
+    True
+    >>> is_conservative(R[2] * R.y)
+    False
+
+    """
+
+    # Field is conservative irrespective of frame
+    # Take the first frame in the result of the separate method of Vector
+    if field == Vector(0):
+        return True
+    frame = list(field.separate())[0]
+    return curl(field, frame).simplify() == Vector(0)
+
+
+def is_solenoidal(field):
+    """
+    Checks if a field is solenoidal.
+
+    Parameters
+    ==========
+
+    field : Vector
+        The field to check for solenoidal property
+
+    Examples
+    ========
+
+    >>> from sympy.physics.vector import ReferenceFrame
+    >>> from sympy.physics.vector import is_solenoidal
+    >>> R = ReferenceFrame('R')
+    >>> is_solenoidal(R[1]*R[2]*R.x + R[0]*R[2]*R.y + R[0]*R[1]*R.z)
+    True
+    >>> is_solenoidal(R[1] * R.y)
+    False
+
+    """
+
+    # Field is solenoidal irrespective of frame
+    # Take the first frame in the result of the separate method in Vector
+    if field == Vector(0):
+        return True
+    frame = list(field.separate())[0]
+    return divergence(field, frame).simplify() is S.Zero
+
+
+def scalar_potential(field, frame):
+    """
+    Returns the scalar potential function of a field in a given frame
+    (without the added integration constant).
+
+    Parameters
+    ==========
+
+    field : Vector
+        The vector field whose scalar potential function is to be
+        calculated
+
+    frame : ReferenceFrame
+        The frame to do the calculation in
+
+    Examples
+    ========
+
+    >>> from sympy.physics.vector import ReferenceFrame
+    >>> from sympy.physics.vector import scalar_potential, gradient
+    >>> R = ReferenceFrame('R')
+    >>> scalar_potential(R.z, R) == R[2]
+    True
+    >>> scalar_field = 2*R[0]**2*R[1]*R[2]
+    >>> grad_field = gradient(scalar_field, R)
+    >>> scalar_potential(grad_field, R)
+    2*R_x**2*R_y*R_z
+
+    """
+
+    # Check whether field is conservative
+    if not is_conservative(field):
+        raise ValueError("Field is not conservative")
+    if field == Vector(0):
+        return S.Zero
+    # Express the field exntirely in frame
+    # Substitute coordinate variables also
+    _check_frame(frame)
+    field = express(field, frame, variables=True)
+    # Make a list of dimensions of the frame
+    dimensions = list(frame)
+    # Calculate scalar potential function
+    temp_function = integrate(field.dot(dimensions[0]), frame[0])
+    for i, dim in enumerate(dimensions[1:]):
+        partial_diff = diff(temp_function, frame[i + 1])
+        partial_diff = field.dot(dim) - partial_diff
+        temp_function += integrate(partial_diff, frame[i + 1])
+    return temp_function
+
+
+def scalar_potential_difference(field, frame, point1, point2, origin):
+    """
+    Returns the scalar potential difference between two points in a
+    certain frame, wrt a given field.
+
+    If a scalar field is provided, its values at the two points are
+    considered. If a conservative vector field is provided, the values
+    of its scalar potential function at the two points are used.
+
+    Returns (potential at position 2) - (potential at position 1)
+
+    Parameters
+    ==========
+
+    field : Vector/sympyfiable
+        The field to calculate wrt
+
+    frame : ReferenceFrame
+        The frame to do the calculations in
+
+    point1 : Point
+        The initial Point in given frame
+
+    position2 : Point
+        The second Point in the given frame
+
+    origin : Point
+        The Point to use as reference point for position vector
+        calculation
+
+    Examples
+    ========
+
+    >>> from sympy.physics.vector import ReferenceFrame, Point
+    >>> from sympy.physics.vector import scalar_potential_difference
+    >>> R = ReferenceFrame('R')
+    >>> O = Point('O')
+    >>> P = O.locatenew('P', R[0]*R.x + R[1]*R.y + R[2]*R.z)
+    >>> vectfield = 4*R[0]*R[1]*R.x + 2*R[0]**2*R.y
+    >>> scalar_potential_difference(vectfield, R, O, P, O)
+    2*R_x**2*R_y
+    >>> Q = O.locatenew('O', 3*R.x + R.y + 2*R.z)
+    >>> scalar_potential_difference(vectfield, R, P, Q, O)
+    -2*R_x**2*R_y + 18
+
+    """
+
+    _check_frame(frame)
+    if isinstance(field, Vector):
+        # Get the scalar potential function
+        scalar_fn = scalar_potential(field, frame)
+    else:
+        # Field is a scalar
+        scalar_fn = field
+    # Express positions in required frame
+    position1 = express(point1.pos_from(origin), frame, variables=True)
+    position2 = express(point2.pos_from(origin), frame, variables=True)
+    # Get the two positions as substitution dicts for coordinate variables
+    subs_dict1 = {}
+    subs_dict2 = {}
+    for i, x in enumerate(frame):
+        subs_dict1[frame[i]] = x.dot(position1)
+        subs_dict2[frame[i]] = x.dot(position2)
+    return scalar_fn.subs(subs_dict2) - scalar_fn.subs(subs_dict1)
diff --git a/llmeval-env/lib/python3.10/site-packages/sympy/physics/vector/frame.py b/llmeval-env/lib/python3.10/site-packages/sympy/physics/vector/frame.py
new file mode 100644
index 0000000000000000000000000000000000000000..23f9c0a841deaab89681e69d3962a48ee94993f8
--- /dev/null
+++ b/llmeval-env/lib/python3.10/site-packages/sympy/physics/vector/frame.py
@@ -0,0 +1,1435 @@
+from sympy.core.backend import (diff, expand, sin, cos, sympify, eye, zeros,
+                                ImmutableMatrix as Matrix, MatrixBase)
+from sympy.core.symbol import Symbol
+from sympy.simplify.trigsimp import trigsimp
+from sympy.physics.vector.vector import Vector, _check_vector
+from sympy.utilities.misc import translate
+
+from warnings import warn
+
+__all__ = ['CoordinateSym', 'ReferenceFrame']
+
+
+class CoordinateSym(Symbol):
+    """
+    A coordinate symbol/base scalar associated wrt a Reference Frame.
+
+    Ideally, users should not instantiate this class. Instances of
+    this class must only be accessed through the corresponding frame
+    as 'frame[index]'.
+
+    CoordinateSyms having the same frame and index parameters are equal
+    (even though they may be instantiated separately).
+
+    Parameters
+    ==========
+
+    name : string
+        The display name of the CoordinateSym
+
+    frame : ReferenceFrame
+        The reference frame this base scalar belongs to
+
+    index : 0, 1 or 2
+        The index of the dimension denoted by this coordinate variable
+
+    Examples
+    ========
+
+    >>> from sympy.physics.vector import ReferenceFrame, CoordinateSym
+    >>> A = ReferenceFrame('A')
+    >>> A[1]
+    A_y
+    >>> type(A[0])
+    
+    >>> a_y = CoordinateSym('a_y', A, 1)
+    >>> a_y == A[1]
+    True
+
+    """
+
+    def __new__(cls, name, frame, index):
+        # We can't use the cached Symbol.__new__ because this class depends on
+        # frame and index, which are not passed to Symbol.__xnew__.
+        assumptions = {}
+        super()._sanitize(assumptions, cls)
+        obj = super().__xnew__(cls, name, **assumptions)
+        _check_frame(frame)
+        if index not in range(0, 3):
+            raise ValueError("Invalid index specified")
+        obj._id = (frame, index)
+        return obj
+
+    @property
+    def frame(self):
+        return self._id[0]
+
+    def __eq__(self, other):
+        # Check if the other object is a CoordinateSym of the same frame and
+        # same index
+        if isinstance(other, CoordinateSym):
+            if other._id == self._id:
+                return True
+        return False
+
+    def __ne__(self, other):
+        return not self == other
+
+    def __hash__(self):
+        return (self._id[0].__hash__(), self._id[1]).__hash__()
+
+
+class ReferenceFrame:
+    """A reference frame in classical mechanics.
+
+    ReferenceFrame is a class used to represent a reference frame in classical
+    mechanics. It has a standard basis of three unit vectors in the frame's
+    x, y, and z directions.
+
+    It also can have a rotation relative to a parent frame; this rotation is
+    defined by a direction cosine matrix relating this frame's basis vectors to
+    the parent frame's basis vectors.  It can also have an angular velocity
+    vector, defined in another frame.
+
+    """
+    _count = 0
+
+    def __init__(self, name, indices=None, latexs=None, variables=None):
+        """ReferenceFrame initialization method.
+
+        A ReferenceFrame has a set of orthonormal basis vectors, along with
+        orientations relative to other ReferenceFrames and angular velocities
+        relative to other ReferenceFrames.
+
+        Parameters
+        ==========
+
+        indices : tuple of str
+            Enables the reference frame's basis unit vectors to be accessed by
+            Python's square bracket indexing notation using the provided three
+            indice strings and alters the printing of the unit vectors to
+            reflect this choice.
+        latexs : tuple of str
+            Alters the LaTeX printing of the reference frame's basis unit
+            vectors to the provided three valid LaTeX strings.
+
+        Examples
+        ========
+
+        >>> from sympy.physics.vector import ReferenceFrame, vlatex
+        >>> N = ReferenceFrame('N')
+        >>> N.x
+        N.x
+        >>> O = ReferenceFrame('O', indices=('1', '2', '3'))
+        >>> O.x
+        O['1']
+        >>> O['1']
+        O['1']
+        >>> P = ReferenceFrame('P', latexs=('A1', 'A2', 'A3'))
+        >>> vlatex(P.x)
+        'A1'
+
+        ``symbols()`` can be used to create multiple Reference Frames in one
+        step, for example:
+
+        >>> from sympy.physics.vector import ReferenceFrame
+        >>> from sympy import symbols
+        >>> A, B, C = symbols('A B C', cls=ReferenceFrame)
+        >>> D, E = symbols('D E', cls=ReferenceFrame, indices=('1', '2', '3'))
+        >>> A[0]
+        A_x
+        >>> D.x
+        D['1']
+        >>> E.y
+        E['2']
+        >>> type(A) == type(D)
+        True
+
+        """
+
+        if not isinstance(name, str):
+            raise TypeError('Need to supply a valid name')
+        # The if statements below are for custom printing of basis-vectors for
+        # each frame.
+        # First case, when custom indices are supplied
+        if indices is not None:
+            if not isinstance(indices, (tuple, list)):
+                raise TypeError('Supply the indices as a list')
+            if len(indices) != 3:
+                raise ValueError('Supply 3 indices')
+            for i in indices:
+                if not isinstance(i, str):
+                    raise TypeError('Indices must be strings')
+            self.str_vecs = [(name + '[\'' + indices[0] + '\']'),
+                             (name + '[\'' + indices[1] + '\']'),
+                             (name + '[\'' + indices[2] + '\']')]
+            self.pretty_vecs = [(name.lower() + "_" + indices[0]),
+                                (name.lower() + "_" + indices[1]),
+                                (name.lower() + "_" + indices[2])]
+            self.latex_vecs = [(r"\mathbf{\hat{%s}_{%s}}" % (name.lower(),
+                                                             indices[0])),
+                               (r"\mathbf{\hat{%s}_{%s}}" % (name.lower(),
+                                                             indices[1])),
+                               (r"\mathbf{\hat{%s}_{%s}}" % (name.lower(),
+                                                             indices[2]))]
+            self.indices = indices
+        # Second case, when no custom indices are supplied
+        else:
+            self.str_vecs = [(name + '.x'), (name + '.y'), (name + '.z')]
+            self.pretty_vecs = [name.lower() + "_x",
+                                name.lower() + "_y",
+                                name.lower() + "_z"]
+            self.latex_vecs = [(r"\mathbf{\hat{%s}_x}" % name.lower()),
+                               (r"\mathbf{\hat{%s}_y}" % name.lower()),
+                               (r"\mathbf{\hat{%s}_z}" % name.lower())]
+            self.indices = ['x', 'y', 'z']
+        # Different step, for custom latex basis vectors
+        if latexs is not None:
+            if not isinstance(latexs, (tuple, list)):
+                raise TypeError('Supply the indices as a list')
+            if len(latexs) != 3:
+                raise ValueError('Supply 3 indices')
+            for i in latexs:
+                if not isinstance(i, str):
+                    raise TypeError('Latex entries must be strings')
+            self.latex_vecs = latexs
+        self.name = name
+        self._var_dict = {}
+        # The _dcm_dict dictionary will only store the dcms of adjacent
+        # parent-child relationships. The _dcm_cache dictionary will store
+        # calculated dcm along with all content of _dcm_dict for faster
+        # retrieval of dcms.
+        self._dcm_dict = {}
+        self._dcm_cache = {}
+        self._ang_vel_dict = {}
+        self._ang_acc_dict = {}
+        self._dlist = [self._dcm_dict, self._ang_vel_dict, self._ang_acc_dict]
+        self._cur = 0
+        self._x = Vector([(Matrix([1, 0, 0]), self)])
+        self._y = Vector([(Matrix([0, 1, 0]), self)])
+        self._z = Vector([(Matrix([0, 0, 1]), self)])
+        # Associate coordinate symbols wrt this frame
+        if variables is not None:
+            if not isinstance(variables, (tuple, list)):
+                raise TypeError('Supply the variable names as a list/tuple')
+            if len(variables) != 3:
+                raise ValueError('Supply 3 variable names')
+            for i in variables:
+                if not isinstance(i, str):
+                    raise TypeError('Variable names must be strings')
+        else:
+            variables = [name + '_x', name + '_y', name + '_z']
+        self.varlist = (CoordinateSym(variables[0], self, 0),
+                        CoordinateSym(variables[1], self, 1),
+                        CoordinateSym(variables[2], self, 2))
+        ReferenceFrame._count += 1
+        self.index = ReferenceFrame._count
+
+    def __getitem__(self, ind):
+        """
+        Returns basis vector for the provided index, if the index is a string.
+
+        If the index is a number, returns the coordinate variable correspon-
+        -ding to that index.
+        """
+        if not isinstance(ind, str):
+            if ind < 3:
+                return self.varlist[ind]
+            else:
+                raise ValueError("Invalid index provided")
+        if self.indices[0] == ind:
+            return self.x
+        if self.indices[1] == ind:
+            return self.y
+        if self.indices[2] == ind:
+            return self.z
+        else:
+            raise ValueError('Not a defined index')
+
+    def __iter__(self):
+        return iter([self.x, self.y, self.z])
+
+    def __str__(self):
+        """Returns the name of the frame. """
+        return self.name
+
+    __repr__ = __str__
+
+    def _dict_list(self, other, num):
+        """Returns an inclusive list of reference frames that connect this
+        reference frame to the provided reference frame.
+
+        Parameters
+        ==========
+        other : ReferenceFrame
+            The other reference frame to look for a connecting relationship to.
+        num : integer
+            ``0``, ``1``, and ``2`` will look for orientation, angular
+            velocity, and angular acceleration relationships between the two
+            frames, respectively.
+
+        Returns
+        =======
+        list
+            Inclusive list of reference frames that connect this reference
+            frame to the other reference frame.
+
+        Examples
+        ========
+
+        >>> from sympy.physics.vector import ReferenceFrame
+        >>> A = ReferenceFrame('A')
+        >>> B = ReferenceFrame('B')
+        >>> C = ReferenceFrame('C')
+        >>> D = ReferenceFrame('D')
+        >>> B.orient_axis(A, A.x, 1.0)
+        >>> C.orient_axis(B, B.x, 1.0)
+        >>> D.orient_axis(C, C.x, 1.0)
+        >>> D._dict_list(A, 0)
+        [D, C, B, A]
+
+        Raises
+        ======
+
+        ValueError
+            When no path is found between the two reference frames or ``num``
+            is an incorrect value.
+
+        """
+
+        connect_type = {0: 'orientation',
+                        1: 'angular velocity',
+                        2: 'angular acceleration'}
+
+        if num not in connect_type.keys():
+            raise ValueError('Valid values for num are 0, 1, or 2.')
+
+        possible_connecting_paths = [[self]]
+        oldlist = [[]]
+        while possible_connecting_paths != oldlist:
+            oldlist = possible_connecting_paths[:]  # make a copy
+            for frame_list in possible_connecting_paths:
+                frames_adjacent_to_last = frame_list[-1]._dlist[num].keys()
+                for adjacent_frame in frames_adjacent_to_last:
+                    if adjacent_frame not in frame_list:
+                        connecting_path = frame_list + [adjacent_frame]
+                        if connecting_path not in possible_connecting_paths:
+                            possible_connecting_paths.append(connecting_path)
+
+        for connecting_path in oldlist:
+            if connecting_path[-1] != other:
+                possible_connecting_paths.remove(connecting_path)
+        possible_connecting_paths.sort(key=len)
+
+        if len(possible_connecting_paths) != 0:
+            return possible_connecting_paths[0]  # selects the shortest path
+
+        msg = 'No connecting {} path found between {} and {}.'
+        raise ValueError(msg.format(connect_type[num], self.name, other.name))
+
+    def _w_diff_dcm(self, otherframe):
+        """Angular velocity from time differentiating the DCM. """
+        from sympy.physics.vector.functions import dynamicsymbols
+        dcm2diff = otherframe.dcm(self)
+        diffed = dcm2diff.diff(dynamicsymbols._t)
+        angvelmat = diffed * dcm2diff.T
+        w1 = trigsimp(expand(angvelmat[7]), recursive=True)
+        w2 = trigsimp(expand(angvelmat[2]), recursive=True)
+        w3 = trigsimp(expand(angvelmat[3]), recursive=True)
+        return Vector([(Matrix([w1, w2, w3]), otherframe)])
+
+    def variable_map(self, otherframe):
+        """
+        Returns a dictionary which expresses the coordinate variables
+        of this frame in terms of the variables of otherframe.
+
+        If Vector.simp is True, returns a simplified version of the mapped
+        values. Else, returns them without simplification.
+
+        Simplification of the expressions may take time.
+
+        Parameters
+        ==========
+
+        otherframe : ReferenceFrame
+            The other frame to map the variables to
+
+        Examples
+        ========
+
+        >>> from sympy.physics.vector import ReferenceFrame, dynamicsymbols
+        >>> A = ReferenceFrame('A')
+        >>> q = dynamicsymbols('q')
+        >>> B = A.orientnew('B', 'Axis', [q, A.z])
+        >>> A.variable_map(B)
+        {A_x: B_x*cos(q(t)) - B_y*sin(q(t)), A_y: B_x*sin(q(t)) + B_y*cos(q(t)), A_z: B_z}
+
+        """
+
+        _check_frame(otherframe)
+        if (otherframe, Vector.simp) in self._var_dict:
+            return self._var_dict[(otherframe, Vector.simp)]
+        else:
+            vars_matrix = self.dcm(otherframe) * Matrix(otherframe.varlist)
+            mapping = {}
+            for i, x in enumerate(self):
+                if Vector.simp:
+                    mapping[self.varlist[i]] = trigsimp(vars_matrix[i],
+                                                        method='fu')
+                else:
+                    mapping[self.varlist[i]] = vars_matrix[i]
+            self._var_dict[(otherframe, Vector.simp)] = mapping
+            return mapping
+
+    def ang_acc_in(self, otherframe):
+        """Returns the angular acceleration Vector of the ReferenceFrame.
+
+        Effectively returns the Vector:
+
+        ``N_alpha_B``
+
+        which represent the angular acceleration of B in N, where B is self,
+        and N is otherframe.
+
+        Parameters
+        ==========
+
+        otherframe : ReferenceFrame
+            The ReferenceFrame which the angular acceleration is returned in.
+
+        Examples
+        ========
+
+        >>> from sympy.physics.vector import ReferenceFrame
+        >>> N = ReferenceFrame('N')
+        >>> A = ReferenceFrame('A')
+        >>> V = 10 * N.x
+        >>> A.set_ang_acc(N, V)
+        >>> A.ang_acc_in(N)
+        10*N.x
+
+        """
+
+        _check_frame(otherframe)
+        if otherframe in self._ang_acc_dict:
+            return self._ang_acc_dict[otherframe]
+        else:
+            return self.ang_vel_in(otherframe).dt(otherframe)
+
+    def ang_vel_in(self, otherframe):
+        """Returns the angular velocity Vector of the ReferenceFrame.
+
+        Effectively returns the Vector:
+
+        ^N omega ^B
+
+        which represent the angular velocity of B in N, where B is self, and
+        N is otherframe.
+
+        Parameters
+        ==========
+
+        otherframe : ReferenceFrame
+            The ReferenceFrame which the angular velocity is returned in.
+
+        Examples
+        ========
+
+        >>> from sympy.physics.vector import ReferenceFrame
+        >>> N = ReferenceFrame('N')
+        >>> A = ReferenceFrame('A')
+        >>> V = 10 * N.x
+        >>> A.set_ang_vel(N, V)
+        >>> A.ang_vel_in(N)
+        10*N.x
+
+        """
+
+        _check_frame(otherframe)
+        flist = self._dict_list(otherframe, 1)
+        outvec = Vector(0)
+        for i in range(len(flist) - 1):
+            outvec += flist[i]._ang_vel_dict[flist[i + 1]]
+        return outvec
+
+    def dcm(self, otherframe):
+        r"""Returns the direction cosine matrix of this reference frame
+        relative to the provided reference frame.
+
+        The returned matrix can be used to express the orthogonal unit vectors
+        of this frame in terms of the orthogonal unit vectors of
+        ``otherframe``.
+
+        Parameters
+        ==========
+
+        otherframe : ReferenceFrame
+            The reference frame which the direction cosine matrix of this frame
+            is formed relative to.
+
+        Examples
+        ========
+
+        The following example rotates the reference frame A relative to N by a
+        simple rotation and then calculates the direction cosine matrix of N
+        relative to A.
+
+        >>> from sympy import symbols, sin, cos
+        >>> from sympy.physics.vector import ReferenceFrame
+        >>> q1 = symbols('q1')
+        >>> N = ReferenceFrame('N')
+        >>> A = ReferenceFrame('A')
+        >>> A.orient_axis(N, q1, N.x)
+        >>> N.dcm(A)
+        Matrix([
+        [1,       0,        0],
+        [0, cos(q1), -sin(q1)],
+        [0, sin(q1),  cos(q1)]])
+
+        The second row of the above direction cosine matrix represents the
+        ``N.y`` unit vector in N expressed in A. Like so:
+
+        >>> Ny = 0*A.x + cos(q1)*A.y - sin(q1)*A.z
+
+        Thus, expressing ``N.y`` in A should return the same result:
+
+        >>> N.y.express(A)
+        cos(q1)*A.y - sin(q1)*A.z
+
+        Notes
+        =====
+
+        It is important to know what form of the direction cosine matrix is
+        returned. If ``B.dcm(A)`` is called, it means the "direction cosine
+        matrix of B rotated relative to A". This is the matrix
+        :math:`{}^B\mathbf{C}^A` shown in the following relationship:
+
+        .. math::
+
+           \begin{bmatrix}
+             \hat{\mathbf{b}}_1 \\
+             \hat{\mathbf{b}}_2 \\
+             \hat{\mathbf{b}}_3
+           \end{bmatrix}
+           =
+           {}^B\mathbf{C}^A
+           \begin{bmatrix}
+             \hat{\mathbf{a}}_1 \\
+             \hat{\mathbf{a}}_2 \\
+             \hat{\mathbf{a}}_3
+           \end{bmatrix}.
+
+        :math:`{}^B\mathbf{C}^A` is the matrix that expresses the B unit
+        vectors in terms of the A unit vectors.
+
+        """
+
+        _check_frame(otherframe)
+        # Check if the dcm wrt that frame has already been calculated
+        if otherframe in self._dcm_cache:
+            return self._dcm_cache[otherframe]
+        flist = self._dict_list(otherframe, 0)
+        outdcm = eye(3)
+        for i in range(len(flist) - 1):
+            outdcm = outdcm * flist[i]._dcm_dict[flist[i + 1]]
+        # After calculation, store the dcm in dcm cache for faster future
+        # retrieval
+        self._dcm_cache[otherframe] = outdcm
+        otherframe._dcm_cache[self] = outdcm.T
+        return outdcm
+
+    def _dcm(self, parent, parent_orient):
+        # If parent.oreint(self) is already defined,then
+        # update the _dcm_dict of parent while over write
+        # all content of self._dcm_dict and self._dcm_cache
+        # with new dcm relation.
+        # Else update _dcm_cache and _dcm_dict of both
+        # self and parent.
+        frames = self._dcm_cache.keys()
+        dcm_dict_del = []
+        dcm_cache_del = []
+        if parent in frames:
+            for frame in frames:
+                if frame in self._dcm_dict:
+                    dcm_dict_del += [frame]
+                dcm_cache_del += [frame]
+            # Reset the _dcm_cache of this frame, and remove it from the
+            # _dcm_caches of the frames it is linked to. Also remove it from
+            # the _dcm_dict of its parent
+            for frame in dcm_dict_del:
+                del frame._dcm_dict[self]
+            for frame in dcm_cache_del:
+                del frame._dcm_cache[self]
+        # Reset the _dcm_dict
+            self._dcm_dict = self._dlist[0] = {}
+        # Reset the _dcm_cache
+            self._dcm_cache = {}
+
+        else:
+            # Check for loops and raise warning accordingly.
+            visited = []
+            queue = list(frames)
+            cont = True  # Flag to control queue loop.
+            while queue and cont:
+                node = queue.pop(0)
+                if node not in visited:
+                    visited.append(node)
+                    neighbors = node._dcm_dict.keys()
+                    for neighbor in neighbors:
+                        if neighbor == parent:
+                            warn('Loops are defined among the orientation of '
+                                 'frames. This is likely not desired and may '
+                                 'cause errors in your calculations.')
+                            cont = False
+                            break
+                        queue.append(neighbor)
+
+        # Add the dcm relationship to _dcm_dict
+        self._dcm_dict.update({parent: parent_orient.T})
+        parent._dcm_dict.update({self: parent_orient})
+        # Update the dcm cache
+        self._dcm_cache.update({parent: parent_orient.T})
+        parent._dcm_cache.update({self: parent_orient})
+
+    def orient_axis(self, parent, axis, angle):
+        """Sets the orientation of this reference frame with respect to a
+        parent reference frame by rotating through an angle about an axis fixed
+        in the parent reference frame.
+
+        Parameters
+        ==========
+
+        parent : ReferenceFrame
+            Reference frame that this reference frame will be rotated relative
+            to.
+        axis : Vector
+            Vector fixed in the parent frame about about which this frame is
+            rotated. It need not be a unit vector and the rotation follows the
+            right hand rule.
+        angle : sympifiable
+            Angle in radians by which it the frame is to be rotated.
+
+        Warns
+        ======
+
+        UserWarning
+            If the orientation creates a kinematic loop.
+
+        Examples
+        ========
+
+        Setup variables for the examples:
+
+        >>> from sympy import symbols
+        >>> from sympy.physics.vector import ReferenceFrame
+        >>> q1 = symbols('q1')
+        >>> N = ReferenceFrame('N')
+        >>> B = ReferenceFrame('B')
+        >>> B.orient_axis(N, N.x, q1)
+
+        The ``orient_axis()`` method generates a direction cosine matrix and
+        its transpose which defines the orientation of B relative to N and vice
+        versa. Once orient is called, ``dcm()`` outputs the appropriate
+        direction cosine matrix:
+
+        >>> B.dcm(N)
+        Matrix([
+        [1,       0,      0],
+        [0,  cos(q1), sin(q1)],
+        [0, -sin(q1), cos(q1)]])
+        >>> N.dcm(B)
+        Matrix([
+        [1,       0,        0],
+        [0, cos(q1), -sin(q1)],
+        [0, sin(q1),  cos(q1)]])
+
+        The following two lines show that the sense of the rotation can be
+        defined by negating the vector direction or the angle. Both lines
+        produce the same result.
+
+        >>> B.orient_axis(N, -N.x, q1)
+        >>> B.orient_axis(N, N.x, -q1)
+
+        """
+
+        from sympy.physics.vector.functions import dynamicsymbols
+        _check_frame(parent)
+
+        if not isinstance(axis, Vector) and isinstance(angle, Vector):
+            axis, angle = angle, axis
+
+        axis = _check_vector(axis)
+        theta = sympify(angle)
+
+        if not axis.dt(parent) == 0:
+            raise ValueError('Axis cannot be time-varying.')
+        unit_axis = axis.express(parent).normalize()
+        unit_col = unit_axis.args[0][0]
+        parent_orient_axis = (
+            (eye(3) - unit_col * unit_col.T) * cos(theta) +
+            Matrix([[0, -unit_col[2], unit_col[1]],
+                    [unit_col[2], 0, -unit_col[0]],
+                    [-unit_col[1], unit_col[0], 0]]) *
+            sin(theta) + unit_col * unit_col.T)
+
+        self._dcm(parent, parent_orient_axis)
+
+        thetad = (theta).diff(dynamicsymbols._t)
+        wvec = thetad*axis.express(parent).normalize()
+        self._ang_vel_dict.update({parent: wvec})
+        parent._ang_vel_dict.update({self: -wvec})
+        self._var_dict = {}
+
+    def orient_explicit(self, parent, dcm):
+        """Sets the orientation of this reference frame relative to a parent
+        reference frame by explicitly setting the direction cosine matrix.
+
+        Parameters
+        ==========
+
+        parent : ReferenceFrame
+            Reference frame that this reference frame will be rotated relative
+            to.
+        dcm : Matrix, shape(3, 3)
+            Direction cosine matrix that specifies the relative rotation
+            between the two reference frames.
+
+        Warns
+        ======
+
+        UserWarning
+            If the orientation creates a kinematic loop.
+
+        Examples
+        ========
+
+        Setup variables for the examples:
+
+        >>> from sympy import symbols, Matrix, sin, cos
+        >>> from sympy.physics.vector import ReferenceFrame
+        >>> q1 = symbols('q1')
+        >>> A = ReferenceFrame('A')
+        >>> B = ReferenceFrame('B')
+        >>> N = ReferenceFrame('N')
+
+        A simple rotation of ``A`` relative to ``N`` about ``N.x`` is defined
+        by the following direction cosine matrix:
+
+        >>> dcm = Matrix([[1, 0, 0],
+        ...               [0, cos(q1), -sin(q1)],
+        ...               [0, sin(q1), cos(q1)]])
+        >>> A.orient_explicit(N, dcm)
+        >>> A.dcm(N)
+        Matrix([
+        [1,       0,      0],
+        [0,  cos(q1), sin(q1)],
+        [0, -sin(q1), cos(q1)]])
+
+        This is equivalent to using ``orient_axis()``:
+
+        >>> B.orient_axis(N, N.x, q1)
+        >>> B.dcm(N)
+        Matrix([
+        [1,       0,      0],
+        [0,  cos(q1), sin(q1)],
+        [0, -sin(q1), cos(q1)]])
+
+        **Note carefully that** ``N.dcm(B)`` **(the transpose) would be passed
+        into** ``orient_explicit()`` **for** ``A.dcm(N)`` **to match**
+        ``B.dcm(N)``:
+
+        >>> A.orient_explicit(N, N.dcm(B))
+        >>> A.dcm(N)
+        Matrix([
+        [1,       0,      0],
+        [0,  cos(q1), sin(q1)],
+        [0, -sin(q1), cos(q1)]])
+
+        """
+
+        _check_frame(parent)
+        # amounts must be a Matrix type object
+        # (e.g. sympy.matrices.dense.MutableDenseMatrix).
+        if not isinstance(dcm, MatrixBase):
+            raise TypeError("Amounts must be a SymPy Matrix type object.")
+
+        parent_orient_dcm = dcm
+
+        self._dcm(parent, parent_orient_dcm)
+
+        wvec = self._w_diff_dcm(parent)
+        self._ang_vel_dict.update({parent: wvec})
+        parent._ang_vel_dict.update({self: -wvec})
+        self._var_dict = {}
+
+    def _rot(self, axis, angle):
+        """DCM for simple axis 1,2,or 3 rotations."""
+        if axis == 1:
+            return Matrix([[1, 0, 0],
+                           [0, cos(angle), -sin(angle)],
+                           [0, sin(angle), cos(angle)]])
+        elif axis == 2:
+            return Matrix([[cos(angle), 0, sin(angle)],
+                           [0, 1, 0],
+                           [-sin(angle), 0, cos(angle)]])
+        elif axis == 3:
+            return Matrix([[cos(angle), -sin(angle), 0],
+                           [sin(angle), cos(angle), 0],
+                           [0, 0, 1]])
+
+    def _parse_consecutive_rotations(self, angles, rotation_order):
+        """Helper for orient_body_fixed and orient_space_fixed.
+
+        Parameters
+        ==========
+        angles : 3-tuple of sympifiable
+            Three angles in radians used for the successive rotations.
+        rotation_order : 3 character string or 3 digit integer
+            Order of the rotations. The order can be specified by the strings
+            ``'XZX'``, ``'131'``, or the integer ``131``. There are 12 unique
+            valid rotation orders.
+
+        Returns
+        =======
+
+        amounts : list
+            List of sympifiables corresponding to the rotation angles.
+        rot_order : list
+            List of integers corresponding to the axis of rotation.
+        rot_matrices : list
+            List of DCM around the given axis with corresponding magnitude.
+
+        """
+        amounts = list(angles)
+        for i, v in enumerate(amounts):
+            if not isinstance(v, Vector):
+                amounts[i] = sympify(v)
+
+        approved_orders = ('123', '231', '312', '132', '213', '321', '121',
+                           '131', '212', '232', '313', '323', '')
+        # make sure XYZ => 123
+        rot_order = translate(str(rotation_order), 'XYZxyz', '123123')
+        if rot_order not in approved_orders:
+            raise TypeError('The rotation order is not a valid order.')
+
+        rot_order = [int(r) for r in rot_order]
+        if not (len(amounts) == 3 & len(rot_order) == 3):
+            raise TypeError('Body orientation takes 3 values & 3 orders')
+        rot_matrices = [self._rot(order, amount)
+                        for (order, amount) in zip(rot_order, amounts)]
+        return amounts, rot_order, rot_matrices
+
+    def orient_body_fixed(self, parent, angles, rotation_order):
+        """Rotates this reference frame relative to the parent reference frame
+        by right hand rotating through three successive body fixed simple axis
+        rotations. Each subsequent axis of rotation is about the "body fixed"
+        unit vectors of a new intermediate reference frame. This type of
+        rotation is also referred to rotating through the `Euler and Tait-Bryan
+        Angles`_.
+
+        .. _Euler and Tait-Bryan Angles: https://en.wikipedia.org/wiki/Euler_angles
+
+        The computed angular velocity in this method is by default expressed in
+        the child's frame, so it is most preferable to use ``u1 * child.x + u2 *
+        child.y + u3 * child.z`` as generalized speeds.
+
+        Parameters
+        ==========
+
+        parent : ReferenceFrame
+            Reference frame that this reference frame will be rotated relative
+            to.
+        angles : 3-tuple of sympifiable
+            Three angles in radians used for the successive rotations.
+        rotation_order : 3 character string or 3 digit integer
+            Order of the rotations about each intermediate reference frames'
+            unit vectors. The Euler rotation about the X, Z', X'' axes can be
+            specified by the strings ``'XZX'``, ``'131'``, or the integer
+            ``131``. There are 12 unique valid rotation orders (6 Euler and 6
+            Tait-Bryan): zxz, xyx, yzy, zyz, xzx, yxy, xyz, yzx, zxy, xzy, zyx,
+            and yxz.
+
+        Warns
+        ======
+
+        UserWarning
+            If the orientation creates a kinematic loop.
+
+        Examples
+        ========
+
+        Setup variables for the examples:
+
+        >>> from sympy import symbols
+        >>> from sympy.physics.vector import ReferenceFrame
+        >>> q1, q2, q3 = symbols('q1, q2, q3')
+        >>> N = ReferenceFrame('N')
+        >>> B = ReferenceFrame('B')
+        >>> B1 = ReferenceFrame('B1')
+        >>> B2 = ReferenceFrame('B2')
+        >>> B3 = ReferenceFrame('B3')
+
+        For example, a classic Euler Angle rotation can be done by:
+
+        >>> B.orient_body_fixed(N, (q1, q2, q3), 'XYX')
+        >>> B.dcm(N)
+        Matrix([
+        [        cos(q2),                            sin(q1)*sin(q2),                           -sin(q2)*cos(q1)],
+        [sin(q2)*sin(q3), -sin(q1)*sin(q3)*cos(q2) + cos(q1)*cos(q3),  sin(q1)*cos(q3) + sin(q3)*cos(q1)*cos(q2)],
+        [sin(q2)*cos(q3), -sin(q1)*cos(q2)*cos(q3) - sin(q3)*cos(q1), -sin(q1)*sin(q3) + cos(q1)*cos(q2)*cos(q3)]])
+
+        This rotates reference frame B relative to reference frame N through
+        ``q1`` about ``N.x``, then rotates B again through ``q2`` about
+        ``B.y``, and finally through ``q3`` about ``B.x``. It is equivalent to
+        three successive ``orient_axis()`` calls:
+
+        >>> B1.orient_axis(N, N.x, q1)
+        >>> B2.orient_axis(B1, B1.y, q2)
+        >>> B3.orient_axis(B2, B2.x, q3)
+        >>> B3.dcm(N)
+        Matrix([
+        [        cos(q2),                            sin(q1)*sin(q2),                           -sin(q2)*cos(q1)],
+        [sin(q2)*sin(q3), -sin(q1)*sin(q3)*cos(q2) + cos(q1)*cos(q3),  sin(q1)*cos(q3) + sin(q3)*cos(q1)*cos(q2)],
+        [sin(q2)*cos(q3), -sin(q1)*cos(q2)*cos(q3) - sin(q3)*cos(q1), -sin(q1)*sin(q3) + cos(q1)*cos(q2)*cos(q3)]])
+
+        Acceptable rotation orders are of length 3, expressed in as a string
+        ``'XYZ'`` or ``'123'`` or integer ``123``. Rotations about an axis
+        twice in a row are prohibited.
+
+        >>> B.orient_body_fixed(N, (q1, q2, 0), 'ZXZ')
+        >>> B.orient_body_fixed(N, (q1, q2, 0), '121')
+        >>> B.orient_body_fixed(N, (q1, q2, q3), 123)
+
+        """
+        from sympy.physics.vector.functions import dynamicsymbols
+
+        _check_frame(parent)
+
+        amounts, rot_order, rot_matrices = self._parse_consecutive_rotations(
+            angles, rotation_order)
+        self._dcm(parent, rot_matrices[0] * rot_matrices[1] * rot_matrices[2])
+
+        rot_vecs = [zeros(3, 1) for _ in range(3)]
+        for i, order in enumerate(rot_order):
+            rot_vecs[i][order - 1] = amounts[i].diff(dynamicsymbols._t)
+        u1, u2, u3 = rot_vecs[2] + rot_matrices[2].T * (
+            rot_vecs[1] + rot_matrices[1].T * rot_vecs[0])
+        wvec = u1 * self.x + u2 * self.y + u3 * self.z  # There is a double -
+        self._ang_vel_dict.update({parent: wvec})
+        parent._ang_vel_dict.update({self: -wvec})
+        self._var_dict = {}
+
+    def orient_space_fixed(self, parent, angles, rotation_order):
+        """Rotates this reference frame relative to the parent reference frame
+        by right hand rotating through three successive space fixed simple axis
+        rotations. Each subsequent axis of rotation is about the "space fixed"
+        unit vectors of the parent reference frame.
+
+        The computed angular velocity in this method is by default expressed in
+        the child's frame, so it is most preferable to use ``u1 * child.x + u2 *
+        child.y + u3 * child.z`` as generalized speeds.
+
+        Parameters
+        ==========
+        parent : ReferenceFrame
+            Reference frame that this reference frame will be rotated relative
+            to.
+        angles : 3-tuple of sympifiable
+            Three angles in radians used for the successive rotations.
+        rotation_order : 3 character string or 3 digit integer
+            Order of the rotations about the parent reference frame's unit
+            vectors. The order can be specified by the strings ``'XZX'``,
+            ``'131'``, or the integer ``131``. There are 12 unique valid
+            rotation orders.
+
+        Warns
+        ======
+
+        UserWarning
+            If the orientation creates a kinematic loop.
+
+        Examples
+        ========
+
+        Setup variables for the examples:
+
+        >>> from sympy import symbols
+        >>> from sympy.physics.vector import ReferenceFrame
+        >>> q1, q2, q3 = symbols('q1, q2, q3')
+        >>> N = ReferenceFrame('N')
+        >>> B = ReferenceFrame('B')
+        >>> B1 = ReferenceFrame('B1')
+        >>> B2 = ReferenceFrame('B2')
+        >>> B3 = ReferenceFrame('B3')
+
+        >>> B.orient_space_fixed(N, (q1, q2, q3), '312')
+        >>> B.dcm(N)
+        Matrix([
+        [ sin(q1)*sin(q2)*sin(q3) + cos(q1)*cos(q3), sin(q1)*cos(q2), sin(q1)*sin(q2)*cos(q3) - sin(q3)*cos(q1)],
+        [-sin(q1)*cos(q3) + sin(q2)*sin(q3)*cos(q1), cos(q1)*cos(q2), sin(q1)*sin(q3) + sin(q2)*cos(q1)*cos(q3)],
+        [                           sin(q3)*cos(q2),        -sin(q2),                           cos(q2)*cos(q3)]])
+
+        is equivalent to:
+
+        >>> B1.orient_axis(N, N.z, q1)
+        >>> B2.orient_axis(B1, N.x, q2)
+        >>> B3.orient_axis(B2, N.y, q3)
+        >>> B3.dcm(N).simplify()
+        Matrix([
+        [ sin(q1)*sin(q2)*sin(q3) + cos(q1)*cos(q3), sin(q1)*cos(q2), sin(q1)*sin(q2)*cos(q3) - sin(q3)*cos(q1)],
+        [-sin(q1)*cos(q3) + sin(q2)*sin(q3)*cos(q1), cos(q1)*cos(q2), sin(q1)*sin(q3) + sin(q2)*cos(q1)*cos(q3)],
+        [                           sin(q3)*cos(q2),        -sin(q2),                           cos(q2)*cos(q3)]])
+
+        It is worth noting that space-fixed and body-fixed rotations are
+        related by the order of the rotations, i.e. the reverse order of body
+        fixed will give space fixed and vice versa.
