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ckpts/universal/global_step80/zero/17.attention.query_key_value.weight/exp_avg.pt

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ckpts/universal/global_step80/zero/17.attention.query_key_value.weight/fp32.pt

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ckpts/universal/global_step80/zero/25.mlp.dense_4h_to_h.weight/exp_avg.pt

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ckpts/universal/global_step80/zero/25.mlp.dense_4h_to_h.weight/fp32.pt

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ckpts/universal/global_step80/zero/4.post_attention_layernorm.weight/exp_avg.pt

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ckpts/universal/global_step80/zero/4.post_attention_layernorm.weight/exp_avg_sq.pt

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ckpts/universal/global_step80/zero/4.post_attention_layernorm.weight/fp32.pt

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venv/lib/python3.10/site-packages/sympy/printing/__init__.py

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+"""Printing subsystem"""
+
+from .pretty import pager_print, pretty, pretty_print, pprint, pprint_use_unicode, pprint_try_use_unicode
+
+from .latex import latex, print_latex, multiline_latex
+
+from .mathml import mathml, print_mathml
+
+from .python import python, print_python
+
+from .pycode import pycode
+
+from .codeprinter import print_ccode, print_fcode
+
+from .codeprinter import ccode, fcode, cxxcode # noqa:F811
+
+from .smtlib import smtlib_code
+
+from .glsl import glsl_code, print_glsl
+
+from .rcode import rcode, print_rcode
+
+from .jscode import jscode, print_jscode
+
+from .julia import julia_code
+
+from .mathematica import mathematica_code
+
+from .octave import octave_code
+
+from .rust import rust_code
+
+from .gtk import print_gtk
+
+from .preview import preview
+
+from .repr import srepr
+
+from .tree import print_tree
+
+from .str import StrPrinter, sstr, sstrrepr
+
+from .tableform import TableForm
+
+from .dot import dotprint
+
+from .maple import maple_code, print_maple_code
+
+__all__ = [
+    # sympy.printing.pretty
+    'pager_print', 'pretty', 'pretty_print', 'pprint', 'pprint_use_unicode',
+    'pprint_try_use_unicode',
+
+    # sympy.printing.latex
+    'latex', 'print_latex', 'multiline_latex',
+
+    # sympy.printing.mathml
+    'mathml', 'print_mathml',
+
+    # sympy.printing.python
+    'python', 'print_python',
+
+    # sympy.printing.pycode
+    'pycode',
+
+    # sympy.printing.codeprinter
+    'ccode', 'print_ccode', 'cxxcode', 'fcode', 'print_fcode',
+
+    # sympy.printing.smtlib
+    'smtlib_code',
+
+    # sympy.printing.glsl
+    'glsl_code', 'print_glsl',
+
+    # sympy.printing.rcode
+    'rcode', 'print_rcode',
+
+    # sympy.printing.jscode
+    'jscode', 'print_jscode',
+
+    # sympy.printing.julia
+    'julia_code',
+
+    # sympy.printing.mathematica
+    'mathematica_code',
+
+    # sympy.printing.octave
+    'octave_code',
+
+    # sympy.printing.rust
+    'rust_code',
+
+    # sympy.printing.gtk
+    'print_gtk',
+
+    # sympy.printing.preview
+    'preview',
+
+    # sympy.printing.repr
+    'srepr',
+
+    # sympy.printing.tree
+    'print_tree',
+
+    # sympy.printing.str
+    'StrPrinter', 'sstr', 'sstrrepr',
+
+    # sympy.printing.tableform
+    'TableForm',
+
+    # sympy.printing.dot
+    'dotprint',
+
+    # sympy.printing.maple
+    'maple_code', 'print_maple_code',
+]

venv/lib/python3.10/site-packages/sympy/printing/aesaracode.py

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+from __future__ import annotations
+from typing import Any
+
+from sympy.external import import_module
+from sympy.printing.printer import Printer
+from sympy.utilities.iterables import is_sequence
+import sympy
+from functools import partial
+
+
+aesara = import_module('aesara')
+
+if aesara:
+    aes = aesara.scalar
+    aet = aesara.tensor
+    from aesara.tensor import nlinalg
+    from aesara.tensor.elemwise import Elemwise
+    from aesara.tensor.elemwise import DimShuffle
+
+    # `true_divide` replaced `true_div` in Aesara 2.8.11 (released 2023) to
+    # match NumPy
+    # XXX: Remove this when not needed to support older versions.
+    true_divide = getattr(aet, 'true_divide', None)
+    if true_divide is None:
+        true_divide = aet.true_div
+
+    mapping = {
+            sympy.Add: aet.add,
+            sympy.Mul: aet.mul,
+            sympy.Abs: aet.abs,
+            sympy.sign: aet.sgn,
+            sympy.ceiling: aet.ceil,
+            sympy.floor: aet.floor,
+            sympy.log: aet.log,
+            sympy.exp: aet.exp,
+            sympy.sqrt: aet.sqrt,
+            sympy.cos: aet.cos,
+            sympy.acos: aet.arccos,
+            sympy.sin: aet.sin,
+            sympy.asin: aet.arcsin,
+            sympy.tan: aet.tan,
+            sympy.atan: aet.arctan,
+            sympy.atan2: aet.arctan2,
+            sympy.cosh: aet.cosh,
+            sympy.acosh: aet.arccosh,
+            sympy.sinh: aet.sinh,
+            sympy.asinh: aet.arcsinh,
+            sympy.tanh: aet.tanh,
+            sympy.atanh: aet.arctanh,
+            sympy.re: aet.real,
+            sympy.im: aet.imag,
+            sympy.arg: aet.angle,
+            sympy.erf: aet.erf,
+            sympy.gamma: aet.gamma,
+            sympy.loggamma: aet.gammaln,
+            sympy.Pow: aet.pow,
+            sympy.Eq: aet.eq,
+            sympy.StrictGreaterThan: aet.gt,
+            sympy.StrictLessThan: aet.lt,
+            sympy.LessThan: aet.le,
+            sympy.GreaterThan: aet.ge,
+            sympy.And: aet.bitwise_and,  # bitwise
+            sympy.Or: aet.bitwise_or,  # bitwise
+            sympy.Not: aet.invert,  # bitwise
+            sympy.Xor: aet.bitwise_xor,  # bitwise
+            sympy.Max: aet.maximum,  # Sympy accept >2 inputs, Aesara only 2
+            sympy.Min: aet.minimum,  # Sympy accept >2 inputs, Aesara only 2
+            sympy.conjugate: aet.conj,
+            sympy.core.numbers.ImaginaryUnit: lambda:aet.complex(0,1),
+            # Matrices
+            sympy.MatAdd: Elemwise(aes.add),
+            sympy.HadamardProduct: Elemwise(aes.mul),
+            sympy.Trace: nlinalg.trace,
+            sympy.Determinant : nlinalg.det,
+            sympy.Inverse: nlinalg.matrix_inverse,
+            sympy.Transpose: DimShuffle((False, False), [1, 0]),
+    }
+
+
+class AesaraPrinter(Printer):
+    """ Code printer which creates Aesara symbolic expression graphs.
+
+    Parameters
+    ==========
+
+    cache : dict
+        Cache dictionary to use. If None (default) will use
+        the global cache. To create a printer which does not depend on or alter
+        global state pass an empty dictionary. Note: the dictionary is not
+        copied on initialization of the printer and will be updated in-place,
+        so using the same dict object when creating multiple printers or making
+        multiple calls to :func:`.aesara_code` or :func:`.aesara_function` means
+        the cache is shared between all these applications.
+
+    Attributes
+    ==========
+
+    cache : dict
+        A cache of Aesara variables which have been created for SymPy
+        symbol-like objects (e.g. :class:`sympy.core.symbol.Symbol` or
+        :class:`sympy.matrices.expressions.MatrixSymbol`). This is used to
+        ensure that all references to a given symbol in an expression (or
+        multiple expressions) are printed as the same Aesara variable, which is
+        created only once. Symbols are differentiated only by name and type. The
+        format of the cache's contents should be considered opaque to the user.
+    """
+    printmethod = "_aesara"
+
+    def __init__(self, *args, **kwargs):
+        self.cache = kwargs.pop('cache', {})
+        super().__init__(*args, **kwargs)
+
+    def _get_key(self, s, name=None, dtype=None, broadcastable=None):
+        """ Get the cache key for a SymPy object.
+
+        Parameters
+        ==========
+
+        s : sympy.core.basic.Basic
+            SymPy object to get key for.
+
+        name : str
+            Name of object, if it does not have a ``name`` attribute.
+        """
+
+        if name is None:
+            name = s.name
+
+        return (name, type(s), s.args, dtype, broadcastable)
+
+    def _get_or_create(self, s, name=None, dtype=None, broadcastable=None):
+        """
+        Get the Aesara variable for a SymPy symbol from the cache, or create it
+        if it does not exist.
+        """
+
+        # Defaults
+        if name is None:
+            name = s.name
+        if dtype is None:
+            dtype = 'floatX'
+        if broadcastable is None:
+            broadcastable = ()
+
+        key = self._get_key(s, name, dtype=dtype, broadcastable=broadcastable)
+
+        if key in self.cache:
+            return self.cache[key]
+
+        value = aet.tensor(name=name, dtype=dtype, broadcastable=broadcastable)
+        self.cache[key] = value
+        return value
+
+    def _print_Symbol(self, s, **kwargs):
+        dtype = kwargs.get('dtypes', {}).get(s)
+        bc = kwargs.get('broadcastables', {}).get(s)
+        return self._get_or_create(s, dtype=dtype, broadcastable=bc)
+
+    def _print_AppliedUndef(self, s, **kwargs):
+        name = str(type(s)) + '_' + str(s.args[0])
+        dtype = kwargs.get('dtypes', {}).get(s)
+        bc = kwargs.get('broadcastables', {}).get(s)
+        return self._get_or_create(s, name=name, dtype=dtype, broadcastable=bc)
+
+    def _print_Basic(self, expr, **kwargs):
+        op = mapping[type(expr)]
+        children = [self._print(arg, **kwargs) for arg in expr.args]
+        return op(*children)
+
+    def _print_Number(self, n, **kwargs):
+        # Integers already taken care of below, interpret as float
+        return float(n.evalf())
+
+    def _print_MatrixSymbol(self, X, **kwargs):
+        dtype = kwargs.get('dtypes', {}).get(X)
+        return self._get_or_create(X, dtype=dtype, broadcastable=(None, None))
+
+    def _print_DenseMatrix(self, X, **kwargs):
+        if not hasattr(aet, 'stacklists'):
+            raise NotImplementedError(
+               "Matrix translation not yet supported in this version of Aesara")
+
+        return aet.stacklists([
+            [self._print(arg, **kwargs) for arg in L]
+            for L in X.tolist()
+        ])
+
+    _print_ImmutableMatrix = _print_ImmutableDenseMatrix = _print_DenseMatrix
+
+    def _print_MatMul(self, expr, **kwargs):
+        children = [self._print(arg, **kwargs) for arg in expr.args]
+        result = children[0]
+        for child in children[1:]:
+            result = aet.dot(result, child)
+        return result
+
+    def _print_MatPow(self, expr, **kwargs):
+        children = [self._print(arg, **kwargs) for arg in expr.args]
+        result = 1
+        if isinstance(children[1], int) and children[1] > 0:
+            for i in range(children[1]):
+                result = aet.dot(result, children[0])
+        else:
+            raise NotImplementedError('''Only non-negative integer
+           powers of matrices can be handled by Aesara at the moment''')
+        return result
+
+    def _print_MatrixSlice(self, expr, **kwargs):
+        parent = self._print(expr.parent, **kwargs)
+        rowslice = self._print(slice(*expr.rowslice), **kwargs)
+        colslice = self._print(slice(*expr.colslice), **kwargs)
+        return parent[rowslice, colslice]
+
+    def _print_BlockMatrix(self, expr, **kwargs):
+        nrows, ncols = expr.blocks.shape
+        blocks = [[self._print(expr.blocks[r, c], **kwargs)
+                        for c in range(ncols)]
+                        for r in range(nrows)]
+        return aet.join(0, *[aet.join(1, *row) for row in blocks])
+
+
+    def _print_slice(self, expr, **kwargs):
+        return slice(*[self._print(i, **kwargs)
+                        if isinstance(i, sympy.Basic) else i
+                        for i in (expr.start, expr.stop, expr.step)])
+
+    def _print_Pi(self, expr, **kwargs):
+        return 3.141592653589793
+
+    def _print_Piecewise(self, expr, **kwargs):
+        import numpy as np
+        e, cond = expr.args[0].args  # First condition and corresponding value
+
+        # Print conditional expression and value for first condition
+        p_cond = self._print(cond, **kwargs)
+        p_e = self._print(e, **kwargs)
+
+        # One condition only
+        if len(expr.args) == 1:
+            # Return value if condition else NaN
+            return aet.switch(p_cond, p_e, np.nan)
+
+        # Return value_1 if condition_1 else evaluate remaining conditions
+        p_remaining = self._print(sympy.Piecewise(*expr.args[1:]), **kwargs)
+        return aet.switch(p_cond, p_e, p_remaining)
+
+    def _print_Rational(self, expr, **kwargs):
+        return true_divide(self._print(expr.p, **kwargs),
+                           self._print(expr.q, **kwargs))
+
+    def _print_Integer(self, expr, **kwargs):
+        return expr.p
+
+    def _print_factorial(self, expr, **kwargs):
+        return self._print(sympy.gamma(expr.args[0] + 1), **kwargs)
+
+    def _print_Derivative(self, deriv, **kwargs):
+        from aesara.gradient import Rop
+
+        rv = self._print(deriv.expr, **kwargs)
+        for var in deriv.variables:
+            var = self._print(var, **kwargs)
+            rv = Rop(rv, var, aet.ones_like(var))
+        return rv
+
+    def emptyPrinter(self, expr):
+        return expr
+
+    def doprint(self, expr, dtypes=None, broadcastables=None):
+        """ Convert a SymPy expression to a Aesara graph variable.
+
+        The ``dtypes`` and ``broadcastables`` arguments are used to specify the
+        data type, dimension, and broadcasting behavior of the Aesara variables
+        corresponding to the free symbols in ``expr``. Each is a mapping from
+        SymPy symbols to the value of the corresponding argument to
+        ``aesara.tensor.var.TensorVariable``.
+
+        See the corresponding `documentation page`__ for more information on
+        broadcasting in Aesara.