+
+        >>> B.orient_space_fixed(N, (q1, q2, q3), '231')
+        >>> B.dcm(N)
+        Matrix([
+        [cos(q1)*cos(q2), sin(q1)*sin(q3) + sin(q2)*cos(q1)*cos(q3), -sin(q1)*cos(q3) + sin(q2)*sin(q3)*cos(q1)],
+        [       -sin(q2),                           cos(q2)*cos(q3),                            sin(q3)*cos(q2)],
+        [sin(q1)*cos(q2), sin(q1)*sin(q2)*cos(q3) - sin(q3)*cos(q1),  sin(q1)*sin(q2)*sin(q3) + cos(q1)*cos(q3)]])
+
+        >>> B.orient_body_fixed(N, (q3, q2, q1), '132')
+        >>> B.dcm(N)
+        Matrix([
+        [cos(q1)*cos(q2), sin(q1)*sin(q3) + sin(q2)*cos(q1)*cos(q3), -sin(q1)*cos(q3) + sin(q2)*sin(q3)*cos(q1)],
+        [       -sin(q2),                           cos(q2)*cos(q3),                            sin(q3)*cos(q2)],
+        [sin(q1)*cos(q2), sin(q1)*sin(q2)*cos(q3) - sin(q3)*cos(q1),  sin(q1)*sin(q2)*sin(q3) + cos(q1)*cos(q3)]])
+
+        """
+        from sympy.physics.vector.functions import dynamicsymbols
+
+        _check_frame(parent)
+
+        amounts, rot_order, rot_matrices = self._parse_consecutive_rotations(
+            angles, rotation_order)
+        self._dcm(parent, rot_matrices[2] * rot_matrices[1] * rot_matrices[0])
+
+        rot_vecs = [zeros(3, 1) for _ in range(3)]
+        for i, order in enumerate(rot_order):
+            rot_vecs[i][order - 1] = amounts[i].diff(dynamicsymbols._t)
+        u1, u2, u3 = rot_vecs[0] + rot_matrices[0].T * (
+            rot_vecs[1] + rot_matrices[1].T * rot_vecs[2])
+        wvec = u1 * self.x + u2 * self.y + u3 * self.z  # There is a double -
+        self._ang_vel_dict.update({parent: wvec})
+        parent._ang_vel_dict.update({self: -wvec})
+        self._var_dict = {}
+
+    def orient_quaternion(self, parent, numbers):
+        """Sets the orientation of this reference frame relative to a parent
+        reference frame via an orientation quaternion. An orientation
+        quaternion is defined as a finite rotation a unit vector, ``(lambda_x,
+        lambda_y, lambda_z)``, by an angle ``theta``. The orientation
+        quaternion is described by four parameters:
+
+        - ``q0 = cos(theta/2)``
+        - ``q1 = lambda_x*sin(theta/2)``
+        - ``q2 = lambda_y*sin(theta/2)``
+        - ``q3 = lambda_z*sin(theta/2)``
+
+        See `Quaternions and Spatial Rotation
+        `_ on
+        Wikipedia for more information.
+
+        Parameters
+        ==========
+        parent : ReferenceFrame
+            Reference frame that this reference frame will be rotated relative
+            to.
+        numbers : 4-tuple of sympifiable
+            The four quaternion scalar numbers as defined above: ``q0``,
+            ``q1``, ``q2``, ``q3``.
+
+        Warns
+        ======
+
+        UserWarning
+            If the orientation creates a kinematic loop.
+
+        Examples
+        ========
+
+        Setup variables for the examples:
+
+        >>> from sympy import symbols
+        >>> from sympy.physics.vector import ReferenceFrame
+        >>> q0, q1, q2, q3 = symbols('q0 q1 q2 q3')
+        >>> N = ReferenceFrame('N')
+        >>> B = ReferenceFrame('B')
+
+        Set the orientation:
+
+        >>> B.orient_quaternion(N, (q0, q1, q2, q3))
+        >>> B.dcm(N)
+        Matrix([
+        [q0**2 + q1**2 - q2**2 - q3**2,             2*q0*q3 + 2*q1*q2,            -2*q0*q2 + 2*q1*q3],
+        [           -2*q0*q3 + 2*q1*q2, q0**2 - q1**2 + q2**2 - q3**2,             2*q0*q1 + 2*q2*q3],
+        [            2*q0*q2 + 2*q1*q3,            -2*q0*q1 + 2*q2*q3, q0**2 - q1**2 - q2**2 + q3**2]])
+
+        """
+
+        from sympy.physics.vector.functions import dynamicsymbols
+        _check_frame(parent)
+
+        numbers = list(numbers)
+        for i, v in enumerate(numbers):
+            if not isinstance(v, Vector):
+                numbers[i] = sympify(v)
+
+        if not (isinstance(numbers, (list, tuple)) & (len(numbers) == 4)):
+            raise TypeError('Amounts are a list or tuple of length 4')
+        q0, q1, q2, q3 = numbers
+        parent_orient_quaternion = (
+            Matrix([[q0**2 + q1**2 - q2**2 - q3**2,
+                     2 * (q1 * q2 - q0 * q3),
+                     2 * (q0 * q2 + q1 * q3)],
+                    [2 * (q1 * q2 + q0 * q3),
+                     q0**2 - q1**2 + q2**2 - q3**2,
+                     2 * (q2 * q3 - q0 * q1)],
+                    [2 * (q1 * q3 - q0 * q2),
+                     2 * (q0 * q1 + q2 * q3),
+                     q0**2 - q1**2 - q2**2 + q3**2]]))
+
+        self._dcm(parent, parent_orient_quaternion)
+
+        t = dynamicsymbols._t
+        q0, q1, q2, q3 = numbers
+        q0d = diff(q0, t)
+        q1d = diff(q1, t)
+        q2d = diff(q2, t)
+        q3d = diff(q3, t)
+        w1 = 2 * (q1d * q0 + q2d * q3 - q3d * q2 - q0d * q1)
+        w2 = 2 * (q2d * q0 + q3d * q1 - q1d * q3 - q0d * q2)
+        w3 = 2 * (q3d * q0 + q1d * q2 - q2d * q1 - q0d * q3)
+        wvec = Vector([(Matrix([w1, w2, w3]), self)])
+
+        self._ang_vel_dict.update({parent: wvec})
+        parent._ang_vel_dict.update({self: -wvec})
+        self._var_dict = {}
+
+    def orient(self, parent, rot_type, amounts, rot_order=''):
+        """Sets the orientation of this reference frame relative to another
+        (parent) reference frame.
+
+        .. note:: It is now recommended to use the ``.orient_axis,
+           .orient_body_fixed, .orient_space_fixed, .orient_quaternion``
+           methods for the different rotation types.
+
+        Parameters
+        ==========
+
+        parent : ReferenceFrame
+            Reference frame that this reference frame will be rotated relative
+            to.
+        rot_type : str
+            The method used to generate the direction cosine matrix. Supported
+            methods are:
+
+            - ``'Axis'``: simple rotations about a single common axis
+            - ``'DCM'``: for setting the direction cosine matrix directly
+            - ``'Body'``: three successive rotations about new intermediate
+              axes, also called "Euler and Tait-Bryan angles"
+            - ``'Space'``: three successive rotations about the parent
+              frames' unit vectors
+            - ``'Quaternion'``: rotations defined by four parameters which
+              result in a singularity free direction cosine matrix
+
+        amounts :
+            Expressions defining the rotation angles or direction cosine
+            matrix. These must match the ``rot_type``. See examples below for
+            details. The input types are:
+
+            - ``'Axis'``: 2-tuple (expr/sym/func, Vector)
+            - ``'DCM'``: Matrix, shape(3,3)
+            - ``'Body'``: 3-tuple of expressions, symbols, or functions
+            - ``'Space'``: 3-tuple of expressions, symbols, or functions
+            - ``'Quaternion'``: 4-tuple of expressions, symbols, or
+              functions
+
+        rot_order : str or int, optional
+            If applicable, the order of the successive of rotations. The string
+            ``'123'`` and integer ``123`` are equivalent, for example. Required
+            for ``'Body'`` and ``'Space'``.
+
+        Warns
+        ======
+
+        UserWarning
+            If the orientation creates a kinematic loop.
+
+        """
+
+        _check_frame(parent)
+
+        approved_orders = ('123', '231', '312', '132', '213', '321', '121',
+                           '131', '212', '232', '313', '323', '')
+        rot_order = translate(str(rot_order), 'XYZxyz', '123123')
+        rot_type = rot_type.upper()
+
+        if rot_order not in approved_orders:
+            raise TypeError('The supplied order is not an approved type')
+
+        if rot_type == 'AXIS':
+            self.orient_axis(parent, amounts[1], amounts[0])
+
+        elif rot_type == 'DCM':
+            self.orient_explicit(parent, amounts)
+
+        elif rot_type == 'BODY':
+            self.orient_body_fixed(parent, amounts, rot_order)
+
+        elif rot_type == 'SPACE':
+            self.orient_space_fixed(parent, amounts, rot_order)
+
+        elif rot_type == 'QUATERNION':
+            self.orient_quaternion(parent, amounts)
+
+        else:
+            raise NotImplementedError('That is not an implemented rotation')
+
+    def orientnew(self, newname, rot_type, amounts, rot_order='',
+                  variables=None, indices=None, latexs=None):
+        r"""Returns a new reference frame oriented with respect to this
+        reference frame.
+
+        See ``ReferenceFrame.orient()`` for detailed examples of how to orient
+        reference frames.
+
+        Parameters
+        ==========
+
+        newname : str
+            Name for the new reference frame.
+        rot_type : str
+            The method used to generate the direction cosine matrix. Supported
+            methods are:
+
+            - ``'Axis'``: simple rotations about a single common axis
+            - ``'DCM'``: for setting the direction cosine matrix directly
+            - ``'Body'``: three successive rotations about new intermediate
+              axes, also called "Euler and Tait-Bryan angles"
+            - ``'Space'``: three successive rotations about the parent
+              frames' unit vectors
+            - ``'Quaternion'``: rotations defined by four parameters which
+              result in a singularity free direction cosine matrix
+
+        amounts :
+            Expressions defining the rotation angles or direction cosine
+            matrix. These must match the ``rot_type``. See examples below for
+            details. The input types are:
+
+            - ``'Axis'``: 2-tuple (expr/sym/func, Vector)
+            - ``'DCM'``: Matrix, shape(3,3)
+            - ``'Body'``: 3-tuple of expressions, symbols, or functions
+            - ``'Space'``: 3-tuple of expressions, symbols, or functions
+            - ``'Quaternion'``: 4-tuple of expressions, symbols, or
+              functions
+
+        rot_order : str or int, optional
+            If applicable, the order of the successive of rotations. The string
+            ``'123'`` and integer ``123`` are equivalent, for example. Required
+            for ``'Body'`` and ``'Space'``.
+        indices : tuple of str
+            Enables the reference frame's basis unit vectors to be accessed by
+            Python's square bracket indexing notation using the provided three
+            indice strings and alters the printing of the unit vectors to
+            reflect this choice.
+        latexs : tuple of str
+            Alters the LaTeX printing of the reference frame's basis unit
+            vectors to the provided three valid LaTeX strings.
+
+        Examples
+        ========
+
+        >>> from sympy import symbols
+        >>> from sympy.physics.vector import ReferenceFrame, vlatex
+        >>> q0, q1, q2, q3 = symbols('q0 q1 q2 q3')
+        >>> N = ReferenceFrame('N')
+
+        Create a new reference frame A rotated relative to N through a simple
+        rotation.
+
+        >>> A = N.orientnew('A', 'Axis', (q0, N.x))
+
+        Create a new reference frame B rotated relative to N through body-fixed
+        rotations.
+
+        >>> B = N.orientnew('B', 'Body', (q1, q2, q3), '123')
+
+        Create a new reference frame C rotated relative to N through a simple
+        rotation with unique indices and LaTeX printing.
+
+        >>> C = N.orientnew('C', 'Axis', (q0, N.x), indices=('1', '2', '3'),
+        ... latexs=(r'\hat{\mathbf{c}}_1',r'\hat{\mathbf{c}}_2',
+        ... r'\hat{\mathbf{c}}_3'))
+        >>> C['1']
+        C['1']
+        >>> print(vlatex(C['1']))
+        \hat{\mathbf{c}}_1
+
+        """
+
+        newframe = self.__class__(newname, variables=variables,
+                                  indices=indices, latexs=latexs)
+
+        approved_orders = ('123', '231', '312', '132', '213', '321', '121',
+                           '131', '212', '232', '313', '323', '')
+        rot_order = translate(str(rot_order), 'XYZxyz', '123123')
+        rot_type = rot_type.upper()
+
+        if rot_order not in approved_orders:
+            raise TypeError('The supplied order is not an approved type')
+
+        if rot_type == 'AXIS':
+            newframe.orient_axis(self, amounts[1], amounts[0])
+
+        elif rot_type == 'DCM':
+            newframe.orient_explicit(self, amounts)
+
+        elif rot_type == 'BODY':
+            newframe.orient_body_fixed(self, amounts, rot_order)
+
+        elif rot_type == 'SPACE':
+            newframe.orient_space_fixed(self, amounts, rot_order)
+
+        elif rot_type == 'QUATERNION':
+            newframe.orient_quaternion(self, amounts)
+
+        else:
+            raise NotImplementedError('That is not an implemented rotation')
+        return newframe
+
+    def set_ang_acc(self, otherframe, value):
+        """Define the angular acceleration Vector in a ReferenceFrame.
+
+        Defines the angular acceleration of this ReferenceFrame, in another.
+        Angular acceleration can be defined with respect to multiple different
+        ReferenceFrames. Care must be taken to not create loops which are
+        inconsistent.
+
+        Parameters
+        ==========
+
+        otherframe : ReferenceFrame
+            A ReferenceFrame to define the angular acceleration in
+        value : Vector
+            The Vector representing angular acceleration
+
+        Examples
+        ========
+
+        >>> from sympy.physics.vector import ReferenceFrame
+        >>> N = ReferenceFrame('N')
+        >>> A = ReferenceFrame('A')
+        >>> V = 10 * N.x
+        >>> A.set_ang_acc(N, V)
+        >>> A.ang_acc_in(N)
+        10*N.x
+
+        """
+
+        if value == 0:
+            value = Vector(0)
+        value = _check_vector(value)
+        _check_frame(otherframe)
+        self._ang_acc_dict.update({otherframe: value})
+        otherframe._ang_acc_dict.update({self: -value})
+
+    def set_ang_vel(self, otherframe, value):
+        """Define the angular velocity vector in a ReferenceFrame.
+
+        Defines the angular velocity of this ReferenceFrame, in another.
+        Angular velocity can be defined with respect to multiple different
+        ReferenceFrames. Care must be taken to not create loops which are
+        inconsistent.
+
+        Parameters
+        ==========
+
+        otherframe : ReferenceFrame
+            A ReferenceFrame to define the angular velocity in
+        value : Vector
+            The Vector representing angular velocity
+
+        Examples
+        ========
+
+        >>> from sympy.physics.vector import ReferenceFrame
+        >>> N = ReferenceFrame('N')
+        >>> A = ReferenceFrame('A')
+        >>> V = 10 * N.x
+        >>> A.set_ang_vel(N, V)
+        >>> A.ang_vel_in(N)
+        10*N.x
+
+        """
+
+        if value == 0:
+            value = Vector(0)
+        value = _check_vector(value)
+        _check_frame(otherframe)
+        self._ang_vel_dict.update({otherframe: value})
+        otherframe._ang_vel_dict.update({self: -value})
+
+    @property
+    def x(self):
+        """The basis Vector for the ReferenceFrame, in the x direction. """
+        return self._x
+
+    @property
+    def y(self):
+        """The basis Vector for the ReferenceFrame, in the y direction. """
+        return self._y
+
+    @property
+    def z(self):
+        """The basis Vector for the ReferenceFrame, in the z direction. """
+        return self._z
+
+    def partial_velocity(self, frame, *gen_speeds):
+        """Returns the partial angular velocities of this frame in the given
+        frame with respect to one or more provided generalized speeds.
+
+        Parameters
+        ==========
+        frame : ReferenceFrame
+            The frame with which the angular velocity is defined in.
+        gen_speeds : functions of time
+            The generalized speeds.
+
+        Returns
+        =======
+        partial_velocities : tuple of Vector
+            The partial angular velocity vectors corresponding to the provided
+            generalized speeds.
+
+        Examples
+        ========
+
+        >>> from sympy.physics.vector import ReferenceFrame, dynamicsymbols
+        >>> N = ReferenceFrame('N')
+        >>> A = ReferenceFrame('A')
+        >>> u1, u2 = dynamicsymbols('u1, u2')
+        >>> A.set_ang_vel(N, u1 * A.x + u2 * N.y)
+        >>> A.partial_velocity(N, u1)
+        A.x
+        >>> A.partial_velocity(N, u1, u2)
+        (A.x, N.y)
+
+        """
+
+        partials = [self.ang_vel_in(frame).diff(speed, frame, var_in_dcm=False)
+                    for speed in gen_speeds]
+
+        if len(partials) == 1:
+            return partials[0]
+        else:
+            return tuple(partials)
+
+
+def _check_frame(other):
+    from .vector import VectorTypeError
+    if not isinstance(other, ReferenceFrame):
+        raise VectorTypeError(other, ReferenceFrame('A'))
diff --git a/llmeval-env/lib/python3.10/site-packages/sympy/physics/vector/functions.py b/llmeval-env/lib/python3.10/site-packages/sympy/physics/vector/functions.py
new file mode 100644
index 0000000000000000000000000000000000000000..d80c6ad4d8cf73f1389220d6f0faa4c7f0cf0b63
--- /dev/null
+++ b/llmeval-env/lib/python3.10/site-packages/sympy/physics/vector/functions.py
@@ -0,0 +1,644 @@
+from functools import reduce
+
+from sympy.core.backend import (sympify, diff, sin, cos, Matrix, symbols,
+                                Function, S, Symbol)
+from sympy.integrals.integrals import integrate
+from sympy.simplify.trigsimp import trigsimp
+from .vector import Vector, _check_vector
+from .frame import CoordinateSym, _check_frame
+from .dyadic import Dyadic
+from .printing import vprint, vsprint, vpprint, vlatex, init_vprinting
+from sympy.utilities.iterables import iterable
+from sympy.utilities.misc import translate
+
+__all__ = ['cross', 'dot', 'express', 'time_derivative', 'outer',
+           'kinematic_equations', 'get_motion_params', 'partial_velocity',
+           'dynamicsymbols', 'vprint', 'vsprint', 'vpprint', 'vlatex',
+           'init_vprinting']
+
+
+def cross(vec1, vec2):
+    """Cross product convenience wrapper for Vector.cross(): \n"""
+    if not isinstance(vec1, (Vector, Dyadic)):
+        raise TypeError('Cross product is between two vectors')
+    return vec1 ^ vec2
+
+
+cross.__doc__ += Vector.cross.__doc__  # type: ignore
+
+
+def dot(vec1, vec2):
+    """Dot product convenience wrapper for Vector.dot(): \n"""
+    if not isinstance(vec1, (Vector, Dyadic)):
+        raise TypeError('Dot product is between two vectors')
+    return vec1 & vec2
+
+
+dot.__doc__ += Vector.dot.__doc__  # type: ignore
+
+
+def express(expr, frame, frame2=None, variables=False):
+    """
+    Global function for 'express' functionality.
+
+    Re-expresses a Vector, scalar(sympyfiable) or Dyadic in given frame.
+
+    Refer to the local methods of Vector and Dyadic for details.
+    If 'variables' is True, then the coordinate variables (CoordinateSym
+    instances) of other frames present in the vector/scalar field or
+    dyadic expression are also substituted in terms of the base scalars of
+    this frame.
+
+    Parameters
+    ==========
+
+    expr : Vector/Dyadic/scalar(sympyfiable)
+        The expression to re-express in ReferenceFrame 'frame'
+
+    frame: ReferenceFrame
+        The reference frame to express expr in
+
+    frame2 : ReferenceFrame
+        The other frame required for re-expression(only for Dyadic expr)
+
+    variables : boolean
+        Specifies whether to substitute the coordinate variables present
+        in expr, in terms of those of frame
+
+    Examples
+    ========
+
+    >>> from sympy.physics.vector import ReferenceFrame, outer, dynamicsymbols
+    >>> from sympy.physics.vector import init_vprinting
+    >>> init_vprinting(pretty_print=False)
+    >>> N = ReferenceFrame('N')
+    >>> q = dynamicsymbols('q')
+    >>> B = N.orientnew('B', 'Axis', [q, N.z])
+    >>> d = outer(N.x, N.x)
+    >>> from sympy.physics.vector import express
+    >>> express(d, B, N)
+    cos(q)*(B.x|N.x) - sin(q)*(B.y|N.x)
+    >>> express(B.x, N)
+    cos(q)*N.x + sin(q)*N.y
+    >>> express(N[0], B, variables=True)
+    B_x*cos(q) - B_y*sin(q)
+
+    """
+
+    _check_frame(frame)
+
+    if expr == 0:
+        return expr
+
+    if isinstance(expr, Vector):
+        # Given expr is a Vector
+        if variables:
+            # If variables attribute is True, substitute the coordinate
+            # variables in the Vector
+            frame_list = [x[-1] for x in expr.args]
+            subs_dict = {}
+            for f in frame_list:
+                subs_dict.update(f.variable_map(frame))
+            expr = expr.subs(subs_dict)
+        # Re-express in this frame
+        outvec = Vector([])
+        for i, v in enumerate(expr.args):
+            if v[1] != frame:
+                temp = frame.dcm(v[1]) * v[0]
+                if Vector.simp:
+                    temp = temp.applyfunc(lambda x:
+                                          trigsimp(x, method='fu'))
+                outvec += Vector([(temp, frame)])
+            else:
+                outvec += Vector([v])
+        return outvec
+
+    if isinstance(expr, Dyadic):
+        if frame2 is None:
+            frame2 = frame
+        _check_frame(frame2)
+        ol = Dyadic(0)
+        for i, v in enumerate(expr.args):
+            ol += express(v[0], frame, variables=variables) * \
+                  (express(v[1], frame, variables=variables) |
+                   express(v[2], frame2, variables=variables))
+        return ol
+
+    else:
+        if variables:
+            # Given expr is a scalar field
+            frame_set = set()
+            expr = sympify(expr)
+            # Substitute all the coordinate variables
+            for x in expr.free_symbols:
+                if isinstance(x, CoordinateSym) and x.frame != frame:
+                    frame_set.add(x.frame)
+            subs_dict = {}
+            for f in frame_set:
+                subs_dict.update(f.variable_map(frame))
+            return expr.subs(subs_dict)
+        return expr
+
+
+def time_derivative(expr, frame, order=1):
+    """
+    Calculate the time derivative of a vector/scalar field function
+    or dyadic expression in given frame.
+
+    References
+    ==========
+
+    https://en.wikipedia.org/wiki/Rotating_reference_frame#Time_derivatives_in_the_two_frames
+
+    Parameters
+    ==========
+
+    expr : Vector/Dyadic/sympifyable
+        The expression whose time derivative is to be calculated
+
+    frame : ReferenceFrame
+        The reference frame to calculate the time derivative in
+
+    order : integer
+        The order of the derivative to be calculated
+
+    Examples
+    ========
+
+    >>> from sympy.physics.vector import ReferenceFrame, dynamicsymbols
+    >>> from sympy.physics.vector import init_vprinting
+    >>> init_vprinting(pretty_print=False)
+    >>> from sympy import Symbol
+    >>> q1 = Symbol('q1')
+    >>> u1 = dynamicsymbols('u1')
+    >>> N = ReferenceFrame('N')
+    >>> A = N.orientnew('A', 'Axis', [q1, N.x])
+    >>> v = u1 * N.x
+    >>> A.set_ang_vel(N, 10*A.x)
+    >>> from sympy.physics.vector import time_derivative
+    >>> time_derivative(v, N)
+    u1'*N.x
+    >>> time_derivative(u1*A[0], N)
+    N_x*u1'
+    >>> B = N.orientnew('B', 'Axis', [u1, N.z])
+    >>> from sympy.physics.vector import outer
+    >>> d = outer(N.x, N.x)
+    >>> time_derivative(d, B)
+    - u1'*(N.y|N.x) - u1'*(N.x|N.y)
+
+    """
+
+    t = dynamicsymbols._t
+    _check_frame(frame)
+
+    if order == 0:
+        return expr
+    if order % 1 != 0 or order < 0:
+        raise ValueError("Unsupported value of order entered")
+
+    if isinstance(expr, Vector):
+        outlist = []
+        for i, v in enumerate(expr.args):
+            if v[1] == frame:
+                outlist += [(express(v[0], frame, variables=True).diff(t),
+                             frame)]
+            else:
+                outlist += (time_derivative(Vector([v]), v[1]) +
+                            (v[1].ang_vel_in(frame) ^ Vector([v]))).args
+        outvec = Vector(outlist)
+        return time_derivative(outvec, frame, order - 1)
+
+    if isinstance(expr, Dyadic):
+        ol = Dyadic(0)
+        for i, v in enumerate(expr.args):
+            ol += (v[0].diff(t) * (v[1] | v[2]))
+            ol += (v[0] * (time_derivative(v[1], frame) | v[2]))
+            ol += (v[0] * (v[1] | time_derivative(v[2], frame)))
+        return time_derivative(ol, frame, order - 1)
+
+    else:
+        return diff(express(expr, frame, variables=True), t, order)
+
+
+def outer(vec1, vec2):
+    """Outer product convenience wrapper for Vector.outer():\n"""
+    if not isinstance(vec1, Vector):
+        raise TypeError('Outer product is between two Vectors')
+    return vec1 | vec2
+
+
+outer.__doc__ += Vector.outer.__doc__  # type: ignore
+
+
+def kinematic_equations(speeds, coords, rot_type, rot_order=''):
+    """Gives equations relating the qdot's to u's for a rotation type.
+
+    Supply rotation type and order as in orient. Speeds are assumed to be
+    body-fixed; if we are defining the orientation of B in A using by rot_type,
+    the angular velocity of B in A is assumed to be in the form: speed[0]*B.x +
+    speed[1]*B.y + speed[2]*B.z
+
+    Parameters
+    ==========
+
+    speeds : list of length 3
+        The body fixed angular velocity measure numbers.
+    coords : list of length 3 or 4
+        The coordinates used to define the orientation of the two frames.
+    rot_type : str
+        The type of rotation used to create the equations. Body, Space, or
+        Quaternion only
+    rot_order : str or int
+        If applicable, the order of a series of rotations.
+
+    Examples
+    ========
+
+    >>> from sympy.physics.vector import dynamicsymbols
+    >>> from sympy.physics.vector import kinematic_equations, vprint
+    >>> u1, u2, u3 = dynamicsymbols('u1 u2 u3')
+    >>> q1, q2, q3 = dynamicsymbols('q1 q2 q3')
+    >>> vprint(kinematic_equations([u1,u2,u3], [q1,q2,q3], 'body', '313'),
+    ...     order=None)
+    [-(u1*sin(q3) + u2*cos(q3))/sin(q2) + q1', -u1*cos(q3) + u2*sin(q3) + q2', (u1*sin(q3) + u2*cos(q3))*cos(q2)/sin(q2) - u3 + q3']
+
+    """
+
+    # Code below is checking and sanitizing input
+    approved_orders = ('123', '231', '312', '132', '213', '321', '121', '131',
+                       '212', '232', '313', '323', '1', '2', '3', '')
+    # make sure XYZ => 123 and rot_type is in lower case
+    rot_order = translate(str(rot_order), 'XYZxyz', '123123')
+    rot_type = rot_type.lower()
+
+    if not isinstance(speeds, (list, tuple)):
+        raise TypeError('Need to supply speeds in a list')
+    if len(speeds) != 3:
+        raise TypeError('Need to supply 3 body-fixed speeds')
+    if not isinstance(coords, (list, tuple)):
+        raise TypeError('Need to supply coordinates in a list')
+    if rot_type in ['body', 'space']:
+        if rot_order not in approved_orders:
+            raise ValueError('Not an acceptable rotation order')
+        if len(coords) != 3:
+            raise ValueError('Need 3 coordinates for body or space')
+        # Actual hard-coded kinematic differential equations
+        w1, w2, w3 = speeds
+        if w1 == w2 == w3 == 0:
+            return [S.Zero]*3
+        q1, q2, q3 = coords
+        q1d, q2d, q3d = [diff(i, dynamicsymbols._t) for i in coords]
+        s1, s2, s3 = [sin(q1), sin(q2), sin(q3)]
+        c1, c2, c3 = [cos(q1), cos(q2), cos(q3)]
+        if rot_type == 'body':
+            if rot_order == '123':
+                return [q1d - (w1 * c3 - w2 * s3) / c2, q2d - w1 * s3 - w2 *
+                        c3, q3d - (-w1 * c3 + w2 * s3) * s2 / c2 - w3]
+            if rot_order == '231':
+                return [q1d - (w2 * c3 - w3 * s3) / c2, q2d - w2 * s3 - w3 *
+                        c3, q3d - w1 - (- w2 * c3 + w3 * s3) * s2 / c2]
+            if rot_order == '312':
+                return [q1d - (-w1 * s3 + w3 * c3) / c2, q2d - w1 * c3 - w3 *
+                        s3, q3d - (w1 * s3 - w3 * c3) * s2 / c2 - w2]
+            if rot_order == '132':
+                return [q1d - (w1 * c3 + w3 * s3) / c2, q2d + w1 * s3 - w3 *
+                        c3, q3d - (w1 * c3 + w3 * s3) * s2 / c2 - w2]
+            if rot_order == '213':
+                return [q1d - (w1 * s3 + w2 * c3) / c2, q2d - w1 * c3 + w2 *
+                        s3, q3d - (w1 * s3 + w2 * c3) * s2 / c2 - w3]
+            if rot_order == '321':
+                return [q1d - (w2 * s3 + w3 * c3) / c2, q2d - w2 * c3 + w3 *
+                        s3, q3d - w1 - (w2 * s3 + w3 * c3) * s2 / c2]
+            if rot_order == '121':
+                return [q1d - (w2 * s3 + w3 * c3) / s2, q2d - w2 * c3 + w3 *
+                        s3, q3d - w1 + (w2 * s3 + w3 * c3) * c2 / s2]
+            if rot_order == '131':
+                return [q1d - (-w2 * c3 + w3 * s3) / s2, q2d - w2 * s3 - w3 *
+                        c3, q3d - w1 - (w2 * c3 - w3 * s3) * c2 / s2]
+            if rot_order == '212':
+                return [q1d - (w1 * s3 - w3 * c3) / s2, q2d - w1 * c3 - w3 *
+                        s3, q3d - (-w1 * s3 + w3 * c3) * c2 / s2 - w2]
+            if rot_order == '232':
+                return [q1d - (w1 * c3 + w3 * s3) / s2, q2d + w1 * s3 - w3 *
+                        c3, q3d + (w1 * c3 + w3 * s3) * c2 / s2 - w2]
+            if rot_order == '313':
+                return [q1d - (w1 * s3 + w2 * c3) / s2, q2d - w1 * c3 + w2 *
+                        s3, q3d + (w1 * s3 + w2 * c3) * c2 / s2 - w3]
+            if rot_order == '323':
+                return [q1d - (-w1 * c3 + w2 * s3) / s2, q2d - w1 * s3 - w2 *
+                        c3, q3d - (w1 * c3 - w2 * s3) * c2 / s2 - w3]
+        if rot_type == 'space':
+            if rot_order == '123':
+                return [q1d - w1 - (w2 * s1 + w3 * c1) * s2 / c2, q2d - w2 *
+                        c1 + w3 * s1, q3d - (w2 * s1 + w3 * c1) / c2]
+            if rot_order == '231':
+                return [q1d - (w1 * c1 + w3 * s1) * s2 / c2 - w2, q2d + w1 *
+                        s1 - w3 * c1, q3d - (w1 * c1 + w3 * s1) / c2]
+            if rot_order == '312':
+                return [q1d - (w1 * s1 + w2 * c1) * s2 / c2 - w3, q2d - w1 *
+                        c1 + w2 * s1, q3d - (w1 * s1 + w2 * c1) / c2]
+            if rot_order == '132':
+                return [q1d - w1 - (-w2 * c1 + w3 * s1) * s2 / c2, q2d - w2 *
+                        s1 - w3 * c1, q3d - (w2 * c1 - w3 * s1) / c2]
+            if rot_order == '213':
+                return [q1d - (w1 * s1 - w3 * c1) * s2 / c2 - w2, q2d - w1 *
+                        c1 - w3 * s1, q3d - (-w1 * s1 + w3 * c1) / c2]
+            if rot_order == '321':
+                return [q1d - (-w1 * c1 + w2 * s1) * s2 / c2 - w3, q2d - w1 *
+                        s1 - w2 * c1, q3d - (w1 * c1 - w2 * s1) / c2]
+            if rot_order == '121':
+                return [q1d - w1 + (w2 * s1 + w3 * c1) * c2 / s2, q2d - w2 *
+                        c1 + w3 * s1, q3d - (w2 * s1 + w3 * c1) / s2]
+            if rot_order == '131':
+                return [q1d - w1 - (w2 * c1 - w3 * s1) * c2 / s2, q2d - w2 *
+                        s1 - w3 * c1, q3d - (-w2 * c1 + w3 * s1) / s2]
+            if rot_order == '212':
+                return [q1d - (-w1 * s1 + w3 * c1) * c2 / s2 - w2, q2d - w1 *
+                        c1 - w3 * s1, q3d - (w1 * s1 - w3 * c1) / s2]
+            if rot_order == '232':
+                return [q1d + (w1 * c1 + w3 * s1) * c2 / s2 - w2, q2d + w1 *
+                        s1 - w3 * c1, q3d - (w1 * c1 + w3 * s1) / s2]
+            if rot_order == '313':
+                return [q1d + (w1 * s1 + w2 * c1) * c2 / s2 - w3, q2d - w1 *
+                        c1 + w2 * s1, q3d - (w1 * s1 + w2 * c1) / s2]
+            if rot_order == '323':
+                return [q1d - (w1 * c1 - w2 * s1) * c2 / s2 - w3, q2d - w1 *
+                        s1 - w2 * c1, q3d - (-w1 * c1 + w2 * s1) / s2]
+    elif rot_type == 'quaternion':
+        if rot_order != '':
+            raise ValueError('Cannot have rotation order for quaternion')
+        if len(coords) != 4:
+            raise ValueError('Need 4 coordinates for quaternion')
+        # Actual hard-coded kinematic differential equations
+        e0, e1, e2, e3 = coords
+        w = Matrix(speeds + [0])
+        E = Matrix([[e0, -e3, e2, e1],
+                    [e3, e0, -e1, e2],
+                    [-e2, e1, e0, e3],
+                    [-e1, -e2, -e3, e0]])
+        edots = Matrix([diff(i, dynamicsymbols._t) for i in [e1, e2, e3, e0]])
+        return list(edots.T - 0.5 * w.T * E.T)
+    else:
+        raise ValueError('Not an approved rotation type for this function')
+
+
+def get_motion_params(frame, **kwargs):
+    """
+    Returns the three motion parameters - (acceleration, velocity, and
+    position) as vectorial functions of time in the given frame.
+
+    If a higher order differential function is provided, the lower order
+    functions are used as boundary conditions. For example, given the
+    acceleration, the velocity and position parameters are taken as
+    boundary conditions.
+
+    The values of time at which the boundary conditions are specified
+    are taken from timevalue1(for position boundary condition) and
+    timevalue2(for velocity boundary condition).
+
+    If any of the boundary conditions are not provided, they are taken
+    to be zero by default (zero vectors, in case of vectorial inputs). If
+    the boundary conditions are also functions of time, they are converted
+    to constants by substituting the time values in the dynamicsymbols._t
+    time Symbol.
+
+    This function can also be used for calculating rotational motion
+    parameters. Have a look at the Parameters and Examples for more clarity.
+
+    Parameters
+    ==========
+
+    frame : ReferenceFrame
+        The frame to express the motion parameters in
+
+    acceleration : Vector
+        Acceleration of the object/frame as a function of time
+
+    velocity : Vector
+        Velocity as function of time or as boundary condition
+        of velocity at time = timevalue1
+
+    position : Vector
+        Velocity as function of time or as boundary condition
+        of velocity at time = timevalue1
+
+    timevalue1 : sympyfiable
+        Value of time for position boundary condition
+
+    timevalue2 : sympyfiable
+        Value of time for velocity boundary condition
+
+    Examples
+    ========
+
+    >>> from sympy.physics.vector import ReferenceFrame, get_motion_params, dynamicsymbols
+    >>> from sympy.physics.vector import init_vprinting
+    >>> init_vprinting(pretty_print=False)
+    >>> from sympy import symbols
+    >>> R = ReferenceFrame('R')
+    >>> v1, v2, v3 = dynamicsymbols('v1 v2 v3')
+    >>> v = v1*R.x + v2*R.y + v3*R.z
+    >>> get_motion_params(R, position = v)
+    (v1''*R.x + v2''*R.y + v3''*R.z, v1'*R.x + v2'*R.y + v3'*R.z, v1*R.x + v2*R.y + v3*R.z)
+    >>> a, b, c = symbols('a b c')
+    >>> v = a*R.x + b*R.y + c*R.z
+    >>> get_motion_params(R, velocity = v)
+    (0, a*R.x + b*R.y + c*R.z, a*t*R.x + b*t*R.y + c*t*R.z)
+    >>> parameters = get_motion_params(R, acceleration = v)
+    >>> parameters[1]
+    a*t*R.x + b*t*R.y + c*t*R.z
+    >>> parameters[2]
+    a*t**2/2*R.x + b*t**2/2*R.y + c*t**2/2*R.z
+
+    """
+
+    def _process_vector_differential(vectdiff, condition, variable, ordinate,
+                                     frame):
+        """
+        Helper function for get_motion methods. Finds derivative of vectdiff
+        wrt variable, and its integral using the specified boundary condition
+        at value of variable = ordinate.
+        Returns a tuple of - (derivative, function and integral) wrt vectdiff
+
+        """
+
+        # Make sure boundary condition is independent of 'variable'
+        if condition != 0:
+            condition = express(condition, frame, variables=True)
+        # Special case of vectdiff == 0
+        if vectdiff == Vector(0):
+            return (0, 0, condition)
+        # Express vectdiff completely in condition's frame to give vectdiff1
+        vectdiff1 = express(vectdiff, frame)
+        # Find derivative of vectdiff
+        vectdiff2 = time_derivative(vectdiff, frame)
+        # Integrate and use boundary condition
+        vectdiff0 = Vector(0)
+        lims = (variable, ordinate, variable)
+        for dim in frame:
+            function1 = vectdiff1.dot(dim)
+            abscissa = dim.dot(condition).subs({variable: ordinate})
+            # Indefinite integral of 'function1' wrt 'variable', using
+            # the given initial condition (ordinate, abscissa).
+            vectdiff0 += (integrate(function1, lims) + abscissa) * dim
+        # Return tuple
+        return (vectdiff2, vectdiff, vectdiff0)
+
+    _check_frame(frame)
+    # Decide mode of operation based on user's input
+    if 'acceleration' in kwargs:
+        mode = 2
+    elif 'velocity' in kwargs:
+        mode = 1
+    else:
+        mode = 0
+    # All the possible parameters in kwargs
+    # Not all are required for every case
+    # If not specified, set to default values(may or may not be used in
+    # calculations)
+    conditions = ['acceleration', 'velocity', 'position',
+                  'timevalue', 'timevalue1', 'timevalue2']
+    for i, x in enumerate(conditions):
+        if x not in kwargs:
+            if i < 3:
+                kwargs[x] = Vector(0)
+            else:
+                kwargs[x] = S.Zero
+        elif i < 3:
+            _check_vector(kwargs[x])
+        else:
+            kwargs[x] = sympify(kwargs[x])
+    if mode == 2:
+        vel = _process_vector_differential(kwargs['acceleration'],
+                                           kwargs['velocity'],
+                                           dynamicsymbols._t,
+                                           kwargs['timevalue2'], frame)[2]
+        pos = _process_vector_differential(vel, kwargs['position'],
+                                           dynamicsymbols._t,
+                                           kwargs['timevalue1'], frame)[2]
+        return (kwargs['acceleration'], vel, pos)
+    elif mode == 1:
+        return _process_vector_differential(kwargs['velocity'],
+                                            kwargs['position'],
+                                            dynamicsymbols._t,
+                                            kwargs['timevalue1'], frame)
+    else:
+        vel = time_derivative(kwargs['position'], frame)
+        acc = time_derivative(vel, frame)
+        return (acc, vel, kwargs['position'])
+
+
+def partial_velocity(vel_vecs, gen_speeds, frame):
+    """Returns a list of partial velocities with respect to the provided
+    generalized speeds in the given reference frame for each of the supplied
+    velocity vectors.