+
+        .. __: https://aesara.readthedocs.io/en/latest/tutorial/broadcasting.html
+
+        Parameters
+        ==========
+
+        expr : sympy.core.expr.Expr
+            SymPy expression to print.
+
+        dtypes : dict
+            Mapping from SymPy symbols to Aesara datatypes to use when creating
+            new Aesara variables for those symbols. Corresponds to the ``dtype``
+            argument to ``aesara.tensor.var.TensorVariable``. Defaults to ``'floatX'``
+            for symbols not included in the mapping.
+
+        broadcastables : dict
+            Mapping from SymPy symbols to the value of the ``broadcastable``
+            argument to ``aesara.tensor.var.TensorVariable`` to use when creating Aesara
+            variables for those symbols. Defaults to the empty tuple for symbols
+            not included in the mapping (resulting in a scalar).
+
+        Returns
+        =======
+
+        aesara.graph.basic.Variable
+            A variable corresponding to the expression's value in a Aesara
+            symbolic expression graph.
+
+        """
+        if dtypes is None:
+            dtypes = {}
+        if broadcastables is None:
+            broadcastables = {}
+
+        return self._print(expr, dtypes=dtypes, broadcastables=broadcastables)
+
+
+global_cache: dict[Any, Any] = {}
+
+
+def aesara_code(expr, cache=None, **kwargs):
+    """
+    Convert a SymPy expression into a Aesara graph variable.
+
+    Parameters
+    ==========
+
+    expr : sympy.core.expr.Expr
+        SymPy expression object to convert.
+
+    cache : dict
+        Cached Aesara variables (see :class:`AesaraPrinter.cache
+        <AesaraPrinter>`). Defaults to the module-level global cache.
+
+    dtypes : dict
+        Passed to :meth:`.AesaraPrinter.doprint`.
+
+    broadcastables : dict
+        Passed to :meth:`.AesaraPrinter.doprint`.
+
+    Returns
+    =======
+
+    aesara.graph.basic.Variable
+        A variable corresponding to the expression's value in a Aesara symbolic
+        expression graph.
+
+    """
+    if not aesara:
+        raise ImportError("aesara is required for aesara_code")
+
+    if cache is None:
+        cache = global_cache
+
+    return AesaraPrinter(cache=cache, settings={}).doprint(expr, **kwargs)
+
+
+def dim_handling(inputs, dim=None, dims=None, broadcastables=None):
+    r"""
+    Get value of ``broadcastables`` argument to :func:`.aesara_code` from
+    keyword arguments to :func:`.aesara_function`.
+
+    Included for backwards compatibility.
+
+    Parameters
+    ==========
+
+    inputs
+        Sequence of input symbols.
+
+    dim : int
+        Common number of dimensions for all inputs. Overrides other arguments
+        if given.
+
+    dims : dict
+        Mapping from input symbols to number of dimensions. Overrides
+        ``broadcastables`` argument if given.
+
+    broadcastables : dict
+        Explicit value of ``broadcastables`` argument to
+        :meth:`.AesaraPrinter.doprint`. If not None function will return this value unchanged.
+
+    Returns
+    =======
+    dict
+        Dictionary mapping elements of ``inputs`` to their "broadcastable"
+        values (tuple of ``bool``\ s).
+    """
+    if dim is not None:
+        return {s: (False,) * dim for s in inputs}
+
+    if dims is not None:
+        maxdim = max(dims.values())
+        return {
+            s: (False,) * d + (True,) * (maxdim - d)
+            for s, d in dims.items()
+        }
+
+    if broadcastables is not None:
+        return broadcastables
+
+    return {}
+
+
+def aesara_function(inputs, outputs, scalar=False, *,
+        dim=None, dims=None, broadcastables=None, **kwargs):
+    """
+    Create a Aesara function from SymPy expressions.
+
+    The inputs and outputs are converted to Aesara variables using
+    :func:`.aesara_code` and then passed to ``aesara.function``.
+
+    Parameters
+    ==========
+
+    inputs
+        Sequence of symbols which constitute the inputs of the function.
+
+    outputs
+        Sequence of expressions which constitute the outputs(s) of the
+        function. The free symbols of each expression must be a subset of
+        ``inputs``.
+
+    scalar : bool
+        Convert 0-dimensional arrays in output to scalars. This will return a
+        Python wrapper function around the Aesara function object.
+
+    cache : dict
+        Cached Aesara variables (see :class:`AesaraPrinter.cache
+        <AesaraPrinter>`). Defaults to the module-level global cache.
+
+    dtypes : dict
+        Passed to :meth:`.AesaraPrinter.doprint`.
+
+    broadcastables : dict
+        Passed to :meth:`.AesaraPrinter.doprint`.
+
+    dims : dict
+        Alternative to ``broadcastables`` argument. Mapping from elements of
+        ``inputs`` to integers indicating the dimension of their associated
+        arrays/tensors. Overrides ``broadcastables`` argument if given.
+
+    dim : int
+        Another alternative to the ``broadcastables`` argument. Common number of
+        dimensions to use for all arrays/tensors.
+        ``aesara_function([x, y], [...], dim=2)`` is equivalent to using
+        ``broadcastables={x: (False, False), y: (False, False)}``.
+
+    Returns
+    =======
+    callable
+        A callable object which takes values of ``inputs`` as positional
+        arguments and returns an output array for each of the expressions
+        in ``outputs``. If ``outputs`` is a single expression the function will
+        return a Numpy array, if it is a list of multiple expressions the
+        function will return a list of arrays. See description of the ``squeeze``
+        argument above for the behavior when a single output is passed in a list.
+        The returned object will either be an instance of
+        ``aesara.compile.function.types.Function`` or a Python wrapper
+        function around one. In both cases, the returned value will have a
+        ``aesara_function`` attribute which points to the return value of
+        ``aesara.function``.
+
+    Examples
+    ========
+
+    >>> from sympy.abc import x, y, z
+    >>> from sympy.printing.aesaracode import aesara_function
+
+    A simple function with one input and one output:
+
+    >>> f1 = aesara_function([x], [x**2 - 1], scalar=True)
+    >>> f1(3)
+    8.0
+
+    A function with multiple inputs and one output:
+
+    >>> f2 = aesara_function([x, y, z], [(x**z + y**z)**(1/z)], scalar=True)
+    >>> f2(3, 4, 2)
+    5.0
+
+    A function with multiple inputs and multiple outputs:
+
+    >>> f3 = aesara_function([x, y], [x**2 + y**2, x**2 - y**2], scalar=True)
+    >>> f3(2, 3)
+    [13.0, -5.0]
+
+    See also
+    ========
+
+    dim_handling
+
+    """
+    if not aesara:
+        raise ImportError("Aesara is required for aesara_function")
+
+    # Pop off non-aesara keyword args
+    cache = kwargs.pop('cache', {})
+    dtypes = kwargs.pop('dtypes', {})
+
+    broadcastables = dim_handling(
+        inputs, dim=dim, dims=dims, broadcastables=broadcastables,
+    )
+
+    # Print inputs/outputs
+    code = partial(aesara_code, cache=cache, dtypes=dtypes,
+                   broadcastables=broadcastables)
+    tinputs = list(map(code, inputs))
+    toutputs = list(map(code, outputs))
+
+    #fix constant expressions as variables
+    toutputs = [output if isinstance(output, aesara.graph.basic.Variable) else aet.as_tensor_variable(output) for output in toutputs]
+
+    if len(toutputs) == 1:
+        toutputs = toutputs[0]
+
+    # Compile aesara func
+    func = aesara.function(tinputs, toutputs, **kwargs)
+
+    is_0d = [len(o.variable.broadcastable) == 0 for o in func.outputs]
+
+    # No wrapper required
+    if not scalar or not any(is_0d):
+        func.aesara_function = func
+        return func
+
+    # Create wrapper to convert 0-dimensional outputs to scalars
+    def wrapper(*args):
+        out = func(*args)
+        # out can be array(1.0) or [array(1.0), array(2.0)]
+
+        if is_sequence(out):
+            return [o[()] if is_0d[i] else o for i, o in enumerate(out)]
+        else:
+            return out[()]
+
+    wrapper.__wrapped__ = func
+    wrapper.__doc__ = func.__doc__
+    wrapper.aesara_function = func
+    return wrapper

venv/lib/python3.10/site-packages/sympy/printing/c.py

@@ -0,0 +1,747 @@
+"""
+C code printer
+
+The C89CodePrinter & C99CodePrinter converts single SymPy expressions into
+single C expressions, using the functions defined in math.h where possible.
+
+A complete code generator, which uses ccode extensively, can be found in
+sympy.utilities.codegen. The codegen module can be used to generate complete
+source code files that are compilable without further modifications.
+
+
+"""
+
+from __future__ import annotations
+from typing import Any
+
+from functools import wraps
+from itertools import chain
+
+from sympy.core import S
+from sympy.core.numbers import equal_valued
+from sympy.codegen.ast import (
+    Assignment, Pointer, Variable, Declaration, Type,
+    real, complex_, integer, bool_, float32, float64, float80,
+    complex64, complex128, intc, value_const, pointer_const,
+    int8, int16, int32, int64, uint8, uint16, uint32, uint64, untyped,
+    none
+)
+from sympy.printing.codeprinter import CodePrinter, requires
+from sympy.printing.precedence import precedence, PRECEDENCE
+from sympy.sets.fancysets import Range
+
+# These are defined in the other file so we can avoid importing sympy.codegen
+# from the top-level 'import sympy'. Export them here as well.
+from sympy.printing.codeprinter import ccode, print_ccode # noqa:F401
+
+# dictionary mapping SymPy function to (argument_conditions, C_function).
+# Used in C89CodePrinter._print_Function(self)
+known_functions_C89 = {
+    "Abs": [(lambda x: not x.is_integer, "fabs"), (lambda x: x.is_integer, "abs")],
+    "sin": "sin",
+    "cos": "cos",
+    "tan": "tan",
+    "asin": "asin",
+    "acos": "acos",
+    "atan": "atan",
+    "atan2": "atan2",
+    "exp": "exp",
+    "log": "log",
+    "sinh": "sinh",
+    "cosh": "cosh",
+    "tanh": "tanh",
+    "floor": "floor",
+    "ceiling": "ceil",
+    "sqrt": "sqrt", # To enable automatic rewrites
+}
+
+known_functions_C99 = dict(known_functions_C89, **{
+    'exp2': 'exp2',
+    'expm1': 'expm1',
+    'log10': 'log10',
+    'log2': 'log2',
+    'log1p': 'log1p',
+    'Cbrt': 'cbrt',
+    'hypot': 'hypot',
+    'fma': 'fma',
+    'loggamma': 'lgamma',
+    'erfc': 'erfc',
+    'Max': 'fmax',
+    'Min': 'fmin',
+    "asinh": "asinh",
+    "acosh": "acosh",
+    "atanh": "atanh",
+    "erf": "erf",
+    "gamma": "tgamma",
+})
+
+# These are the core reserved words in the C language. Taken from:
+# https://en.cppreference.com/w/c/keyword
+
+reserved_words = [
+    'auto', 'break', 'case', 'char', 'const', 'continue', 'default', 'do',
+    'double', 'else', 'enum', 'extern', 'float', 'for', 'goto', 'if', 'int',
+    'long', 'register', 'return', 'short', 'signed', 'sizeof', 'static',
+    'struct', 'entry',  # never standardized, we'll leave it here anyway
+    'switch', 'typedef', 'union', 'unsigned', 'void', 'volatile', 'while'
+]
+
+reserved_words_c99 = ['inline', 'restrict']
+
+def get_math_macros():
+    """ Returns a dictionary with math-related macros from math.h/cmath
+
+    Note that these macros are not strictly required by the C/C++-standard.
+    For MSVC they are enabled by defining "_USE_MATH_DEFINES" (preferably
+    via a compilation flag).
+
+    Returns
+    =======
+
+    Dictionary mapping SymPy expressions to strings (macro names)
+
+    """
+    from sympy.codegen.cfunctions import log2, Sqrt
+    from sympy.functions.elementary.exponential import log
+    from sympy.functions.elementary.miscellaneous import sqrt
+
+    return {
+        S.Exp1: 'M_E',
+        log2(S.Exp1): 'M_LOG2E',
+        1/log(2): 'M_LOG2E',
+        log(2): 'M_LN2',
+        log(10): 'M_LN10',
+        S.Pi: 'M_PI',
+        S.Pi/2: 'M_PI_2',
+        S.Pi/4: 'M_PI_4',
+        1/S.Pi: 'M_1_PI',
+        2/S.Pi: 'M_2_PI',
+        2/sqrt(S.Pi): 'M_2_SQRTPI',
+        2/Sqrt(S.Pi): 'M_2_SQRTPI',
+        sqrt(2): 'M_SQRT2',
+        Sqrt(2): 'M_SQRT2',
+        1/sqrt(2): 'M_SQRT1_2',
+        1/Sqrt(2): 'M_SQRT1_2'
+    }
+
+
+def _as_macro_if_defined(meth):
+    """ Decorator for printer methods
+
+    When a Printer's method is decorated using this decorator the expressions printed
+    will first be looked for in the attribute ``math_macros``, and if present it will
+    print the macro name in ``math_macros`` followed by a type suffix for the type
+    ``real``. e.g. printing ``sympy.pi`` would print ``M_PIl`` if real is mapped to float80.