+
+    The output is a list of lists. The outer list has a number of elements
+    equal to the number of supplied velocity vectors. The inner lists are, for
+    each velocity vector, the partial derivatives of that velocity vector with
+    respect to the generalized speeds supplied.
+
+    Parameters
+    ==========
+
+    vel_vecs : iterable
+        An iterable of velocity vectors (angular or linear).
+    gen_speeds : iterable
+        An iterable of generalized speeds.
+    frame : ReferenceFrame
+        The reference frame that the partial derivatives are going to be taken
+        in.
+
+    Examples
+    ========
+
+    >>> from sympy.physics.vector import Point, ReferenceFrame
+    >>> from sympy.physics.vector import dynamicsymbols
+    >>> from sympy.physics.vector import partial_velocity
+    >>> u = dynamicsymbols('u')
+    >>> N = ReferenceFrame('N')
+    >>> P = Point('P')
+    >>> P.set_vel(N, u * N.x)
+    >>> vel_vecs = [P.vel(N)]
+    >>> gen_speeds = [u]
+    >>> partial_velocity(vel_vecs, gen_speeds, N)
+    [[N.x]]
+
+    """
+
+    if not iterable(vel_vecs):
+        raise TypeError('Velocity vectors must be contained in an iterable.')
+
+    if not iterable(gen_speeds):
+        raise TypeError('Generalized speeds must be contained in an iterable')
+
+    vec_partials = []
+    for vec in vel_vecs:
+        partials = []
+        for speed in gen_speeds:
+            partials.append(vec.diff(speed, frame, var_in_dcm=False))
+        vec_partials.append(partials)
+
+    return vec_partials
+
+
+def dynamicsymbols(names, level=0, **assumptions):
+    """Uses symbols and Function for functions of time.
+
+    Creates a SymPy UndefinedFunction, which is then initialized as a function
+    of a variable, the default being Symbol('t').
+
+    Parameters
+    ==========
+
+    names : str
+        Names of the dynamic symbols you want to create; works the same way as
+        inputs to symbols
+    level : int
+        Level of differentiation of the returned function; d/dt once of t,
+        twice of t, etc.
+    assumptions :
+        - real(bool) : This is used to set the dynamicsymbol as real,
+                    by default is False.
+        - positive(bool) : This is used to set the dynamicsymbol as positive,
+                    by default is False.
+        - commutative(bool) : This is used to set the commutative property of
+                    a dynamicsymbol, by default is True.
+        - integer(bool) : This is used to set the dynamicsymbol as integer,
+                    by default is False.
+
+    Examples
+    ========
+
+    >>> from sympy.physics.vector import dynamicsymbols
+    >>> from sympy import diff, Symbol
+    >>> q1 = dynamicsymbols('q1')
+    >>> q1
+    q1(t)
+    >>> q2 = dynamicsymbols('q2', real=True)
+    >>> q2.is_real
+    True
+    >>> q3 = dynamicsymbols('q3', positive=True)
+    >>> q3.is_positive
+    True
+    >>> q4, q5 = dynamicsymbols('q4,q5', commutative=False)
+    >>> bool(q4*q5 != q5*q4)
+    True
+    >>> q6 = dynamicsymbols('q6', integer=True)
+    >>> q6.is_integer
+    True
+    >>> diff(q1, Symbol('t'))
+    Derivative(q1(t), t)
+
+    """
+    esses = symbols(names, cls=Function, **assumptions)
+    t = dynamicsymbols._t
+    if iterable(esses):
+        esses = [reduce(diff, [t] * level, e(t)) for e in esses]
+        return esses
+    else:
+        return reduce(diff, [t] * level, esses(t))
+
+
+dynamicsymbols._t = Symbol('t')  # type: ignore
+dynamicsymbols._str = '\''  # type: ignore
diff --git a/llmeval-env/lib/python3.10/site-packages/sympy/physics/vector/point.py b/llmeval-env/lib/python3.10/site-packages/sympy/physics/vector/point.py
new file mode 100644
index 0000000000000000000000000000000000000000..14e5db08da9b7bb0cc9a10291422c3d17c6ea87b
--- /dev/null
+++ b/llmeval-env/lib/python3.10/site-packages/sympy/physics/vector/point.py
@@ -0,0 +1,629 @@
+from .vector import Vector, _check_vector
+from .frame import _check_frame
+from warnings import warn
+
+__all__ = ['Point']
+
+
+class Point:
+    """This object represents a point in a dynamic system.
+
+    It stores the: position, velocity, and acceleration of a point.
+    The position is a vector defined as the vector distance from a parent
+    point to this point.
+
+    Parameters
+    ==========
+
+    name : string
+        The display name of the Point
+
+    Examples
+    ========
+
+    >>> from sympy.physics.vector import Point, ReferenceFrame, dynamicsymbols
+    >>> from sympy.physics.vector import init_vprinting
+    >>> init_vprinting(pretty_print=False)
+    >>> N = ReferenceFrame('N')
+    >>> O = Point('O')
+    >>> P = Point('P')
+    >>> u1, u2, u3 = dynamicsymbols('u1 u2 u3')
+    >>> O.set_vel(N, u1 * N.x + u2 * N.y + u3 * N.z)
+    >>> O.acc(N)
+    u1'*N.x + u2'*N.y + u3'*N.z
+
+    ``symbols()`` can be used to create multiple Points in a single step, for
+    example:
+
+    >>> from sympy.physics.vector import Point, ReferenceFrame, dynamicsymbols
+    >>> from sympy.physics.vector import init_vprinting
+    >>> init_vprinting(pretty_print=False)
+    >>> from sympy import symbols
+    >>> N = ReferenceFrame('N')
+    >>> u1, u2 = dynamicsymbols('u1 u2')
+    >>> A, B = symbols('A B', cls=Point)
+    >>> type(A)
+    
+    >>> A.set_vel(N, u1 * N.x + u2 * N.y)
+    >>> B.set_vel(N, u2 * N.x + u1 * N.y)
+    >>> A.acc(N) - B.acc(N)
+    (u1' - u2')*N.x + (-u1' + u2')*N.y
+
+    """
+
+    def __init__(self, name):
+        """Initialization of a Point object. """
+        self.name = name
+        self._pos_dict = {}
+        self._vel_dict = {}
+        self._acc_dict = {}
+        self._pdlist = [self._pos_dict, self._vel_dict, self._acc_dict]
+
+    def __str__(self):
+        return self.name
+
+    __repr__ = __str__
+
+    def _check_point(self, other):
+        if not isinstance(other, Point):
+            raise TypeError('A Point must be supplied')
+
+    def _pdict_list(self, other, num):
+        """Returns a list of points that gives the shortest path with respect
+        to position, velocity, or acceleration from this point to the provided
+        point.
+
+        Parameters
+        ==========
+        other : Point
+            A point that may be related to this point by position, velocity, or
+            acceleration.
+        num : integer
+            0 for searching the position tree, 1 for searching the velocity
+            tree, and 2 for searching the acceleration tree.
+
+        Returns
+        =======
+        list of Points
+            A sequence of points from self to other.
+
+        Notes
+        =====
+
+        It is not clear if num = 1 or num = 2 actually works because the keys
+        to ``_vel_dict`` and ``_acc_dict`` are :class:`ReferenceFrame` objects
+        which do not have the ``_pdlist`` attribute.
+
+        """
+        outlist = [[self]]
+        oldlist = [[]]
+        while outlist != oldlist:
+            oldlist = outlist[:]
+            for i, v in enumerate(outlist):
+                templist = v[-1]._pdlist[num].keys()
+                for i2, v2 in enumerate(templist):
+                    if not v.__contains__(v2):
+                        littletemplist = v + [v2]
+                        if not outlist.__contains__(littletemplist):
+                            outlist.append(littletemplist)
+        for i, v in enumerate(oldlist):
+            if v[-1] != other:
+                outlist.remove(v)
+        outlist.sort(key=len)
+        if len(outlist) != 0:
+            return outlist[0]
+        raise ValueError('No Connecting Path found between ' + other.name +
+                         ' and ' + self.name)
+
+    def a1pt_theory(self, otherpoint, outframe, interframe):
+        """Sets the acceleration of this point with the 1-point theory.
+
+        The 1-point theory for point acceleration looks like this:
+
+        ^N a^P = ^B a^P + ^N a^O + ^N alpha^B x r^OP + ^N omega^B x (^N omega^B
+        x r^OP) + 2 ^N omega^B x ^B v^P
+
+        where O is a point fixed in B, P is a point moving in B, and B is
+        rotating in frame N.
+
+        Parameters
+        ==========
+
+        otherpoint : Point
+            The first point of the 1-point theory (O)
+        outframe : ReferenceFrame
+            The frame we want this point's acceleration defined in (N)
+        fixedframe : ReferenceFrame
+            The intermediate frame in this calculation (B)
+
+        Examples
+        ========
+
+        >>> from sympy.physics.vector import Point, ReferenceFrame
+        >>> from sympy.physics.vector import dynamicsymbols
+        >>> from sympy.physics.vector import init_vprinting
+        >>> init_vprinting(pretty_print=False)
+        >>> q = dynamicsymbols('q')
+        >>> q2 = dynamicsymbols('q2')
+        >>> qd = dynamicsymbols('q', 1)
+        >>> q2d = dynamicsymbols('q2', 1)
+        >>> N = ReferenceFrame('N')
+        >>> B = ReferenceFrame('B')
+        >>> B.set_ang_vel(N, 5 * B.y)
+        >>> O = Point('O')
+        >>> P = O.locatenew('P', q * B.x)
+        >>> P.set_vel(B, qd * B.x + q2d * B.y)
+        >>> O.set_vel(N, 0)
+        >>> P.a1pt_theory(O, N, B)
+        (-25*q + q'')*B.x + q2''*B.y - 10*q'*B.z
+
+        """
+
+        _check_frame(outframe)
+        _check_frame(interframe)
+        self._check_point(otherpoint)
+        dist = self.pos_from(otherpoint)
+        v = self.vel(interframe)
+        a1 = otherpoint.acc(outframe)
+        a2 = self.acc(interframe)
+        omega = interframe.ang_vel_in(outframe)
+        alpha = interframe.ang_acc_in(outframe)
+        self.set_acc(outframe, a2 + 2 * (omega ^ v) + a1 + (alpha ^ dist) +
+                     (omega ^ (omega ^ dist)))
+        return self.acc(outframe)
+
+    def a2pt_theory(self, otherpoint, outframe, fixedframe):
+        """Sets the acceleration of this point with the 2-point theory.
+
+        The 2-point theory for point acceleration looks like this:
+
+        ^N a^P = ^N a^O + ^N alpha^B x r^OP + ^N omega^B x (^N omega^B x r^OP)
+
+        where O and P are both points fixed in frame B, which is rotating in
+        frame N.
+
+        Parameters
+        ==========
+
+        otherpoint : Point
+            The first point of the 2-point theory (O)
+        outframe : ReferenceFrame
+            The frame we want this point's acceleration defined in (N)
+        fixedframe : ReferenceFrame
+            The frame in which both points are fixed (B)
+
+        Examples
+        ========
+
+        >>> from sympy.physics.vector import Point, ReferenceFrame, dynamicsymbols
+        >>> from sympy.physics.vector import init_vprinting
+        >>> init_vprinting(pretty_print=False)
+        >>> q = dynamicsymbols('q')
+        >>> qd = dynamicsymbols('q', 1)
+        >>> N = ReferenceFrame('N')
+        >>> B = N.orientnew('B', 'Axis', [q, N.z])
+        >>> O = Point('O')
+        >>> P = O.locatenew('P', 10 * B.x)
+        >>> O.set_vel(N, 5 * N.x)
+        >>> P.a2pt_theory(O, N, B)
+        - 10*q'**2*B.x + 10*q''*B.y
+
+        """
+
+        _check_frame(outframe)
+        _check_frame(fixedframe)
+        self._check_point(otherpoint)
+        dist = self.pos_from(otherpoint)
+        a = otherpoint.acc(outframe)
+        omega = fixedframe.ang_vel_in(outframe)
+        alpha = fixedframe.ang_acc_in(outframe)
+        self.set_acc(outframe, a + (alpha ^ dist) + (omega ^ (omega ^ dist)))
+        return self.acc(outframe)
+
+    def acc(self, frame):
+        """The acceleration Vector of this Point in a ReferenceFrame.
+
+        Parameters
+        ==========
+
+        frame : ReferenceFrame
+            The frame in which the returned acceleration vector will be defined
+            in.
+
+        Examples
+        ========
+
+        >>> from sympy.physics.vector import Point, ReferenceFrame
+        >>> N = ReferenceFrame('N')
+        >>> p1 = Point('p1')
+        >>> p1.set_acc(N, 10 * N.x)
+        >>> p1.acc(N)
+        10*N.x
+
+        """
+
+        _check_frame(frame)
+        if not (frame in self._acc_dict):
+            if self.vel(frame) != 0:
+                return (self._vel_dict[frame]).dt(frame)
+            else:
+                return Vector(0)
+        return self._acc_dict[frame]
+
+    def locatenew(self, name, value):
+        """Creates a new point with a position defined from this point.
+
+        Parameters
+        ==========
+
+        name : str
+            The name for the new point
+        value : Vector
+            The position of the new point relative to this point
+
+        Examples
+        ========
+
+        >>> from sympy.physics.vector import ReferenceFrame, Point
+        >>> N = ReferenceFrame('N')
+        >>> P1 = Point('P1')
+        >>> P2 = P1.locatenew('P2', 10 * N.x)
+
+        """
+
+        if not isinstance(name, str):
+            raise TypeError('Must supply a valid name')
+        if value == 0:
+            value = Vector(0)
+        value = _check_vector(value)
+        p = Point(name)
+        p.set_pos(self, value)
+        self.set_pos(p, -value)
+        return p
+
+    def pos_from(self, otherpoint):
+        """Returns a Vector distance between this Point and the other Point.
+
+        Parameters
+        ==========
+
+        otherpoint : Point
+            The otherpoint we are locating this one relative to
+
+        Examples
+        ========
+
+        >>> from sympy.physics.vector import Point, ReferenceFrame
+        >>> N = ReferenceFrame('N')
+        >>> p1 = Point('p1')
+        >>> p2 = Point('p2')
+        >>> p1.set_pos(p2, 10 * N.x)
+        >>> p1.pos_from(p2)
+        10*N.x
+
+        """
+
+        outvec = Vector(0)
+        plist = self._pdict_list(otherpoint, 0)
+        for i in range(len(plist) - 1):
+            outvec += plist[i]._pos_dict[plist[i + 1]]
+        return outvec
+
+    def set_acc(self, frame, value):
+        """Used to set the acceleration of this Point in a ReferenceFrame.
+
+        Parameters
+        ==========
+
+        frame : ReferenceFrame
+            The frame in which this point's acceleration is defined
+        value : Vector
+            The vector value of this point's acceleration in the frame
+
+        Examples
+        ========
+
+        >>> from sympy.physics.vector import Point, ReferenceFrame
+        >>> N = ReferenceFrame('N')
+        >>> p1 = Point('p1')
+        >>> p1.set_acc(N, 10 * N.x)
+        >>> p1.acc(N)
+        10*N.x
+
+        """
+
+        if value == 0:
+            value = Vector(0)
+        value = _check_vector(value)
+        _check_frame(frame)
+        self._acc_dict.update({frame: value})
+
+    def set_pos(self, otherpoint, value):
+        """Used to set the position of this point w.r.t. another point.
+
+        Parameters
+        ==========
+
+        otherpoint : Point
+            The other point which this point's location is defined relative to
+        value : Vector
+            The vector which defines the location of this point
+
+        Examples
+        ========
+
+        >>> from sympy.physics.vector import Point, ReferenceFrame
+        >>> N = ReferenceFrame('N')
+        >>> p1 = Point('p1')
+        >>> p2 = Point('p2')
+        >>> p1.set_pos(p2, 10 * N.x)
+        >>> p1.pos_from(p2)
+        10*N.x
+
+        """
+
+        if value == 0:
+            value = Vector(0)
+        value = _check_vector(value)
+        self._check_point(otherpoint)
+        self._pos_dict.update({otherpoint: value})
+        otherpoint._pos_dict.update({self: -value})
+
+    def set_vel(self, frame, value):
+        """Sets the velocity Vector of this Point in a ReferenceFrame.
+
+        Parameters
+        ==========
+
+        frame : ReferenceFrame
+            The frame in which this point's velocity is defined
+        value : Vector
+            The vector value of this point's velocity in the frame
+
+        Examples
+        ========
+
+        >>> from sympy.physics.vector import Point, ReferenceFrame
+        >>> N = ReferenceFrame('N')
+        >>> p1 = Point('p1')
+        >>> p1.set_vel(N, 10 * N.x)
+        >>> p1.vel(N)
+        10*N.x
+
+        """
+
+        if value == 0:
+            value = Vector(0)
+        value = _check_vector(value)
+        _check_frame(frame)
+        self._vel_dict.update({frame: value})
+
+    def v1pt_theory(self, otherpoint, outframe, interframe):
+        """Sets the velocity of this point with the 1-point theory.
+
+        The 1-point theory for point velocity looks like this:
+
+        ^N v^P = ^B v^P + ^N v^O + ^N omega^B x r^OP
+
+        where O is a point fixed in B, P is a point moving in B, and B is
+        rotating in frame N.
+
+        Parameters
+        ==========
+
+        otherpoint : Point
+            The first point of the 1-point theory (O)
+        outframe : ReferenceFrame
+            The frame we want this point's velocity defined in (N)
+        interframe : ReferenceFrame
+            The intermediate frame in this calculation (B)
+
+        Examples
+        ========
+
+        >>> from sympy.physics.vector import Point, ReferenceFrame
+        >>> from sympy.physics.vector import dynamicsymbols
+        >>> from sympy.physics.vector import init_vprinting
+        >>> init_vprinting(pretty_print=False)
+        >>> q = dynamicsymbols('q')
+        >>> q2 = dynamicsymbols('q2')
+        >>> qd = dynamicsymbols('q', 1)
+        >>> q2d = dynamicsymbols('q2', 1)
+        >>> N = ReferenceFrame('N')
+        >>> B = ReferenceFrame('B')
+        >>> B.set_ang_vel(N, 5 * B.y)
+        >>> O = Point('O')
+        >>> P = O.locatenew('P', q * B.x)
+        >>> P.set_vel(B, qd * B.x + q2d * B.y)
+        >>> O.set_vel(N, 0)
+        >>> P.v1pt_theory(O, N, B)
+        q'*B.x + q2'*B.y - 5*q*B.z
+
+        """
+
+        _check_frame(outframe)
+        _check_frame(interframe)
+        self._check_point(otherpoint)
+        dist = self.pos_from(otherpoint)
+        v1 = self.vel(interframe)
+        v2 = otherpoint.vel(outframe)
+        omega = interframe.ang_vel_in(outframe)
+        self.set_vel(outframe, v1 + v2 + (omega ^ dist))
+        return self.vel(outframe)
+
+    def v2pt_theory(self, otherpoint, outframe, fixedframe):
+        """Sets the velocity of this point with the 2-point theory.
+
+        The 2-point theory for point velocity looks like this:
+
+        ^N v^P = ^N v^O + ^N omega^B x r^OP
+
+        where O and P are both points fixed in frame B, which is rotating in
+        frame N.
+
+        Parameters
+        ==========
+
+        otherpoint : Point
+            The first point of the 2-point theory (O)
+        outframe : ReferenceFrame
+            The frame we want this point's velocity defined in (N)
+        fixedframe : ReferenceFrame
+            The frame in which both points are fixed (B)
+
+        Examples
+        ========
+
+        >>> from sympy.physics.vector import Point, ReferenceFrame, dynamicsymbols
+        >>> from sympy.physics.vector import init_vprinting
+        >>> init_vprinting(pretty_print=False)
+        >>> q = dynamicsymbols('q')
+        >>> qd = dynamicsymbols('q', 1)
+        >>> N = ReferenceFrame('N')
+        >>> B = N.orientnew('B', 'Axis', [q, N.z])
+        >>> O = Point('O')
+        >>> P = O.locatenew('P', 10 * B.x)
+        >>> O.set_vel(N, 5 * N.x)
+        >>> P.v2pt_theory(O, N, B)
+        5*N.x + 10*q'*B.y
+
+        """
+
+        _check_frame(outframe)
+        _check_frame(fixedframe)
+        self._check_point(otherpoint)
+        dist = self.pos_from(otherpoint)
+        v = otherpoint.vel(outframe)
+        omega = fixedframe.ang_vel_in(outframe)
+        self.set_vel(outframe, v + (omega ^ dist))
+        return self.vel(outframe)
+
+    def vel(self, frame):
+        """The velocity Vector of this Point in the ReferenceFrame.
+
+        Parameters
+        ==========
+
+        frame : ReferenceFrame
+            The frame in which the returned velocity vector will be defined in
+
+        Examples
+        ========
+
+        >>> from sympy.physics.vector import Point, ReferenceFrame, dynamicsymbols
+        >>> N = ReferenceFrame('N')
+        >>> p1 = Point('p1')
+        >>> p1.set_vel(N, 10 * N.x)
+        >>> p1.vel(N)
+        10*N.x
+
+        Velocities will be automatically calculated if possible, otherwise a
+        ``ValueError`` will be returned. If it is possible to calculate
+        multiple different velocities from the relative points, the points
+        defined most directly relative to this point will be used. In the case
+        of inconsistent relative positions of points, incorrect velocities may
+        be returned. It is up to the user to define prior relative positions
+        and velocities of points in a self-consistent way.
+
+        >>> p = Point('p')
+        >>> q = dynamicsymbols('q')
+        >>> p.set_vel(N, 10 * N.x)
+        >>> p2 = Point('p2')
+        >>> p2.set_pos(p, q*N.x)
+        >>> p2.vel(N)
+        (Derivative(q(t), t) + 10)*N.x
+
+        """
+
+        _check_frame(frame)
+        if not (frame in self._vel_dict):
+            valid_neighbor_found = False
+            is_cyclic = False
+            visited = []
+            queue = [self]
+            candidate_neighbor = []
+            while queue:  # BFS to find nearest point
+                node = queue.pop(0)
+                if node not in visited:
+                    visited.append(node)
+                    for neighbor, neighbor_pos in node._pos_dict.items():
+                        if neighbor in visited:
+                            continue
+                        try:
+                            # Checks if pos vector is valid
+                            neighbor_pos.express(frame)
+                        except ValueError:
+                            continue
+                        if neighbor in queue:
+                            is_cyclic = True
+                        try:
+                            # Checks if point has its vel defined in req frame
+                            neighbor_velocity = neighbor._vel_dict[frame]
+                        except KeyError:
+                            queue.append(neighbor)
+                            continue
+                        candidate_neighbor.append(neighbor)
+                        if not valid_neighbor_found:
+                            self.set_vel(frame, self.pos_from(neighbor).dt(frame) + neighbor_velocity)
+                            valid_neighbor_found = True
+            if is_cyclic:
+                warn('Kinematic loops are defined among the positions of '
+                     'points. This is likely not desired and may cause errors '
+                     'in your calculations.')
+            if len(candidate_neighbor) > 1:
+                warn('Velocity automatically calculated based on point ' +
+                     candidate_neighbor[0].name +
+                     ' but it is also possible from points(s):' +
+                     str(candidate_neighbor[1:]) +
+                     '. Velocities from these points are not necessarily the '
+                     'same. This may cause errors in your calculations.')
+            if valid_neighbor_found:
+                return self._vel_dict[frame]
+            else:
+                raise ValueError('Velocity of point ' + self.name +
+                                 ' has not been'
+                                 ' defined in ReferenceFrame ' + frame.name)
+
+        return self._vel_dict[frame]
+
+    def partial_velocity(self, frame, *gen_speeds):
+        """Returns the partial velocities of the linear velocity vector of this
+        point in the given frame with respect to one or more provided
+        generalized speeds.
+
+        Parameters
+        ==========
+        frame : ReferenceFrame
+            The frame with which the velocity is defined in.
+        gen_speeds : functions of time
+            The generalized speeds.
+
+        Returns
+        =======
+        partial_velocities : tuple of Vector
+            The partial velocity vectors corresponding to the provided
+            generalized speeds.
+
+        Examples
+        ========
+
+        >>> from sympy.physics.vector import ReferenceFrame, Point
+        >>> from sympy.physics.vector import dynamicsymbols
+        >>> N = ReferenceFrame('N')
+        >>> A = ReferenceFrame('A')
+        >>> p = Point('p')
+        >>> u1, u2 = dynamicsymbols('u1, u2')
+        >>> p.set_vel(N, u1 * N.x + u2 * A.y)
+        >>> p.partial_velocity(N, u1)
+        N.x
+        >>> p.partial_velocity(N, u1, u2)
+        (N.x, A.y)
+
+        """
+        partials = [self.vel(frame).diff(speed, frame, var_in_dcm=False) for
+                    speed in gen_speeds]
+
+        if len(partials) == 1:
+            return partials[0]
+        else:
+            return tuple(partials)
diff --git a/llmeval-env/lib/python3.10/site-packages/sympy/physics/vector/printing.py b/llmeval-env/lib/python3.10/site-packages/sympy/physics/vector/printing.py
new file mode 100644
index 0000000000000000000000000000000000000000..59efcd90e3e5bad64a2180efab4ce31d3ae94ad3
--- /dev/null
+++ b/llmeval-env/lib/python3.10/site-packages/sympy/physics/vector/printing.py
@@ -0,0 +1,371 @@
+from sympy.core.function import Derivative
+from sympy.core.function import UndefinedFunction, AppliedUndef
+from sympy.core.symbol import Symbol
+from sympy.interactive.printing import init_printing
+from sympy.printing.latex import LatexPrinter
+from sympy.printing.pretty.pretty import PrettyPrinter
+from sympy.printing.pretty.pretty_symbology import center_accent
+from sympy.printing.str import StrPrinter
+from sympy.printing.precedence import PRECEDENCE
+
+__all__ = ['vprint', 'vsstrrepr', 'vsprint', 'vpprint', 'vlatex',
+           'init_vprinting']
+
+
+class VectorStrPrinter(StrPrinter):
+    """String Printer for vector expressions. """
+
+    def _print_Derivative(self, e):
+        from sympy.physics.vector.functions import dynamicsymbols
+        t = dynamicsymbols._t
+        if (bool(sum([i == t for i in e.variables])) &
+                isinstance(type(e.args[0]), UndefinedFunction)):
+            ol = str(e.args[0].func)
+            for i, v in enumerate(e.variables):
+                ol += dynamicsymbols._str
+            return ol
+        else:
+            return StrPrinter().doprint(e)
+
+    def _print_Function(self, e):
+        from sympy.physics.vector.functions import dynamicsymbols
+        t = dynamicsymbols._t
+        if isinstance(type(e), UndefinedFunction):
+            return StrPrinter().doprint(e).replace("(%s)" % t, '')
+        return e.func.__name__ + "(%s)" % self.stringify(e.args, ", ")
+
+
+class VectorStrReprPrinter(VectorStrPrinter):
+    """String repr printer for vector expressions."""
+    def _print_str(self, s):
+        return repr(s)
+
+
+class VectorLatexPrinter(LatexPrinter):
+    """Latex Printer for vector expressions. """
+
+    def _print_Function(self, expr, exp=None):
+        from sympy.physics.vector.functions import dynamicsymbols
+        func = expr.func.__name__
+        t = dynamicsymbols._t
+
+        if (hasattr(self, '_print_' + func) and not
+            isinstance(type(expr), UndefinedFunction)):
+            return getattr(self, '_print_' + func)(expr, exp)
+        elif isinstance(type(expr), UndefinedFunction) and (expr.args == (t,)):
+            # treat this function like a symbol
+            expr = Symbol(func)
+            if exp is not None:
+                # copied from LatexPrinter._helper_print_standard_power, which
+                # we can't call because we only have exp as a string.
+                base = self.parenthesize(expr, PRECEDENCE['Pow'])
+                base = self.parenthesize_super(base)
+                return r"%s^{%s}" % (base, exp)
+            else:
+                return super()._print(expr)
+        else:
+            return super()._print_Function(expr, exp)
+
+    def _print_Derivative(self, der_expr):
+        from sympy.physics.vector.functions import dynamicsymbols
+        # make sure it is in the right form
+        der_expr = der_expr.doit()
+        if not isinstance(der_expr, Derivative):
+            return r"\left(%s\right)" % self.doprint(der_expr)
+
+        # check if expr is a dynamicsymbol
+        t = dynamicsymbols._t
+        expr = der_expr.expr
+        red = expr.atoms(AppliedUndef)
+        syms = der_expr.variables
+        test1 = not all(True for i in red if i.free_symbols == {t})
+        test2 = not all(t == i for i in syms)
+        if test1 or test2:
+            return super()._print_Derivative(der_expr)
+
+        # done checking
+        dots = len(syms)
+        base = self._print_Function(expr)
+        base_split = base.split('_', 1)
+        base = base_split[0]
+        if dots == 1:
+            base = r"\dot{%s}" % base
+        elif dots == 2:
+            base = r"\ddot{%s}" % base
+        elif dots == 3:
+            base = r"\dddot{%s}" % base
+        elif dots == 4:
+            base = r"\ddddot{%s}" % base
+        else:  # Fallback to standard printing
+            return super()._print_Derivative(der_expr)
+        if len(base_split) != 1:
+            base += '_' + base_split[1]
+        return base
+
+
+class VectorPrettyPrinter(PrettyPrinter):
+    """Pretty Printer for vectorialexpressions. """
+
+    def _print_Derivative(self, deriv):
+        from sympy.physics.vector.functions import dynamicsymbols
+        # XXX use U('PARTIAL DIFFERENTIAL') here ?
+        t = dynamicsymbols._t
+        dot_i = 0
+        syms = list(reversed(deriv.variables))
+
+        while len(syms) > 0:
+            if syms[-1] == t:
+                syms.pop()
+                dot_i += 1
+            else:
+                return super()._print_Derivative(deriv)
+
+        if not (isinstance(type(deriv.expr), UndefinedFunction) and
+                (deriv.expr.args == (t,))):
+            return super()._print_Derivative(deriv)
+        else:
+            pform = self._print_Function(deriv.expr)
+
+        # the following condition would happen with some sort of non-standard
+        # dynamic symbol I guess, so we'll just print the SymPy way
+        if len(pform.picture) > 1:
+            return super()._print_Derivative(deriv)
+
+        # There are only special symbols up to fourth-order derivatives
+        if dot_i >= 5:
+            return super()._print_Derivative(deriv)
+
+        # Deal with special symbols
+        dots = {0: "",
+                1: "\N{COMBINING DOT ABOVE}",
+                2: "\N{COMBINING DIAERESIS}",
+                3: "\N{COMBINING THREE DOTS ABOVE}",
+                4: "\N{COMBINING FOUR DOTS ABOVE}"}
+
+        d = pform.__dict__
+        # if unicode is false then calculate number of apostrophes needed and
+        # add to output
+        if not self._use_unicode:
+            apostrophes = ""
+            for i in range(0, dot_i):
+                apostrophes += "'"
+            d['picture'][0] += apostrophes + "(t)"
+        else:
+            d['picture'] = [center_accent(d['picture'][0], dots[dot_i])]
+        return pform
+
+    def _print_Function(self, e):
+        from sympy.physics.vector.functions import dynamicsymbols
+        t = dynamicsymbols._t
+        # XXX works only for applied functions
+        func = e.func
+        args = e.args
+        func_name = func.__name__
+        pform = self._print_Symbol(Symbol(func_name))
+        # If this function is an Undefined function of t, it is probably a
+        # dynamic symbol, so we'll skip the (t). The rest of the code is
+        # identical to the normal PrettyPrinter code
+        if not (isinstance(func, UndefinedFunction) and (args == (t,))):
+            return super()._print_Function(e)
+        return pform
+
+
+def vprint(expr, **settings):
+    r"""Function for printing of expressions generated in the
+    sympy.physics vector package.
+
+    Extends SymPy's StrPrinter, takes the same setting accepted by SymPy's
+    :func:`~.sstr`, and is equivalent to ``print(sstr(foo))``.
+
+    Parameters
+    ==========
+
+    expr : valid SymPy object
+        SymPy expression to print.
+    settings : args
+        Same as the settings accepted by SymPy's sstr().
+
+    Examples
+    ========
+
+    >>> from sympy.physics.vector import vprint, dynamicsymbols
+    >>> u1 = dynamicsymbols('u1')
+    >>> print(u1)
+    u1(t)
+    >>> vprint(u1)
+    u1
+
+    """
+
+    outstr = vsprint(expr, **settings)
+
+    import builtins
+    if (outstr != 'None'):
+        builtins._ = outstr
+        print(outstr)
+
+
+def vsstrrepr(expr, **settings):
+    """Function for displaying expression representation's with vector
+    printing enabled.
+
+    Parameters
+    ==========
+
+    expr : valid SymPy object
+        SymPy expression to print.
+    settings : args
+        Same as the settings accepted by SymPy's sstrrepr().
+
+    """
+    p = VectorStrReprPrinter(settings)
+    return p.doprint(expr)
+
+
+def vsprint(expr, **settings):
+    r"""Function for displaying expressions generated in the
+    sympy.physics vector package.
+
+    Returns the output of vprint() as a string.
+
+    Parameters
+    ==========
+
+    expr : valid SymPy object
+        SymPy expression to print
+    settings : args
+        Same as the settings accepted by SymPy's sstr().
+
+    Examples
+    ========
+
+    >>> from sympy.physics.vector import vsprint, dynamicsymbols
+    >>> u1, u2 = dynamicsymbols('u1 u2')
+    >>> u2d = dynamicsymbols('u2', level=1)
+    >>> print("%s = %s" % (u1, u2 + u2d))
+    u1(t) = u2(t) + Derivative(u2(t), t)
+    >>> print("%s = %s" % (vsprint(u1), vsprint(u2 + u2d)))
+    u1 = u2 + u2'
+
+    """
+
+    string_printer = VectorStrPrinter(settings)
+    return string_printer.doprint(expr)
+
+
+def vpprint(expr, **settings):
+    r"""Function for pretty printing of expressions generated in the
+    sympy.physics vector package.
+
+    Mainly used for expressions not inside a vector; the output of running
+    scripts and generating equations of motion. Takes the same options as
+    SymPy's :func:`~.pretty_print`; see that function for more information.
+
+    Parameters
+    ==========
+
+    expr : valid SymPy object
+        SymPy expression to pretty print
+    settings : args
+        Same as those accepted by SymPy's pretty_print.
+
+
+    """
+
+    pp = VectorPrettyPrinter(settings)
+
+    # Note that this is copied from sympy.printing.pretty.pretty_print:
+
+    # XXX: this is an ugly hack, but at least it works
+    use_unicode = pp._settings['use_unicode']
+    from sympy.printing.pretty.pretty_symbology import pretty_use_unicode
+    uflag = pretty_use_unicode(use_unicode)
+
+    try:
+        return pp.doprint(expr)
+    finally:
+        pretty_use_unicode(uflag)
+
+
+def vlatex(expr, **settings):
+    r"""Function for printing latex representation of sympy.physics.vector
+    objects.
+
+    For latex representation of Vectors, Dyadics, and dynamicsymbols. Takes the
+    same options as SymPy's :func:`~.latex`; see that function for more
+    information;
+
+    Parameters
+    ==========
+
+    expr : valid SymPy object
+        SymPy expression to represent in LaTeX form
+    settings : args
+        Same as latex()
+
+    Examples
+    ========
+
+    >>> from sympy.physics.vector import vlatex, ReferenceFrame, dynamicsymbols
+    >>> N = ReferenceFrame('N')
+    >>> q1, q2 = dynamicsymbols('q1 q2')
+    >>> q1d, q2d = dynamicsymbols('q1 q2', 1)
+    >>> q1dd, q2dd = dynamicsymbols('q1 q2', 2)
+    >>> vlatex(N.x + N.y)
+    '\\mathbf{\\hat{n}_x} + \\mathbf{\\hat{n}_y}'
+    >>> vlatex(q1 + q2)
+    'q_{1} + q_{2}'
+    >>> vlatex(q1d)
+    '\\dot{q}_{1}'
+    >>> vlatex(q1 * q2d)
+    'q_{1} \\dot{q}_{2}'
+    >>> vlatex(q1dd * q1 / q1d)
+    '\\frac{q_{1} \\ddot{q}_{1}}{\\dot{q}_{1}}'
+
+    """
+    latex_printer = VectorLatexPrinter(settings)
+
+    return latex_printer.doprint(expr)
+
+
+def init_vprinting(**kwargs):
+    """Initializes time derivative printing for all SymPy objects, i.e. any
+    functions of time will be displayed in a more compact notation. The main
+    benefit of this is for printing of time derivatives; instead of
+    displaying as ``Derivative(f(t),t)``, it will display ``f'``. This is
+    only actually needed for when derivatives are present and are not in a
+    physics.vector.Vector or physics.vector.Dyadic object. This function is a
+    light wrapper to :func:`~.init_printing`. Any keyword
+    arguments for it are valid here.