+
+    """
+    @wraps(meth)
+    def _meth_wrapper(self, expr, **kwargs):
+        if expr in self.math_macros:
+            return '%s%s' % (self.math_macros[expr], self._get_math_macro_suffix(real))
+        else:
+            return meth(self, expr, **kwargs)
+
+    return _meth_wrapper
+
+
+class C89CodePrinter(CodePrinter):
+    """A printer to convert Python expressions to strings of C code"""
+    printmethod = "_ccode"
+    language = "C"
+    standard = "C89"
+    reserved_words = set(reserved_words)
+
+    _default_settings: dict[str, Any] = {
+        'order': None,
+        'full_prec': 'auto',
+        'precision': 17,
+        'user_functions': {},
+        'human': True,
+        'allow_unknown_functions': False,
+        'contract': True,
+        'dereference': set(),
+        'error_on_reserved': False,
+        'reserved_word_suffix': '_',
+    }
+
+    type_aliases = {
+        real: float64,
+        complex_: complex128,
+        integer: intc
+    }
+
+    type_mappings: dict[Type, Any] = {
+        real: 'double',
+        intc: 'int',
+        float32: 'float',
+        float64: 'double',
+        integer: 'int',
+        bool_: 'bool',
+        int8: 'int8_t',
+        int16: 'int16_t',
+        int32: 'int32_t',
+        int64: 'int64_t',
+        uint8: 'int8_t',
+        uint16: 'int16_t',
+        uint32: 'int32_t',
+        uint64: 'int64_t',
+    }
+
+    type_headers = {
+        bool_: {'stdbool.h'},
+        int8: {'stdint.h'},
+        int16: {'stdint.h'},
+        int32: {'stdint.h'},
+        int64: {'stdint.h'},
+        uint8: {'stdint.h'},
+        uint16: {'stdint.h'},
+        uint32: {'stdint.h'},
+        uint64: {'stdint.h'},
+    }
+
+    # Macros needed to be defined when using a Type
+    type_macros: dict[Type, tuple[str, ...]] = {}
+
+    type_func_suffixes = {
+        float32: 'f',
+        float64: '',
+        float80: 'l'
+    }
+
+    type_literal_suffixes = {
+        float32: 'F',
+        float64: '',
+        float80: 'L'
+    }
+
+    type_math_macro_suffixes = {
+        float80: 'l'
+    }
+
+    math_macros = None
+
+    _ns = ''  # namespace, C++ uses 'std::'
+    # known_functions-dict to copy
+    _kf: dict[str, Any] = known_functions_C89
+
+    def __init__(self, settings=None):
+        settings = settings or {}
+        if self.math_macros is None:
+            self.math_macros = settings.pop('math_macros', get_math_macros())
+        self.type_aliases = dict(chain(self.type_aliases.items(),
+                                       settings.pop('type_aliases', {}).items()))
+        self.type_mappings = dict(chain(self.type_mappings.items(),
+                                        settings.pop('type_mappings', {}).items()))
+        self.type_headers = dict(chain(self.type_headers.items(),
+                                       settings.pop('type_headers', {}).items()))
+        self.type_macros = dict(chain(self.type_macros.items(),
+                                       settings.pop('type_macros', {}).items()))
+        self.type_func_suffixes = dict(chain(self.type_func_suffixes.items(),
+                                        settings.pop('type_func_suffixes', {}).items()))
+        self.type_literal_suffixes = dict(chain(self.type_literal_suffixes.items(),
+                                        settings.pop('type_literal_suffixes', {}).items()))
+        self.type_math_macro_suffixes = dict(chain(self.type_math_macro_suffixes.items(),
+                                        settings.pop('type_math_macro_suffixes', {}).items()))
+        super().__init__(settings)
+        self.known_functions = dict(self._kf, **settings.get('user_functions', {}))
+        self._dereference = set(settings.get('dereference', []))
+        self.headers = set()
+        self.libraries = set()
+        self.macros = set()
+
+    def _rate_index_position(self, p):
+        return p*5
+
+    def _get_statement(self, codestring):
+        """ Get code string as a statement - i.e. ending with a semicolon. """
+        return codestring if codestring.endswith(';') else codestring + ';'
+
+    def _get_comment(self, text):
+        return "/* {} */".format(text)
+
+    def _declare_number_const(self, name, value):
+        type_ = self.type_aliases[real]
+        var = Variable(name, type=type_, value=value.evalf(type_.decimal_dig), attrs={value_const})
+        decl = Declaration(var)
+        return self._get_statement(self._print(decl))
+
+    def _format_code(self, lines):
+        return self.indent_code(lines)
+
+    def _traverse_matrix_indices(self, mat):
+        rows, cols = mat.shape
+        return ((i, j) for i in range(rows) for j in range(cols))
+
+    @_as_macro_if_defined
+    def _print_Mul(self, expr, **kwargs):
+        return super()._print_Mul(expr, **kwargs)
+
+    @_as_macro_if_defined
+    def _print_Pow(self, expr):
+        if "Pow" in self.known_functions:
+            return self._print_Function(expr)
+        PREC = precedence(expr)
+        suffix = self._get_func_suffix(real)
+        if equal_valued(expr.exp, -1):
+            literal_suffix = self._get_literal_suffix(real)
+            return '1.0%s/%s' % (literal_suffix, self.parenthesize(expr.base, PREC))
+        elif equal_valued(expr.exp, 0.5):
+            return '%ssqrt%s(%s)' % (self._ns, suffix, self._print(expr.base))
+        elif expr.exp == S.One/3 and self.standard != 'C89':
+            return '%scbrt%s(%s)' % (self._ns, suffix, self._print(expr.base))
+        else:
+            return '%spow%s(%s, %s)' % (self._ns, suffix, self._print(expr.base),
+                                   self._print(expr.exp))
+
+    def _print_Mod(self, expr):
+        num, den = expr.args
+        if num.is_integer and den.is_integer:
+            PREC = precedence(expr)
+            snum, sden = [self.parenthesize(arg, PREC) for arg in expr.args]
+            # % is remainder (same sign as numerator), not modulo (same sign as
+            # denominator), in C. Hence, % only works as modulo if both numbers
+            # have the same sign
+            if (num.is_nonnegative and den.is_nonnegative or
+                num.is_nonpositive and den.is_nonpositive):
+                return f"{snum} % {sden}"
+            return f"(({snum} % {sden}) + {sden}) % {sden}"
+        # Not guaranteed integer
+        return self._print_math_func(expr, known='fmod')
+
+    def _print_Rational(self, expr):
+        p, q = int(expr.p), int(expr.q)
+        suffix = self._get_literal_suffix(real)
+        return '%d.0%s/%d.0%s' % (p, suffix, q, suffix)
+
+    def _print_Indexed(self, expr):
+        # calculate index for 1d array
+        offset = getattr(expr.base, 'offset', S.Zero)
+        strides = getattr(expr.base, 'strides', None)
+        indices = expr.indices
+
+        if strides is None or isinstance(strides, str):
+            dims = expr.shape
+            shift = S.One
+            temp = ()
+            if strides == 'C' or strides is None:
+                traversal = reversed(range(expr.rank))
+                indices = indices[::-1]
+            elif strides == 'F':
+                traversal = range(expr.rank)
+
+            for i in traversal:
+                temp += (shift,)
+                shift *= dims[i]
+            strides = temp
+        flat_index = sum([x[0]*x[1] for x in zip(indices, strides)]) + offset
+        return "%s[%s]" % (self._print(expr.base.label),
+                           self._print(flat_index))
+
+    def _print_Idx(self, expr):
+        return self._print(expr.label)
+
+    @_as_macro_if_defined
+    def _print_NumberSymbol(self, expr):
+        return super()._print_NumberSymbol(expr)
+
+    def _print_Infinity(self, expr):
+        return 'HUGE_VAL'
+
+    def _print_NegativeInfinity(self, expr):
+        return '-HUGE_VAL'
+
+    def _print_Piecewise(self, expr):
+        if expr.args[-1].cond != True:
+            # We need the last conditional to be a True, otherwise the resulting
+            # function may not return a result.
+            raise ValueError("All Piecewise expressions must contain an "
+                             "(expr, True) statement to be used as a default "
+                             "condition. Without one, the generated "
+                             "expression may not evaluate to anything under "
+                             "some condition.")
+        lines = []
+        if expr.has(Assignment):
+            for i, (e, c) in enumerate(expr.args):
+                if i == 0:
+                    lines.append("if (%s) {" % self._print(c))
+                elif i == len(expr.args) - 1 and c == True:
+                    lines.append("else {")
+                else:
+                    lines.append("else if (%s) {" % self._print(c))
+                code0 = self._print(e)
+                lines.append(code0)
+                lines.append("}")
+            return "\n".join(lines)
+        else:
+            # The piecewise was used in an expression, need to do inline
+            # operators. This has the downside that inline operators will
+            # not work for statements that span multiple lines (Matrix or
+            # Indexed expressions).
+            ecpairs = ["((%s) ? (\n%s\n)\n" % (self._print(c),
+                                               self._print(e))
+                    for e, c in expr.args[:-1]]
+            last_line = ": (\n%s\n)" % self._print(expr.args[-1].expr)
+            return ": ".join(ecpairs) + last_line + " ".join([")"*len(ecpairs)])
+
+    def _print_ITE(self, expr):
+        from sympy.functions import Piecewise
+        return self._print(expr.rewrite(Piecewise, deep=False))
+
+    def _print_MatrixElement(self, expr):
+        return "{}[{}]".format(self.parenthesize(expr.parent, PRECEDENCE["Atom"],
+            strict=True), expr.j + expr.i*expr.parent.shape[1])
+
+    def _print_Symbol(self, expr):
+        name = super()._print_Symbol(expr)
+        if expr in self._settings['dereference']:
+            return '(*{})'.format(name)
+        else:
+            return name
+
+    def _print_Relational(self, expr):
+        lhs_code = self._print(expr.lhs)
+        rhs_code = self._print(expr.rhs)
+        op = expr.rel_op
+        return "{} {} {}".format(lhs_code, op, rhs_code)
+
+    def _print_For(self, expr):
+        target = self._print(expr.target)
+        if isinstance(expr.iterable, Range):
+            start, stop, step = expr.iterable.args
+        else:
+            raise NotImplementedError("Only iterable currently supported is Range")
+        body = self._print(expr.body)
+        return ('for ({target} = {start}; {target} < {stop}; {target} += '
+                '{step}) {{\n{body}\n}}').format(target=target, start=start,
+                stop=stop, step=step, body=body)
+
+    def _print_sign(self, func):
+        return '((({0}) > 0) - (({0}) < 0))'.format(self._print(func.args[0]))
+
+    def _print_Max(self, expr):
+        if "Max" in self.known_functions:
+            return self._print_Function(expr)
+        def inner_print_max(args): # The more natural abstraction of creating
+            if len(args) == 1:     # and printing smaller Max objects is slow
+                return self._print(args[0]) # when there are many arguments.
+            half = len(args) // 2
+            return "((%(a)s > %(b)s) ? %(a)s : %(b)s)" % {
+                'a': inner_print_max(args[:half]),
+                'b': inner_print_max(args[half:])
+            }
+        return inner_print_max(expr.args)
+
+    def _print_Min(self, expr):
+        if "Min" in self.known_functions:
+            return self._print_Function(expr)
+        def inner_print_min(args): # The more natural abstraction of creating
+            if len(args) == 1:     # and printing smaller Min objects is slow
+                return self._print(args[0]) # when there are many arguments.
+            half = len(args) // 2
+            return "((%(a)s < %(b)s) ? %(a)s : %(b)s)" % {
+                'a': inner_print_min(args[:half]),
+                'b': inner_print_min(args[half:])
+            }
+        return inner_print_min(expr.args)
+
+    def indent_code(self, code):
+        """Accepts a string of code or a list of code lines"""
+
+        if isinstance(code, str):
+            code_lines = self.indent_code(code.splitlines(True))
+            return ''.join(code_lines)
+
+        tab = "   "
+        inc_token = ('{', '(', '{\n', '(\n')
+        dec_token = ('}', ')')
+
+        code = [line.lstrip(' \t') for line in code]
+
+        increase = [int(any(map(line.endswith, inc_token))) for line in code]
+        decrease = [int(any(map(line.startswith, dec_token))) for line in code]
+
+        pretty = []
+        level = 0
+        for n, line in enumerate(code):
+            if line in ('', '\n'):
+                pretty.append(line)
+                continue
+            level -= decrease[n]
+            pretty.append("%s%s" % (tab*level, line))
+            level += increase[n]
+        return pretty
+
+    def _get_func_suffix(self, type_):
+        return self.type_func_suffixes[self.type_aliases.get(type_, type_)]
+
+    def _get_literal_suffix(self, type_):
+        return self.type_literal_suffixes[self.type_aliases.get(type_, type_)]
+
+    def _get_math_macro_suffix(self, type_):
+        alias = self.type_aliases.get(type_, type_)
+        dflt = self.type_math_macro_suffixes.get(alias, '')
+        return self.type_math_macro_suffixes.get(type_, dflt)
+
+    def _print_Tuple(self, expr):
+        return '{'+', '.join(self._print(e) for e in expr)+'}'
+
+    _print_List = _print_Tuple
+
+    def _print_Type(self, type_):
+        self.headers.update(self.type_headers.get(type_, set()))
+        self.macros.update(self.type_macros.get(type_, set()))
+        return self._print(self.type_mappings.get(type_, type_.name))
+
+    def _print_Declaration(self, decl):
+        from sympy.codegen.cnodes import restrict
+        var = decl.variable
+        val = var.value
+        if var.type == untyped:
+            raise ValueError("C does not support untyped variables")
+
+        if isinstance(var, Pointer):
+            result = '{vc}{t} *{pc} {r}{s}'.format(
+                vc='const ' if value_const in var.attrs else '',
+                t=self._print(var.type),
+                pc=' const' if pointer_const in var.attrs else '',
+                r='restrict ' if restrict in var.attrs else '',
+                s=self._print(var.symbol)
+            )
+        elif isinstance(var, Variable):
+            result = '{vc}{t} {s}'.format(
+                vc='const ' if value_const in var.attrs else '',
+                t=self._print(var.type),
+                s=self._print(var.symbol)
+            )
+        else:
+            raise NotImplementedError("Unknown type of var: %s" % type(var))
+        if val != None: # Must be "!= None", cannot be "is not None"
+            result += ' = %s' % self._print(val)
+        return result
+
+    def _print_Float(self, flt):
+        type_ = self.type_aliases.get(real, real)
+        self.macros.update(self.type_macros.get(type_, set()))
+        suffix = self._get_literal_suffix(type_)
+        num = str(flt.evalf(type_.decimal_dig))
+        if 'e' not in num and '.' not in num:
+            num += '.0'
+        num_parts = num.split('e')
+        num_parts[0] = num_parts[0].rstrip('0')
+        if num_parts[0].endswith('.'):
+            num_parts[0] += '0'
+        return 'e'.join(num_parts) + suffix
+
+    @requires(headers={'stdbool.h'})
+    def _print_BooleanTrue(self, expr):
+        return 'true'
+
+    @requires(headers={'stdbool.h'})
+    def _print_BooleanFalse(self, expr):
+        return 'false'
+
+    def _print_Element(self, elem):
+        if elem.strides == None: # Must be "== None", cannot be "is None"
+            if elem.offset != None: # Must be "!= None", cannot be "is not None"
+                raise ValueError("Expected strides when offset is given")
+            idxs = ']['.join((self._print(arg) for arg in elem.indices))
+        else:
+            global_idx = sum([i*s for i, s in zip(elem.indices, elem.strides)])
+            if elem.offset != None: # Must be "!= None", cannot be "is not None"
+                global_idx += elem.offset
+            idxs = self._print(global_idx)
+
+        return "{symb}[{idxs}]".format(