+
+    {0}
+
+    Examples
+    ========
+
+    >>> from sympy import Function, symbols
+    >>> t, x = symbols('t, x')
+    >>> omega = Function('omega')
+    >>> omega(x).diff()
+    Derivative(omega(x), x)
+    >>> omega(t).diff()
+    Derivative(omega(t), t)
+
+    Now use the string printer:
+
+    >>> from sympy.physics.vector import init_vprinting
+    >>> init_vprinting(pretty_print=False)
+    >>> omega(x).diff()
+    Derivative(omega(x), x)
+    >>> omega(t).diff()
+    omega'
+
+    """
+    kwargs['str_printer'] = vsstrrepr
+    kwargs['pretty_printer'] = vpprint
+    kwargs['latex_printer'] = vlatex
+    init_printing(**kwargs)
+
+
+params = init_printing.__doc__.split('Examples\n    ========')[0]  # type: ignore
+init_vprinting.__doc__ = init_vprinting.__doc__.format(params)  # type: ignore
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diff --git a/llmeval-env/lib/python3.10/site-packages/sympy/physics/vector/tests/test_dyadic.py b/llmeval-env/lib/python3.10/site-packages/sympy/physics/vector/tests/test_dyadic.py
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index 0000000000000000000000000000000000000000..e10f8a7293df7d8818dd1ef87aa19b075904c859
--- /dev/null
+++ b/llmeval-env/lib/python3.10/site-packages/sympy/physics/vector/tests/test_dyadic.py
@@ -0,0 +1,124 @@
+from sympy.core.numbers import (Float, pi)
+from sympy.core.symbol import symbols
+from sympy.functions.elementary.trigonometric import (cos, sin)
+from sympy.matrices.immutable import ImmutableDenseMatrix as Matrix
+from sympy.physics.vector import ReferenceFrame, Vector, dynamicsymbols, outer
+from sympy.physics.vector.dyadic import _check_dyadic
+from sympy.testing.pytest import raises
+
+Vector.simp = True
+A = ReferenceFrame('A')
+
+
+def test_dyadic():
+    d1 = A.x | A.x
+    d2 = A.y | A.y
+    d3 = A.x | A.y
+    assert d1 * 0 == 0
+    assert d1 != 0
+    assert d1 * 2 == 2 * A.x | A.x
+    assert d1 / 2. == 0.5 * d1
+    assert d1 & (0 * d1) == 0
+    assert d1 & d2 == 0
+    assert d1 & A.x == A.x
+    assert d1 ^ A.x == 0
+    assert d1 ^ A.y == A.x | A.z
+    assert d1 ^ A.z == - A.x | A.y
+    assert d2 ^ A.x == - A.y | A.z
+    assert A.x ^ d1 == 0
+    assert A.y ^ d1 == - A.z | A.x
+    assert A.z ^ d1 == A.y | A.x
+    assert A.x & d1 == A.x
+    assert A.y & d1 == 0
+    assert A.y & d2 == A.y
+    assert d1 & d3 == A.x | A.y
+    assert d3 & d1 == 0
+    assert d1.dt(A) == 0
+    q = dynamicsymbols('q')
+    qd = dynamicsymbols('q', 1)
+    B = A.orientnew('B', 'Axis', [q, A.z])
+    assert d1.express(B) == d1.express(B, B)
+    assert d1.express(B) == ((cos(q)**2) * (B.x | B.x) + (-sin(q) * cos(q)) *
+            (B.x | B.y) + (-sin(q) * cos(q)) * (B.y | B.x) + (sin(q)**2) *
+            (B.y | B.y))
+    assert d1.express(B, A) == (cos(q)) * (B.x | A.x) + (-sin(q)) * (B.y | A.x)
+    assert d1.express(A, B) == (cos(q)) * (A.x | B.x) + (-sin(q)) * (A.x | B.y)
+    assert d1.dt(B) == (-qd) * (A.y | A.x) + (-qd) * (A.x | A.y)
+
+    assert d1.to_matrix(A) == Matrix([[1, 0, 0], [0, 0, 0], [0, 0, 0]])
+    assert d1.to_matrix(A, B) == Matrix([[cos(q), -sin(q), 0],
+                                         [0, 0, 0],
+                                         [0, 0, 0]])
+    assert d3.to_matrix(A) == Matrix([[0, 1, 0], [0, 0, 0], [0, 0, 0]])
+    a, b, c, d, e, f = symbols('a, b, c, d, e, f')
+    v1 = a * A.x + b * A.y + c * A.z
+    v2 = d * A.x + e * A.y + f * A.z
+    d4 = v1.outer(v2)
+    assert d4.to_matrix(A) == Matrix([[a * d, a * e, a * f],
+                                      [b * d, b * e, b * f],
+                                      [c * d, c * e, c * f]])
+    d5 = v1.outer(v1)
+    C = A.orientnew('C', 'Axis', [q, A.x])
+    for expected, actual in zip(C.dcm(A) * d5.to_matrix(A) * C.dcm(A).T,
+                                d5.to_matrix(C)):
+        assert (expected - actual).simplify() == 0
+
+    raises(TypeError, lambda: d1.applyfunc(0))
+
+
+def test_dyadic_simplify():
+    x, y, z, k, n, m, w, f, s, A = symbols('x, y, z, k, n, m, w, f, s, A')
+    N = ReferenceFrame('N')
+
+    dy = N.x | N.x
+    test1 = (1 / x + 1 / y) * dy
+    assert (N.x & test1 & N.x) != (x + y) / (x * y)
+    test1 = test1.simplify()
+    assert (N.x & test1 & N.x) == (x + y) / (x * y)
+
+    test2 = (A**2 * s**4 / (4 * pi * k * m**3)) * dy
+    test2 = test2.simplify()
+    assert (N.x & test2 & N.x) == (A**2 * s**4 / (4 * pi * k * m**3))
+
+    test3 = ((4 + 4 * x - 2 * (2 + 2 * x)) / (2 + 2 * x)) * dy
+    test3 = test3.simplify()
+    assert (N.x & test3 & N.x) == 0
+
+    test4 = ((-4 * x * y**2 - 2 * y**3 - 2 * x**2 * y) / (x + y)**2) * dy
+    test4 = test4.simplify()
+    assert (N.x & test4 & N.x) == -2 * y
+
+
+def test_dyadic_subs():
+    N = ReferenceFrame('N')
+    s = symbols('s')
+    a = s*(N.x | N.x)
+    assert a.subs({s: 2}) == 2*(N.x | N.x)
+
+
+def test_check_dyadic():
+    raises(TypeError, lambda: _check_dyadic(0))
+
+
+def test_dyadic_evalf():
+    N = ReferenceFrame('N')
+    a = pi * (N.x | N.x)
+    assert a.evalf(3) == Float('3.1416', 3) * (N.x | N.x)
+    s = symbols('s')
+    a = 5 * s * pi* (N.x | N.x)
+    assert a.evalf(2) == Float('5', 2) * Float('3.1416', 2) * s * (N.x | N.x)
+    assert a.evalf(9, subs={s: 5.124}) == Float('80.48760378', 9) * (N.x | N.x)
+
+
+def test_dyadic_xreplace():
+    x, y, z = symbols('x y z')
+    N = ReferenceFrame('N')
+    D = outer(N.x, N.x)
+    v = x*y * D
+    assert v.xreplace({x : cos(x)}) == cos(x)*y * D
+    assert v.xreplace({x*y : pi}) == pi * D
+    v = (x*y)**z * D
+    assert v.xreplace({(x*y)**z : 1}) == D
+    assert v.xreplace({x:1, z:0}) == D
+    raises(TypeError, lambda: v.xreplace())
+    raises(TypeError, lambda: v.xreplace([x, y]))
diff --git a/llmeval-env/lib/python3.10/site-packages/sympy/physics/vector/tests/test_fieldfunctions.py b/llmeval-env/lib/python3.10/site-packages/sympy/physics/vector/tests/test_fieldfunctions.py
new file mode 100644
index 0000000000000000000000000000000000000000..4e5c67aad44ca972dac6e455c57b60a74bae207a
--- /dev/null
+++ b/llmeval-env/lib/python3.10/site-packages/sympy/physics/vector/tests/test_fieldfunctions.py
@@ -0,0 +1,133 @@
+from sympy.core.singleton import S
+from sympy.core.symbol import Symbol
+from sympy.functions.elementary.trigonometric import (cos, sin)
+from sympy.physics.vector import ReferenceFrame, Vector, Point, \
+     dynamicsymbols
+from sympy.physics.vector.fieldfunctions import divergence, \
+     gradient, curl, is_conservative, is_solenoidal, \
+     scalar_potential, scalar_potential_difference
+from sympy.testing.pytest import raises
+
+R = ReferenceFrame('R')
+q = dynamicsymbols('q')
+P = R.orientnew('P', 'Axis', [q, R.z])
+
+
+def test_curl():
+    assert curl(Vector(0), R) == Vector(0)
+    assert curl(R.x, R) == Vector(0)
+    assert curl(2*R[1]**2*R.y, R) == Vector(0)
+    assert curl(R[0]*R[1]*R.z, R) == R[0]*R.x - R[1]*R.y
+    assert curl(R[0]*R[1]*R[2] * (R.x+R.y+R.z), R) == \
+           (-R[0]*R[1] + R[0]*R[2])*R.x + (R[0]*R[1] - R[1]*R[2])*R.y + \
+           (-R[0]*R[2] + R[1]*R[2])*R.z
+    assert curl(2*R[0]**2*R.y, R) == 4*R[0]*R.z
+    assert curl(P[0]**2*R.x + P.y, R) == \
+           - 2*(R[0]*cos(q) + R[1]*sin(q))*sin(q)*R.z
+    assert curl(P[0]*R.y, P) == cos(q)*P.z
+
+
+def test_divergence():
+    assert divergence(Vector(0), R) is S.Zero
+    assert divergence(R.x, R) is S.Zero
+    assert divergence(R[0]**2*R.x, R) == 2*R[0]
+    assert divergence(R[0]*R[1]*R[2] * (R.x+R.y+R.z), R) == \
+           R[0]*R[1] + R[0]*R[2] + R[1]*R[2]
+    assert divergence((1/(R[0]*R[1]*R[2])) * (R.x+R.y+R.z), R) == \
+           -1/(R[0]*R[1]*R[2]**2) - 1/(R[0]*R[1]**2*R[2]) - \
+           1/(R[0]**2*R[1]*R[2])
+    v = P[0]*P.x + P[1]*P.y + P[2]*P.z
+    assert divergence(v, P) == 3
+    assert divergence(v, R).simplify() == 3
+    assert divergence(P[0]*R.x + R[0]*P.x, R) == 2*cos(q)
+
+
+def test_gradient():
+    a = Symbol('a')
+    assert gradient(0, R) == Vector(0)
+    assert gradient(R[0], R) == R.x
+    assert gradient(R[0]*R[1]*R[2], R) == \
+           R[1]*R[2]*R.x + R[0]*R[2]*R.y + R[0]*R[1]*R.z
+    assert gradient(2*R[0]**2, R) == 4*R[0]*R.x
+    assert gradient(a*sin(R[1])/R[0], R) == \
+           - a*sin(R[1])/R[0]**2*R.x + a*cos(R[1])/R[0]*R.y
+    assert gradient(P[0]*P[1], R) == \
+           ((-R[0]*sin(q) + R[1]*cos(q))*cos(q) - (R[0]*cos(q) + R[1]*sin(q))*sin(q))*R.x + \
+           ((-R[0]*sin(q) + R[1]*cos(q))*sin(q) + (R[0]*cos(q) + R[1]*sin(q))*cos(q))*R.y
+    assert gradient(P[0]*R[2], P) == P[2]*P.x + P[0]*P.z
+
+
+scalar_field = 2*R[0]**2*R[1]*R[2]
+grad_field = gradient(scalar_field, R)
+vector_field = R[1]**2*R.x + 3*R[0]*R.y + 5*R[1]*R[2]*R.z
+curl_field = curl(vector_field, R)
+
+
+def test_conservative():
+    assert is_conservative(0) is True
+    assert is_conservative(R.x) is True
+    assert is_conservative(2 * R.x + 3 * R.y + 4 * R.z) is True
+    assert is_conservative(R[1]*R[2]*R.x + R[0]*R[2]*R.y + R[0]*R[1]*R.z) is \
+           True
+    assert is_conservative(R[0] * R.y) is False
+    assert is_conservative(grad_field) is True
+    assert is_conservative(curl_field) is False
+    assert is_conservative(4*R[0]*R[1]*R[2]*R.x + 2*R[0]**2*R[2]*R.y) is \
+                           False
+    assert is_conservative(R[2]*P.x + P[0]*R.z) is True
+
+
+def test_solenoidal():
+    assert is_solenoidal(0) is True
+    assert is_solenoidal(R.x) is True
+    assert is_solenoidal(2 * R.x + 3 * R.y + 4 * R.z) is True
+    assert is_solenoidal(R[1]*R[2]*R.x + R[0]*R[2]*R.y + R[0]*R[1]*R.z) is \
+           True
+    assert is_solenoidal(R[1] * R.y) is False
+    assert is_solenoidal(grad_field) is False
+    assert is_solenoidal(curl_field) is True
+    assert is_solenoidal((-2*R[1] + 3)*R.z) is True
+    assert is_solenoidal(cos(q)*R.x + sin(q)*R.y + cos(q)*P.z) is True
+    assert is_solenoidal(R[2]*P.x + P[0]*R.z) is True
+
+
+def test_scalar_potential():
+    assert scalar_potential(0, R) == 0
+    assert scalar_potential(R.x, R) == R[0]
+    assert scalar_potential(R.y, R) == R[1]
+    assert scalar_potential(R.z, R) == R[2]
+    assert scalar_potential(R[1]*R[2]*R.x + R[0]*R[2]*R.y + \
+                            R[0]*R[1]*R.z, R) == R[0]*R[1]*R[2]
+    assert scalar_potential(grad_field, R) == scalar_field
+    assert scalar_potential(R[2]*P.x + P[0]*R.z, R) == \
+           R[0]*R[2]*cos(q) + R[1]*R[2]*sin(q)
+    assert scalar_potential(R[2]*P.x + P[0]*R.z, P) == P[0]*P[2]
+    raises(ValueError, lambda: scalar_potential(R[0] * R.y, R))
+
+
+def test_scalar_potential_difference():
+    origin = Point('O')
+    point1 = origin.locatenew('P1', 1*R.x + 2*R.y + 3*R.z)
+    point2 = origin.locatenew('P2', 4*R.x + 5*R.y + 6*R.z)
+    genericpointR = origin.locatenew('RP', R[0]*R.x + R[1]*R.y + R[2]*R.z)
+    genericpointP = origin.locatenew('PP', P[0]*P.x + P[1]*P.y + P[2]*P.z)
+    assert scalar_potential_difference(S.Zero, R, point1, point2, \
+                                       origin) == 0
+    assert scalar_potential_difference(scalar_field, R, origin, \
+                                       genericpointR, origin) == \
+                                       scalar_field
+    assert scalar_potential_difference(grad_field, R, origin, \
+                                       genericpointR, origin) == \
+                                       scalar_field
+    assert scalar_potential_difference(grad_field, R, point1, point2,
+                                       origin) == 948
+    assert scalar_potential_difference(R[1]*R[2]*R.x + R[0]*R[2]*R.y + \
+                                       R[0]*R[1]*R.z, R, point1,
+                                       genericpointR, origin) == \
+                                       R[0]*R[1]*R[2] - 6
+    potential_diff_P = 2*P[2]*(P[0]*sin(q) + P[1]*cos(q))*\
+                       (P[0]*cos(q) - P[1]*sin(q))**2
+    assert scalar_potential_difference(grad_field, P, origin, \
+                                       genericpointP, \
+                                       origin).simplify() == \
+                                       potential_diff_P
diff --git a/llmeval-env/lib/python3.10/site-packages/sympy/physics/vector/tests/test_frame.py b/llmeval-env/lib/python3.10/site-packages/sympy/physics/vector/tests/test_frame.py
new file mode 100644
index 0000000000000000000000000000000000000000..69cbc97d745139038ee255b48ec2c0a4e88ce67c
--- /dev/null
+++ b/llmeval-env/lib/python3.10/site-packages/sympy/physics/vector/tests/test_frame.py
@@ -0,0 +1,660 @@
+from sympy.core.numbers import pi
+from sympy.core.symbol import symbols
+from sympy.functions.elementary.trigonometric import (cos, sin)
+from sympy.matrices.dense import (eye, zeros)
+from sympy.matrices.immutable import ImmutableDenseMatrix as Matrix
+from sympy.simplify.simplify import simplify
+from sympy.physics.vector import (ReferenceFrame, Vector, CoordinateSym,
+                                  dynamicsymbols, time_derivative, express,
+                                  dot)
+from sympy.physics.vector.frame import _check_frame
+from sympy.physics.vector.vector import VectorTypeError
+from sympy.testing.pytest import raises
+import warnings
+
+Vector.simp = True
+
+
+def test_dict_list():
+
+    A = ReferenceFrame('A')
+    B = ReferenceFrame('B')
+    C = ReferenceFrame('C')
+    D = ReferenceFrame('D')
+    E = ReferenceFrame('E')
+    F = ReferenceFrame('F')
+
+    B.orient_axis(A, A.x, 1.0)
+    C.orient_axis(B, B.x, 1.0)
+    D.orient_axis(C, C.x, 1.0)
+
+    assert D._dict_list(A, 0) == [D, C, B, A]
+
+    E.orient_axis(D, D.x, 1.0)
+
+    assert C._dict_list(A, 0) == [C, B, A]
+    assert C._dict_list(E, 0) == [C, D, E]
+
+    # only 0, 1, 2 permitted for second argument
+    raises(ValueError, lambda: C._dict_list(E, 5))
+    # no connecting path
+    raises(ValueError, lambda: F._dict_list(A, 0))
+
+
+def test_coordinate_vars():
+    """Tests the coordinate variables functionality"""
+    A = ReferenceFrame('A')
+    assert CoordinateSym('Ax', A, 0) == A[0]
+    assert CoordinateSym('Ax', A, 1) == A[1]
+    assert CoordinateSym('Ax', A, 2) == A[2]
+    raises(ValueError, lambda: CoordinateSym('Ax', A, 3))
+    q = dynamicsymbols('q')
+    qd = dynamicsymbols('q', 1)
+    assert isinstance(A[0], CoordinateSym) and \
+           isinstance(A[0], CoordinateSym) and \
+           isinstance(A[0], CoordinateSym)
+    assert A.variable_map(A) == {A[0]:A[0], A[1]:A[1], A[2]:A[2]}
+    assert A[0].frame == A
+    B = A.orientnew('B', 'Axis', [q, A.z])
+    assert B.variable_map(A) == {B[2]: A[2], B[1]: -A[0]*sin(q) + A[1]*cos(q),
+                                 B[0]: A[0]*cos(q) + A[1]*sin(q)}
+    assert A.variable_map(B) == {A[0]: B[0]*cos(q) - B[1]*sin(q),
+                                 A[1]: B[0]*sin(q) + B[1]*cos(q), A[2]: B[2]}
+    assert time_derivative(B[0], A) == -A[0]*sin(q)*qd + A[1]*cos(q)*qd
+    assert time_derivative(B[1], A) == -A[0]*cos(q)*qd - A[1]*sin(q)*qd
+    assert time_derivative(B[2], A) == 0
+    assert express(B[0], A, variables=True) == A[0]*cos(q) + A[1]*sin(q)
+    assert express(B[1], A, variables=True) == -A[0]*sin(q) + A[1]*cos(q)
+    assert express(B[2], A, variables=True) == A[2]
+    assert time_derivative(A[0]*A.x + A[1]*A.y + A[2]*A.z, B) == A[1]*qd*A.x - A[0]*qd*A.y
+    assert time_derivative(B[0]*B.x + B[1]*B.y + B[2]*B.z, A) == - B[1]*qd*B.x + B[0]*qd*B.y
+    assert express(B[0]*B[1]*B[2], A, variables=True) == \
+           A[2]*(-A[0]*sin(q) + A[1]*cos(q))*(A[0]*cos(q) + A[1]*sin(q))
+    assert (time_derivative(B[0]*B[1]*B[2], A) -
+            (A[2]*(-A[0]**2*cos(2*q) -
+             2*A[0]*A[1]*sin(2*q) +
+             A[1]**2*cos(2*q))*qd)).trigsimp() == 0
+    assert express(B[0]*B.x + B[1]*B.y + B[2]*B.z, A) == \
+           (B[0]*cos(q) - B[1]*sin(q))*A.x + (B[0]*sin(q) + \
+           B[1]*cos(q))*A.y + B[2]*A.z
+    assert express(B[0]*B.x + B[1]*B.y + B[2]*B.z, A, variables=True) == \
+           A[0]*A.x + A[1]*A.y + A[2]*A.z
+    assert express(A[0]*A.x + A[1]*A.y + A[2]*A.z, B) == \
+           (A[0]*cos(q) + A[1]*sin(q))*B.x + \
+           (-A[0]*sin(q) + A[1]*cos(q))*B.y + A[2]*B.z
+    assert express(A[0]*A.x + A[1]*A.y + A[2]*A.z, B, variables=True) == \
+           B[0]*B.x + B[1]*B.y + B[2]*B.z
+    N = B.orientnew('N', 'Axis', [-q, B.z])
+    assert N.variable_map(A) == {N[0]: A[0], N[2]: A[2], N[1]: A[1]}
+    C = A.orientnew('C', 'Axis', [q, A.x + A.y + A.z])
+    mapping = A.variable_map(C)
+    assert mapping[A[0]] == 2*C[0]*cos(q)/3 + C[0]/3 - 2*C[1]*sin(q + pi/6)/3 +\
+           C[1]/3 - 2*C[2]*cos(q + pi/3)/3 + C[2]/3
+    assert mapping[A[1]] == -2*C[0]*cos(q + pi/3)/3 + \
+           C[0]/3 + 2*C[1]*cos(q)/3 + C[1]/3 - 2*C[2]*sin(q + pi/6)/3 + C[2]/3
+    assert mapping[A[2]] == -2*C[0]*sin(q + pi/6)/3 + C[0]/3 - \
+           2*C[1]*cos(q + pi/3)/3 + C[1]/3 + 2*C[2]*cos(q)/3 + C[2]/3
+
+
+def test_ang_vel():
+    q1, q2, q3, q4 = dynamicsymbols('q1 q2 q3 q4')
+    q1d, q2d, q3d, q4d = dynamicsymbols('q1 q2 q3 q4', 1)
+    N = ReferenceFrame('N')
+    A = N.orientnew('A', 'Axis', [q1, N.z])
+    B = A.orientnew('B', 'Axis', [q2, A.x])
+    C = B.orientnew('C', 'Axis', [q3, B.y])
+    D = N.orientnew('D', 'Axis', [q4, N.y])
+    u1, u2, u3 = dynamicsymbols('u1 u2 u3')
+    assert A.ang_vel_in(N) == (q1d)*A.z
+    assert B.ang_vel_in(N) == (q2d)*B.x + (q1d)*A.z
+    assert C.ang_vel_in(N) == (q3d)*C.y + (q2d)*B.x + (q1d)*A.z
+
+    A2 = N.orientnew('A2', 'Axis', [q4, N.y])
+    assert N.ang_vel_in(N) == 0
+    assert N.ang_vel_in(A) == -q1d*N.z
+    assert N.ang_vel_in(B) == -q1d*A.z - q2d*B.x
+    assert N.ang_vel_in(C) == -q1d*A.z - q2d*B.x - q3d*B.y
+    assert N.ang_vel_in(A2) == -q4d*N.y
+
+    assert A.ang_vel_in(N) == q1d*N.z
+    assert A.ang_vel_in(A) == 0
+    assert A.ang_vel_in(B) == - q2d*B.x
+    assert A.ang_vel_in(C) == - q2d*B.x - q3d*B.y
+    assert A.ang_vel_in(A2) == q1d*N.z - q4d*N.y
+
+    assert B.ang_vel_in(N) == q1d*A.z + q2d*A.x
+    assert B.ang_vel_in(A) == q2d*A.x
+    assert B.ang_vel_in(B) == 0
+    assert B.ang_vel_in(C) == -q3d*B.y
+    assert B.ang_vel_in(A2) == q1d*A.z + q2d*A.x - q4d*N.y
+
+    assert C.ang_vel_in(N) == q1d*A.z + q2d*A.x + q3d*B.y
+    assert C.ang_vel_in(A) == q2d*A.x + q3d*C.y
+    assert C.ang_vel_in(B) == q3d*B.y
+    assert C.ang_vel_in(C) == 0
+    assert C.ang_vel_in(A2) == q1d*A.z + q2d*A.x + q3d*B.y - q4d*N.y
+
+    assert A2.ang_vel_in(N) == q4d*A2.y
+    assert A2.ang_vel_in(A) == q4d*A2.y - q1d*N.z
+    assert A2.ang_vel_in(B) == q4d*N.y - q1d*A.z - q2d*A.x
+    assert A2.ang_vel_in(C) == q4d*N.y - q1d*A.z - q2d*A.x - q3d*B.y
+    assert A2.ang_vel_in(A2) == 0
+
+    C.set_ang_vel(N, u1*C.x + u2*C.y + u3*C.z)
+    assert C.ang_vel_in(N) == (u1)*C.x + (u2)*C.y + (u3)*C.z
+    assert N.ang_vel_in(C) == (-u1)*C.x + (-u2)*C.y + (-u3)*C.z
+    assert C.ang_vel_in(D) == (u1)*C.x + (u2)*C.y + (u3)*C.z + (-q4d)*D.y
+    assert D.ang_vel_in(C) == (-u1)*C.x + (-u2)*C.y + (-u3)*C.z + (q4d)*D.y
+
+    q0 = dynamicsymbols('q0')
+    q0d = dynamicsymbols('q0', 1)
+    E = N.orientnew('E', 'Quaternion', (q0, q1, q2, q3))
+    assert E.ang_vel_in(N) == (
+        2 * (q1d * q0 + q2d * q3 - q3d * q2 - q0d * q1) * E.x +
+        2 * (q2d * q0 + q3d * q1 - q1d * q3 - q0d * q2) * E.y +
+        2 * (q3d * q0 + q1d * q2 - q2d * q1 - q0d * q3) * E.z)
+
+    F = N.orientnew('F', 'Body', (q1, q2, q3), 313)
+    assert F.ang_vel_in(N) == ((sin(q2)*sin(q3)*q1d + cos(q3)*q2d)*F.x +
+        (sin(q2)*cos(q3)*q1d - sin(q3)*q2d)*F.y + (cos(q2)*q1d + q3d)*F.z)
+    G = N.orientnew('G', 'Axis', (q1, N.x + N.y))
+    assert G.ang_vel_in(N) == q1d * (N.x + N.y).normalize()
+    assert N.ang_vel_in(G) == -q1d * (N.x + N.y).normalize()
+
+
+def test_dcm():
+    q1, q2, q3, q4 = dynamicsymbols('q1 q2 q3 q4')
+    N = ReferenceFrame('N')
+    A = N.orientnew('A', 'Axis', [q1, N.z])
+    B = A.orientnew('B', 'Axis', [q2, A.x])
+    C = B.orientnew('C', 'Axis', [q3, B.y])
+    D = N.orientnew('D', 'Axis', [q4, N.y])
+    E = N.orientnew('E', 'Space', [q1, q2, q3], '123')
+    assert N.dcm(C) == Matrix([
+        [- sin(q1) * sin(q2) * sin(q3) + cos(q1) * cos(q3), - sin(q1) *
+        cos(q2), sin(q1) * sin(q2) * cos(q3) + sin(q3) * cos(q1)], [sin(q1) *
+        cos(q3) + sin(q2) * sin(q3) * cos(q1), cos(q1) * cos(q2), sin(q1) *
+            sin(q3) - sin(q2) * cos(q1) * cos(q3)], [- sin(q3) * cos(q2), sin(q2),
+        cos(q2) * cos(q3)]])
+    # This is a little touchy.  Is it ok to use simplify in assert?
+    test_mat = D.dcm(C) - Matrix(
+        [[cos(q1) * cos(q3) * cos(q4) - sin(q3) * (- sin(q4) * cos(q2) +
+        sin(q1) * sin(q2) * cos(q4)), - sin(q2) * sin(q4) - sin(q1) *
+            cos(q2) * cos(q4), sin(q3) * cos(q1) * cos(q4) + cos(q3) * (- sin(q4) *
+        cos(q2) + sin(q1) * sin(q2) * cos(q4))], [sin(q1) * cos(q3) +
+        sin(q2) * sin(q3) * cos(q1), cos(q1) * cos(q2), sin(q1) * sin(q3) -
+            sin(q2) * cos(q1) * cos(q3)], [sin(q4) * cos(q1) * cos(q3) -
+        sin(q3) * (cos(q2) * cos(q4) + sin(q1) * sin(q2) * sin(q4)), sin(q2) *
+                cos(q4) - sin(q1) * sin(q4) * cos(q2), sin(q3) * sin(q4) * cos(q1) +
+                cos(q3) * (cos(q2) * cos(q4) + sin(q1) * sin(q2) * sin(q4))]])
+    assert test_mat.expand() == zeros(3, 3)
+    assert E.dcm(N) == Matrix(
+        [[cos(q2)*cos(q3), sin(q3)*cos(q2), -sin(q2)],
+        [sin(q1)*sin(q2)*cos(q3) - sin(q3)*cos(q1), sin(q1)*sin(q2)*sin(q3) +
+        cos(q1)*cos(q3), sin(q1)*cos(q2)], [sin(q1)*sin(q3) +
+        sin(q2)*cos(q1)*cos(q3), - sin(q1)*cos(q3) + sin(q2)*sin(q3)*cos(q1),
+         cos(q1)*cos(q2)]])
+
+def test_w_diff_dcm1():
+    # Ref:
+    # Dynamics Theory and Applications, Kane 1985
+    # Sec. 2.1 ANGULAR VELOCITY
+    A = ReferenceFrame('A')
+    B = ReferenceFrame('B')
+
+    c11, c12, c13 = dynamicsymbols('C11 C12 C13')
+    c21, c22, c23 = dynamicsymbols('C21 C22 C23')
+    c31, c32, c33 = dynamicsymbols('C31 C32 C33')
+
+    c11d, c12d, c13d = dynamicsymbols('C11 C12 C13', level=1)
+    c21d, c22d, c23d = dynamicsymbols('C21 C22 C23', level=1)
+    c31d, c32d, c33d = dynamicsymbols('C31 C32 C33', level=1)
+
+    DCM = Matrix([
+        [c11, c12, c13],
+        [c21, c22, c23],
+        [c31, c32, c33]
+    ])
+
+    B.orient(A, 'DCM', DCM)
+    b1a = (B.x).express(A)
+    b2a = (B.y).express(A)
+    b3a = (B.z).express(A)
+
+    # Equation (2.1.1)
+    B.set_ang_vel(A, B.x*(dot((b3a).dt(A), B.y))
+                   + B.y*(dot((b1a).dt(A), B.z))
+                   + B.z*(dot((b2a).dt(A), B.x)))
+
+    # Equation (2.1.21)
+    expr = (  (c12*c13d + c22*c23d + c32*c33d)*B.x
+            + (c13*c11d + c23*c21d + c33*c31d)*B.y
+            + (c11*c12d + c21*c22d + c31*c32d)*B.z)
+    assert B.ang_vel_in(A) - expr == 0
+
+def test_w_diff_dcm2():
+    q1, q2, q3 = dynamicsymbols('q1:4')
+    N = ReferenceFrame('N')
+    A = N.orientnew('A', 'axis', [q1, N.x])
+    B = A.orientnew('B', 'axis', [q2, A.y])
+    C = B.orientnew('C', 'axis', [q3, B.z])
+
+    DCM = C.dcm(N).T
+    D = N.orientnew('D', 'DCM', DCM)
+
+    # Frames D and C are the same ReferenceFrame,
+    # since they have equal DCM respect to frame N.
+    # Therefore, D and C should have same angle velocity in N.
+    assert D.dcm(N) == C.dcm(N) == Matrix([
+        [cos(q2)*cos(q3), sin(q1)*sin(q2)*cos(q3) +
+        sin(q3)*cos(q1), sin(q1)*sin(q3) -
+        sin(q2)*cos(q1)*cos(q3)], [-sin(q3)*cos(q2),
+        -sin(q1)*sin(q2)*sin(q3) + cos(q1)*cos(q3),
+        sin(q1)*cos(q3) + sin(q2)*sin(q3)*cos(q1)],
+        [sin(q2), -sin(q1)*cos(q2), cos(q1)*cos(q2)]])
+    assert (D.ang_vel_in(N) - C.ang_vel_in(N)).express(N).simplify() == 0
+
+def test_orientnew_respects_parent_class():
+    class MyReferenceFrame(ReferenceFrame):
+        pass
+    B = MyReferenceFrame('B')
+    C = B.orientnew('C', 'Axis', [0, B.x])
+    assert isinstance(C, MyReferenceFrame)
+
+
+def test_orientnew_respects_input_indices():
+    N = ReferenceFrame('N')
+    q1 = dynamicsymbols('q1')
+    A = N.orientnew('a', 'Axis', [q1, N.z])
+    #modify default indices:
+    minds = [x+'1' for x in N.indices]
+    B = N.orientnew('b', 'Axis', [q1, N.z], indices=minds)
+
+    assert N.indices == A.indices
+    assert B.indices == minds
+
+def test_orientnew_respects_input_latexs():
+    N = ReferenceFrame('N')
+    q1 = dynamicsymbols('q1')
+    A = N.orientnew('a', 'Axis', [q1, N.z])
+
+    #build default and alternate latex_vecs:
+    def_latex_vecs = [(r"\mathbf{\hat{%s}_%s}" % (A.name.lower(),
+                      A.indices[0])), (r"\mathbf{\hat{%s}_%s}" %
+                      (A.name.lower(), A.indices[1])),
+                      (r"\mathbf{\hat{%s}_%s}" % (A.name.lower(),
+                      A.indices[2]))]
+
+    name = 'b'
+    indices = [x+'1' for x in N.indices]
+    new_latex_vecs = [(r"\mathbf{\hat{%s}_{%s}}" % (name.lower(),
+                      indices[0])), (r"\mathbf{\hat{%s}_{%s}}" %
+                      (name.lower(), indices[1])),
+                      (r"\mathbf{\hat{%s}_{%s}}" % (name.lower(),
+                      indices[2]))]
+
+    B = N.orientnew(name, 'Axis', [q1, N.z], latexs=new_latex_vecs)
+
+    assert A.latex_vecs == def_latex_vecs
+    assert B.latex_vecs == new_latex_vecs
+    assert B.indices != indices
+
+def test_orientnew_respects_input_variables():
+    N = ReferenceFrame('N')
+    q1 = dynamicsymbols('q1')
+    A = N.orientnew('a', 'Axis', [q1, N.z])
+
+    #build non-standard variable names
+    name = 'b'
+    new_variables = ['notb_'+x+'1' for x in N.indices]
+    B = N.orientnew(name, 'Axis', [q1, N.z], variables=new_variables)
+
+    for j,var in enumerate(A.varlist):
+        assert var.name == A.name + '_' + A.indices[j]
+
+    for j,var in enumerate(B.varlist):
+        assert var.name == new_variables[j]
+
+def test_issue_10348():
+    u = dynamicsymbols('u:3')
+    I = ReferenceFrame('I')
+    I.orientnew('A', 'space', u, 'XYZ')
+
+
+def test_issue_11503():
+    A = ReferenceFrame("A")
+    A.orientnew("B", "Axis", [35, A.y])
+    C = ReferenceFrame("C")
+    A.orient(C, "Axis", [70, C.z])
+
+
+def test_partial_velocity():
+
+    N = ReferenceFrame('N')
+    A = ReferenceFrame('A')
+
+    u1, u2 = dynamicsymbols('u1, u2')
+
+    A.set_ang_vel(N, u1 * A.x + u2 * N.y)
+
+    assert N.partial_velocity(A, u1) == -A.x
+    assert N.partial_velocity(A, u1, u2) == (-A.x, -N.y)
+
+    assert A.partial_velocity(N, u1) == A.x
+    assert A.partial_velocity(N, u1, u2) == (A.x, N.y)
+
+    assert N.partial_velocity(N, u1) == 0
+    assert A.partial_velocity(A, u1) == 0
+
+
+def test_issue_11498():
+    A = ReferenceFrame('A')
+    B = ReferenceFrame('B')
+
+    # Identity transformation
+    A.orient(B, 'DCM', eye(3))
+    assert A.dcm(B) == Matrix([[1, 0, 0], [0, 1, 0], [0, 0, 1]])
+    assert B.dcm(A) == Matrix([[1, 0, 0], [0, 1, 0], [0, 0, 1]])
+
+    # x -> y
+    # y -> -z
+    # z -> -x
+    A.orient(B, 'DCM', Matrix([[0, 1, 0], [0, 0, -1], [-1, 0, 0]]))
+    assert B.dcm(A) == Matrix([[0, 1, 0], [0, 0, -1], [-1, 0, 0]])
+    assert A.dcm(B) == Matrix([[0, 0, -1], [1, 0, 0], [0, -1, 0]])
+    assert B.dcm(A).T == A.dcm(B)
+
+
+def test_reference_frame():
+    raises(TypeError, lambda: ReferenceFrame(0))
+    raises(TypeError, lambda: ReferenceFrame('N', 0))
+    raises(ValueError, lambda: ReferenceFrame('N', [0, 1]))
+    raises(TypeError, lambda: ReferenceFrame('N', [0, 1, 2]))
+    raises(TypeError, lambda: ReferenceFrame('N', ['a', 'b', 'c'], 0))
+    raises(ValueError, lambda: ReferenceFrame('N', ['a', 'b', 'c'], [0, 1]))
+    raises(TypeError, lambda: ReferenceFrame('N', ['a', 'b', 'c'], [0, 1, 2]))
+    raises(TypeError, lambda: ReferenceFrame('N', ['a', 'b', 'c'],
+                                                 ['a', 'b', 'c'], 0))
+    raises(ValueError, lambda: ReferenceFrame('N', ['a', 'b', 'c'],
+                                              ['a', 'b', 'c'], [0, 1]))
+    raises(TypeError, lambda: ReferenceFrame('N', ['a', 'b', 'c'],
+                                             ['a', 'b', 'c'], [0, 1, 2]))
+    N = ReferenceFrame('N')
+    assert N[0] == CoordinateSym('N_x', N, 0)
+    assert N[1] == CoordinateSym('N_y', N, 1)
+    assert N[2] == CoordinateSym('N_z', N, 2)
+    raises(ValueError, lambda: N[3])
+    N = ReferenceFrame('N', ['a', 'b', 'c'])
+    assert N['a'] == N.x
+    assert N['b'] == N.y
+    assert N['c'] == N.z
+    raises(ValueError, lambda: N['d'])
+    assert str(N) == 'N'
+
+    A = ReferenceFrame('A')
+    B = ReferenceFrame('B')
+    q0, q1, q2, q3 = symbols('q0 q1 q2 q3')
+    raises(TypeError, lambda: A.orient(B, 'DCM', 0))
+    raises(TypeError, lambda: B.orient(N, 'Space', [q1, q2, q3], '222'))
+    raises(TypeError, lambda: B.orient(N, 'Axis', [q1, N.x + 2 * N.y], '222'))
+    raises(TypeError, lambda: B.orient(N, 'Axis', q1))
+    raises(IndexError, lambda: B.orient(N, 'Axis', [q1]))
+    raises(TypeError, lambda: B.orient(N, 'Quaternion', [q0, q1, q2, q3], '222'))
+    raises(TypeError, lambda: B.orient(N, 'Quaternion', q0))
+    raises(TypeError, lambda: B.orient(N, 'Quaternion', [q0, q1, q2]))
+    raises(NotImplementedError, lambda: B.orient(N, 'Foo', [q0, q1, q2]))
+    raises(TypeError, lambda: B.orient(N, 'Body', [q1, q2], '232'))
+    raises(TypeError, lambda: B.orient(N, 'Space', [q1, q2], '232'))
+
+    N.set_ang_acc(B, 0)
+    assert N.ang_acc_in(B) == Vector(0)
+    N.set_ang_vel(B, 0)
+    assert N.ang_vel_in(B) == Vector(0)
+
+
+def test_check_frame():
+    raises(VectorTypeError, lambda: _check_frame(0))
+
+
+def test_dcm_diff_16824():
+    # NOTE : This is a regression test for the bug introduced in PR 14758,
+    # identified in 16824, and solved by PR 16828.
+
+    # This is the solution to Problem 2.2 on page 264 in Kane & Lenvinson's
+    # 1985 book.
+
+    q1, q2, q3 = dynamicsymbols('q1:4')
+
+    s1 = sin(q1)
+    c1 = cos(q1)
+    s2 = sin(q2)
+    c2 = cos(q2)
+    s3 = sin(q3)
+    c3 = cos(q3)
+
+    dcm = Matrix([[c2*c3, s1*s2*c3 - s3*c1, c1*s2*c3 + s3*s1],
+                  [c2*s3, s1*s2*s3 + c3*c1, c1*s2*s3 - c3*s1],
+                  [-s2,   s1*c2,            c1*c2]])
+
+    A = ReferenceFrame('A')
+    B = ReferenceFrame('B')
+    B.orient(A, 'DCM', dcm)
+
+    AwB = B.ang_vel_in(A)
+
+    alpha2 = s3*c2*q1.diff() + c3*q2.diff()
+    beta2 = s1*c2*q3.diff() + c1*q2.diff()
+
+    assert simplify(AwB.dot(A.y) - alpha2) == 0
+    assert simplify(AwB.dot(B.y) - beta2) == 0
+
+def test_orient_explicit():
+    A = ReferenceFrame('A')
+    B = ReferenceFrame('B')
+    A.orient_explicit(B, eye(3))
+    assert A.dcm(B) == Matrix([[1, 0, 0], [0, 1, 0], [0, 0, 1]])
+
+def test_orient_axis():
+    A = ReferenceFrame('A')
+    B = ReferenceFrame('B')
+    A.orient_axis(B,-B.x, 1)
+    A1 = A.dcm(B)
+    A.orient_axis(B, B.x, -1)
+    A2 = A.dcm(B)
+    A.orient_axis(B, 1, -B.x)
+    A3 = A.dcm(B)
+    assert A1 == A2
+    assert A2 == A3
+    raises(TypeError, lambda: A.orient_axis(B, 1, 1))
+
+def test_orient_body():
+    A = ReferenceFrame('A')
+    B = ReferenceFrame('B')
+    B.orient_body_fixed(A, (1,1,0), 'XYX')
+    assert B.dcm(A) == Matrix([[cos(1), sin(1)**2, -sin(1)*cos(1)], [0, cos(1), sin(1)], [sin(1), -sin(1)*cos(1), cos(1)**2]])
+
+
+def test_orient_body_advanced():
+    q1, q2, q3 = dynamicsymbols('q1:4')
+    c1, c2, c3 = symbols('c1:4')
+    u1, u2, u3 = dynamicsymbols('q1:4', 1)
+
+    # Test with everything as dynamicsymbols
+    A, B = ReferenceFrame('A'), ReferenceFrame('B')
+    B.orient_body_fixed(A, (q1, q2, q3), 'zxy')
+    assert A.dcm(B) == Matrix([
+        [-sin(q1) * sin(q2) * sin(q3) + cos(q1) * cos(q3), -sin(q1) * cos(q2),
+         sin(q1) * sin(q2) * cos(q3) + sin(q3) * cos(q1)],
+        [sin(q1) * cos(q3) + sin(q2) * sin(q3) * cos(q1), cos(q1) * cos(q2),
+         sin(q1) * sin(q3) - sin(q2) * cos(q1) * cos(q3)],
+        [-sin(q3) * cos(q2), sin(q2), cos(q2) * cos(q3)]])
+    assert B.ang_vel_in(A).to_matrix(B) == Matrix([
+        [-sin(q3) * cos(q2) * u1 + cos(q3) * u2],
+        [sin(q2) * u1 + u3],
+        [sin(q3) * u2 + cos(q2) * cos(q3) * u1]])
+
+    # Test with constant symbol
+    A, B = ReferenceFrame('A'), ReferenceFrame('B')
+    B.orient_body_fixed(A, (q1, c2, q3), 131)
+    assert A.dcm(B) == Matrix([
+        [cos(c2), -sin(c2) * cos(q3), sin(c2) * sin(q3)],
+        [sin(c2) * cos(q1), -sin(q1) * sin(q3) + cos(c2) * cos(q1) * cos(q3),
+         -sin(q1) * cos(q3) - sin(q3) * cos(c2) * cos(q1)],
+        [sin(c2) * sin(q1), sin(q1) * cos(c2) * cos(q3) + sin(q3) * cos(q1),
+         -sin(q1) * sin(q3) * cos(c2) + cos(q1) * cos(q3)]])
+    assert B.ang_vel_in(A).to_matrix(B) == Matrix([
+        [cos(c2) * u1 + u3],
+        [-sin(c2) * cos(q3) * u1],
+        [sin(c2) * sin(q3) * u1]])
+
+    # Test all symbols not time dependent
+    A, B = ReferenceFrame('A'), ReferenceFrame('B')
+    B.orient_body_fixed(A, (c1, c2, c3), 123)
+    assert B.ang_vel_in(A) == Vector(0)
+
+
+def test_orient_space_advanced():
+    # space fixed is in the end like body fixed only in opposite order
+    q1, q2, q3 = dynamicsymbols('q1:4')
+    c1, c2, c3 = symbols('c1:4')
+    u1, u2, u3 = dynamicsymbols('q1:4', 1)
+
+    # Test with everything as dynamicsymbols
+    A, B = ReferenceFrame('A'), ReferenceFrame('B')
+    B.orient_space_fixed(A, (q3, q2, q1), 'yxz')
+    assert A.dcm(B) == Matrix([
+        [-sin(q1) * sin(q2) * sin(q3) + cos(q1) * cos(q3), -sin(q1) * cos(q2),
+         sin(q1) * sin(q2) * cos(q3) + sin(q3) * cos(q1)],
+        [sin(q1) * cos(q3) + sin(q2) * sin(q3) * cos(q1), cos(q1) * cos(q2),
+         sin(q1) * sin(q3) - sin(q2) * cos(q1) * cos(q3)],
+        [-sin(q3) * cos(q2), sin(q2), cos(q2) * cos(q3)]])
+    assert B.ang_vel_in(A).to_matrix(B) == Matrix([
+        [-sin(q3) * cos(q2) * u1 + cos(q3) * u2],
+        [sin(q2) * u1 + u3],
+        [sin(q3) * u2 + cos(q2) * cos(q3) * u1]])
+
+    # Test with constant symbol
+    A, B = ReferenceFrame('A'), ReferenceFrame('B')
+    B.orient_space_fixed(A, (q3, c2, q1), 131)
+    assert A.dcm(B) == Matrix([
+        [cos(c2), -sin(c2) * cos(q3), sin(c2) * sin(q3)],
+        [sin(c2) * cos(q1), -sin(q1) * sin(q3) + cos(c2) * cos(q1) * cos(q3),
+         -sin(q1) * cos(q3) - sin(q3) * cos(c2) * cos(q1)],
+        [sin(c2) * sin(q1), sin(q1) * cos(c2) * cos(q3) + sin(q3) * cos(q1),
+         -sin(q1) * sin(q3) * cos(c2) + cos(q1) * cos(q3)]])
+    assert B.ang_vel_in(A).to_matrix(B) == Matrix([
+        [cos(c2) * u1 + u3],
+        [-sin(c2) * cos(q3) * u1],
+        [sin(c2) * sin(q3) * u1]])
+
+    # Test all symbols not time dependent
+    A, B = ReferenceFrame('A'), ReferenceFrame('B')
+    B.orient_space_fixed(A, (c1, c2, c3), 123)
+    assert B.ang_vel_in(A) == Vector(0)
+
+
+def test_orient_body_simple_ang_vel():
+    """This test ensures that the simplest form of that linear system solution
+    is returned, thus the == for the expression comparison."""