+            symb=self._print(elem.symbol),
+            idxs=idxs
+        )
+
+    def _print_CodeBlock(self, expr):
+        """ Elements of code blocks printed as statements. """
+        return '\n'.join([self._get_statement(self._print(i)) for i in expr.args])
+
+    def _print_While(self, expr):
+        return 'while ({condition}) {{\n{body}\n}}'.format(**expr.kwargs(
+            apply=lambda arg: self._print(arg)))
+
+    def _print_Scope(self, expr):
+        return '{\n%s\n}' % self._print_CodeBlock(expr.body)
+
+    @requires(headers={'stdio.h'})
+    def _print_Print(self, expr):
+        return 'printf({fmt}, {pargs})'.format(
+            fmt=self._print(expr.format_string),
+            pargs=', '.join((self._print(arg) for arg in expr.print_args))
+        )
+
+    def _print_FunctionPrototype(self, expr):
+        pars = ', '.join((self._print(Declaration(arg)) for arg in expr.parameters))
+        return "%s %s(%s)" % (
+            tuple((self._print(arg) for arg in (expr.return_type, expr.name))) + (pars,)
+        )
+
+    def _print_FunctionDefinition(self, expr):
+        return "%s%s" % (self._print_FunctionPrototype(expr),
+                         self._print_Scope(expr))
+
+    def _print_Return(self, expr):
+        arg, = expr.args
+        return 'return %s' % self._print(arg)
+
+    def _print_CommaOperator(self, expr):
+        return '(%s)' % ', '.join((self._print(arg) for arg in expr.args))
+
+    def _print_Label(self, expr):
+        if expr.body == none:
+            return '%s:' % str(expr.name)
+        if len(expr.body.args) == 1:
+            return '%s:\n%s' % (str(expr.name), self._print_CodeBlock(expr.body))
+        return '%s:\n{\n%s\n}' % (str(expr.name), self._print_CodeBlock(expr.body))
+
+    def _print_goto(self, expr):
+        return 'goto %s' % expr.label.name
+
+    def _print_PreIncrement(self, expr):
+        arg, = expr.args
+        return '++(%s)' % self._print(arg)
+
+    def _print_PostIncrement(self, expr):
+        arg, = expr.args
+        return '(%s)++' % self._print(arg)
+
+    def _print_PreDecrement(self, expr):
+        arg, = expr.args
+        return '--(%s)' % self._print(arg)
+
+    def _print_PostDecrement(self, expr):
+        arg, = expr.args
+        return '(%s)--' % self._print(arg)
+
+    def _print_struct(self, expr):
+        return "%(keyword)s %(name)s {\n%(lines)s}" % {
+            "keyword": expr.__class__.__name__, "name": expr.name, "lines": ';\n'.join(
+                [self._print(decl) for decl in expr.declarations] + [''])
+        }
+
+    def _print_BreakToken(self, _):
+        return 'break'
+
+    def _print_ContinueToken(self, _):
+        return 'continue'
+
+    _print_union = _print_struct
+
+class C99CodePrinter(C89CodePrinter):
+    standard = 'C99'
+    reserved_words = set(reserved_words + reserved_words_c99)
+    type_mappings=dict(chain(C89CodePrinter.type_mappings.items(), {
+        complex64: 'float complex',
+        complex128: 'double complex',
+    }.items()))
+    type_headers = dict(chain(C89CodePrinter.type_headers.items(), {
+        complex64: {'complex.h'},
+        complex128: {'complex.h'}
+    }.items()))
+
+    # known_functions-dict to copy
+    _kf: dict[str, Any] = known_functions_C99
+
+    # functions with versions with 'f' and 'l' suffixes:
+    _prec_funcs = ('fabs fmod remainder remquo fma fmax fmin fdim nan exp exp2'
+                   ' expm1 log log10 log2 log1p pow sqrt cbrt hypot sin cos tan'
+                   ' asin acos atan atan2 sinh cosh tanh asinh acosh atanh erf'
+                   ' erfc tgamma lgamma ceil floor trunc round nearbyint rint'
+                   ' frexp ldexp modf scalbn ilogb logb nextafter copysign').split()
+
+    def _print_Infinity(self, expr):
+        return 'INFINITY'
+
+    def _print_NegativeInfinity(self, expr):
+        return '-INFINITY'
+
+    def _print_NaN(self, expr):
+        return 'NAN'
+
+    # tgamma was already covered by 'known_functions' dict
+
+    @requires(headers={'math.h'}, libraries={'m'})
+    @_as_macro_if_defined
+    def _print_math_func(self, expr, nest=False, known=None):
+        if known is None:
+            known = self.known_functions[expr.__class__.__name__]
+        if not isinstance(known, str):
+            for cb, name in known:
+                if cb(*expr.args):
+                    known = name
+                    break
+            else:
+                raise ValueError("No matching printer")
+        try:
+            return known(self, *expr.args)
+        except TypeError:
+            suffix = self._get_func_suffix(real) if self._ns + known in self._prec_funcs else ''
+
+        if nest:
+            args = self._print(expr.args[0])
+            if len(expr.args) > 1:
+                paren_pile = ''
+                for curr_arg in expr.args[1:-1]:
+                    paren_pile += ')'
+                    args += ', {ns}{name}{suffix}({next}'.format(
+                        ns=self._ns,
+                        name=known,
+                        suffix=suffix,
+                        next = self._print(curr_arg)
+                    )
+                args += ', %s%s' % (
+                    self._print(expr.func(expr.args[-1])),
+                    paren_pile
+                )
+        else:
+            args = ', '.join((self._print(arg) for arg in expr.args))
+        return '{ns}{name}{suffix}({args})'.format(
+            ns=self._ns,
+            name=known,
+            suffix=suffix,
+            args=args
+        )
+
+    def _print_Max(self, expr):
+        return self._print_math_func(expr, nest=True)
+
+    def _print_Min(self, expr):
+        return self._print_math_func(expr, nest=True)
+
+    def _get_loop_opening_ending(self, indices):
+        open_lines = []
+        close_lines = []
+        loopstart = "for (int %(var)s=%(start)s; %(var)s<%(end)s; %(var)s++){"  # C99
+        for i in indices:
+            # C arrays start at 0 and end at dimension-1
+            open_lines.append(loopstart % {
+                'var': self._print(i.label),
+                'start': self._print(i.lower),
+                'end': self._print(i.upper + 1)})
+            close_lines.append("}")
+        return open_lines, close_lines
+
+
+for k in ('Abs Sqrt exp exp2 expm1 log log10 log2 log1p Cbrt hypot fma'
+          ' loggamma sin cos tan asin acos atan atan2 sinh cosh tanh asinh acosh '
+          'atanh erf erfc loggamma gamma ceiling floor').split():
+    setattr(C99CodePrinter, '_print_%s' % k, C99CodePrinter._print_math_func)
+
+
+class C11CodePrinter(C99CodePrinter):
+
+    @requires(headers={'stdalign.h'})
+    def _print_alignof(self, expr):
+        arg, = expr.args
+        return 'alignof(%s)' % self._print(arg)
+
+
+c_code_printers = {
+    'c89': C89CodePrinter,
+    'c99': C99CodePrinter,
+    'c11': C11CodePrinter
+}

venv/lib/python3.10/site-packages/sympy/printing/codeprinter.py

@@ -0,0 +1,875 @@
+from __future__ import annotations
+from typing import Any
+
+from functools import wraps
+
+from sympy.core import Add, Mul, Pow, S, sympify, Float
+from sympy.core.basic import Basic
+from sympy.core.expr import UnevaluatedExpr
+from sympy.core.function import Lambda
+from sympy.core.mul import _keep_coeff
+from sympy.core.sorting import default_sort_key
+from sympy.core.symbol import Symbol
+from sympy.functions.elementary.complexes import re
+from sympy.printing.str import StrPrinter
+from sympy.printing.precedence import precedence, PRECEDENCE
+
+
+class requires:
+    """ Decorator for registering requirements on print methods. """
+    def __init__(self, **kwargs):
+        self._req = kwargs
+
+    def __call__(self, method):
+        def _method_wrapper(self_, *args, **kwargs):
+            for k, v in self._req.items():
+                getattr(self_, k).update(v)
+            return method(self_, *args, **kwargs)
+        return wraps(method)(_method_wrapper)
+
+
+class AssignmentError(Exception):
+    """
+    Raised if an assignment variable for a loop is missing.