+
+    psi, theta, phi = dynamicsymbols('psi, theta, varphi')
+    t = dynamicsymbols._t
+    A = ReferenceFrame('A')
+    B = ReferenceFrame('B')
+    B.orient_body_fixed(A, (psi, theta, phi), 'ZXZ')
+    A_w_B = B.ang_vel_in(A)
+    assert A_w_B.args[0][1] == B
+    assert A_w_B.args[0][0][0] == (sin(theta)*sin(phi)*psi.diff(t) +
+                                   cos(phi)*theta.diff(t))
+    assert A_w_B.args[0][0][1] == (sin(theta)*cos(phi)*psi.diff(t) -
+                                   sin(phi)*theta.diff(t))
+    assert A_w_B.args[0][0][2] == cos(theta)*psi.diff(t) + phi.diff(t)
+
+
+def test_orient_space():
+    A = ReferenceFrame('A')
+    B = ReferenceFrame('B')
+    B.orient_space_fixed(A, (0,0,0), '123')
+    assert B.dcm(A) == Matrix([[1, 0, 0], [0, 1, 0], [0, 0, 1]])
+
+def test_orient_quaternion():
+    A = ReferenceFrame('A')
+    B = ReferenceFrame('B')
+    B.orient_quaternion(A, (0,0,0,0))
+    assert B.dcm(A) == Matrix([[0, 0, 0], [0, 0, 0], [0, 0, 0]])
+
+def test_looped_frame_warning():
+    A = ReferenceFrame('A')
+    B = ReferenceFrame('B')
+    C = ReferenceFrame('C')
+
+    a, b, c = symbols('a b c')
+    B.orient_axis(A, A.x, a)
+    C.orient_axis(B, B.x, b)
+
+    with warnings.catch_warnings(record = True) as w:
+        warnings.simplefilter("always")
+        A.orient_axis(C, C.x, c)
+        assert issubclass(w[-1].category, UserWarning)
+        assert 'Loops are defined among the orientation of frames. ' + \
+            'This is likely not desired and may cause errors in your calculations.' in str(w[-1].message)
+
+def test_frame_dict():
+    A = ReferenceFrame('A')
+    B = ReferenceFrame('B')
+    C = ReferenceFrame('C')
+
+    a, b, c = symbols('a b c')
+
+    B.orient_axis(A, A.x, a)
+    assert A._dcm_dict == {B: Matrix([[1, 0, 0],[0, cos(a), -sin(a)],[0, sin(a),  cos(a)]])}
+    assert B._dcm_dict == {A: Matrix([[1, 0, 0],[0,  cos(a), sin(a)],[0, -sin(a), cos(a)]])}
+    assert C._dcm_dict == {}
+
+    B.orient_axis(C, C.x, b)
+    # Previous relation is not wiped
+    assert A._dcm_dict == {B: Matrix([[1, 0, 0],[0, cos(a), -sin(a)],[0, sin(a),  cos(a)]])}
+    assert B._dcm_dict == {A: Matrix([[1, 0, 0],[0,  cos(a), sin(a)],[0, -sin(a), cos(a)]]), \
+        C: Matrix([[1, 0, 0],[0,  cos(b), sin(b)],[0, -sin(b), cos(b)]])}
+    assert C._dcm_dict == {B: Matrix([[1, 0, 0],[0, cos(b), -sin(b)],[0, sin(b),  cos(b)]])}
+
+    A.orient_axis(B, B.x, c)
+    # Previous relation is updated
+    assert B._dcm_dict == {C: Matrix([[1, 0, 0],[0,  cos(b), sin(b)],[0, -sin(b), cos(b)]]),\
+        A: Matrix([[1, 0, 0],[0, cos(c), -sin(c)],[0, sin(c),  cos(c)]])}
+    assert A._dcm_dict == {B: Matrix([[1, 0, 0],[0,  cos(c), sin(c)],[0, -sin(c), cos(c)]])}
+    assert C._dcm_dict == {B: Matrix([[1, 0, 0],[0, cos(b), -sin(b)],[0, sin(b),  cos(b)]])}
+
+def test_dcm_cache_dict():
+    A = ReferenceFrame('A')
+    B = ReferenceFrame('B')
+    C = ReferenceFrame('C')
+    D = ReferenceFrame('D')
+
+    a, b, c = symbols('a b c')
+
+    B.orient_axis(A, A.x, a)
+    C.orient_axis(B, B.x, b)
+    D.orient_axis(C, C.x, c)
+
+    assert D._dcm_dict == {C: Matrix([[1, 0, 0],[0,  cos(c), sin(c)],[0, -sin(c), cos(c)]])}
+    assert C._dcm_dict == {B: Matrix([[1, 0, 0],[0,  cos(b), sin(b)],[0, -sin(b), cos(b)]]), \
+        D: Matrix([[1, 0, 0],[0, cos(c), -sin(c)],[0, sin(c),  cos(c)]])}
+    assert B._dcm_dict == {A: Matrix([[1, 0, 0],[0,  cos(a), sin(a)],[0, -sin(a), cos(a)]]), \
+        C: Matrix([[1, 0, 0],[0, cos(b), -sin(b)],[0, sin(b),  cos(b)]])}
+    assert A._dcm_dict == {B: Matrix([[1, 0, 0],[0, cos(a), -sin(a)],[0, sin(a),  cos(a)]])}
+
+    assert D._dcm_dict == D._dcm_cache
+
+    D.dcm(A) # Check calculated dcm relation is stored in _dcm_cache and not in _dcm_dict
+    assert list(A._dcm_cache.keys()) == [A, B, D]
+    assert list(D._dcm_cache.keys()) == [C, A]
+    assert list(A._dcm_dict.keys()) == [B]
+    assert list(D._dcm_dict.keys()) == [C]
+    assert A._dcm_dict != A._dcm_cache
+
+    A.orient_axis(B, B.x, b) # _dcm_cache of A is wiped out and new relation is stored.
+    assert A._dcm_dict == {B: Matrix([[1, 0, 0],[0,  cos(b), sin(b)],[0, -sin(b), cos(b)]])}
+    assert A._dcm_dict == A._dcm_cache
+    assert B._dcm_dict == {C: Matrix([[1, 0, 0],[0, cos(b), -sin(b)],[0, sin(b),  cos(b)]]), \
+        A: Matrix([[1, 0, 0],[0, cos(b), -sin(b)],[0, sin(b),  cos(b)]])}
diff --git a/llmeval-env/lib/python3.10/site-packages/sympy/physics/vector/tests/test_functions.py b/llmeval-env/lib/python3.10/site-packages/sympy/physics/vector/tests/test_functions.py
new file mode 100644
index 0000000000000000000000000000000000000000..4c37a1890c2448995a4e5e8b7ea2dddda040f518
--- /dev/null
+++ b/llmeval-env/lib/python3.10/site-packages/sympy/physics/vector/tests/test_functions.py
@@ -0,0 +1,508 @@
+from sympy.core.numbers import pi
+from sympy.core.singleton import S
+from sympy.core.symbol import symbols
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.functions.elementary.trigonometric import (cos, sin)
+from sympy.integrals.integrals import Integral
+from sympy.physics.vector import Dyadic, Point, ReferenceFrame, Vector
+from sympy.physics.vector.functions import (cross, dot, express,
+                                            time_derivative,
+                                            kinematic_equations, outer,
+                                            partial_velocity,
+                                            get_motion_params, dynamicsymbols)
+from sympy.testing.pytest import raises
+
+Vector.simp = True
+q1, q2, q3, q4, q5 = symbols('q1 q2 q3 q4 q5')
+N = ReferenceFrame('N')
+A = N.orientnew('A', 'Axis', [q1, N.z])
+B = A.orientnew('B', 'Axis', [q2, A.x])
+C = B.orientnew('C', 'Axis', [q3, B.y])
+
+
+def test_dot():
+    assert dot(A.x, A.x) == 1
+    assert dot(A.x, A.y) == 0
+    assert dot(A.x, A.z) == 0
+
+    assert dot(A.y, A.x) == 0
+    assert dot(A.y, A.y) == 1
+    assert dot(A.y, A.z) == 0
+
+    assert dot(A.z, A.x) == 0
+    assert dot(A.z, A.y) == 0
+    assert dot(A.z, A.z) == 1
+
+
+def test_dot_different_frames():
+    assert dot(N.x, A.x) == cos(q1)
+    assert dot(N.x, A.y) == -sin(q1)
+    assert dot(N.x, A.z) == 0
+    assert dot(N.y, A.x) == sin(q1)
+    assert dot(N.y, A.y) == cos(q1)
+    assert dot(N.y, A.z) == 0
+    assert dot(N.z, A.x) == 0
+    assert dot(N.z, A.y) == 0
+    assert dot(N.z, A.z) == 1
+
+    assert dot(N.x, A.x + A.y) == sqrt(2)*cos(q1 + pi/4) == dot(A.x + A.y, N.x)
+
+    assert dot(A.x, C.x) == cos(q3)
+    assert dot(A.x, C.y) == 0
+    assert dot(A.x, C.z) == sin(q3)
+    assert dot(A.y, C.x) == sin(q2)*sin(q3)
+    assert dot(A.y, C.y) == cos(q2)
+    assert dot(A.y, C.z) == -sin(q2)*cos(q3)
+    assert dot(A.z, C.x) == -cos(q2)*sin(q3)
+    assert dot(A.z, C.y) == sin(q2)
+    assert dot(A.z, C.z) == cos(q2)*cos(q3)
+
+
+def test_cross():
+    assert cross(A.x, A.x) == 0
+    assert cross(A.x, A.y) == A.z
+    assert cross(A.x, A.z) == -A.y
+
+    assert cross(A.y, A.x) == -A.z
+    assert cross(A.y, A.y) == 0
+    assert cross(A.y, A.z) == A.x
+
+    assert cross(A.z, A.x) == A.y
+    assert cross(A.z, A.y) == -A.x
+    assert cross(A.z, A.z) == 0
+
+
+def test_cross_different_frames():
+    assert cross(N.x, A.x) == sin(q1)*A.z
+    assert cross(N.x, A.y) == cos(q1)*A.z
+    assert cross(N.x, A.z) == -sin(q1)*A.x - cos(q1)*A.y
+    assert cross(N.y, A.x) == -cos(q1)*A.z
+    assert cross(N.y, A.y) == sin(q1)*A.z
+    assert cross(N.y, A.z) == cos(q1)*A.x - sin(q1)*A.y
+    assert cross(N.z, A.x) == A.y
+    assert cross(N.z, A.y) == -A.x
+    assert cross(N.z, A.z) == 0
+
+    assert cross(N.x, A.x) == sin(q1)*A.z
+    assert cross(N.x, A.y) == cos(q1)*A.z
+    assert cross(N.x, A.x + A.y) == sin(q1)*A.z + cos(q1)*A.z
+    assert cross(A.x + A.y, N.x) == -sin(q1)*A.z - cos(q1)*A.z
+
+    assert cross(A.x, C.x) == sin(q3)*C.y
+    assert cross(A.x, C.y) == -sin(q3)*C.x + cos(q3)*C.z
+    assert cross(A.x, C.z) == -cos(q3)*C.y
+    assert cross(C.x, A.x) == -sin(q3)*C.y
+    assert cross(C.y, A.x) == sin(q3)*C.x - cos(q3)*C.z
+    assert cross(C.z, A.x) == cos(q3)*C.y
+
+def test_operator_match():
+    """Test that the output of dot, cross, outer functions match
+    operator behavior.
+    """
+    A = ReferenceFrame('A')
+    v = A.x + A.y
+    d = v | v
+    zerov = Vector(0)
+    zerod = Dyadic(0)
+
+    # dot products
+    assert d & d == dot(d, d)
+    assert d & zerod == dot(d, zerod)
+    assert zerod & d == dot(zerod, d)
+    assert d & v == dot(d, v)
+    assert v & d == dot(v, d)
+    assert d & zerov == dot(d, zerov)
+    assert zerov & d == dot(zerov, d)
+    raises(TypeError, lambda: dot(d, S.Zero))
+    raises(TypeError, lambda: dot(S.Zero, d))
+    raises(TypeError, lambda: dot(d, 0))
+    raises(TypeError, lambda: dot(0, d))
+    assert v & v == dot(v, v)
+    assert v & zerov == dot(v, zerov)
+    assert zerov & v == dot(zerov, v)
+    raises(TypeError, lambda: dot(v, S.Zero))
+    raises(TypeError, lambda: dot(S.Zero, v))
+    raises(TypeError, lambda: dot(v, 0))
+    raises(TypeError, lambda: dot(0, v))
+
+    # cross products
+    raises(TypeError, lambda: cross(d, d))
+    raises(TypeError, lambda: cross(d, zerod))
+    raises(TypeError, lambda: cross(zerod, d))
+    assert d ^ v == cross(d, v)
+    assert v ^ d == cross(v, d)
+    assert d ^ zerov == cross(d, zerov)
+    assert zerov ^ d == cross(zerov, d)
+    assert zerov ^ d == cross(zerov, d)
+    raises(TypeError, lambda: cross(d, S.Zero))
+    raises(TypeError, lambda: cross(S.Zero, d))
+    raises(TypeError, lambda: cross(d, 0))
+    raises(TypeError, lambda: cross(0, d))
+    assert v ^ v == cross(v, v)
+    assert v ^ zerov == cross(v, zerov)
+    assert zerov ^ v == cross(zerov, v)
+    raises(TypeError, lambda: cross(v, S.Zero))
+    raises(TypeError, lambda: cross(S.Zero, v))
+    raises(TypeError, lambda: cross(v, 0))
+    raises(TypeError, lambda: cross(0, v))
+
+    # outer products
+    raises(TypeError, lambda: outer(d, d))
+    raises(TypeError, lambda: outer(d, zerod))
+    raises(TypeError, lambda: outer(zerod, d))
+    raises(TypeError, lambda: outer(d, v))
+    raises(TypeError, lambda: outer(v, d))
+    raises(TypeError, lambda: outer(d, zerov))
+    raises(TypeError, lambda: outer(zerov, d))
+    raises(TypeError, lambda: outer(zerov, d))
+    raises(TypeError, lambda: outer(d, S.Zero))
+    raises(TypeError, lambda: outer(S.Zero, d))
+    raises(TypeError, lambda: outer(d, 0))
+    raises(TypeError, lambda: outer(0, d))
+    assert v | v == outer(v, v)
+    assert v | zerov == outer(v, zerov)
+    assert zerov | v == outer(zerov, v)
+    raises(TypeError, lambda: outer(v, S.Zero))
+    raises(TypeError, lambda: outer(S.Zero, v))
+    raises(TypeError, lambda: outer(v, 0))
+    raises(TypeError, lambda: outer(0, v))
+
+
+def test_express():
+    assert express(Vector(0), N) == Vector(0)
+    assert express(S.Zero, N) is S.Zero
+    assert express(A.x, C) == cos(q3)*C.x + sin(q3)*C.z
+    assert express(A.y, C) == sin(q2)*sin(q3)*C.x + cos(q2)*C.y - \
+        sin(q2)*cos(q3)*C.z
+    assert express(A.z, C) == -sin(q3)*cos(q2)*C.x + sin(q2)*C.y + \
+        cos(q2)*cos(q3)*C.z
+    assert express(A.x, N) == cos(q1)*N.x + sin(q1)*N.y
+    assert express(A.y, N) == -sin(q1)*N.x + cos(q1)*N.y
+    assert express(A.z, N) == N.z
+    assert express(A.x, A) == A.x
+    assert express(A.y, A) == A.y
+    assert express(A.z, A) == A.z
+    assert express(A.x, B) == B.x
+    assert express(A.y, B) == cos(q2)*B.y - sin(q2)*B.z
+    assert express(A.z, B) == sin(q2)*B.y + cos(q2)*B.z
+    assert express(A.x, C) == cos(q3)*C.x + sin(q3)*C.z
+    assert express(A.y, C) == sin(q2)*sin(q3)*C.x + cos(q2)*C.y - \
+        sin(q2)*cos(q3)*C.z
+    assert express(A.z, C) == -sin(q3)*cos(q2)*C.x + sin(q2)*C.y + \
+        cos(q2)*cos(q3)*C.z
+    # Check to make sure UnitVectors get converted properly
+    assert express(N.x, N) == N.x
+    assert express(N.y, N) == N.y
+    assert express(N.z, N) == N.z
+    assert express(N.x, A) == (cos(q1)*A.x - sin(q1)*A.y)
+    assert express(N.y, A) == (sin(q1)*A.x + cos(q1)*A.y)
+    assert express(N.z, A) == A.z
+    assert express(N.x, B) == (cos(q1)*B.x - sin(q1)*cos(q2)*B.y +
+            sin(q1)*sin(q2)*B.z)
+    assert express(N.y, B) == (sin(q1)*B.x + cos(q1)*cos(q2)*B.y -
+            sin(q2)*cos(q1)*B.z)
+    assert express(N.z, B) == (sin(q2)*B.y + cos(q2)*B.z)
+    assert express(N.x, C) == (
+        (cos(q1)*cos(q3) - sin(q1)*sin(q2)*sin(q3))*C.x -
+        sin(q1)*cos(q2)*C.y +
+        (sin(q3)*cos(q1) + sin(q1)*sin(q2)*cos(q3))*C.z)
+    assert express(N.y, C) == (
+        (sin(q1)*cos(q3) + sin(q2)*sin(q3)*cos(q1))*C.x +
+        cos(q1)*cos(q2)*C.y +
+        (sin(q1)*sin(q3) - sin(q2)*cos(q1)*cos(q3))*C.z)
+    assert express(N.z, C) == (-sin(q3)*cos(q2)*C.x + sin(q2)*C.y +
+            cos(q2)*cos(q3)*C.z)
+
+    assert express(A.x, N) == (cos(q1)*N.x + sin(q1)*N.y)
+    assert express(A.y, N) == (-sin(q1)*N.x + cos(q1)*N.y)
+    assert express(A.z, N) == N.z
+    assert express(A.x, A) == A.x
+    assert express(A.y, A) == A.y
+    assert express(A.z, A) == A.z
+    assert express(A.x, B) == B.x
+    assert express(A.y, B) == (cos(q2)*B.y - sin(q2)*B.z)
+    assert express(A.z, B) == (sin(q2)*B.y + cos(q2)*B.z)
+    assert express(A.x, C) == (cos(q3)*C.x + sin(q3)*C.z)
+    assert express(A.y, C) == (sin(q2)*sin(q3)*C.x + cos(q2)*C.y -
+            sin(q2)*cos(q3)*C.z)
+    assert express(A.z, C) == (-sin(q3)*cos(q2)*C.x + sin(q2)*C.y +
+            cos(q2)*cos(q3)*C.z)
+
+    assert express(B.x, N) == (cos(q1)*N.x + sin(q1)*N.y)
+    assert express(B.y, N) == (-sin(q1)*cos(q2)*N.x +
+            cos(q1)*cos(q2)*N.y + sin(q2)*N.z)
+    assert express(B.z, N) == (sin(q1)*sin(q2)*N.x -
+            sin(q2)*cos(q1)*N.y + cos(q2)*N.z)
+    assert express(B.x, A) == A.x
+    assert express(B.y, A) == (cos(q2)*A.y + sin(q2)*A.z)
+    assert express(B.z, A) == (-sin(q2)*A.y + cos(q2)*A.z)
+    assert express(B.x, B) == B.x
+    assert express(B.y, B) == B.y
+    assert express(B.z, B) == B.z
+    assert express(B.x, C) == (cos(q3)*C.x + sin(q3)*C.z)
+    assert express(B.y, C) == C.y
+    assert express(B.z, C) == (-sin(q3)*C.x + cos(q3)*C.z)
+
+    assert express(C.x, N) == (
+        (cos(q1)*cos(q3) - sin(q1)*sin(q2)*sin(q3))*N.x +
+        (sin(q1)*cos(q3) + sin(q2)*sin(q3)*cos(q1))*N.y -
+        sin(q3)*cos(q2)*N.z)
+    assert express(C.y, N) == (
+        -sin(q1)*cos(q2)*N.x + cos(q1)*cos(q2)*N.y + sin(q2)*N.z)
+    assert express(C.z, N) == (
+        (sin(q3)*cos(q1) + sin(q1)*sin(q2)*cos(q3))*N.x +
+        (sin(q1)*sin(q3) - sin(q2)*cos(q1)*cos(q3))*N.y +
+        cos(q2)*cos(q3)*N.z)
+    assert express(C.x, A) == (cos(q3)*A.x + sin(q2)*sin(q3)*A.y -
+            sin(q3)*cos(q2)*A.z)
+    assert express(C.y, A) == (cos(q2)*A.y + sin(q2)*A.z)
+    assert express(C.z, A) == (sin(q3)*A.x - sin(q2)*cos(q3)*A.y +
+            cos(q2)*cos(q3)*A.z)
+    assert express(C.x, B) == (cos(q3)*B.x - sin(q3)*B.z)
+    assert express(C.y, B) == B.y
+    assert express(C.z, B) == (sin(q3)*B.x + cos(q3)*B.z)
+    assert express(C.x, C) == C.x
+    assert express(C.y, C) == C.y
+    assert express(C.z, C) == C.z == (C.z)
+
+    #  Check to make sure Vectors get converted back to UnitVectors
+    assert N.x == express((cos(q1)*A.x - sin(q1)*A.y), N)
+    assert N.y == express((sin(q1)*A.x + cos(q1)*A.y), N)
+    assert N.x == express((cos(q1)*B.x - sin(q1)*cos(q2)*B.y +
+            sin(q1)*sin(q2)*B.z), N)
+    assert N.y == express((sin(q1)*B.x + cos(q1)*cos(q2)*B.y -
+        sin(q2)*cos(q1)*B.z), N)
+    assert N.z == express((sin(q2)*B.y + cos(q2)*B.z), N)
+
+    """
+    These don't really test our code, they instead test the auto simplification
+    (or lack thereof) of SymPy.
+    assert N.x == express((
+            (cos(q1)*cos(q3)-sin(q1)*sin(q2)*sin(q3))*C.x -
+            sin(q1)*cos(q2)*C.y +
+            (sin(q3)*cos(q1)+sin(q1)*sin(q2)*cos(q3))*C.z), N)
+    assert N.y == express((
+            (sin(q1)*cos(q3) + sin(q2)*sin(q3)*cos(q1))*C.x +
+            cos(q1)*cos(q2)*C.y +
+            (sin(q1)*sin(q3) - sin(q2)*cos(q1)*cos(q3))*C.z), N)
+    assert N.z == express((-sin(q3)*cos(q2)*C.x + sin(q2)*C.y +
+            cos(q2)*cos(q3)*C.z), N)
+    """
+
+    assert A.x == express((cos(q1)*N.x + sin(q1)*N.y), A)
+    assert A.y == express((-sin(q1)*N.x + cos(q1)*N.y), A)
+
+    assert A.y == express((cos(q2)*B.y - sin(q2)*B.z), A)
+    assert A.z == express((sin(q2)*B.y + cos(q2)*B.z), A)
+
+    assert A.x == express((cos(q3)*C.x + sin(q3)*C.z), A)
+
+    # Tripsimp messes up here too.
+    #print express((sin(q2)*sin(q3)*C.x + cos(q2)*C.y -
+    #        sin(q2)*cos(q3)*C.z), A)
+    assert A.y == express((sin(q2)*sin(q3)*C.x + cos(q2)*C.y -
+            sin(q2)*cos(q3)*C.z), A)
+
+    assert A.z == express((-sin(q3)*cos(q2)*C.x + sin(q2)*C.y +
+            cos(q2)*cos(q3)*C.z), A)
+    assert B.x == express((cos(q1)*N.x + sin(q1)*N.y), B)
+    assert B.y == express((-sin(q1)*cos(q2)*N.x +
+            cos(q1)*cos(q2)*N.y + sin(q2)*N.z), B)
+
+    assert B.z == express((sin(q1)*sin(q2)*N.x -
+            sin(q2)*cos(q1)*N.y + cos(q2)*N.z), B)
+
+    assert B.y == express((cos(q2)*A.y + sin(q2)*A.z), B)
+    assert B.z == express((-sin(q2)*A.y + cos(q2)*A.z), B)
+    assert B.x == express((cos(q3)*C.x + sin(q3)*C.z), B)
+    assert B.z == express((-sin(q3)*C.x + cos(q3)*C.z), B)
+
+    """
+    assert C.x == express((
+            (cos(q1)*cos(q3)-sin(q1)*sin(q2)*sin(q3))*N.x +
+            (sin(q1)*cos(q3)+sin(q2)*sin(q3)*cos(q1))*N.y -
+                sin(q3)*cos(q2)*N.z), C)
+    assert C.y == express((
+            -sin(q1)*cos(q2)*N.x + cos(q1)*cos(q2)*N.y + sin(q2)*N.z), C)
+    assert C.z == express((
+            (sin(q3)*cos(q1)+sin(q1)*sin(q2)*cos(q3))*N.x +
+            (sin(q1)*sin(q3)-sin(q2)*cos(q1)*cos(q3))*N.y +
+            cos(q2)*cos(q3)*N.z), C)
+    """
+    assert C.x == express((cos(q3)*A.x + sin(q2)*sin(q3)*A.y -
+            sin(q3)*cos(q2)*A.z), C)
+    assert C.y == express((cos(q2)*A.y + sin(q2)*A.z), C)
+    assert C.z == express((sin(q3)*A.x - sin(q2)*cos(q3)*A.y +
+            cos(q2)*cos(q3)*A.z), C)
+    assert C.x == express((cos(q3)*B.x - sin(q3)*B.z), C)
+    assert C.z == express((sin(q3)*B.x + cos(q3)*B.z), C)
+
+
+def test_time_derivative():
+    #The use of time_derivative for calculations pertaining to scalar
+    #fields has been tested in test_coordinate_vars in test_essential.py
+    A = ReferenceFrame('A')
+    q = dynamicsymbols('q')
+    qd = dynamicsymbols('q', 1)
+    B = A.orientnew('B', 'Axis', [q, A.z])
+    d = A.x | A.x
+    assert time_derivative(d, B) == (-qd) * (A.y | A.x) + \
+           (-qd) * (A.x | A.y)
+    d1 = A.x | B.y
+    assert time_derivative(d1, A) == - qd*(A.x|B.x)
+    assert time_derivative(d1, B) == - qd*(A.y|B.y)
+    d2 = A.x | B.x
+    assert time_derivative(d2, A) == qd*(A.x|B.y)
+    assert time_derivative(d2, B) == - qd*(A.y|B.x)
+    d3 = A.x | B.z
+    assert time_derivative(d3, A) == 0
+    assert time_derivative(d3, B) == - qd*(A.y|B.z)
+    q1, q2, q3, q4 = dynamicsymbols('q1 q2 q3 q4')
+    q1d, q2d, q3d, q4d = dynamicsymbols('q1 q2 q3 q4', 1)
+    q1dd, q2dd, q3dd, q4dd = dynamicsymbols('q1 q2 q3 q4', 2)
+    C = B.orientnew('C', 'Axis', [q4, B.x])
+    v1 = q1 * A.z
+    v2 = q2*A.x + q3*B.y
+    v3 = q1*A.x + q2*A.y + q3*A.z
+    assert time_derivative(B.x, C) == 0
+    assert time_derivative(B.y, C) == - q4d*B.z
+    assert time_derivative(B.z, C) == q4d*B.y
+    assert time_derivative(v1, B) == q1d*A.z
+    assert time_derivative(v1, C) == - q1*sin(q)*q4d*A.x + \
+           q1*cos(q)*q4d*A.y + q1d*A.z
+    assert time_derivative(v2, A) == q2d*A.x - q3*qd*B.x + q3d*B.y
+    assert time_derivative(v2, C) == q2d*A.x - q2*qd*A.y + \
+           q2*sin(q)*q4d*A.z + q3d*B.y - q3*q4d*B.z
+    assert time_derivative(v3, B) == (q2*qd + q1d)*A.x + \
+           (-q1*qd + q2d)*A.y + q3d*A.z
+    assert time_derivative(d, C) == - qd*(A.y|A.x) + \
+           sin(q)*q4d*(A.z|A.x) - qd*(A.x|A.y) + sin(q)*q4d*(A.x|A.z)
+    raises(ValueError, lambda: time_derivative(B.x, C, order=0.5))
+    raises(ValueError, lambda: time_derivative(B.x, C, order=-1))
+
+
+def test_get_motion_methods():
+    #Initialization
+    t = dynamicsymbols._t
+    s1, s2, s3 = symbols('s1 s2 s3')
+    S1, S2, S3 = symbols('S1 S2 S3')
+    S4, S5, S6 = symbols('S4 S5 S6')
+    t1, t2 = symbols('t1 t2')
+    a, b, c = dynamicsymbols('a b c')
+    ad, bd, cd = dynamicsymbols('a b c', 1)
+    a2d, b2d, c2d = dynamicsymbols('a b c', 2)
+    v0 = S1*N.x + S2*N.y + S3*N.z
+    v01 = S4*N.x + S5*N.y + S6*N.z
+    v1 = s1*N.x + s2*N.y + s3*N.z
+    v2 = a*N.x + b*N.y + c*N.z
+    v2d = ad*N.x + bd*N.y + cd*N.z
+    v2dd = a2d*N.x + b2d*N.y + c2d*N.z
+    #Test position parameter
+    assert get_motion_params(frame = N) == (0, 0, 0)
+    assert get_motion_params(N, position=v1) == (0, 0, v1)
+    assert get_motion_params(N, position=v2) == (v2dd, v2d, v2)
+    #Test velocity parameter
+    assert get_motion_params(N, velocity=v1) == (0, v1, v1 * t)
+    assert get_motion_params(N, velocity=v1, position=v0, timevalue1=t1) == \
+           (0, v1, v0 + v1*(t - t1))
+    answer = get_motion_params(N, velocity=v1, position=v2, timevalue1=t1)
+    answer_expected = (0, v1, v1*t - v1*t1 + v2.subs(t, t1))
+    assert answer == answer_expected
+
+    answer = get_motion_params(N, velocity=v2, position=v0, timevalue1=t1)
+    integral_vector = Integral(a, (t, t1, t))*N.x + Integral(b, (t, t1, t))*N.y \
+            + Integral(c, (t, t1, t))*N.z
+    answer_expected = (v2d, v2, v0 + integral_vector)
+    assert answer == answer_expected
+
+    #Test acceleration parameter
+    assert get_motion_params(N, acceleration=v1) == \
+           (v1, v1 * t, v1 * t**2/2)
+    assert get_motion_params(N, acceleration=v1, velocity=v0,
+                          position=v2, timevalue1=t1, timevalue2=t2) == \
+           (v1, (v0 + v1*t - v1*t2),
+            -v0*t1 + v1*t**2/2 + v1*t2*t1 - \
+            v1*t1**2/2 + t*(v0 - v1*t2) + \
+            v2.subs(t, t1))
+    assert get_motion_params(N, acceleration=v1, velocity=v0,
+                             position=v01, timevalue1=t1, timevalue2=t2) == \
+           (v1, v0 + v1*t - v1*t2,
+            -v0*t1 + v01 + v1*t**2/2 + \
+            v1*t2*t1 - v1*t1**2/2 + \
+            t*(v0 - v1*t2))
+    answer = get_motion_params(N, acceleration=a*N.x, velocity=S1*N.x,
+                          position=S2*N.x, timevalue1=t1, timevalue2=t2)
+    i1 = Integral(a, (t, t2, t))
+    answer_expected = (a*N.x, (S1 + i1)*N.x, \
+        (S2 + Integral(S1 + i1, (t, t1, t)))*N.x)
+    assert answer == answer_expected
+
+
+def test_kin_eqs():
+    q0, q1, q2, q3 = dynamicsymbols('q0 q1 q2 q3')
+    q0d, q1d, q2d, q3d = dynamicsymbols('q0 q1 q2 q3', 1)
+    u1, u2, u3 = dynamicsymbols('u1 u2 u3')
+    ke = kinematic_equations([u1,u2,u3], [q1,q2,q3], 'body', 313)
+    assert ke == kinematic_equations([u1,u2,u3], [q1,q2,q3], 'body', '313')
+    kds = kinematic_equations([u1, u2, u3], [q0, q1, q2, q3], 'quaternion')
+    assert kds == [-0.5 * q0 * u1 - 0.5 * q2 * u3 + 0.5 * q3 * u2 + q1d,
+            -0.5 * q0 * u2 + 0.5 * q1 * u3 - 0.5 * q3 * u1 + q2d,
+            -0.5 * q0 * u3 - 0.5 * q1 * u2 + 0.5 * q2 * u1 + q3d,
+            0.5 * q1 * u1 + 0.5 * q2 * u2 + 0.5 * q3 * u3 + q0d]
+    raises(ValueError, lambda: kinematic_equations([u1, u2, u3], [q0, q1, q2], 'quaternion'))
+    raises(ValueError, lambda: kinematic_equations([u1, u2, u3], [q0, q1, q2, q3], 'quaternion', '123'))
+    raises(ValueError, lambda: kinematic_equations([u1, u2, u3], [q0, q1, q2, q3], 'foo'))
+    raises(TypeError, lambda: kinematic_equations(u1, [q0, q1, q2, q3], 'quaternion'))
+    raises(TypeError, lambda: kinematic_equations([u1], [q0, q1, q2, q3], 'quaternion'))
+    raises(TypeError, lambda: kinematic_equations([u1, u2, u3], q0, 'quaternion'))
+    raises(ValueError, lambda: kinematic_equations([u1, u2, u3], [q0, q1, q2, q3], 'body'))
+    raises(ValueError, lambda: kinematic_equations([u1, u2, u3], [q0, q1, q2, q3], 'space'))
+    raises(ValueError, lambda: kinematic_equations([u1, u2, u3], [q0, q1, q2], 'body', '222'))
+    assert kinematic_equations([0, 0, 0], [q0, q1, q2], 'space') == [S.Zero, S.Zero, S.Zero]
+
+
+def test_partial_velocity():
+    q1, q2, q3, u1, u2, u3 = dynamicsymbols('q1 q2 q3 u1 u2 u3')
+    u4, u5 = dynamicsymbols('u4, u5')
+    r = symbols('r')
+
+    N = ReferenceFrame('N')
+    Y = N.orientnew('Y', 'Axis', [q1, N.z])
+    L = Y.orientnew('L', 'Axis', [q2, Y.x])
+    R = L.orientnew('R', 'Axis', [q3, L.y])
+    R.set_ang_vel(N, u1 * L.x + u2 * L.y + u3 * L.z)
+
+    C = Point('C')
+    C.set_vel(N, u4 * L.x + u5 * (Y.z ^ L.x))
+    Dmc = C.locatenew('Dmc', r * L.z)
+    Dmc.v2pt_theory(C, N, R)
+
+    vel_list = [Dmc.vel(N), C.vel(N), R.ang_vel_in(N)]
+    u_list = [u1, u2, u3, u4, u5]
+    assert (partial_velocity(vel_list, u_list, N) ==
+            [[- r*L.y, r*L.x, 0, L.x, cos(q2)*L.y - sin(q2)*L.z],
+            [0, 0, 0, L.x, cos(q2)*L.y - sin(q2)*L.z],
+            [L.x, L.y, L.z, 0, 0]])
+
+    # Make sure that partial velocities can be computed regardless if the
+    # orientation between frames is defined or not.
+    A = ReferenceFrame('A')
+    B = ReferenceFrame('B')
+    v = u4 * A.x + u5 * B.y
+    assert partial_velocity((v, ), (u4, u5), A) == [[A.x, B.y]]
+
+    raises(TypeError, lambda: partial_velocity(Dmc.vel(N), u_list, N))
+    raises(TypeError, lambda: partial_velocity(vel_list, u1, N))
+
+def test_dynamicsymbols():
+    #Tests to check the assumptions applied to dynamicsymbols
+    f1 = dynamicsymbols('f1')
+    f2 = dynamicsymbols('f2', real=True)
+    f3 = dynamicsymbols('f3', positive=True)
+    f4, f5 = dynamicsymbols('f4,f5', commutative=False)
+    f6 = dynamicsymbols('f6', integer=True)
+    assert f1.is_real is None
+    assert f2.is_real
+    assert f3.is_positive
+    assert f4*f5 != f5*f4
+    assert f6.is_integer
diff --git a/llmeval-env/lib/python3.10/site-packages/sympy/physics/vector/tests/test_output.py b/llmeval-env/lib/python3.10/site-packages/sympy/physics/vector/tests/test_output.py
new file mode 100644
index 0000000000000000000000000000000000000000..162bfa30ec6a9944e9ef9faf545cc44b2534b509
--- /dev/null
+++ b/llmeval-env/lib/python3.10/site-packages/sympy/physics/vector/tests/test_output.py
@@ -0,0 +1,76 @@
+from sympy.core.singleton import S
+from sympy.physics.vector import Vector, ReferenceFrame, Dyadic
+from sympy.testing.pytest import raises
+
+Vector.simp = True
+A = ReferenceFrame('A')
+
+
+def test_output_type():
+    A = ReferenceFrame('A')
+    v = A.x + A.y
+    d = v | v
+    zerov = Vector(0)
+    zerod = Dyadic(0)
+
+    # dot products
+    assert isinstance(d & d, Dyadic)
+    assert isinstance(d & zerod, Dyadic)
+    assert isinstance(zerod & d, Dyadic)
+    assert isinstance(d & v, Vector)
+    assert isinstance(v & d, Vector)
+    assert isinstance(d & zerov, Vector)
+    assert isinstance(zerov & d, Vector)
+    raises(TypeError, lambda: d & S.Zero)
+    raises(TypeError, lambda: S.Zero & d)
+    raises(TypeError, lambda: d & 0)
+    raises(TypeError, lambda: 0 & d)
+    assert not isinstance(v & v, (Vector, Dyadic))
+    assert not isinstance(v & zerov, (Vector, Dyadic))
+    assert not isinstance(zerov & v, (Vector, Dyadic))
+    raises(TypeError, lambda: v & S.Zero)
+    raises(TypeError, lambda: S.Zero & v)
+    raises(TypeError, lambda: v & 0)
+    raises(TypeError, lambda: 0 & v)
+
+    # cross products
+    raises(TypeError, lambda: d ^ d)
+    raises(TypeError, lambda: d ^ zerod)
+    raises(TypeError, lambda: zerod ^ d)
+    assert isinstance(d ^ v, Dyadic)
+    assert isinstance(v ^ d, Dyadic)
+    assert isinstance(d ^ zerov, Dyadic)
+    assert isinstance(zerov ^ d, Dyadic)
+    assert isinstance(zerov ^ d, Dyadic)
+    raises(TypeError, lambda: d ^ S.Zero)
+    raises(TypeError, lambda: S.Zero ^ d)
+    raises(TypeError, lambda: d ^ 0)
+    raises(TypeError, lambda: 0 ^ d)
+    assert isinstance(v ^ v, Vector)
+    assert isinstance(v ^ zerov, Vector)
+    assert isinstance(zerov ^ v, Vector)
+    raises(TypeError, lambda: v ^ S.Zero)
+    raises(TypeError, lambda: S.Zero ^ v)
+    raises(TypeError, lambda: v ^ 0)
+    raises(TypeError, lambda: 0 ^ v)
+
+    # outer products
+    raises(TypeError, lambda: d | d)
+    raises(TypeError, lambda: d | zerod)
+    raises(TypeError, lambda: zerod | d)
+    raises(TypeError, lambda: d | v)
+    raises(TypeError, lambda: v | d)
+    raises(TypeError, lambda: d | zerov)
+    raises(TypeError, lambda: zerov | d)
+    raises(TypeError, lambda: zerov | d)
+    raises(TypeError, lambda: d | S.Zero)
+    raises(TypeError, lambda: S.Zero | d)
+    raises(TypeError, lambda: d | 0)
+    raises(TypeError, lambda: 0 | d)
+    assert isinstance(v | v, Dyadic)
+    assert isinstance(v | zerov, Dyadic)
+    assert isinstance(zerov | v, Dyadic)
+    raises(TypeError, lambda: v | S.Zero)
+    raises(TypeError, lambda: S.Zero | v)
+    raises(TypeError, lambda: v | 0)
+    raises(TypeError, lambda: 0 | v)
diff --git a/llmeval-env/lib/python3.10/site-packages/sympy/physics/vector/tests/test_point.py b/llmeval-env/lib/python3.10/site-packages/sympy/physics/vector/tests/test_point.py
new file mode 100644
index 0000000000000000000000000000000000000000..e12edd925f22d77d2fdba7ec7e9b6a037e03eff4
--- /dev/null
+++ b/llmeval-env/lib/python3.10/site-packages/sympy/physics/vector/tests/test_point.py
@@ -0,0 +1,379 @@
+from sympy.physics.vector import dynamicsymbols, Point, ReferenceFrame
+from sympy.testing.pytest import raises, ignore_warnings
+import warnings
+
+def test_point_v1pt_theorys():
+    q, q2 = dynamicsymbols('q q2')
+    qd, q2d = dynamicsymbols('q q2', 1)
+    qdd, q2dd = dynamicsymbols('q q2', 2)
+    N = ReferenceFrame('N')
+    B = ReferenceFrame('B')
+    B.set_ang_vel(N, qd * B.z)
+    O = Point('O')
+    P = O.locatenew('P', B.x)
+    P.set_vel(B, 0)
+    O.set_vel(N, 0)
+    assert P.v1pt_theory(O, N, B) == qd * B.y
+    O.set_vel(N, N.x)
+    assert P.v1pt_theory(O, N, B) == N.x + qd * B.y
+    P.set_vel(B, B.z)
+    assert P.v1pt_theory(O, N, B) == B.z + N.x + qd * B.y
+
+
+def test_point_a1pt_theorys():
+    q, q2 = dynamicsymbols('q q2')
+    qd, q2d = dynamicsymbols('q q2', 1)
+    qdd, q2dd = dynamicsymbols('q q2', 2)
+    N = ReferenceFrame('N')
+    B = ReferenceFrame('B')
+    B.set_ang_vel(N, qd * B.z)
+    O = Point('O')
+    P = O.locatenew('P', B.x)
+    P.set_vel(B, 0)
+    O.set_vel(N, 0)
+    assert P.a1pt_theory(O, N, B) == -(qd**2) * B.x + qdd * B.y
+    P.set_vel(B, q2d * B.z)
+    assert P.a1pt_theory(O, N, B) == -(qd**2) * B.x + qdd * B.y + q2dd * B.z
+    O.set_vel(N, q2d * B.x)
+    assert P.a1pt_theory(O, N, B) == ((q2dd - qd**2) * B.x + (q2d * qd + qdd) * B.y +
+                               q2dd * B.z)
+
+
+def test_point_v2pt_theorys():
+    q = dynamicsymbols('q')
+    qd = dynamicsymbols('q', 1)
+    N = ReferenceFrame('N')
+    B = N.orientnew('B', 'Axis', [q, N.z])
+    O = Point('O')
+    P = O.locatenew('P', 0)
+    O.set_vel(N, 0)
+    assert P.v2pt_theory(O, N, B) == 0
+    P = O.locatenew('P', B.x)
+    assert P.v2pt_theory(O, N, B) == (qd * B.z ^ B.x)
+    O.set_vel(N, N.x)
+    assert P.v2pt_theory(O, N, B) == N.x + qd * B.y
+
+
+def test_point_a2pt_theorys():
+    q = dynamicsymbols('q')
+    qd = dynamicsymbols('q', 1)
+    qdd = dynamicsymbols('q', 2)
+    N = ReferenceFrame('N')
+    B = N.orientnew('B', 'Axis', [q, N.z])
+    O = Point('O')
+    P = O.locatenew('P', 0)
+    O.set_vel(N, 0)
+    assert P.a2pt_theory(O, N, B) == 0
+    P.set_pos(O, B.x)
+    assert P.a2pt_theory(O, N, B) == (-qd**2) * B.x + (qdd) * B.y
+
+
+def test_point_funcs():
+    q, q2 = dynamicsymbols('q q2')
+    qd, q2d = dynamicsymbols('q q2', 1)
+    qdd, q2dd = dynamicsymbols('q q2', 2)
+    N = ReferenceFrame('N')
+    B = ReferenceFrame('B')
+    B.set_ang_vel(N, 5 * B.y)
+    O = Point('O')
+    P = O.locatenew('P', q * B.x)
+    assert P.pos_from(O) == q * B.x
+    P.set_vel(B, qd * B.x + q2d * B.y)
+    assert P.vel(B) == qd * B.x + q2d * B.y
+    O.set_vel(N, 0)
+    assert O.vel(N) == 0
+    assert P.a1pt_theory(O, N, B) == ((-25 * q + qdd) * B.x + (q2dd) * B.y +
+                               (-10 * qd) * B.z)
+
+    B = N.orientnew('B', 'Axis', [q, N.z])
+    O = Point('O')
+    P = O.locatenew('P', 10 * B.x)
+    O.set_vel(N, 5 * N.x)
+    assert O.vel(N) == 5 * N.x
+    assert P.a2pt_theory(O, N, B) == (-10 * qd**2) * B.x + (10 * qdd) * B.y
+
+    B.set_ang_vel(N, 5 * B.y)
+    O = Point('O')
+    P = O.locatenew('P', q * B.x)
+    P.set_vel(B, qd * B.x + q2d * B.y)
+    O.set_vel(N, 0)
+    assert P.v1pt_theory(O, N, B) == qd * B.x + q2d * B.y - 5 * q * B.z
+
+
+def test_point_pos():
+    q = dynamicsymbols('q')
+    N = ReferenceFrame('N')
+    B = N.orientnew('B', 'Axis', [q, N.z])
+    O = Point('O')
+    P = O.locatenew('P', 10 * N.x + 5 * B.x)
+    assert P.pos_from(O) == 10 * N.x + 5 * B.x
+    Q = P.locatenew('Q', 10 * N.y + 5 * B.y)
+    assert Q.pos_from(P) == 10 * N.y + 5 * B.y
+    assert Q.pos_from(O) == 10 * N.x + 10 * N.y + 5 * B.x + 5 * B.y
+    assert O.pos_from(Q) == -10 * N.x - 10 * N.y - 5 * B.x - 5 * B.y
+
+def test_point_partial_velocity():
+
+    N = ReferenceFrame('N')
+    A = ReferenceFrame('A')
+
+    p = Point('p')
+
+    u1, u2 = dynamicsymbols('u1, u2')
+
+    p.set_vel(N, u1 * A.x + u2 * N.y)
+
+    assert p.partial_velocity(N, u1) == A.x
+    assert p.partial_velocity(N, u1, u2) == (A.x, N.y)
+    raises(ValueError, lambda: p.partial_velocity(A, u1))
+
+def test_point_vel(): #Basic functionality
+    q1, q2 = dynamicsymbols('q1 q2')
+    N = ReferenceFrame('N')
+    B = ReferenceFrame('B')
+    Q = Point('Q')
+    O = Point('O')
+    Q.set_pos(O, q1 * N.x)
+    raises(ValueError , lambda: Q.vel(N)) # Velocity of O in N is not defined
+    O.set_vel(N, q2 * N.y)
+    assert O.vel(N) == q2 * N.y
+    raises(ValueError , lambda : O.vel(B)) #Velocity of O is not defined in B
+
+def test_auto_point_vel():
+    t = dynamicsymbols._t
+    q1, q2 = dynamicsymbols('q1 q2')
+    N = ReferenceFrame('N')
+    B = ReferenceFrame('B')
+    O = Point('O')
+    Q = Point('Q')
+    Q.set_pos(O, q1 * N.x)
+    O.set_vel(N, q2 * N.y)
+    assert Q.vel(N) == q1.diff(t) * N.x + q2 * N.y  # Velocity of Q using O
+    P1 = Point('P1')
+    P1.set_pos(O, q1 * B.x)
+    P2 = Point('P2')
+    P2.set_pos(P1, q2 * B.z)
+    raises(ValueError, lambda : P2.vel(B)) # O's velocity is defined in different frame, and no
+    #point in between has its velocity defined
+    raises(ValueError, lambda: P2.vel(N)) # Velocity of O not defined in N
+
+def test_auto_point_vel_multiple_point_path():
+    t = dynamicsymbols._t
+    q1, q2 = dynamicsymbols('q1 q2')
+    B = ReferenceFrame('B')
+    P = Point('P')
+    P.set_vel(B, q1 * B.x)
+    P1 = Point('P1')
+    P1.set_pos(P, q2 * B.y)
+    P1.set_vel(B, q1 * B.z)
+    P2 = Point('P2')
+    P2.set_pos(P1, q1 * B.z)
+    P3 = Point('P3')
+    P3.set_pos(P2, 10 * q1 * B.y)
+    assert P3.vel(B) == 10 * q1.diff(t) * B.y + (q1 + q1.diff(t)) * B.z
+
+def test_auto_vel_dont_overwrite():
+    t = dynamicsymbols._t
+    q1, q2, u1 = dynamicsymbols('q1, q2, u1')
+    N = ReferenceFrame('N')
+    P = Point('P1')
+    P.set_vel(N, u1 * N.x)
+    P1 = Point('P1')
+    P1.set_pos(P, q2 * N.y)
+    assert P1.vel(N) == q2.diff(t) * N.y + u1 * N.x
+    assert P.vel(N) == u1 * N.x
+    P1.set_vel(N, u1 * N.z)
+    assert P1.vel(N) == u1 * N.z
+
+def test_auto_point_vel_if_tree_has_vel_but_inappropriate_pos_vector():
+    q1, q2 = dynamicsymbols('q1 q2')
+    B = ReferenceFrame('B')
+    S = ReferenceFrame('S')
+    P = Point('P')
+    P.set_vel(B, q1 * B.x)
+    P1 = Point('P1')
+    P1.set_pos(P, S.y)
+    raises(ValueError, lambda : P1.vel(B)) # P1.pos_from(P) can't be expressed in B
+    raises(ValueError, lambda : P1.vel(S)) # P.vel(S) not defined
+
+def test_auto_point_vel_shortest_path():
+    t = dynamicsymbols._t
+    q1, q2, u1, u2 = dynamicsymbols('q1 q2 u1 u2')
+    B = ReferenceFrame('B')
+    P = Point('P')
+    P.set_vel(B, u1 * B.x)
+    P1 = Point('P1')
+    P1.set_pos(P, q2 * B.y)
+    P1.set_vel(B, q1 * B.z)
+    P2 = Point('P2')
+    P2.set_pos(P1, q1 * B.z)
+    P3 = Point('P3')
+    P3.set_pos(P2, 10 * q1 * B.y)
+    P4 = Point('P4')
+    P4.set_pos(P3, q1 * B.x)
+    O = Point('O')
+    O.set_vel(B, u2 * B.y)
+    O1 = Point('O1')
+    O1.set_pos(O, q2 * B.z)
+    P4.set_pos(O1, q1 * B.x + q2 * B.z)
+    with warnings.catch_warnings(): #There are two possible paths in this point tree, thus a warning is raised
+        warnings.simplefilter('error')
+        with ignore_warnings(UserWarning):
+            assert P4.vel(B) == q1.diff(t) * B.x + u2 * B.y + 2 * q2.diff(t) * B.z
+
+def test_auto_point_vel_connected_frames():
+    t = dynamicsymbols._t
+    q, q1, q2, u = dynamicsymbols('q q1 q2 u')
+    N = ReferenceFrame('N')
+    B = ReferenceFrame('B')
+    O = Point('O')
+    O.set_vel(N, u * N.x)
+    P = Point('P')
+    P.set_pos(O, q1 * N.x + q2 * B.y)
+    raises(ValueError, lambda: P.vel(N))
+    N.orient(B, 'Axis', (q, B.x))
+    assert P.vel(N) == (u + q1.diff(t)) * N.x + q2.diff(t) * B.y - q2 * q.diff(t) * B.z
+
+def test_auto_point_vel_multiple_paths_warning_arises():
+    q, u = dynamicsymbols('q u')
+    N = ReferenceFrame('N')
+    O = Point('O')
+    P = Point('P')
+    Q = Point('Q')
+    R = Point('R')
+    P.set_vel(N, u * N.x)
+    Q.set_vel(N, u *N.y)
+    R.set_vel(N, u * N.z)
+    O.set_pos(P, q * N.z)
+    O.set_pos(Q, q * N.y)
+    O.set_pos(R, q * N.x)
+    with warnings.catch_warnings(): #There are two possible paths in this point tree, thus a warning is raised
+        warnings.simplefilter("error")
+        raises(UserWarning ,lambda: O.vel(N))
+
+def test_auto_vel_cyclic_warning_arises():
+    P = Point('P')
+    P1 = Point('P1')
+    P2 = Point('P2')
+    P3 = Point('P3')
+    N = ReferenceFrame('N')
+    P.set_vel(N, N.x)
+    P1.set_pos(P, N.x)
+    P2.set_pos(P1, N.y)
+    P3.set_pos(P2, N.z)
+    P1.set_pos(P3, N.x + N.y)
+    with warnings.catch_warnings(): #The path is cyclic at P1, thus a warning is raised
+        warnings.simplefilter("error")
+        raises(UserWarning ,lambda: P2.vel(N))
+
+def test_auto_vel_cyclic_warning_msg():
+    P = Point('P')
+    P1 = Point('P1')
+    P2 = Point('P2')
+    P3 = Point('P3')
+    N = ReferenceFrame('N')
+    P.set_vel(N, N.x)
+    P1.set_pos(P, N.x)
+    P2.set_pos(P1, N.y)
+    P3.set_pos(P2, N.z)
+    P1.set_pos(P3, N.x + N.y)
+    with warnings.catch_warnings(record = True) as w: #The path is cyclic at P1, thus a warning is raised
+        warnings.simplefilter("always")
+        P2.vel(N)
+        assert issubclass(w[-1].category, UserWarning)
+        assert 'Kinematic loops are defined among the positions of points. This is likely not desired and may cause errors in your calculations.' in str(w[-1].message)
+
+def test_auto_vel_multiple_path_warning_msg():
+    N = ReferenceFrame('N')
+    O = Point('O')
+    P = Point('P')
+    Q = Point('Q')
+    P.set_vel(N, N.x)
+    Q.set_vel(N, N.y)
+    O.set_pos(P, N.z)
+    O.set_pos(Q, N.y)
+    with warnings.catch_warnings(record = True) as w: #There are two possible paths in this point tree, thus a warning is raised
+        warnings.simplefilter("always")
+        O.vel(N)
+        assert issubclass(w[-1].category, UserWarning)
+        assert 'Velocity automatically calculated based on point' in str(w[-1].message)
+        assert 'Velocities from these points are not necessarily the same. This may cause errors in your calculations.' in str(w[-1].message)
+
+def test_auto_vel_derivative():
+    q1, q2 = dynamicsymbols('q1:3')
+    u1, u2 = dynamicsymbols('u1:3', 1)
+    A = ReferenceFrame('A')
+    B = ReferenceFrame('B')
+    C = ReferenceFrame('C')
+    B.orient_axis(A, A.z, q1)
+    B.set_ang_vel(A, u1 * A.z)
+    C.orient_axis(B, B.z, q2)
+    C.set_ang_vel(B, u2 * B.z)
+
+    Am = Point('Am')
+    Am.set_vel(A, 0)
+    Bm = Point('Bm')
+    Bm.set_pos(Am, B.x)
+    Bm.set_vel(B, 0)
+    Bm.set_vel(C, 0)
+    Cm = Point('Cm')
+    Cm.set_pos(Bm, C.x)
+    Cm.set_vel(C, 0)
+    temp = Cm._vel_dict.copy()
+    assert Cm.vel(A) == (u1 * B.y + (u1 + u2) * C.y)
+    Cm._vel_dict = temp
+    Cm.v2pt_theory(Bm, B, C)
+    assert Cm.vel(A) == (u1 * B.y + (u1 + u2) * C.y)
+
+def test_auto_point_acc_zero_vel():
+    N = ReferenceFrame('N')
+    O = Point('O')
+    O.set_vel(N, 0)
+    assert O.acc(N) == 0 * N.x
+
+def test_auto_point_acc_compute_vel():
+    t = dynamicsymbols._t
+    q1 = dynamicsymbols('q1')
+    N = ReferenceFrame('N')
+    A = ReferenceFrame('A')
+    A.orient_axis(N, N.z, q1)
+
+    O = Point('O')
+    O.set_vel(N, 0)
+    P = Point('P')
+    P.set_pos(O, A.x)
+    assert P.acc(N) == -q1.diff(t) ** 2 * A.x + q1.diff(t, 2) * A.y
+
+def test_auto_acc_derivative():
+    # Tests whether the Point.acc method gives the correct acceleration of the
+    # end point of two linkages in series, while getting minimal information.
+    q1, q2 = dynamicsymbols('q1:3')
+    u1, u2 = dynamicsymbols('q1:3', 1)
+    v1, v2 = dynamicsymbols('q1:3', 2)
+    A = ReferenceFrame('A')
+    B = ReferenceFrame('B')
+    C = ReferenceFrame('C')
+    B.orient_axis(A, A.z, q1)
+    C.orient_axis(B, B.z, q2)
+
+    Am = Point('Am')
+    Am.set_vel(A, 0)
+    Bm = Point('Bm')
+    Bm.set_pos(Am, B.x)
+    Bm.set_vel(B, 0)
+    Bm.set_vel(C, 0)
+    Cm = Point('Cm')
+    Cm.set_pos(Bm, C.x)
+    Cm.set_vel(C, 0)
+
+    # Copy dictionaries to later check the calculation using the 2pt_theories
+    Bm_vel_dict, Cm_vel_dict = Bm._vel_dict.copy(), Cm._vel_dict.copy()
+    Bm_acc_dict, Cm_acc_dict = Bm._acc_dict.copy(), Cm._acc_dict.copy()
+    check = -u1 ** 2 * B.x + v1 * B.y - (u1 + u2) ** 2 * C.x + (v1 + v2) * C.y
+    assert Cm.acc(A) == check
+    Bm._vel_dict, Cm._vel_dict = Bm_vel_dict, Cm_vel_dict
+    Bm._acc_dict, Cm._acc_dict = Bm_acc_dict, Cm_acc_dict
+    Bm.v2pt_theory(Am, A, B)
+    Cm.v2pt_theory(Bm, A, C)
+    Bm.a2pt_theory(Am, A, B)
+    assert Cm.a2pt_theory(Bm, A, C) == check
diff --git a/llmeval-env/lib/python3.10/site-packages/sympy/physics/vector/tests/test_printing.py b/llmeval-env/lib/python3.10/site-packages/sympy/physics/vector/tests/test_printing.py
new file mode 100644
index 0000000000000000000000000000000000000000..b0c60c5d17ab30e8c9d4c42e7ed70bd74e30e20a
--- /dev/null
+++ b/llmeval-env/lib/python3.10/site-packages/sympy/physics/vector/tests/test_printing.py
@@ -0,0 +1,331 @@
+# -*- coding: utf-8 -*-
+
+from sympy.core.function import Function
+from sympy.core.symbol import symbols
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.functions.elementary.trigonometric import (asin, cos, sin)
+from sympy.physics.vector import ReferenceFrame, dynamicsymbols, Dyadic
+from sympy.physics.vector.printing import (VectorLatexPrinter, vpprint,
+                                           vsprint, vsstrrepr, vlatex)
+
+
+a, b, c = symbols('a, b, c')
+alpha, omega, beta = dynamicsymbols('alpha, omega, beta')
+
+A = ReferenceFrame('A')
+N = ReferenceFrame('N')
+
+v = a ** 2 * N.x + b * N.y + c * sin(alpha) * N.z
+w = alpha * N.x + sin(omega) * N.y + alpha * beta * N.z
+ww = alpha * N.x + asin(omega) * N.y - alpha.diff() * beta * N.z
+o = a/b * N.x + (c+b)/a * N.y + c**2/b * N.z
+
+y = a ** 2 * (N.x | N.y) + b * (N.y | N.y) + c * sin(alpha) * (N.z | N.y)
+x = alpha * (N.x | N.x) + sin(omega) * (N.y | N.z) + alpha * beta * (N.z | N.x)
+xx = N.x | (-N.y - N.z)
+xx2 = N.x | (N.y + N.z)
+
+def ascii_vpretty(expr):
+    return vpprint(expr, use_unicode=False, wrap_line=False)
+
+
+def unicode_vpretty(expr):
+    return vpprint(expr, use_unicode=True, wrap_line=False)
+
+
+def test_latex_printer():
+    r = Function('r')('t')
+    assert VectorLatexPrinter().doprint(r ** 2) == "r^{2}"
+    r2 = Function('r^2')('t')
+    assert VectorLatexPrinter().doprint(r2.diff()) == r'\dot{r^{2}}'
+    ra = Function('r__a')('t')
+    assert VectorLatexPrinter().doprint(ra.diff().diff()) == r'\ddot{r^{a}}'
+
+
+def test_vector_pretty_print():
+
+    # TODO : The unit vectors should print with subscripts but they just
+    # print as `n_x` instead of making `x` a subscript with unicode.
+
+    # TODO : The pretty print division does not print correctly here:
+    # w = alpha * N.x + sin(omega) * N.y + alpha / beta * N.z
+
+    expected = """\
+ 2
+a  n_x + b n_y + c*sin(alpha) n_z\
+"""
+    uexpected = """\
+ 2
+a  n_x + b n_y + c⋅sin(α) n_z\
+"""
+
+    assert ascii_vpretty(v) == expected
+    assert unicode_vpretty(v) == uexpected
+
+    expected = 'alpha n_x + sin(omega) n_y + alpha*beta n_z'
+    uexpected = 'α n_x + sin(ω) n_y + α⋅β n_z'
+
+    assert ascii_vpretty(w) == expected
+    assert unicode_vpretty(w) == uexpected
+
+    expected = """\
+                     2
+a       b + c       c
+- n_x + ----- n_y + -- n_z
+b         a         b\
+"""
+    uexpected = """\
+                     2
+a       b + c       c
+─ n_x + ───── n_y + ── n_z
+b         a         b\
+"""
+
+    assert ascii_vpretty(o) == expected
+    assert unicode_vpretty(o) == uexpected
+
+
+def test_vector_latex():
+
+    a, b, c, d, omega = symbols('a, b, c, d, omega')
+
+    v = (a ** 2 + b / c) * A.x + sqrt(d) * A.y + cos(omega) * A.z
+
+    assert vlatex(v) == (r'(a^{2} + \frac{b}{c})\mathbf{\hat{a}_x} + '
+                         r'\sqrt{d}\mathbf{\hat{a}_y} + '
+                         r'\cos{\left(\omega \right)}'
+                         r'\mathbf{\hat{a}_z}')
+
+    theta, omega, alpha, q = dynamicsymbols('theta, omega, alpha, q')
+
+    v = theta * A.x + omega * omega * A.y + (q * alpha) * A.z
+
+    assert vlatex(v) == (r'\theta\mathbf{\hat{a}_x} + '
+                         r'\omega^{2}\mathbf{\hat{a}_y} + '
+                         r'\alpha q\mathbf{\hat{a}_z}')
+
+    phi1, phi2, phi3 = dynamicsymbols('phi1, phi2, phi3')
+    theta1, theta2, theta3 = symbols('theta1, theta2, theta3')
+
+    v = (sin(theta1) * A.x +
+         cos(phi1) * cos(phi2) * A.y +
+         cos(theta1 + phi3) * A.z)
+
+    assert vlatex(v) == (r'\sin{\left(\theta_{1} \right)}'
+                         r'\mathbf{\hat{a}_x} + \cos{'
+                         r'\left(\phi_{1} \right)} \cos{'
+                         r'\left(\phi_{2} \right)}\mathbf{\hat{a}_y} + '
+                         r'\cos{\left(\theta_{1} + '
+                         r'\phi_{3} \right)}\mathbf{\hat{a}_z}')
+
+    N = ReferenceFrame('N')
+
+    a, b, c, d, omega = symbols('a, b, c, d, omega')
+
+    v = (a ** 2 + b / c) * N.x + sqrt(d) * N.y + cos(omega) * N.z
+
+    expected = (r'(a^{2} + \frac{b}{c})\mathbf{\hat{n}_x} + '
+                r'\sqrt{d}\mathbf{\hat{n}_y} + '
+                r'\cos{\left(\omega \right)}'
+                r'\mathbf{\hat{n}_z}')
+
+    assert vlatex(v) == expected
+
+    # Try custom unit vectors.
+
+    N = ReferenceFrame('N', latexs=(r'\hat{i}', r'\hat{j}', r'\hat{k}'))
+
+    v = (a ** 2 + b / c) * N.x + sqrt(d) * N.y + cos(omega) * N.z
+
+    expected = (r'(a^{2} + \frac{b}{c})\hat{i} + '
+                r'\sqrt{d}\hat{j} + '
+                r'\cos{\left(\omega \right)}\hat{k}')
+    assert vlatex(v) == expected
+
+    expected = r'\alpha\mathbf{\hat{n}_x} + \operatorname{asin}{\left(\omega ' \
+        r'\right)}\mathbf{\hat{n}_y} -  \beta \dot{\alpha}\mathbf{\hat{n}_z}'
+    assert vlatex(ww) == expected
+
+    expected = r'- \mathbf{\hat{n}_x}\otimes \mathbf{\hat{n}_y} - ' \
+        r'\mathbf{\hat{n}_x}\otimes \mathbf{\hat{n}_z}'
+    assert vlatex(xx) == expected
+
+    expected = r'\mathbf{\hat{n}_x}\otimes \mathbf{\hat{n}_y} + ' \
+        r'\mathbf{\hat{n}_x}\otimes \mathbf{\hat{n}_z}'
+    assert vlatex(xx2) == expected
+
+
+def test_vector_latex_arguments():
+    assert vlatex(N.x * 3.0, full_prec=False) == r'3.0\mathbf{\hat{n}_x}'
+    assert vlatex(N.x * 3.0, full_prec=True) == r'3.00000000000000\mathbf{\hat{n}_x}'
+
+
+def test_vector_latex_with_functions():
+
+    N = ReferenceFrame('N')
+
+    omega, alpha = dynamicsymbols('omega, alpha')
+
+    v = omega.diff() * N.x
+
+    assert vlatex(v) == r'\dot{\omega}\mathbf{\hat{n}_x}'
+
+    v = omega.diff() ** alpha * N.x
+
+    assert vlatex(v) == (r'\dot{\omega}^{\alpha}'
+                          r'\mathbf{\hat{n}_x}')
+
+
+def test_dyadic_pretty_print():
+
+    expected = """\
+ 2
+a  n_x|n_y + b n_y|n_y + c*sin(alpha) n_z|n_y\
+"""
+
+    uexpected = """\
+ 2
+a  n_x⊗n_y + b n_y⊗n_y + c⋅sin(α) n_z⊗n_y\
+"""
+    assert ascii_vpretty(y) == expected
+    assert unicode_vpretty(y) == uexpected
+
+    expected = 'alpha n_x|n_x + sin(omega) n_y|n_z + alpha*beta n_z|n_x'
+    uexpected = 'α n_x⊗n_x + sin(ω) n_y⊗n_z + α⋅β n_z⊗n_x'
+    assert ascii_vpretty(x) == expected
+    assert unicode_vpretty(x) == uexpected
+
+    assert ascii_vpretty(Dyadic([])) == '0'
+    assert unicode_vpretty(Dyadic([])) == '0'
+
+    assert ascii_vpretty(xx) == '- n_x|n_y - n_x|n_z'
+    assert unicode_vpretty(xx) == '- n_x⊗n_y - n_x⊗n_z'
+
+    assert ascii_vpretty(xx2) == 'n_x|n_y + n_x|n_z'
+    assert unicode_vpretty(xx2) == 'n_x⊗n_y + n_x⊗n_z'
+
+
+def test_dyadic_latex():
+
+    expected = (r'a^{2}\mathbf{\hat{n}_x}\otimes \mathbf{\hat{n}_y} + '
+                r'b\mathbf{\hat{n}_y}\otimes \mathbf{\hat{n}_y} + '
+                r'c \sin{\left(\alpha \right)}'
+                r'\mathbf{\hat{n}_z}\otimes \mathbf{\hat{n}_y}')
+
+    assert vlatex(y) == expected
+
+    expected = (r'\alpha\mathbf{\hat{n}_x}\otimes \mathbf{\hat{n}_x} + '
+                r'\sin{\left(\omega \right)}\mathbf{\hat{n}_y}'
+                r'\otimes \mathbf{\hat{n}_z} + '
+                r'\alpha \beta\mathbf{\hat{n}_z}\otimes \mathbf{\hat{n}_x}')
+
+    assert vlatex(x) == expected
+
+    assert vlatex(Dyadic([])) == '0'
+
+
+def test_dyadic_str():
+    assert vsprint(Dyadic([])) == '0'
+    assert vsprint(y) == 'a**2*(N.x|N.y) + b*(N.y|N.y) + c*sin(alpha)*(N.z|N.y)'
+    assert vsprint(x) == 'alpha*(N.x|N.x) + sin(omega)*(N.y|N.z) + alpha*beta*(N.z|N.x)'
+    assert vsprint(ww) == "alpha*N.x + asin(omega)*N.y - beta*alpha'*N.z"
+    assert vsprint(xx) == '- (N.x|N.y) - (N.x|N.z)'
+    assert vsprint(xx2) == '(N.x|N.y) + (N.x|N.z)'
+
+
+def test_vlatex(): # vlatex is broken #12078
+    from sympy.physics.vector import vlatex
+
+    x = symbols('x')
+    J = symbols('J')
+
+    f = Function('f')
+    g = Function('g')
+    h = Function('h')
+
+    expected = r'J \left(\frac{d}{d x} g{\left(x \right)} - \frac{d}{d x} h{\left(x \right)}\right)'
+
+    expr = J*f(x).diff(x).subs(f(x), g(x)-h(x))
+
+    assert vlatex(expr) == expected
+
+
+def test_issue_13354():
+    """
+    Test for proper pretty printing of physics vectors with ADD
+    instances in arguments.
+
+    Test is exactly the one suggested in the original bug report by
+    @moorepants.
+    """
+
+    a, b, c = symbols('a, b, c')
+    A = ReferenceFrame('A')
+    v = a * A.x + b * A.y + c * A.z
+    w = b * A.x + c * A.y + a * A.z
+    z = w + v
+
+    expected = """(a + b) a_x + (b + c) a_y + (a + c) a_z"""
+
+    assert ascii_vpretty(z) == expected
+
+
+def test_vector_derivative_printing():
+    # First order
+    v = omega.diff() * N.x
+    assert unicode_vpretty(v) == 'ω̇ n_x'
+    assert ascii_vpretty(v) == "omega'(t) n_x"
+
+    # Second order
+    v = omega.diff().diff() * N.x
+
+    assert vlatex(v) == r'\ddot{\omega}\mathbf{\hat{n}_x}'
+    assert unicode_vpretty(v) == 'ω̈ n_x'
+    assert ascii_vpretty(v) == "omega''(t) n_x"
+
+    # Third order
+    v = omega.diff().diff().diff() * N.x
+
+    assert vlatex(v) == r'\dddot{\omega}\mathbf{\hat{n}_x}'
+    assert unicode_vpretty(v) == 'ω⃛ n_x'
+    assert ascii_vpretty(v) == "omega'''(t) n_x"
+
+    # Fourth order
+    v = omega.diff().diff().diff().diff() * N.x
+
+    assert vlatex(v) == r'\ddddot{\omega}\mathbf{\hat{n}_x}'
+    assert unicode_vpretty(v) == 'ω⃜ n_x'
+    assert ascii_vpretty(v) == "omega''''(t) n_x"
+
+    # Fifth order
+    v = omega.diff().diff().diff().diff().diff() * N.x
+
+    assert vlatex(v) == r'\frac{d^{5}}{d t^{5}} \omega\mathbf{\hat{n}_x}'
+    assert unicode_vpretty(v) == '  5\n d\n───(ω) n_x\n  5\ndt'
+    assert ascii_vpretty(v) == '  5\n d\n---(omega) n_x\n  5\ndt'
+
+
+def test_vector_str_printing():
+    assert vsprint(w) == 'alpha*N.x + sin(omega)*N.y + alpha*beta*N.z'
+    assert vsprint(omega.diff() * N.x) == "omega'*N.x"
+    assert vsstrrepr(w) == 'alpha*N.x + sin(omega)*N.y + alpha*beta*N.z'
+
+
+def test_vector_str_arguments():
+    assert vsprint(N.x * 3.0, full_prec=False) == '3.0*N.x'
+    assert vsprint(N.x * 3.0, full_prec=True) == '3.00000000000000*N.x'
+
+
+def test_issue_14041():
+    import sympy.physics.mechanics as me
+
+    A_frame = me.ReferenceFrame('A')
+    thetad, phid = me.dynamicsymbols('theta, phi', 1)
+    L = symbols('L')
+
+    assert vlatex(L*(phid + thetad)**2*A_frame.x) == \
+        r"L \left(\dot{\phi} + \dot{\theta}\right)^{2}\mathbf{\hat{a}_x}"
+    assert vlatex((phid + thetad)**2*A_frame.x) == \
+        r"\left(\dot{\phi} + \dot{\theta}\right)^{2}\mathbf{\hat{a}_x}"
+    assert vlatex((phid*thetad)**a*A_frame.x) == \
+        r"\left(\dot{\phi} \dot{\theta}\right)^{a}\mathbf{\hat{a}_x}"
diff --git a/llmeval-env/lib/python3.10/site-packages/sympy/physics/vector/tests/test_vector.py b/llmeval-env/lib/python3.10/site-packages/sympy/physics/vector/tests/test_vector.py
new file mode 100644
index 0000000000000000000000000000000000000000..19701ddf250a97649758a0994ad3c49c742fe800
--- /dev/null
+++ b/llmeval-env/lib/python3.10/site-packages/sympy/physics/vector/tests/test_vector.py
@@ -0,0 +1,247 @@
+from sympy.core.numbers import (Float, pi)
+from sympy.core.symbol import symbols
+from sympy.core.sorting import ordered
+from sympy.functions.elementary.trigonometric import (cos, sin)
+from sympy.matrices.immutable import ImmutableDenseMatrix as Matrix
+from sympy.physics.vector import ReferenceFrame, Vector, dynamicsymbols, dot
+from sympy.physics.vector.vector import VectorTypeError
+from sympy.abc import x, y, z
+from sympy.testing.pytest import raises
+
+
+Vector.simp = True
+A = ReferenceFrame('A')
+
+
+def test_free_dynamicsymbols():
+    A, B, C, D = symbols('A, B, C, D', cls=ReferenceFrame)
+    a, b, c, d, e, f = dynamicsymbols('a, b, c, d, e, f')
+    B.orient_axis(A, a, A.x)
+    C.orient_axis(B, b, B.y)
+    D.orient_axis(C, c, C.x)
+
+    v = d*D.x + e*D.y + f*D.z
+
+    assert set(ordered(v.free_dynamicsymbols(A))) == {a, b, c, d, e, f}
+    assert set(ordered(v.free_dynamicsymbols(B))) == {b, c, d, e, f}
+    assert set(ordered(v.free_dynamicsymbols(C))) == {c, d, e, f}
+    assert set(ordered(v.free_dynamicsymbols(D))) == {d, e, f}
+
+
+def test_Vector():
+    assert A.x != A.y
+    assert A.y != A.z
+    assert A.z != A.x
+
+    assert A.x + 0 == A.x
+
+    v1 = x*A.x + y*A.y + z*A.z
+    v2 = x**2*A.x + y**2*A.y + z**2*A.z
+    v3 = v1 + v2
+    v4 = v1 - v2
+
+    assert isinstance(v1, Vector)
+    assert dot(v1, A.x) == x
+    assert dot(v1, A.y) == y
+    assert dot(v1, A.z) == z
+
+    assert isinstance(v2, Vector)
+    assert dot(v2, A.x) == x**2
+    assert dot(v2, A.y) == y**2
+    assert dot(v2, A.z) == z**2
+
+    assert isinstance(v3, Vector)
+    # We probably shouldn't be using simplify in dot...
+    assert dot(v3, A.x) == x**2 + x
+    assert dot(v3, A.y) == y**2 + y
+    assert dot(v3, A.z) == z**2 + z
+
+    assert isinstance(v4, Vector)
+    # We probably shouldn't be using simplify in dot...
+    assert dot(v4, A.x) == x - x**2
+    assert dot(v4, A.y) == y - y**2
+    assert dot(v4, A.z) == z - z**2
+
+    assert v1.to_matrix(A) == Matrix([[x], [y], [z]])
+    q = symbols('q')
+    B = A.orientnew('B', 'Axis', (q, A.x))
+    assert v1.to_matrix(B) == Matrix([[x],
+                                      [ y * cos(q) + z * sin(q)],
+                                      [-y * sin(q) + z * cos(q)]])
+
+    #Test the separate method
+    B = ReferenceFrame('B')
+    v5 = x*A.x + y*A.y + z*B.z
+    assert Vector(0).separate() == {}
+    assert v1.separate() == {A: v1}
+    assert v5.separate() == {A: x*A.x + y*A.y, B: z*B.z}
+
+    #Test the free_symbols property
+    v6 = x*A.x + y*A.y + z*A.z
+    assert v6.free_symbols(A) == {x,y,z}
+
+    raises(TypeError, lambda: v3.applyfunc(v1))
+
+
+def test_Vector_diffs():
+    q1, q2, q3, q4 = dynamicsymbols('q1 q2 q3 q4')
+    q1d, q2d, q3d, q4d = dynamicsymbols('q1 q2 q3 q4', 1)
+    q1dd, q2dd, q3dd, q4dd = dynamicsymbols('q1 q2 q3 q4', 2)
+    N = ReferenceFrame('N')
+    A = N.orientnew('A', 'Axis', [q3, N.z])
+    B = A.orientnew('B', 'Axis', [q2, A.x])
+    v1 = q2 * A.x + q3 * N.y
+    v2 = q3 * B.x + v1
+    v3 = v1.dt(B)
+    v4 = v2.dt(B)
+    v5 = q1*A.x + q2*A.y + q3*A.z
+
+    assert v1.dt(N) == q2d * A.x + q2 * q3d * A.y + q3d * N.y
+    assert v1.dt(A) == q2d * A.x + q3 * q3d * N.x + q3d * N.y
+    assert v1.dt(B) == (q2d * A.x + q3 * q3d * N.x + q3d *
+                        N.y - q3 * cos(q3) * q2d * N.z)
+    assert v2.dt(N) == (q2d * A.x + (q2 + q3) * q3d * A.y + q3d * B.x + q3d *
+                        N.y)
+    assert v2.dt(A) == q2d * A.x + q3d * B.x + q3 * q3d * N.x + q3d * N.y
+    assert v2.dt(B) == (q2d * A.x + q3d * B.x + q3 * q3d * N.x + q3d * N.y -
+                        q3 * cos(q3) * q2d * N.z)
+    assert v3.dt(N) == (q2dd * A.x + q2d * q3d * A.y + (q3d**2 + q3 * q3dd) *
+                        N.x + q3dd * N.y + (q3 * sin(q3) * q2d * q3d -
+                        cos(q3) * q2d * q3d - q3 * cos(q3) * q2dd) * N.z)
+    assert v3.dt(A) == (q2dd * A.x + (2 * q3d**2 + q3 * q3dd) * N.x + (q3dd -
+                        q3 * q3d**2) * N.y + (q3 * sin(q3) * q2d * q3d -
+                        cos(q3) * q2d * q3d - q3 * cos(q3) * q2dd) * N.z)
+    assert v3.dt(B) == (q2dd * A.x - q3 * cos(q3) * q2d**2 * A.y + (2 *
+                        q3d**2 + q3 * q3dd) * N.x + (q3dd - q3 * q3d**2) *
+                        N.y + (2 * q3 * sin(q3) * q2d * q3d - 2 * cos(q3) *
+                        q2d * q3d - q3 * cos(q3) * q2dd) * N.z)
+    assert v4.dt(N) == (q2dd * A.x + q3d * (q2d + q3d) * A.y + q3dd * B.x +
+                        (q3d**2 + q3 * q3dd) * N.x + q3dd * N.y + (q3 *
+                        sin(q3) * q2d * q3d - cos(q3) * q2d * q3d - q3 *
+                        cos(q3) * q2dd) * N.z)
+    assert v4.dt(A) == (q2dd * A.x + q3dd * B.x + (2 * q3d**2 + q3 * q3dd) *
+                        N.x + (q3dd - q3 * q3d**2) * N.y + (q3 * sin(q3) *
+                        q2d * q3d - cos(q3) * q2d * q3d - q3 * cos(q3) *
+                        q2dd) * N.z)
+    assert v4.dt(B) == (q2dd * A.x - q3 * cos(q3) * q2d**2 * A.y + q3dd * B.x +
+                        (2 * q3d**2 + q3 * q3dd) * N.x + (q3dd - q3 * q3d**2) *
+                        N.y + (2 * q3 * sin(q3) * q2d * q3d - 2 * cos(q3) *
+                        q2d * q3d - q3 * cos(q3) * q2dd) * N.z)
+    assert v5.dt(B) == q1d*A.x + (q3*q2d + q2d)*A.y + (-q2*q2d + q3d)*A.z
+    assert v5.dt(A) == q1d*A.x + q2d*A.y + q3d*A.z
+    assert v5.dt(N) == (-q2*q3d + q1d)*A.x + (q1*q3d + q2d)*A.y + q3d*A.z
+    assert v3.diff(q1d, N) == 0
+    assert v3.diff(q2d, N) == A.x - q3 * cos(q3) * N.z
+    assert v3.diff(q3d, N) == q3 * N.x + N.y
+    assert v3.diff(q1d, A) == 0
+    assert v3.diff(q2d, A) == A.x - q3 * cos(q3) * N.z
+    assert v3.diff(q3d, A) == q3 * N.x + N.y
+    assert v3.diff(q1d, B) == 0
+    assert v3.diff(q2d, B) == A.x - q3 * cos(q3) * N.z
+    assert v3.diff(q3d, B) == q3 * N.x + N.y
+    assert v4.diff(q1d, N) == 0
+    assert v4.diff(q2d, N) == A.x - q3 * cos(q3) * N.z
+    assert v4.diff(q3d, N) == B.x + q3 * N.x + N.y
+    assert v4.diff(q1d, A) == 0
+    assert v4.diff(q2d, A) == A.x - q3 * cos(q3) * N.z
+    assert v4.diff(q3d, A) == B.x + q3 * N.x + N.y
+    assert v4.diff(q1d, B) == 0
+    assert v4.diff(q2d, B) == A.x - q3 * cos(q3) * N.z
+    assert v4.diff(q3d, B) == B.x + q3 * N.x + N.y
+
+    # diff() should only express vector components in the derivative frame if
+    # the orientation of the component's frame depends on the variable
+    v6 = q2**2*N.y + q2**2*A.y + q2**2*B.y
+    # already expressed in N
+    n_measy = 2*q2
+    # A_C_N does not depend on q2, so don't express in N
+    a_measy = 2*q2
+    # B_C_N depends on q2, so express in N
+    b_measx = (q2**2*B.y).dot(N.x).diff(q2)
+    b_measy = (q2**2*B.y).dot(N.y).diff(q2)
+    b_measz = (q2**2*B.y).dot(N.z).diff(q2)
+    n_comp, a_comp = v6.diff(q2, N).args
+    assert len(v6.diff(q2, N).args) == 2  # only N and A parts
+    assert n_comp[1] == N
+    assert a_comp[1] == A
+    assert n_comp[0] == Matrix([b_measx, b_measy + n_measy, b_measz])
+    assert a_comp[0] == Matrix([0, a_measy, 0])
+
+
+def test_vector_var_in_dcm():
+
+    N = ReferenceFrame('N')
+    A = ReferenceFrame('A')
+    B = ReferenceFrame('B')
+    u1, u2, u3, u4 = dynamicsymbols('u1 u2 u3 u4')
+
+    v = u1 * u2 * A.x + u3 * N.y + u4**2 * N.z
+
+    assert v.diff(u1, N, var_in_dcm=False) == u2 * A.x
+    assert v.diff(u1, A, var_in_dcm=False) == u2 * A.x
+    assert v.diff(u3, N, var_in_dcm=False) == N.y
+    assert v.diff(u3, A, var_in_dcm=False) == N.y
+    assert v.diff(u3, B, var_in_dcm=False) == N.y
+    assert v.diff(u4, N, var_in_dcm=False) == 2 * u4 * N.z
+
+    raises(ValueError, lambda: v.diff(u1, N))
+
+
+def test_vector_simplify():
+    x, y, z, k, n, m, w, f, s, A = symbols('x, y, z, k, n, m, w, f, s, A')
+    N = ReferenceFrame('N')
+
+    test1 = (1 / x + 1 / y) * N.x
+    assert (test1 & N.x) != (x + y) / (x * y)
+    test1 = test1.simplify()
+    assert (test1 & N.x) == (x + y) / (x * y)
+
+    test2 = (A**2 * s**4 / (4 * pi * k * m**3)) * N.x
+    test2 = test2.simplify()
+    assert (test2 & N.x) == (A**2 * s**4 / (4 * pi * k * m**3))
+
+    test3 = ((4 + 4 * x - 2 * (2 + 2 * x)) / (2 + 2 * x)) * N.x
+    test3 = test3.simplify()
+    assert (test3 & N.x) == 0
+
+    test4 = ((-4 * x * y**2 - 2 * y**3 - 2 * x**2 * y) / (x + y)**2) * N.x
+    test4 = test4.simplify()
+    assert (test4 & N.x) == -2 * y
+
+
+def test_vector_evalf():
+    a, b = symbols('a b')
+    v = pi * A.x
+    assert v.evalf(2) == Float('3.1416', 2) * A.x
+    v = pi * A.x + 5 * a * A.y - b * A.z
+    assert v.evalf(3) == Float('3.1416', 3) * A.x + Float('5', 3) * a * A.y - b * A.z
+    assert v.evalf(5, subs={a: 1.234, b:5.8973}) == Float('3.1415926536', 5) * A.x + Float('6.17', 5) * A.y - Float('5.8973', 5) * A.z
+
+
+def test_vector_angle():
+    A = ReferenceFrame('A')
+    v1 = A.x + A.y
+    v2 = A.z
+    assert v1.angle_between(v2) == pi/2
+    B = ReferenceFrame('B')
+    B.orient_axis(A, A.x, pi)
+    v3 = A.x
+    v4 = B.x
+    assert v3.angle_between(v4) == 0
+
+
+def test_vector_xreplace():
+    x, y, z = symbols('x y z')
+    v = x**2 * A.x + x*y * A.y + x*y*z * A.z
+    assert v.xreplace({x : cos(x)}) == cos(x)**2 * A.x + y*cos(x) * A.y + y*z*cos(x) * A.z
+    assert v.xreplace({x*y : pi}) == x**2 * A.x + pi * A.y + x*y*z * A.z
+    assert v.xreplace({x*y*z : 1}) == x**2*A.x + x*y*A.y + A.z
+    assert v.xreplace({x:1, z:0}) == A.x + y * A.y
+    raises(TypeError, lambda: v.xreplace())
+    raises(TypeError, lambda: v.xreplace([x, y]))
+
+def test_issue_23366():
+    u1 = dynamicsymbols('u1')
+    N = ReferenceFrame('N')
+    N_v_A = u1*N.x
+    raises(VectorTypeError, lambda: N_v_A.diff(N, u1))
diff --git a/llmeval-env/lib/python3.10/site-packages/sympy/physics/vector/vector.py b/llmeval-env/lib/python3.10/site-packages/sympy/physics/vector/vector.py
new file mode 100644
index 0000000000000000000000000000000000000000..2130587a569dbb258556aca93bc3a293cef98ea2
--- /dev/null
+++ b/llmeval-env/lib/python3.10/site-packages/sympy/physics/vector/vector.py
@@ -0,0 +1,858 @@
+from sympy.core.backend import (S, sympify, expand, sqrt, Add, zeros, acos,
+                                ImmutableMatrix as Matrix, _simplify_matrix)
+from sympy.simplify.trigsimp import trigsimp
+from sympy.printing.defaults import Printable
+from sympy.utilities.misc import filldedent
+from sympy.core.evalf import EvalfMixin
+
+from mpmath.libmp.libmpf import prec_to_dps
+
+
+__all__ = ['Vector']
+
+
+class Vector(Printable, EvalfMixin):
+    """The class used to define vectors.
+
+    It along with ReferenceFrame are the building blocks of describing a
+    classical mechanics system in PyDy and sympy.physics.vector.
+
+    Attributes
+    ==========
+
+    simp : Boolean
+        Let certain methods use trigsimp on their outputs
+
+    """
+
+    simp = False
+    is_number = False
+
+    def __init__(self, inlist):
+        """This is the constructor for the Vector class.  You should not be
+        calling this, it should only be used by other functions. You should be
+        treating Vectors like you would with if you were doing the math by
+        hand, and getting the first 3 from the standard basis vectors from a
+        ReferenceFrame.
+
+        The only exception is to create a zero vector:
+        zv = Vector(0)
+
+        """
+
+        self.args = []
+        if inlist == 0:
+            inlist = []
+        if isinstance(inlist, dict):
+            d = inlist
+        else:
+            d = {}
+            for inp in inlist:
+                if inp[1] in d:
+                    d[inp[1]] += inp[0]
+                else:
+                    d[inp[1]] = inp[0]
+
+        for k, v in d.items():
+            if v != Matrix([0, 0, 0]):
+                self.args.append((v, k))
+
+    @property
+    def func(self):
+        """Returns the class Vector. """
+        return Vector
+
+    def __hash__(self):
+        return hash(tuple(self.args))
+
+    def __add__(self, other):
+        """The add operator for Vector. """
+        if other == 0:
+            return self
+        other = _check_vector(other)
+        return Vector(self.args + other.args)
+
+    def __and__(self, other):
+        """Dot product of two vectors.
+
+        Returns a scalar, the dot product of the two Vectors
+
+        Parameters
+        ==========
+
+        other : Vector
+            The Vector which we are dotting with
+
+        Examples
+        ========
+
+        >>> from sympy.physics.vector import ReferenceFrame, dot
+        >>> from sympy import symbols
+        >>> q1 = symbols('q1')
+        >>> N = ReferenceFrame('N')
+        >>> dot(N.x, N.x)
+        1
+        >>> dot(N.x, N.y)
+        0
+        >>> A = N.orientnew('A', 'Axis', [q1, N.x])
+        >>> dot(N.y, A.y)
+        cos(q1)
+
+        """
+
+        from sympy.physics.vector.dyadic import Dyadic
+        if isinstance(other, Dyadic):
+            return NotImplemented
+        other = _check_vector(other)
+        out = S.Zero
+        for i, v1 in enumerate(self.args):
+            for j, v2 in enumerate(other.args):
+                out += ((v2[0].T)
+                        * (v2[1].dcm(v1[1]))
+                        * (v1[0]))[0]
+        if Vector.simp:
+            return trigsimp(out, recursive=True)
+        else:
+            return out
+
+    def __truediv__(self, other):
+        """This uses mul and inputs self and 1 divided by other. """
+        return self.__mul__(S.One / other)
+
+    def __eq__(self, other):
+        """Tests for equality.
+
+        It is very import to note that this is only as good as the SymPy
+        equality test; False does not always mean they are not equivalent
+        Vectors.
+        If other is 0, and self is empty, returns True.
+        If other is 0 and self is not empty, returns False.
+        If none of the above, only accepts other as a Vector.
+
+        """
+
+        if other == 0:
+            other = Vector(0)
+        try:
+            other = _check_vector(other)
+        except TypeError:
+            return False
+        if (self.args == []) and (other.args == []):
+            return True
+        elif (self.args == []) or (other.args == []):
+            return False
+
+        frame = self.args[0][1]
+        for v in frame:
+            if expand((self - other) & v) != 0:
+                return False
+        return True
+
+    def __mul__(self, other):
+        """Multiplies the Vector by a sympifyable expression.
+
+        Parameters
+        ==========
+
+        other : Sympifyable
+            The scalar to multiply this Vector with
+
+        Examples
+        ========
+
+        >>> from sympy.physics.vector import ReferenceFrame
+        >>> from sympy import Symbol
+        >>> N = ReferenceFrame('N')
+        >>> b = Symbol('b')
+        >>> V = 10 * b * N.x
+        >>> print(V)
+        10*b*N.x
+
+        """
+
+        newlist = list(self.args)
+        other = sympify(other)
+        for i, v in enumerate(newlist):
+            newlist[i] = (other * newlist[i][0], newlist[i][1])
+        return Vector(newlist)
+
+    def __neg__(self):
+        return self * -1
+
+    def __or__(self, other):
+        """Outer product between two Vectors.
+
+        A rank increasing operation, which returns a Dyadic from two Vectors
+
+        Parameters
+        ==========
+
+        other : Vector
+            The Vector to take the outer product with
+
+        Examples
+        ========
+
+        >>> from sympy.physics.vector import ReferenceFrame, outer
+        >>> N = ReferenceFrame('N')
+        >>> outer(N.x, N.x)
+        (N.x|N.x)
+
+        """
+
+        from sympy.physics.vector.dyadic import Dyadic
+        other = _check_vector(other)
+        ol = Dyadic(0)
+        for i, v in enumerate(self.args):
+            for i2, v2 in enumerate(other.args):
+                # it looks this way because if we are in the same frame and
+                # use the enumerate function on the same frame in a nested
+                # fashion, then bad things happen
+                ol += Dyadic([(v[0][0] * v2[0][0], v[1].x, v2[1].x)])
+                ol += Dyadic([(v[0][0] * v2[0][1], v[1].x, v2[1].y)])
+                ol += Dyadic([(v[0][0] * v2[0][2], v[1].x, v2[1].z)])
+                ol += Dyadic([(v[0][1] * v2[0][0], v[1].y, v2[1].x)])
+                ol += Dyadic([(v[0][1] * v2[0][1], v[1].y, v2[1].y)])
+                ol += Dyadic([(v[0][1] * v2[0][2], v[1].y, v2[1].z)])
+                ol += Dyadic([(v[0][2] * v2[0][0], v[1].z, v2[1].x)])
+                ol += Dyadic([(v[0][2] * v2[0][1], v[1].z, v2[1].y)])
+                ol += Dyadic([(v[0][2] * v2[0][2], v[1].z, v2[1].z)])
+        return ol
+
+    def _latex(self, printer):
+        """Latex Printing method. """
+
+        ar = self.args  # just to shorten things
+        if len(ar) == 0:
+            return str(0)
+        ol = []  # output list, to be concatenated to a string
+        for i, v in enumerate(ar):
+            for j in 0, 1, 2:
+                # if the coef of the basis vector is 1, we skip the 1
+                if ar[i][0][j] == 1:
+                    ol.append(' + ' + ar[i][1].latex_vecs[j])
+                # if the coef of the basis vector is -1, we skip the 1
+                elif ar[i][0][j] == -1:
+                    ol.append(' - ' + ar[i][1].latex_vecs[j])
+                elif ar[i][0][j] != 0:
+                    # If the coefficient of the basis vector is not 1 or -1;
+                    # also, we might wrap it in parentheses, for readability.
+                    arg_str = printer._print(ar[i][0][j])
+                    if isinstance(ar[i][0][j], Add):
+                        arg_str = "(%s)" % arg_str
+                    if arg_str[0] == '-':
+                        arg_str = arg_str[1:]
+                        str_start = ' - '
+                    else:
+                        str_start = ' + '
+                    ol.append(str_start + arg_str + ar[i][1].latex_vecs[j])
+        outstr = ''.join(ol)
+        if outstr.startswith(' + '):
+            outstr = outstr[3:]
+        elif outstr.startswith(' '):
+            outstr = outstr[1:]
+        return outstr
+
+    def _pretty(self, printer):
+        """Pretty Printing method. """
+        from sympy.printing.pretty.stringpict import prettyForm
+        e = self
+
+        class Fake:
+
+            def render(self, *args, **kwargs):
+                ar = e.args  # just to shorten things
+                if len(ar) == 0:
+                    return str(0)
+                pforms = []  # output list, to be concatenated to a string
+                for i, v in enumerate(ar):
+                    for j in 0, 1, 2:
+                        # if the coef of the basis vector is 1, we skip the 1
+                        if ar[i][0][j] == 1:
+                            pform = printer._print(ar[i][1].pretty_vecs[j])
+                        # if the coef of the basis vector is -1, we skip the 1
+                        elif ar[i][0][j] == -1:
+                            pform = printer._print(ar[i][1].pretty_vecs[j])
+                            pform = prettyForm(*pform.left(" - "))
+                            bin = prettyForm.NEG
+                            pform = prettyForm(binding=bin, *pform)
+                        elif ar[i][0][j] != 0:
+                            # If the basis vector coeff is not 1 or -1,
+                            # we might wrap it in parentheses, for readability.
+                            pform = printer._print(ar[i][0][j])
+
+                            if isinstance(ar[i][0][j], Add):
+                                tmp = pform.parens()
+                                pform = prettyForm(tmp[0], tmp[1])
+
+                            pform = prettyForm(*pform.right(
+                                " ", ar[i][1].pretty_vecs[j]))
+                        else:
+                            continue
+                        pforms.append(pform)
+
+                pform = prettyForm.__add__(*pforms)
+                kwargs["wrap_line"] = kwargs.get("wrap_line")
+                kwargs["num_columns"] = kwargs.get("num_columns")
+                out_str = pform.render(*args, **kwargs)
+                mlines = [line.rstrip() for line in out_str.split("\n")]
+                return "\n".join(mlines)
+
+        return Fake()
+
+    def __ror__(self, other):
+        """Outer product between two Vectors.
+
+        A rank increasing operation, which returns a Dyadic from two Vectors
+
+        Parameters
+        ==========
+
+        other : Vector
+            The Vector to take the outer product with
+
+        Examples
+        ========
+
+        >>> from sympy.physics.vector import ReferenceFrame, outer
+        >>> N = ReferenceFrame('N')
+        >>> outer(N.x, N.x)
+        (N.x|N.x)
+
+        """
+
+        from sympy.physics.vector.dyadic import Dyadic
+        other = _check_vector(other)
+        ol = Dyadic(0)
+        for i, v in enumerate(other.args):
+            for i2, v2 in enumerate(self.args):
+                # it looks this way because if we are in the same frame and
+                # use the enumerate function on the same frame in a nested
+                # fashion, then bad things happen
+                ol += Dyadic([(v[0][0] * v2[0][0], v[1].x, v2[1].x)])
+                ol += Dyadic([(v[0][0] * v2[0][1], v[1].x, v2[1].y)])
+                ol += Dyadic([(v[0][0] * v2[0][2], v[1].x, v2[1].z)])
+                ol += Dyadic([(v[0][1] * v2[0][0], v[1].y, v2[1].x)])
+                ol += Dyadic([(v[0][1] * v2[0][1], v[1].y, v2[1].y)])
+                ol += Dyadic([(v[0][1] * v2[0][2], v[1].y, v2[1].z)])
+                ol += Dyadic([(v[0][2] * v2[0][0], v[1].z, v2[1].x)])
+                ol += Dyadic([(v[0][2] * v2[0][1], v[1].z, v2[1].y)])
+                ol += Dyadic([(v[0][2] * v2[0][2], v[1].z, v2[1].z)])
+        return ol
+
+    def __rsub__(self, other):
+        return (-1 * self) + other
+
+    def _sympystr(self, printer, order=True):
+        """Printing method. """
+        if not order or len(self.args) == 1:
+            ar = list(self.args)
+        elif len(self.args) == 0:
+            return printer._print(0)
+        else:
+            d = {v[1]: v[0] for v in self.args}
+            keys = sorted(d.keys(), key=lambda x: x.index)
+            ar = []
+            for key in keys:
+                ar.append((d[key], key))
+        ol = []  # output list, to be concatenated to a string
+        for i, v in enumerate(ar):
+            for j in 0, 1, 2:
+                # if the coef of the basis vector is 1, we skip the 1
+                if ar[i][0][j] == 1:
+                    ol.append(' + ' + ar[i][1].str_vecs[j])
+                # if the coef of the basis vector is -1, we skip the 1
+                elif ar[i][0][j] == -1:
+                    ol.append(' - ' + ar[i][1].str_vecs[j])
+                elif ar[i][0][j] != 0:
+                    # If the coefficient of the basis vector is not 1 or -1;
+                    # also, we might wrap it in parentheses, for readability.
+                    arg_str = printer._print(ar[i][0][j])
+                    if isinstance(ar[i][0][j], Add):
+                        arg_str = "(%s)" % arg_str
+                    if arg_str[0] == '-':
+                        arg_str = arg_str[1:]
+                        str_start = ' - '
+                    else:
+                        str_start = ' + '
+                    ol.append(str_start + arg_str + '*' + ar[i][1].str_vecs[j])
+        outstr = ''.join(ol)
+        if outstr.startswith(' + '):
+            outstr = outstr[3:]
+        elif outstr.startswith(' '):
+            outstr = outstr[1:]
+        return outstr
+
+    def __sub__(self, other):
+        """The subtraction operator. """
+        return self.__add__(other * -1)
+
+    def __xor__(self, other):
+        """The cross product operator for two Vectors.
+
+        Returns a Vector, expressed in the same ReferenceFrames as self.
+
+        Parameters
+        ==========
+
+        other : Vector
+            The Vector which we are crossing with
+
+        Examples
+        ========
+
+        >>> from sympy import symbols
+        >>> from sympy.physics.vector import ReferenceFrame, cross
+        >>> q1 = symbols('q1')
+        >>> N = ReferenceFrame('N')
+        >>> cross(N.x, N.y)
+        N.z
+        >>> A = ReferenceFrame('A')
+        >>> A.orient_axis(N, q1, N.x)
+        >>> cross(A.x, N.y)
+        N.z
+        >>> cross(N.y, A.x)
+        - sin(q1)*A.y - cos(q1)*A.z
+
+        """
+
+        from sympy.physics.vector.dyadic import Dyadic
+        if isinstance(other, Dyadic):
+            return NotImplemented
+        other = _check_vector(other)
+        if other.args == []:
+            return Vector(0)
+
+        def _det(mat):
+            """This is needed as a little method for to find the determinant
+            of a list in python; needs to work for a 3x3 list.
+            SymPy's Matrix will not take in Vector, so need a custom function.
+            You should not be calling this.
+
+            """
+
+            return (mat[0][0] * (mat[1][1] * mat[2][2] - mat[1][2] * mat[2][1])
+                    + mat[0][1] * (mat[1][2] * mat[2][0] - mat[1][0] *
+                    mat[2][2]) + mat[0][2] * (mat[1][0] * mat[2][1] -
+                    mat[1][1] * mat[2][0]))
+
+        outlist = []
+        ar = other.args  # For brevity
+        for i, v in enumerate(ar):
+            tempx = v[1].x
+            tempy = v[1].y
+            tempz = v[1].z
+            tempm = ([[tempx, tempy, tempz],
+                      [self & tempx, self & tempy, self & tempz],
+                      [Vector([ar[i]]) & tempx, Vector([ar[i]]) & tempy,
+                       Vector([ar[i]]) & tempz]])
+            outlist += _det(tempm).args
+        return Vector(outlist)
+
+    __radd__ = __add__
+    __rand__ = __and__
+    __rmul__ = __mul__
+
+    def separate(self):
+        """
+        The constituents of this vector in different reference frames,
+        as per its definition.
+
+        Returns a dict mapping each ReferenceFrame to the corresponding
+        constituent Vector.
+
+        Examples
+        ========
+
+        >>> from sympy.physics.vector import ReferenceFrame
+        >>> R1 = ReferenceFrame('R1')
+        >>> R2 = ReferenceFrame('R2')
+        >>> v = R1.x + R2.x
+        >>> v.separate() == {R1: R1.x, R2: R2.x}
+        True
+
+        """
+
+        components = {}
+        for x in self.args:
+            components[x[1]] = Vector([x])
+        return components
+
+    def dot(self, other):
+        return self & other
+    dot.__doc__ = __and__.__doc__
+
+    def cross(self, other):
+        return self ^ other
+    cross.__doc__ = __xor__.__doc__
+
+    def outer(self, other):
+        return self | other
+    outer.__doc__ = __or__.__doc__
+
+    def diff(self, var, frame, var_in_dcm=True):
+        """Returns the partial derivative of the vector with respect to a
+        variable in the provided reference frame.
+
+        Parameters
+        ==========
+        var : Symbol
+            What the partial derivative is taken with respect to.
+        frame : ReferenceFrame
+            The reference frame that the partial derivative is taken in.
+        var_in_dcm : boolean
+            If true, the differentiation algorithm assumes that the variable
+            may be present in any of the direction cosine matrices that relate
+            the frame to the frames of any component of the vector. But if it
+            is known that the variable is not present in the direction cosine
+            matrices, false can be set to skip full reexpression in the desired
+            frame.
+
+        Examples
+        ========
+
+        >>> from sympy import Symbol
+        >>> from sympy.physics.vector import dynamicsymbols, ReferenceFrame
+        >>> from sympy.physics.vector import Vector
+        >>> from sympy.physics.vector import init_vprinting
+        >>> init_vprinting(pretty_print=False)
+        >>> Vector.simp = True
+        >>> t = Symbol('t')
+        >>> q1 = dynamicsymbols('q1')
+        >>> N = ReferenceFrame('N')
+        >>> A = N.orientnew('A', 'Axis', [q1, N.y])
+        >>> A.x.diff(t, N)
+        - sin(q1)*q1'*N.x - cos(q1)*q1'*N.z
+        >>> A.x.diff(t, N).express(A)
+        - q1'*A.z
+        >>> B = ReferenceFrame('B')
+        >>> u1, u2 = dynamicsymbols('u1, u2')
+        >>> v = u1 * A.x + u2 * B.y
+        >>> v.diff(u2, N, var_in_dcm=False)
+        B.y
+
+        """
+
+        from sympy.physics.vector.frame import _check_frame
+
+        _check_frame(frame)
+        var = sympify(var)
+
+        inlist = []
+
+        for vector_component in self.args:
+            measure_number = vector_component[0]
+            component_frame = vector_component[1]
+            if component_frame == frame:
+                inlist += [(measure_number.diff(var), frame)]
+            else:
+                # If the direction cosine matrix relating the component frame
+                # with the derivative frame does not contain the variable.
+                if not var_in_dcm or (frame.dcm(component_frame).diff(var) ==
+                                      zeros(3, 3)):
+                    inlist += [(measure_number.diff(var), component_frame)]
+                else:  # else express in the frame
+                    reexp_vec_comp = Vector([vector_component]).express(frame)
+                    deriv = reexp_vec_comp.args[0][0].diff(var)
+                    inlist += Vector([(deriv, frame)]).args
+
+        return Vector(inlist)
+
+    def express(self, otherframe, variables=False):
+        """
+        Returns a Vector equivalent to this one, expressed in otherframe.
+        Uses the global express method.
+
+        Parameters
+        ==========
+
+        otherframe : ReferenceFrame
+            The frame for this Vector to be described in
+
+        variables : boolean
+            If True, the coordinate symbols(if present) in this Vector
+            are re-expressed in terms otherframe
+
+        Examples
+        ========
+
+        >>> from sympy.physics.vector import ReferenceFrame, dynamicsymbols
+        >>> from sympy.physics.vector import init_vprinting
+        >>> init_vprinting(pretty_print=False)
+        >>> q1 = dynamicsymbols('q1')
+        >>> N = ReferenceFrame('N')
+        >>> A = N.orientnew('A', 'Axis', [q1, N.y])
+        >>> A.x.express(N)
+        cos(q1)*N.x - sin(q1)*N.z
+
+        """
+        from sympy.physics.vector import express
+        return express(self, otherframe, variables=variables)
+
+    def to_matrix(self, reference_frame):
+        """Returns the matrix form of the vector with respect to the given
+        frame.
+
+        Parameters
+        ----------
+        reference_frame : ReferenceFrame
+            The reference frame that the rows of the matrix correspond to.
+
+        Returns
+        -------
+        matrix : ImmutableMatrix, shape(3,1)
+            The matrix that gives the 1D vector.
+
+        Examples
+        ========
+
+        >>> from sympy import symbols
+        >>> from sympy.physics.vector import ReferenceFrame
+        >>> a, b, c = symbols('a, b, c')
+        >>> N = ReferenceFrame('N')
+        >>> vector = a * N.x + b * N.y + c * N.z
+        >>> vector.to_matrix(N)
+        Matrix([
+        [a],
+        [b],
+        [c]])
+        >>> beta = symbols('beta')
+        >>> A = N.orientnew('A', 'Axis', (beta, N.x))
+        >>> vector.to_matrix(A)
+        Matrix([
+        [                         a],
+        [ b*cos(beta) + c*sin(beta)],
+        [-b*sin(beta) + c*cos(beta)]])
+
+        """
+
+        return Matrix([self.dot(unit_vec) for unit_vec in
+                       reference_frame]).reshape(3, 1)
+
+    def doit(self, **hints):
+        """Calls .doit() on each term in the Vector"""
+        d = {}
+        for v in self.args:
+            d[v[1]] = v[0].applyfunc(lambda x: x.doit(**hints))
+        return Vector(d)
+
+    def dt(self, otherframe):
+        """
+        Returns a Vector which is the time derivative of
+        the self Vector, taken in frame otherframe.
+
+        Calls the global time_derivative method
+
+        Parameters
+        ==========
+
+        otherframe : ReferenceFrame
+            The frame to calculate the time derivative in
+
+        """
+        from sympy.physics.vector import time_derivative
+        return time_derivative(self, otherframe)
+
+    def simplify(self):
+        """Returns a simplified Vector."""
+        d = {}
+        for v in self.args:
+            d[v[1]] = _simplify_matrix(v[0])
+        return Vector(d)
+
+    def subs(self, *args, **kwargs):
+        """Substitution on the Vector.
+
+        Examples
+        ========
+
+        >>> from sympy.physics.vector import ReferenceFrame
+        >>> from sympy import Symbol
+        >>> N = ReferenceFrame('N')
+        >>> s = Symbol('s')
+        >>> a = N.x * s
+        >>> a.subs({s: 2})
+        2*N.x
+
+        """
+
+        d = {}
+        for v in self.args:
+            d[v[1]] = v[0].subs(*args, **kwargs)
+        return Vector(d)
+
+    def magnitude(self):
+        """Returns the magnitude (Euclidean norm) of self.
+
+        Warnings
+        ========
+
+        Python ignores the leading negative sign so that might
+        give wrong results.
+        ``-A.x.magnitude()`` would be treated as ``-(A.x.magnitude())``,
+        instead of ``(-A.x).magnitude()``.
+
+        """
+        return sqrt(self & self)
+
+    def normalize(self):
+        """Returns a Vector of magnitude 1, codirectional with self."""
+        return Vector(self.args + []) / self.magnitude()
+
+    def applyfunc(self, f):
+        """Apply a function to each component of a vector."""
+        if not callable(f):
+            raise TypeError("`f` must be callable.")
+
+        d = {}
+        for v in self.args:
+            d[v[1]] = v[0].applyfunc(f)
+        return Vector(d)
+
+    def angle_between(self, vec):
+        """
+        Returns the smallest angle between Vector 'vec' and self.
+
+        Parameter
+        =========
+
+        vec : Vector
+            The Vector between which angle is needed.
+
+        Examples
+        ========
+
+        >>> from sympy.physics.vector import ReferenceFrame
+        >>> A = ReferenceFrame("A")
+        >>> v1 = A.x
+        >>> v2 = A.y
+        >>> v1.angle_between(v2)
+        pi/2
+
+        >>> v3 = A.x + A.y + A.z
+        >>> v1.angle_between(v3)
+        acos(sqrt(3)/3)
+
+        Warnings
+        ========
+
+        Python ignores the leading negative sign so that might give wrong
+        results. ``-A.x.angle_between()`` would be treated as
+        ``-(A.x.angle_between())``, instead of ``(-A.x).angle_between()``.
+
+        """
+
+        vec1 = self.normalize()
+        vec2 = vec.normalize()
+        angle = acos(vec1.dot(vec2))
+        return angle
+
+    def free_symbols(self, reference_frame):
+        """Returns the free symbols in the measure numbers of the vector
+        expressed in the given reference frame.
+
+        Parameters
+        ==========
+        reference_frame : ReferenceFrame
+            The frame with respect to which the free symbols of the given
+            vector is to be determined.
+
+        Returns
+        =======
+        set of Symbol
+            set of symbols present in the measure numbers of
+            ``reference_frame``.
+
+        """
+
+        return self.to_matrix(reference_frame).free_symbols
+
+    def free_dynamicsymbols(self, reference_frame):
+        """Returns the free dynamic symbols (functions of time ``t``) in the
+        measure numbers of the vector expressed in the given reference frame.
+
+        Parameters
+        ==========
+        reference_frame : ReferenceFrame
+            The frame with respect to which the free dynamic symbols of the
+            given vector is to be determined.
+
+        Returns
+        =======
+        set
+            Set of functions of time ``t``, e.g.
+            ``Function('f')(me.dynamicsymbols._t)``.
+
+        """
+        # TODO : Circular dependency if imported at top. Should move
+        # find_dynamicsymbols into physics.vector.functions.
+        from sympy.physics.mechanics.functions import find_dynamicsymbols
+
+        return find_dynamicsymbols(self, reference_frame=reference_frame)
+
+    def _eval_evalf(self, prec):
+        if not self.args:
+            return self
+        new_args = []
+        dps = prec_to_dps(prec)
+        for mat, frame in self.args:
+            new_args.append([mat.evalf(n=dps), frame])
+        return Vector(new_args)
+
+    def xreplace(self, rule):
+        """Replace occurrences of objects within the measure numbers of the
+        vector.
+
+        Parameters
+        ==========
+
+        rule : dict-like
+            Expresses a replacement rule.
+
+        Returns
+        =======
+
+        Vector
+            Result of the replacement.
+
+        Examples
+        ========
+
+        >>> from sympy import symbols, pi
+        >>> from sympy.physics.vector import ReferenceFrame
+        >>> A = ReferenceFrame('A')
+        >>> x, y, z = symbols('x y z')
+        >>> ((1 + x*y) * A.x).xreplace({x: pi})
+        (pi*y + 1)*A.x
+        >>> ((1 + x*y) * A.x).xreplace({x: pi, y: 2})
+        (1 + 2*pi)*A.x
+
+        Replacements occur only if an entire node in the expression tree is
+        matched:
+
+        >>> ((x*y + z) * A.x).xreplace({x*y: pi})
+        (z + pi)*A.x
+        >>> ((x*y*z) * A.x).xreplace({x*y: pi})
+        x*y*z*A.x
+
+        """
+
+        new_args = []
+        for mat, frame in self.args:
+            mat = mat.xreplace(rule)
+            new_args.append([mat, frame])
+        return Vector(new_args)
+
+
+class VectorTypeError(TypeError):
+
+    def __init__(self, other, want):
+        msg = filldedent("Expected an instance of %s, but received object "
+                         "'%s' of %s." % (type(want), other, type(other)))
+        super().__init__(msg)
+
+
+def _check_vector(other):
+    if not isinstance(other, Vector):
+        raise TypeError('A Vector must be supplied')
+    return other
diff --git a/llmeval-env/lib/python3.10/site-packages/sympy/physics/wigner.py b/llmeval-env/lib/python3.10/site-packages/sympy/physics/wigner.py
new file mode 100644
index 0000000000000000000000000000000000000000..ef404b98acee9893cb582c1790622603b805d866
--- /dev/null
+++ b/llmeval-env/lib/python3.10/site-packages/sympy/physics/wigner.py
@@ -0,0 +1,1159 @@
+# -*- coding: utf-8 -*-
+r"""
+Wigner, Clebsch-Gordan, Racah, and Gaunt coefficients
+
+Collection of functions for calculating Wigner 3j, 6j, 9j,
+Clebsch-Gordan, Racah as well as Gaunt coefficients exactly, all
+evaluating to a rational number times the square root of a rational
+number [Rasch03]_.
+
+Please see the description of the individual functions for further
+details and examples.
+
+References
+==========
+
+.. [Regge58] 'Symmetry Properties of Clebsch-Gordan Coefficients',
+  T. Regge, Nuovo Cimento, Volume 10, pp. 544 (1958)
+.. [Regge59] 'Symmetry Properties of Racah Coefficients',
+  T. Regge, Nuovo Cimento, Volume 11, pp. 116 (1959)
+.. [Edmonds74] A. R. Edmonds. Angular momentum in quantum mechanics.
+  Investigations in physics, 4.; Investigations in physics, no. 4.
+  Princeton, N.J., Princeton University Press, 1957.
+.. [Rasch03] J. Rasch and A. C. H. Yu, 'Efficient Storage Scheme for
+  Pre-calculated Wigner 3j, 6j and Gaunt Coefficients', SIAM
+  J. Sci. Comput. Volume 25, Issue 4, pp. 1416-1428 (2003)
+.. [Liberatodebrito82] 'FORTRAN program for the integral of three
+  spherical harmonics', A. Liberato de Brito,
+  Comput. Phys. Commun., Volume 25, pp. 81-85 (1982)
+.. [Homeier96] 'Some Properties of the Coupling Coefficients of Real
+  Spherical Harmonics and Their Relation to Gaunt Coefficients',
+  H. H. H. Homeier and E. O. Steinborn J. Mol. Struct., Volume 368,
+  pp. 31-37 (1996)
+
+Credits and Copyright
+=====================
+
+This code was taken from Sage with the permission of all authors:
+
+https://groups.google.com/forum/#!topic/sage-devel/M4NZdu-7O38
+
+Authors
+=======
+
+- Jens Rasch (2009-03-24): initial version for Sage
+
+- Jens Rasch (2009-05-31): updated to sage-4.0
+
+- Oscar Gerardo Lazo Arjona (2017-06-18): added Wigner D matrices
+
+- Phil Adam LeMaitre (2022-09-19): added real Gaunt coefficient
+
+Copyright (C) 2008 Jens Rasch 
+
+"""
+from sympy.concrete.summations import Sum
+from sympy.core.add import Add
+from sympy.core.function import Function
+from sympy.core.numbers import (I, Integer, pi)
+from sympy.core.singleton import S
+from sympy.core.symbol import Dummy
+from sympy.core.sympify import sympify
+from sympy.functions.combinatorial.factorials import (binomial, factorial)
+from sympy.functions.elementary.complexes import re
+from sympy.functions.elementary.exponential import exp
+from sympy.functions.elementary.miscellaneous import sqrt
+from sympy.functions.elementary.trigonometric import (cos, sin)
+from sympy.functions.special.spherical_harmonics import Ynm
+from sympy.matrices.dense import zeros
+from sympy.matrices.immutable import ImmutableMatrix
+from sympy.utilities.misc import as_int
+
+# This list of precomputed factorials is needed to massively
+# accelerate future calculations of the various coefficients
+_Factlist = [1]
+
+
+def _calc_factlist(nn):
+    r"""
+    Function calculates a list of precomputed factorials in order to
+    massively accelerate future calculations of the various
+    coefficients.
+
+    Parameters
+    ==========
+
+    nn : integer
+        Highest factorial to be computed.
+
+    Returns
+    =======
+
+    list of integers :
+        The list of precomputed factorials.
+
+    Examples
+    ========
+
+    Calculate list of factorials::
+
+        sage: from sage.functions.wigner import _calc_factlist
+        sage: _calc_factlist(10)
+        [1, 1, 2, 6, 24, 120, 720, 5040, 40320, 362880, 3628800]
+    """
+    if nn >= len(_Factlist):
+        for ii in range(len(_Factlist), int(nn + 1)):
+            _Factlist.append(_Factlist[ii - 1] * ii)
+    return _Factlist[:int(nn) + 1]
+
+
+def wigner_3j(j_1, j_2, j_3, m_1, m_2, m_3):
+    r"""
+    Calculate the Wigner 3j symbol `\operatorname{Wigner3j}(j_1,j_2,j_3,m_1,m_2,m_3)`.
+
+    Parameters
+    ==========
+
+    j_1, j_2, j_3, m_1, m_2, m_3 :
+        Integer or half integer.
+
+    Returns
+    =======
+
+    Rational number times the square root of a rational number.
+
+    Examples
+    ========
+
+    >>> from sympy.physics.wigner import wigner_3j
+    >>> wigner_3j(2, 6, 4, 0, 0, 0)
+    sqrt(715)/143
+    >>> wigner_3j(2, 6, 4, 0, 0, 1)
+    0
+
+    It is an error to have arguments that are not integer or half
+    integer values::
+
+        sage: wigner_3j(2.1, 6, 4, 0, 0, 0)
+        Traceback (most recent call last):
+        ...
+        ValueError: j values must be integer or half integer
+        sage: wigner_3j(2, 6, 4, 1, 0, -1.1)
+        Traceback (most recent call last):
+        ...
+        ValueError: m values must be integer or half integer
+
+    Notes
+    =====
+
+    The Wigner 3j symbol obeys the following symmetry rules:
+
+    - invariant under any permutation of the columns (with the
+      exception of a sign change where `J:=j_1+j_2+j_3`):
+
+      .. math::
+
+         \begin{aligned}
+         \operatorname{Wigner3j}(j_1,j_2,j_3,m_1,m_2,m_3)
+          &=\operatorname{Wigner3j}(j_3,j_1,j_2,m_3,m_1,m_2) \\
+          &=\operatorname{Wigner3j}(j_2,j_3,j_1,m_2,m_3,m_1) \\
+          &=(-1)^J \operatorname{Wigner3j}(j_3,j_2,j_1,m_3,m_2,m_1) \\
+          &=(-1)^J \operatorname{Wigner3j}(j_1,j_3,j_2,m_1,m_3,m_2) \\
+          &=(-1)^J \operatorname{Wigner3j}(j_2,j_1,j_3,m_2,m_1,m_3)
+         \end{aligned}
+
+    - invariant under space inflection, i.e.
+
+      .. math::
+
+         \operatorname{Wigner3j}(j_1,j_2,j_3,m_1,m_2,m_3)
+         =(-1)^J \operatorname{Wigner3j}(j_1,j_2,j_3,-m_1,-m_2,-m_3)
+
+    - symmetric with respect to the 72 additional symmetries based on
+      the work by [Regge58]_
+
+    - zero for `j_1`, `j_2`, `j_3` not fulfilling triangle relation
+
+    - zero for `m_1 + m_2 + m_3 \neq 0`
+
+    - zero for violating any one of the conditions
+      `j_1 \ge |m_1|`,  `j_2 \ge |m_2|`,  `j_3 \ge |m_3|`
+
+    Algorithm
+    =========
+
+    This function uses the algorithm of [Edmonds74]_ to calculate the
+    value of the 3j symbol exactly. Note that the formula contains
+    alternating sums over large factorials and is therefore unsuitable
+    for finite precision arithmetic and only useful for a computer
+    algebra system [Rasch03]_.
+
+    Authors
+    =======
+
+    - Jens Rasch (2009-03-24): initial version
+    """
+    if int(j_1 * 2) != j_1 * 2 or int(j_2 * 2) != j_2 * 2 or \
+            int(j_3 * 2) != j_3 * 2:
+        raise ValueError("j values must be integer or half integer")
+    if int(m_1 * 2) != m_1 * 2 or int(m_2 * 2) != m_2 * 2 or \
+            int(m_3 * 2) != m_3 * 2:
+        raise ValueError("m values must be integer or half integer")
+    if m_1 + m_2 + m_3 != 0:
+        return S.Zero
+    prefid = Integer((-1) ** int(j_1 - j_2 - m_3))
+    m_3 = -m_3
+    a1 = j_1 + j_2 - j_3
+    if a1 < 0:
+        return S.Zero
+    a2 = j_1 - j_2 + j_3
+    if a2 < 0:
+        return S.Zero
+    a3 = -j_1 + j_2 + j_3
+    if a3 < 0:
+        return S.Zero
+    if (abs(m_1) > j_1) or (abs(m_2) > j_2) or (abs(m_3) > j_3):
+        return S.Zero
+
+    maxfact = max(j_1 + j_2 + j_3 + 1, j_1 + abs(m_1), j_2 + abs(m_2),
+                  j_3 + abs(m_3))
+    _calc_factlist(int(maxfact))
+
+    argsqrt = Integer(_Factlist[int(j_1 + j_2 - j_3)] *
+                     _Factlist[int(j_1 - j_2 + j_3)] *
+                     _Factlist[int(-j_1 + j_2 + j_3)] *
+                     _Factlist[int(j_1 - m_1)] *
+                     _Factlist[int(j_1 + m_1)] *
+                     _Factlist[int(j_2 - m_2)] *
+                     _Factlist[int(j_2 + m_2)] *
+                     _Factlist[int(j_3 - m_3)] *
+                     _Factlist[int(j_3 + m_3)]) / \
+        _Factlist[int(j_1 + j_2 + j_3 + 1)]
+
+    ressqrt = sqrt(argsqrt)
+    if ressqrt.is_complex or ressqrt.is_infinite:
+        ressqrt = ressqrt.as_real_imag()[0]
+
+    imin = max(-j_3 + j_1 + m_2, -j_3 + j_2 - m_1, 0)
+    imax = min(j_2 + m_2, j_1 - m_1, j_1 + j_2 - j_3)
+    sumres = 0
+    for ii in range(int(imin), int(imax) + 1):
+        den = _Factlist[ii] * \
+            _Factlist[int(ii + j_3 - j_1 - m_2)] * \
+            _Factlist[int(j_2 + m_2 - ii)] * \
+            _Factlist[int(j_1 - ii - m_1)] * \
+            _Factlist[int(ii + j_3 - j_2 + m_1)] * \
+            _Factlist[int(j_1 + j_2 - j_3 - ii)]
+        sumres = sumres + Integer((-1) ** ii) / den
+
+    res = ressqrt * sumres * prefid
+    return res
+
+
+def clebsch_gordan(j_1, j_2, j_3, m_1, m_2, m_3):
+    r"""
+    Calculates the Clebsch-Gordan coefficient.
+    `\left\langle j_1 m_1 \; j_2 m_2 | j_3 m_3 \right\rangle`.
+
+    The reference for this function is [Edmonds74]_.
+
+    Parameters
+    ==========
+
+    j_1, j_2, j_3, m_1, m_2, m_3 :
+        Integer or half integer.
+
+    Returns
+    =======
+
+    Rational number times the square root of a rational number.
+
+    Examples
+    ========
+
+    >>> from sympy import S
+    >>> from sympy.physics.wigner import clebsch_gordan
+    >>> clebsch_gordan(S(3)/2, S(1)/2, 2, S(3)/2, S(1)/2, 2)
+    1
+    >>> clebsch_gordan(S(3)/2, S(1)/2, 1, S(3)/2, -S(1)/2, 1)
+    sqrt(3)/2
+    >>> clebsch_gordan(S(3)/2, S(1)/2, 1, -S(1)/2, S(1)/2, 0)
+    -sqrt(2)/2
+
+    Notes
+    =====
+
+    The Clebsch-Gordan coefficient will be evaluated via its relation
+    to Wigner 3j symbols:
+
+    .. math::
+
+        \left\langle j_1 m_1 \; j_2 m_2 | j_3 m_3 \right\rangle
+        =(-1)^{j_1-j_2+m_3} \sqrt{2j_3+1}
+        \operatorname{Wigner3j}(j_1,j_2,j_3,m_1,m_2,-m_3)
+
+    See also the documentation on Wigner 3j symbols which exhibit much
+    higher symmetry relations than the Clebsch-Gordan coefficient.
+
+    Authors
+    =======
+
+    - Jens Rasch (2009-03-24): initial version
+    """
+    res = (-1) ** sympify(j_1 - j_2 + m_3) * sqrt(2 * j_3 + 1) * \
+        wigner_3j(j_1, j_2, j_3, m_1, m_2, -m_3)
+    return res
+
+
+def _big_delta_coeff(aa, bb, cc, prec=None):
+    r"""
+    Calculates the Delta coefficient of the 3 angular momenta for
+    Racah symbols. Also checks that the differences are of integer
+    value.
+
+    Parameters
+    ==========
+
+    aa :
+        First angular momentum, integer or half integer.
+    bb :
+        Second angular momentum, integer or half integer.
+    cc :
+        Third angular momentum, integer or half integer.
+    prec :
+        Precision of the ``sqrt()`` calculation.
+
+    Returns
+    =======
+
+    double : Value of the Delta coefficient.
+
+    Examples
+    ========
+
+        sage: from sage.functions.wigner import _big_delta_coeff
+        sage: _big_delta_coeff(1,1,1)
+        1/2*sqrt(1/6)
+    """
+
+    if int(aa + bb - cc) != (aa + bb - cc):
+        raise ValueError("j values must be integer or half integer and fulfill the triangle relation")
+    if int(aa + cc - bb) != (aa + cc - bb):
+        raise ValueError("j values must be integer or half integer and fulfill the triangle relation")
+    if int(bb + cc - aa) != (bb + cc - aa):
+        raise ValueError("j values must be integer or half integer and fulfill the triangle relation")
+    if (aa + bb - cc) < 0:
+        return S.Zero
+    if (aa + cc - bb) < 0:
+        return S.Zero
+    if (bb + cc - aa) < 0:
+        return S.Zero
+
+    maxfact = max(aa + bb - cc, aa + cc - bb, bb + cc - aa, aa + bb + cc + 1)
+    _calc_factlist(maxfact)
+
+    argsqrt = Integer(_Factlist[int(aa + bb - cc)] *
+                     _Factlist[int(aa + cc - bb)] *
+                     _Factlist[int(bb + cc - aa)]) / \
+        Integer(_Factlist[int(aa + bb + cc + 1)])
+
+    ressqrt = sqrt(argsqrt)
+    if prec:
+        ressqrt = ressqrt.evalf(prec).as_real_imag()[0]
+    return ressqrt
+
+
+def racah(aa, bb, cc, dd, ee, ff, prec=None):
+    r"""
+    Calculate the Racah symbol `W(a,b,c,d;e,f)`.
+
+    Parameters
+    ==========
+
+    a, ..., f :
+        Integer or half integer.
+    prec :
+        Precision, default: ``None``. Providing a precision can
+        drastically speed up the calculation.
+
+    Returns
+    =======
+
+    Rational number times the square root of a rational number
+    (if ``prec=None``), or real number if a precision is given.
+
+    Examples
+    ========
+
+    >>> from sympy.physics.wigner import racah
+    >>> racah(3,3,3,3,3,3)
+    -1/14
+
+    Notes
+    =====
+
+    The Racah symbol is related to the Wigner 6j symbol:
+
+    .. math::
+
+       \operatorname{Wigner6j}(j_1,j_2,j_3,j_4,j_5,j_6)
+       =(-1)^{j_1+j_2+j_4+j_5} W(j_1,j_2,j_5,j_4,j_3,j_6)
+
+    Please see the 6j symbol for its much richer symmetries and for
+    additional properties.
+
+    Algorithm
+    =========
+
+    This function uses the algorithm of [Edmonds74]_ to calculate the
+    value of the 6j symbol exactly. Note that the formula contains
+    alternating sums over large factorials and is therefore unsuitable
+    for finite precision arithmetic and only useful for a computer
+    algebra system [Rasch03]_.
+
+    Authors
+    =======
+
+    - Jens Rasch (2009-03-24): initial version
+    """
+    prefac = _big_delta_coeff(aa, bb, ee, prec) * \
+        _big_delta_coeff(cc, dd, ee, prec) * \
+        _big_delta_coeff(aa, cc, ff, prec) * \
+        _big_delta_coeff(bb, dd, ff, prec)
+    if prefac == 0:
+        return S.Zero
+    imin = max(aa + bb + ee, cc + dd + ee, aa + cc + ff, bb + dd + ff)
+    imax = min(aa + bb + cc + dd, aa + dd + ee + ff, bb + cc + ee + ff)
+
+    maxfact = max(imax + 1, aa + bb + cc + dd, aa + dd + ee + ff,
+                 bb + cc + ee + ff)
+    _calc_factlist(maxfact)
+
+    sumres = 0
+    for kk in range(int(imin), int(imax) + 1):
+        den = _Factlist[int(kk - aa - bb - ee)] * \
+            _Factlist[int(kk - cc - dd - ee)] * \
+            _Factlist[int(kk - aa - cc - ff)] * \
+            _Factlist[int(kk - bb - dd - ff)] * \
+            _Factlist[int(aa + bb + cc + dd - kk)] * \
+            _Factlist[int(aa + dd + ee + ff - kk)] * \
+            _Factlist[int(bb + cc + ee + ff - kk)]
+        sumres = sumres + Integer((-1) ** kk * _Factlist[kk + 1]) / den
+
+    res = prefac * sumres * (-1) ** int(aa + bb + cc + dd)
+    return res
+
+
+def wigner_6j(j_1, j_2, j_3, j_4, j_5, j_6, prec=None):
+    r"""
+    Calculate the Wigner 6j symbol `\operatorname{Wigner6j}(j_1,j_2,j_3,j_4,j_5,j_6)`.
+
+    Parameters
+    ==========
+
+    j_1, ..., j_6 :
+        Integer or half integer.
+    prec :
+        Precision, default: ``None``. Providing a precision can
+        drastically speed up the calculation.
+
+    Returns
+    =======
+
+    Rational number times the square root of a rational number
+    (if ``prec=None``), or real number if a precision is given.
+
+    Examples
+    ========
+
+    >>> from sympy.physics.wigner import wigner_6j
+    >>> wigner_6j(3,3,3,3,3,3)
+    -1/14
+    >>> wigner_6j(5,5,5,5,5,5)
+    1/52
+
+    It is an error to have arguments that are not integer or half
+    integer values or do not fulfill the triangle relation::
+
+        sage: wigner_6j(2.5,2.5,2.5,2.5,2.5,2.5)
+        Traceback (most recent call last):
+        ...
+        ValueError: j values must be integer or half integer and fulfill the triangle relation
+        sage: wigner_6j(0.5,0.5,1.1,0.5,0.5,1.1)
+        Traceback (most recent call last):
+        ...
+        ValueError: j values must be integer or half integer and fulfill the triangle relation
+
+    Notes
+    =====
+
+    The Wigner 6j symbol is related to the Racah symbol but exhibits
+    more symmetries as detailed below.
+
+    .. math::
+
+       \operatorname{Wigner6j}(j_1,j_2,j_3,j_4,j_5,j_6)
+        =(-1)^{j_1+j_2+j_4+j_5} W(j_1,j_2,j_5,j_4,j_3,j_6)
+
+    The Wigner 6j symbol obeys the following symmetry rules:
+
+    - Wigner 6j symbols are left invariant under any permutation of
+      the columns:
+
+      .. math::
+
+         \begin{aligned}
+         \operatorname{Wigner6j}(j_1,j_2,j_3,j_4,j_5,j_6)
+          &=\operatorname{Wigner6j}(j_3,j_1,j_2,j_6,j_4,j_5) \\
+          &=\operatorname{Wigner6j}(j_2,j_3,j_1,j_5,j_6,j_4) \\
+          &=\operatorname{Wigner6j}(j_3,j_2,j_1,j_6,j_5,j_4) \\
+          &=\operatorname{Wigner6j}(j_1,j_3,j_2,j_4,j_6,j_5) \\
+          &=\operatorname{Wigner6j}(j_2,j_1,j_3,j_5,j_4,j_6)
+         \end{aligned}
+
+    - They are invariant under the exchange of the upper and lower
+      arguments in each of any two columns, i.e.
+
+      .. math::
+
+         \operatorname{Wigner6j}(j_1,j_2,j_3,j_4,j_5,j_6)
+          =\operatorname{Wigner6j}(j_1,j_5,j_6,j_4,j_2,j_3)
+          =\operatorname{Wigner6j}(j_4,j_2,j_6,j_1,j_5,j_3)
+          =\operatorname{Wigner6j}(j_4,j_5,j_3,j_1,j_2,j_6)
+
+    - additional 6 symmetries [Regge59]_ giving rise to 144 symmetries
+      in total
+
+    - only non-zero if any triple of `j`'s fulfill a triangle relation
+
+    Algorithm
+    =========
+
+    This function uses the algorithm of [Edmonds74]_ to calculate the
+    value of the 6j symbol exactly. Note that the formula contains
+    alternating sums over large factorials and is therefore unsuitable
+    for finite precision arithmetic and only useful for a computer
+    algebra system [Rasch03]_.
+
+    """
+    res = (-1) ** int(j_1 + j_2 + j_4 + j_5) * \
+        racah(j_1, j_2, j_5, j_4, j_3, j_6, prec)
+    return res
+
+
+def wigner_9j(j_1, j_2, j_3, j_4, j_5, j_6, j_7, j_8, j_9, prec=None):
+    r"""
+    Calculate the Wigner 9j symbol
+    `\operatorname{Wigner9j}(j_1,j_2,j_3,j_4,j_5,j_6,j_7,j_8,j_9)`.
+
+    Parameters
+    ==========
+
+    j_1, ..., j_9 :
+        Integer or half integer.
+    prec : precision, default
+        ``None``. Providing a precision can
+        drastically speed up the calculation.
+
+    Returns
+    =======
+
+    Rational number times the square root of a rational number
+    (if ``prec=None``), or real number if a precision is given.
+
+    Examples
+    ========
+
+    >>> from sympy.physics.wigner import wigner_9j
+    >>> wigner_9j(1,1,1, 1,1,1, 1,1,0, prec=64) # ==1/18
+    0.05555555...
+
+    >>> wigner_9j(1/2,1/2,0, 1/2,3/2,1, 0,1,1, prec=64) # ==1/6
+    0.1666666...
+
+    It is an error to have arguments that are not integer or half
+    integer values or do not fulfill the triangle relation::
+
+        sage: wigner_9j(0.5,0.5,0.5, 0.5,0.5,0.5, 0.5,0.5,0.5,prec=64)
+        Traceback (most recent call last):
+        ...
+        ValueError: j values must be integer or half integer and fulfill the triangle relation
+        sage: wigner_9j(1,1,1, 0.5,1,1.5, 0.5,1,2.5,prec=64)
+        Traceback (most recent call last):
+        ...
+        ValueError: j values must be integer or half integer and fulfill the triangle relation
+
+    Algorithm
+    =========
+
+    This function uses the algorithm of [Edmonds74]_ to calculate the
+    value of the 3j symbol exactly. Note that the formula contains
+    alternating sums over large factorials and is therefore unsuitable
+    for finite precision arithmetic and only useful for a computer
+    algebra system [Rasch03]_.
+    """
+    imax = int(min(j_1 + j_9, j_2 + j_6, j_4 + j_8) * 2)
+    imin = imax % 2
+    sumres = 0
+    for kk in range(imin, int(imax) + 1, 2):
+        sumres = sumres + (kk + 1) * \
+            racah(j_1, j_2, j_9, j_6, j_3, kk / 2, prec) * \
+            racah(j_4, j_6, j_8, j_2, j_5, kk / 2, prec) * \
+            racah(j_1, j_4, j_9, j_8, j_7, kk / 2, prec)
+    return sumres
+
+
+def gaunt(l_1, l_2, l_3, m_1, m_2, m_3, prec=None):
+    r"""
+    Calculate the Gaunt coefficient.
+
+    Explanation
+    ===========
+
+    The Gaunt coefficient is defined as the integral over three
+    spherical harmonics:
+
+    .. math::
+
+        \begin{aligned}
+        \operatorname{Gaunt}(l_1,l_2,l_3,m_1,m_2,m_3)
+        &=\int Y_{l_1,m_1}(\Omega)
+         Y_{l_2,m_2}(\Omega) Y_{l_3,m_3}(\Omega) \,d\Omega \\
+        &=\sqrt{\frac{(2l_1+1)(2l_2+1)(2l_3+1)}{4\pi}}
+         \operatorname{Wigner3j}(l_1,l_2,l_3,0,0,0)
+         \operatorname{Wigner3j}(l_1,l_2,l_3,m_1,m_2,m_3)
+        \end{aligned}
+
+    Parameters
+    ==========
+
+    l_1, l_2, l_3, m_1, m_2, m_3 :
+        Integer.
+    prec - precision, default: ``None``.
+        Providing a precision can
+        drastically speed up the calculation.
+
+    Returns
+    =======
+
+    Rational number times the square root of a rational number
+    (if ``prec=None``), or real number if a precision is given.
+
+    Examples
+    ========
+
+    >>> from sympy.physics.wigner import gaunt
+    >>> gaunt(1,0,1,1,0,-1)
+    -1/(2*sqrt(pi))
+    >>> gaunt(1000,1000,1200,9,3,-12).n(64)
+    0.00689500421922113448...
+
+    It is an error to use non-integer values for `l` and `m`::
+
+        sage: gaunt(1.2,0,1.2,0,0,0)
+        Traceback (most recent call last):
+        ...
+        ValueError: l values must be integer
+        sage: gaunt(1,0,1,1.1,0,-1.1)
+        Traceback (most recent call last):
+        ...
+        ValueError: m values must be integer
+
+    Notes
+    =====
+
+    The Gaunt coefficient obeys the following symmetry rules:
+
+    - invariant under any permutation of the columns
+
+      .. math::
+        \begin{aligned}
+          Y(l_1,l_2,l_3,m_1,m_2,m_3)
+          &=Y(l_3,l_1,l_2,m_3,m_1,m_2) \\
+          &=Y(l_2,l_3,l_1,m_2,m_3,m_1) \\
+          &=Y(l_3,l_2,l_1,m_3,m_2,m_1) \\
+          &=Y(l_1,l_3,l_2,m_1,m_3,m_2) \\
+          &=Y(l_2,l_1,l_3,m_2,m_1,m_3)
+        \end{aligned}
+
+    - invariant under space inflection, i.e.
+
+      .. math::
+          Y(l_1,l_2,l_3,m_1,m_2,m_3)
+          =Y(l_1,l_2,l_3,-m_1,-m_2,-m_3)
+
+    - symmetric with respect to the 72 Regge symmetries as inherited
+      for the `3j` symbols [Regge58]_
+
+    - zero for `l_1`, `l_2`, `l_3` not fulfilling triangle relation
+
+    - zero for violating any one of the conditions: `l_1 \ge |m_1|`,
+      `l_2 \ge |m_2|`, `l_3 \ge |m_3|`
+
+    - non-zero only for an even sum of the `l_i`, i.e.
+      `L = l_1 + l_2 + l_3 = 2n` for `n` in `\mathbb{N}`
+
+    Algorithms
+    ==========
+
+    This function uses the algorithm of [Liberatodebrito82]_ to
+    calculate the value of the Gaunt coefficient exactly. Note that
+    the formula contains alternating sums over large factorials and is
+    therefore unsuitable for finite precision arithmetic and only
+    useful for a computer algebra system [Rasch03]_.
+
+    Authors
+    =======
+
+    Jens Rasch (2009-03-24): initial version for Sage.
+    """
+    l_1, l_2, l_3, m_1, m_2, m_3 = [
+        as_int(i) for i in (l_1, l_2, l_3, m_1, m_2, m_3)]
+
+    if l_1 + l_2 - l_3 < 0:
+        return S.Zero
+    if l_1 - l_2 + l_3 < 0:
+        return S.Zero
+    if -l_1 + l_2 + l_3 < 0:
+        return S.Zero
+    if (m_1 + m_2 + m_3) != 0:
+        return S.Zero
+    if (abs(m_1) > l_1) or (abs(m_2) > l_2) or (abs(m_3) > l_3):
+        return S.Zero
+    bigL, remL = divmod(l_1 + l_2 + l_3, 2)
+    if remL % 2:
+        return S.Zero
+
+    imin = max(-l_3 + l_1 + m_2, -l_3 + l_2 - m_1, 0)
+    imax = min(l_2 + m_2, l_1 - m_1, l_1 + l_2 - l_3)
+
+    _calc_factlist(max(l_1 + l_2 + l_3 + 1, imax + 1))
+
+    ressqrt = sqrt((2 * l_1 + 1) * (2 * l_2 + 1) * (2 * l_3 + 1) * \
+        _Factlist[l_1 - m_1] * _Factlist[l_1 + m_1] * _Factlist[l_2 - m_2] * \
+        _Factlist[l_2 + m_2] * _Factlist[l_3 - m_3] * _Factlist[l_3 + m_3] / \
+        (4*pi))
+
+    prefac = Integer(_Factlist[bigL] * _Factlist[l_2 - l_1 + l_3] *
+                     _Factlist[l_1 - l_2 + l_3] * _Factlist[l_1 + l_2 - l_3])/ \
+        _Factlist[2 * bigL + 1]/ \
+        (_Factlist[bigL - l_1] *
+         _Factlist[bigL - l_2] * _Factlist[bigL - l_3])
+
+    sumres = 0
+    for ii in range(int(imin), int(imax) + 1):
+        den = _Factlist[ii] * _Factlist[ii + l_3 - l_1 - m_2] * \
+            _Factlist[l_2 + m_2 - ii] * _Factlist[l_1 - ii - m_1] * \
+            _Factlist[ii + l_3 - l_2 + m_1] * _Factlist[l_1 + l_2 - l_3 - ii]
+        sumres = sumres + Integer((-1) ** ii) / den
+
+    res = ressqrt * prefac * sumres * Integer((-1) ** (bigL + l_3 + m_1 - m_2))
+    if prec is not None:
+        res = res.n(prec)
+    return res
+
+
+def real_gaunt(l_1, l_2, l_3, m_1, m_2, m_3, prec=None):
+    r"""
+    Calculate the real Gaunt coefficient.
+
+    Explanation
+    ===========
+
+    The real Gaunt coefficient is defined as the integral over three
+    real spherical harmonics:
+
+    .. math::
+        \begin{aligned}
+        \operatorname{RealGaunt}(l_1,l_2,l_3,m_1,m_2,m_3)
+        &=\int Z^{m_1}_{l_1}(\Omega)
+         Z^{m_2}_{l_2}(\Omega) Z^{m_3}_{l_3}(\Omega) \,d\Omega \\
+        \end{aligned}
+
+    Alternatively, it can be defined in terms of the standard Gaunt
+    coefficient by relating the real spherical harmonics to the standard
+    spherical harmonics via a unitary transformation `U`, i.e.
+    `Z^{m}_{l}(\Omega)=\sum_{m'}U^{m}_{m'}Y^{m'}_{l}(\Omega)` [Homeier96]_.
+    The real Gaunt coefficient is then defined as
+
+    .. math::
+        \begin{aligned}
+        \operatorname{RealGaunt}(l_1,l_2,l_3,m_1,m_2,m_3)
+        &=\int Z^{m_1}_{l_1}(\Omega)
+         Z^{m_2}_{l_2}(\Omega) Z^{m_3}_{l_3}(\Omega) \,d\Omega \\
+        &=\sum_{m'_1 m'_2 m'_3} U^{m_1}_{m'_1}U^{m_2}_{m'_2}U^{m_3}_{m'_3}
+         \operatorname{Gaunt}(l_1,l_2,l_3,m'_1,m'_2,m'_3)
+        \end{aligned}
+
+    The unitary matrix `U` has components
+
+    .. math::
+        \begin{aligned}
+        U^m_{m'} = \delta_{|m||m'|}*(\delta_{m'0}\delta_{m0} + \frac{1}{\sqrt{2}}\big[\Theta(m)
+        \big(\delta_{m'm}+(-1)^{m'}\delta_{m'-m}\big)+i\Theta(-m)\big((-1)^{-m}
+        \delta_{m'-m}-\delta_{m'm}*(-1)^{m'-m}\big)\big])
+        \end{aligned}
+
+    where `\delta_{ij}` is the Kronecker delta symbol and `\Theta` is a step
+    function defined as
+
+    .. math::
+        \begin{aligned}
+        \Theta(x) = \begin{cases} 1 \,\text{for}\, x > 0 \\ 0 \,\text{for}\, x \leq 0 \end{cases}
+        \end{aligned}
+
+    Parameters
+    ==========
+
+    l_1, l_2, l_3, m_1, m_2, m_3 :
+        Integer.
+
+    prec - precision, default: ``None``.
+        Providing a precision can
+        drastically speed up the calculation.
+
+    Returns
+    =======
+
+    Rational number times the square root of a rational number.
+
+    Examples
+    ========
+
+    >>> from sympy.physics.wigner import real_gaunt
+    >>> real_gaunt(2,2,4,-1,-1,0)
+    -2/(7*sqrt(pi))
+    >>> real_gaunt(10,10,20,-9,-9,0).n(64)
+    -0.00002480019791932209313156167...
+
+    It is an error to use non-integer values for `l` and `m`::
+        real_gaunt(2.8,0.5,1.3,0,0,0)
+        Traceback (most recent call last):
+        ...
+        ValueError: l values must be integer
+        real_gaunt(2,2,4,0.7,1,-3.4)
+        Traceback (most recent call last):
+        ...
+        ValueError: m values must be integer
+
+    Notes
+    =====
+
+    The real Gaunt coefficient inherits from the standard Gaunt coefficient,
+    the invariance under any permutation of the pairs `(l_i, m_i)` and the
+    requirement that the sum of the `l_i` be even to yield a non-zero value.
+    It also obeys the following symmetry rules:
+
+    - zero for `l_1`, `l_2`, `l_3` not fulfiling the condition
+      `l_1 \in \{l_{\text{max}}, l_{\text{max}}-2, \ldots, l_{\text{min}}\}`,
+      where `l_{\text{max}} = l_2+l_3`,
+
+      .. math::
+          \begin{aligned}
+          l_{\text{min}} = \begin{cases} \kappa(l_2, l_3, m_2, m_3) & \text{if}\,
+          \kappa(l_2, l_3, m_2, m_3) + l_{\text{max}}\, \text{is even} \\
+          \kappa(l_2, l_3, m_2, m_3)+1 & \text{if}\, \kappa(l_2, l_3, m_2, m_3) +
+          l_{\text{max}}\, \text{is odd}\end{cases}
+          \end{aligned}
+
+      and `\kappa(l_2, l_3, m_2, m_3) = \max{\big(|l_2-l_3|, \min{\big(|m_2+m_3|,
+      |m_2-m_3|\big)}\big)}`
+
+    - zero for an odd number of negative `m_i`
+
+    Algorithms
+    ==========
+
+    This function uses the algorithms of [Homeier96]_ and [Rasch03]_ to
+    calculate the value of the real Gaunt coefficient exactly. Note that
+    the formula used in [Rasch03]_ contains alternating sums over large
+    factorials and is therefore unsuitable for finite precision arithmetic
+    and only useful for a computer algebra system [Rasch03]_. However, this
+    function can in principle use any algorithm that computes the Gaunt
+    coefficient, so it is suitable for finite precision arithmetic in so far
+    as the algorithm which computes the Gaunt coefficient is.
+    """
+    l_1, l_2, l_3, m_1, m_2, m_3 = [
+        as_int(i) for i in (l_1, l_2, l_3, m_1, m_2, m_3)]
+
+    # check for quick exits
+    if sum(1 for i in (m_1, m_2, m_3) if i < 0) % 2:
+        return S.Zero  # odd number of negative m
+    if (l_1 + l_2 + l_3) % 2:
+        return S.Zero  # sum of l is odd
+    lmax = l_2 + l_3
+    lmin = max(abs(l_2 - l_3), min(abs(m_2 + m_3), abs(m_2 - m_3)))
+    if (lmin + lmax) % 2:
+        lmin += 1
+    if lmin not in range(lmax, lmin - 2, -2):
+        return S.Zero
+
+    kron_del = lambda i, j: 1 if i == j else 0
+    s = lambda e: -1 if e % 2 else 1  #  (-1)**e to give +/-1, avoiding float when e<0
+    A = lambda a, b: (-kron_del(a, b)*s(a-b) + kron_del(a, -b)*
+                      s(b)) if b < 0 else 0
+    B = lambda a, b: (kron_del(a, b) + kron_del(a, -b)*s(a)) if b > 0 else 0
+    C = lambda a, b: kron_del(abs(a), abs(b))*(kron_del(a, 0)*kron_del(b, 0) +
+                                          (B(a, b) + I*A(a, b))/sqrt(2))
+    ugnt = 0
+    for i in range(-l_1, l_1+1):
+        U1 = C(i, m_1)
+        for j in range(-l_2, l_2+1):
+            U2 = C(j, m_2)
+            U3 = C(-i-j, m_3)
+            ugnt = ugnt + re(U1*U2*U3)*gaunt(l_1, l_2, l_3, i, j, -i-j)
+
+    if prec is not None:
+        ugnt = ugnt.n(prec)
+    return ugnt
+
+
+class Wigner3j(Function):
+
+    def doit(self, **hints):
+        if all(obj.is_number for obj in self.args):
+            return wigner_3j(*self.args)
+        else:
+            return self
+
+def dot_rot_grad_Ynm(j, p, l, m, theta, phi):
+    r"""
+    Returns dot product of rotational gradients of spherical harmonics.
+
+    Explanation
+    ===========
+
+    This function returns the right hand side of the following expression:
+
+    .. math ::
+        \vec{R}Y{_j^{p}} \cdot \vec{R}Y{_l^{m}} = (-1)^{m+p}
+        \sum\limits_{k=|l-j|}^{l+j}Y{_k^{m+p}}  * \alpha_{l,m,j,p,k} *
+        \frac{1}{2} (k^2-j^2-l^2+k-j-l)
+
+
+    Arguments
+    =========
+
+    j, p, l, m .... indices in spherical harmonics (expressions or integers)
+    theta, phi .... angle arguments in spherical harmonics
+
+    Example
+    =======
+
+    >>> from sympy import symbols
+    >>> from sympy.physics.wigner import dot_rot_grad_Ynm
+    >>> theta, phi = symbols("theta phi")
+    >>> dot_rot_grad_Ynm(3, 2, 2, 0, theta, phi).doit()
+    3*sqrt(55)*Ynm(5, 2, theta, phi)/(11*sqrt(pi))
+
+    """
+    j = sympify(j)
+    p = sympify(p)
+    l = sympify(l)
+    m = sympify(m)
+    theta = sympify(theta)
+    phi = sympify(phi)
+    k = Dummy("k")
+
+    def alpha(l,m,j,p,k):
+        return sqrt((2*l+1)*(2*j+1)*(2*k+1)/(4*pi)) * \
+                Wigner3j(j, l, k, S.Zero, S.Zero, S.Zero) * \
+                Wigner3j(j, l, k, p, m, -m-p)
+
+    return (S.NegativeOne)**(m+p) * Sum(Ynm(k, m+p, theta, phi) * alpha(l,m,j,p,k) / 2 \
+        *(k**2-j**2-l**2+k-j-l), (k, abs(l-j), l+j))
+
+
+def wigner_d_small(J, beta):
+    """Return the small Wigner d matrix for angular momentum J.
+
+    Explanation
+    ===========
+
+    J : An integer, half-integer, or SymPy symbol for the total angular
+        momentum of the angular momentum space being rotated.
+    beta : A real number representing the Euler angle of rotation about
+        the so-called line of nodes. See [Edmonds74]_.
+
+    Returns
+    =======
+
+    A matrix representing the corresponding Euler angle rotation( in the basis
+    of eigenvectors of `J_z`).
+
+    .. math ::
+        \\mathcal{d}_{\\beta} = \\exp\\big( \\frac{i\\beta}{\\hbar} J_y\\big)
+
+    The components are calculated using the general form [Edmonds74]_,
+    equation 4.1.15.
+
+    Examples
+    ========
+
+    >>> from sympy import Integer, symbols, pi, pprint
+    >>> from sympy.physics.wigner import wigner_d_small
+    >>> half = 1/Integer(2)
+    >>> beta = symbols("beta", real=True)
+    >>> pprint(wigner_d_small(half, beta), use_unicode=True)
+    ⎡   ⎛β⎞      ⎛β⎞⎤
+    ⎢cos⎜─⎟   sin⎜─⎟⎥
+    ⎢   ⎝2⎠      ⎝2⎠⎥
+    ⎢               ⎥
+    ⎢    ⎛β⎞     ⎛β⎞⎥
+    ⎢-sin⎜─⎟  cos⎜─⎟⎥
+    ⎣    ⎝2⎠     ⎝2⎠⎦
+
+    >>> pprint(wigner_d_small(2*half, beta), use_unicode=True)
+    ⎡        2⎛β⎞              ⎛β⎞    ⎛β⎞           2⎛β⎞     ⎤
+    ⎢     cos ⎜─⎟        √2⋅sin⎜─⎟⋅cos⎜─⎟        sin ⎜─⎟     ⎥
+    ⎢         ⎝2⎠              ⎝2⎠    ⎝2⎠            ⎝2⎠     ⎥
+    ⎢                                                        ⎥
+    ⎢       ⎛β⎞    ⎛β⎞       2⎛β⎞      2⎛β⎞        ⎛β⎞    ⎛β⎞⎥
+    ⎢-√2⋅sin⎜─⎟⋅cos⎜─⎟  - sin ⎜─⎟ + cos ⎜─⎟  √2⋅sin⎜─⎟⋅cos⎜─⎟⎥
+    ⎢       ⎝2⎠    ⎝2⎠        ⎝2⎠       ⎝2⎠        ⎝2⎠    ⎝2⎠⎥
+    ⎢                                                        ⎥
+    ⎢        2⎛β⎞               ⎛β⎞    ⎛β⎞          2⎛β⎞     ⎥
+    ⎢     sin ⎜─⎟        -√2⋅sin⎜─⎟⋅cos⎜─⎟       cos ⎜─⎟     ⎥
+    ⎣         ⎝2⎠               ⎝2⎠    ⎝2⎠           ⎝2⎠     ⎦
+
+    From table 4 in [Edmonds74]_
+
+    >>> pprint(wigner_d_small(half, beta).subs({beta:pi/2}), use_unicode=True)
+    ⎡ √2   √2⎤
+    ⎢ ──   ──⎥
+    ⎢ 2    2 ⎥
+    ⎢        ⎥
+    ⎢-√2   √2⎥
+    ⎢────  ──⎥
+    ⎣ 2    2 ⎦
+
+    >>> pprint(wigner_d_small(2*half, beta).subs({beta:pi/2}),
+    ... use_unicode=True)
+    ⎡       √2      ⎤
+    ⎢1/2    ──   1/2⎥
+    ⎢       2       ⎥
+    ⎢               ⎥
+    ⎢-√2         √2 ⎥
+    ⎢────   0    ── ⎥
+    ⎢ 2          2  ⎥
+    ⎢               ⎥
+    ⎢      -√2      ⎥
+    ⎢1/2   ────  1/2⎥
+    ⎣       2       ⎦
+
+    >>> pprint(wigner_d_small(3*half, beta).subs({beta:pi/2}),
+    ... use_unicode=True)
+    ⎡ √2    √6    √6   √2⎤
+    ⎢ ──    ──    ──   ──⎥
+    ⎢ 4     4     4    4 ⎥
+    ⎢                    ⎥
+    ⎢-√6   -√2    √2   √6⎥
+    ⎢────  ────   ──   ──⎥
+    ⎢ 4     4     4    4 ⎥
+    ⎢                    ⎥
+    ⎢ √6   -√2   -√2   √6⎥
+    ⎢ ──   ────  ────  ──⎥
+    ⎢ 4     4     4    4 ⎥
+    ⎢                    ⎥
+    ⎢-√2    √6   -√6   √2⎥
+    ⎢────   ──   ────  ──⎥
+    ⎣ 4     4     4    4 ⎦
+
+    >>> pprint(wigner_d_small(4*half, beta).subs({beta:pi/2}),
+    ... use_unicode=True)
+    ⎡             √6            ⎤
+    ⎢1/4   1/2    ──   1/2   1/4⎥
+    ⎢             4             ⎥
+    ⎢                           ⎥
+    ⎢-1/2  -1/2   0    1/2   1/2⎥
+    ⎢                           ⎥
+    ⎢ √6                     √6 ⎥
+    ⎢ ──    0    -1/2   0    ── ⎥
+    ⎢ 4                      4  ⎥
+    ⎢                           ⎥
+    ⎢-1/2  1/2    0    -1/2  1/2⎥
+    ⎢                           ⎥
+    ⎢             √6            ⎥
+    ⎢1/4   -1/2   ──   -1/2  1/4⎥
+    ⎣             4             ⎦
+
+    """
+    M = [J-i for i in range(2*J+1)]
+    d = zeros(2*J+1)
+    for i, Mi in enumerate(M):
+        for j, Mj in enumerate(M):
+
+            # We get the maximum and minimum value of sigma.
+            sigmamax = max([-Mi-Mj, J-Mj])
+            sigmamin = min([0, J-Mi])
+
+            dij = sqrt(factorial(J+Mi)*factorial(J-Mi) /
+                       factorial(J+Mj)/factorial(J-Mj))
+            terms = [(-1)**(J-Mi-s) *
+                     binomial(J+Mj, J-Mi-s) *
+                     binomial(J-Mj, s) *
+                     cos(beta/2)**(2*s+Mi+Mj) *
+                     sin(beta/2)**(2*J-2*s-Mj-Mi)
+                     for s in range(sigmamin, sigmamax+1)]
+
+            d[i, j] = dij*Add(*terms)
+
+    return ImmutableMatrix(d)
+
+
+def wigner_d(J, alpha, beta, gamma):
+    """Return the Wigner D matrix for angular momentum J.
+
+    Explanation
+    ===========
+
+    J :
+        An integer, half-integer, or SymPy symbol for the total angular
+        momentum of the angular momentum space being rotated.
+    alpha, beta, gamma - Real numbers representing the Euler.
+        Angles of rotation about the so-called vertical, line of nodes, and
+        figure axes. See [Edmonds74]_.
+
+    Returns
+    =======
+
+    A matrix representing the corresponding Euler angle rotation( in the basis
+    of eigenvectors of `J_z`).
+
+    .. math ::
+        \\mathcal{D}_{\\alpha \\beta \\gamma} =
+        \\exp\\big( \\frac{i\\alpha}{\\hbar} J_z\\big)
+        \\exp\\big( \\frac{i\\beta}{\\hbar} J_y\\big)
+        \\exp\\big( \\frac{i\\gamma}{\\hbar} J_z\\big)
+
+    The components are calculated using the general form [Edmonds74]_,
+    equation 4.1.12.
+
+    Examples
+    ========
+
+    The simplest possible example:
+
+    >>> from sympy.physics.wigner import wigner_d
+    >>> from sympy import Integer, symbols, pprint
+    >>> half = 1/Integer(2)
+    >>> alpha, beta, gamma = symbols("alpha, beta, gamma", real=True)
+    >>> pprint(wigner_d(half, alpha, beta, gamma), use_unicode=True)
+    ⎡  ⅈ⋅α  ⅈ⋅γ             ⅈ⋅α  -ⅈ⋅γ         ⎤
+    ⎢  ───  ───             ───  ─────        ⎥
+    ⎢   2    2     ⎛β⎞       2     2      ⎛β⎞ ⎥
+    ⎢ ℯ   ⋅ℯ   ⋅cos⎜─⎟     ℯ   ⋅ℯ     ⋅sin⎜─⎟ ⎥
+    ⎢              ⎝2⎠                    ⎝2⎠ ⎥
+    ⎢                                         ⎥
+    ⎢  -ⅈ⋅α   ⅈ⋅γ          -ⅈ⋅α   -ⅈ⋅γ        ⎥
+    ⎢  ─────  ───          ─────  ─────       ⎥
+    ⎢    2     2     ⎛β⎞     2      2      ⎛β⎞⎥
+    ⎢-ℯ     ⋅ℯ   ⋅sin⎜─⎟  ℯ     ⋅ℯ     ⋅cos⎜─⎟⎥
+    ⎣                ⎝2⎠                   ⎝2⎠⎦
+
+    """
+    d = wigner_d_small(J, beta)
+    M = [J-i for i in range(2*J+1)]
+    D = [[exp(I*Mi*alpha)*d[i, j]*exp(I*Mj*gamma)
+          for j, Mj in enumerate(M)] for i, Mi in enumerate(M)]
+    return ImmutableMatrix(D)