+    """
+    pass
+
+
+def _convert_python_lists(arg):
+    if isinstance(arg, list):
+        from sympy.codegen.abstract_nodes import List
+        return List(*(_convert_python_lists(e) for e in arg))
+    elif isinstance(arg, tuple):
+        return tuple(_convert_python_lists(e) for e in arg)
+    else:
+        return arg
+
+
+class CodePrinter(StrPrinter):
+    """
+    The base class for code-printing subclasses.
+    """
+
+    _operators = {
+        'and': '&&',
+        'or': '||',
+        'not': '!',
+    }
+
+    _default_settings: dict[str, Any] = {
+        'order': None,
+        'full_prec': 'auto',
+        'error_on_reserved': False,
+        'reserved_word_suffix': '_',
+        'human': True,
+        'inline': False,
+        'allow_unknown_functions': False,
+    }
+
+    # Functions which are "simple" to rewrite to other functions that
+    # may be supported
+    # function_to_rewrite : (function_to_rewrite_to, iterable_with_other_functions_required)
+    _rewriteable_functions = {
+            'cot': ('tan', []),
+            'csc': ('sin', []),
+            'sec': ('cos', []),
+            'acot': ('atan', []),
+            'acsc': ('asin', []),
+            'asec': ('acos', []),
+            'coth': ('exp', []),
+            'csch': ('exp', []),
+            'sech': ('exp', []),
+            'acoth': ('log', []),
+            'acsch': ('log', []),
+            'asech': ('log', []),
+            'catalan': ('gamma', []),
+            'fibonacci': ('sqrt', []),
+            'lucas': ('sqrt', []),
+            'beta': ('gamma', []),
+            'sinc': ('sin', ['Piecewise']),
+            'Mod': ('floor', []),
+            'factorial': ('gamma', []),
+            'factorial2': ('gamma', ['Piecewise']),
+            'subfactorial': ('uppergamma', []),
+            'RisingFactorial': ('gamma', ['Piecewise']),
+            'FallingFactorial': ('gamma', ['Piecewise']),
+            'binomial': ('gamma', []),
+            'frac': ('floor', []),
+            'Max': ('Piecewise', []),
+            'Min': ('Piecewise', []),
+            'Heaviside': ('Piecewise', []),
+            'erf2': ('erf', []),
+            'erfc': ('erf', []),
+            'Li': ('li', []),
+            'Ei': ('li', []),
+            'dirichlet_eta': ('zeta', []),
+            'riemann_xi': ('zeta', ['gamma']),
+    }
+
+    def __init__(self, settings=None):
+
+        super().__init__(settings=settings)
+        if not hasattr(self, 'reserved_words'):
+            self.reserved_words = set()
+
+    def _handle_UnevaluatedExpr(self, expr):
+        return expr.replace(re, lambda arg: arg if isinstance(
+            arg, UnevaluatedExpr) and arg.args[0].is_real else re(arg))
+
+    def doprint(self, expr, assign_to=None):
+        """
+        Print the expression as code.
+
+        Parameters
+        ----------
+        expr : Expression
+            The expression to be printed.
+
+        assign_to : Symbol, string, MatrixSymbol, list of strings or Symbols (optional)
+            If provided, the printed code will set the expression to a variable or multiple variables
+            with the name or names given in ``assign_to``.
+        """
+        from sympy.matrices.expressions.matexpr import MatrixSymbol
+        from sympy.codegen.ast import CodeBlock, Assignment
+
+        def _handle_assign_to(expr, assign_to):
+            if assign_to is None:
+                return sympify(expr)
+            if isinstance(assign_to, (list, tuple)):
+                if len(expr) != len(assign_to):
+                    raise ValueError('Failed to assign an expression of length {} to {} variables'.format(len(expr), len(assign_to)))
+                return CodeBlock(*[_handle_assign_to(lhs, rhs) for lhs, rhs in zip(expr, assign_to)])
+            if isinstance(assign_to, str):
+                if expr.is_Matrix:
+                    assign_to = MatrixSymbol(assign_to, *expr.shape)
+                else:
+                    assign_to = Symbol(assign_to)
+            elif not isinstance(assign_to, Basic):
+                raise TypeError("{} cannot assign to object of type {}".format(
+                        type(self).__name__, type(assign_to)))
+            return Assignment(assign_to, expr)
+
+        expr = _convert_python_lists(expr)
+        expr = _handle_assign_to(expr, assign_to)
+
+        # Remove re(...) nodes due to UnevaluatedExpr.is_real always is None:
+        expr = self._handle_UnevaluatedExpr(expr)
+
+        # keep a set of expressions that are not strictly translatable to Code
+        # and number constants that must be declared and initialized
+        self._not_supported = set()
+        self._number_symbols = set()
+
+        lines = self._print(expr).splitlines()
+
+        # format the output
+        if self._settings["human"]:
+            frontlines = []
+            if self._not_supported:
+                frontlines.append(self._get_comment(
+                        "Not supported in {}:".format(self.language)))
+                for expr in sorted(self._not_supported, key=str):
+                    frontlines.append(self._get_comment(type(expr).__name__))
+            for name, value in sorted(self._number_symbols, key=str):
+                frontlines.append(self._declare_number_const(name, value))
+            lines = frontlines + lines
+            lines = self._format_code(lines)
+            result = "\n".join(lines)
+        else:
+            lines = self._format_code(lines)
+            num_syms = {(k, self._print(v)) for k, v in self._number_symbols}
+            result = (num_syms, self._not_supported, "\n".join(lines))
+        self._not_supported = set()
+        self._number_symbols = set()
+        return result
+
+    def _doprint_loops(self, expr, assign_to=None):
+        # Here we print an expression that contains Indexed objects, they
+        # correspond to arrays in the generated code.  The low-level implementation
+        # involves looping over array elements and possibly storing results in temporary
+        # variables or accumulate it in the assign_to object.
+
+        if self._settings.get('contract', True):
+            from sympy.tensor import get_contraction_structure
+            # Setup loops over non-dummy indices  --  all terms need these
+            indices = self._get_expression_indices(expr, assign_to)
+            # Setup loops over dummy indices  --  each term needs separate treatment
+            dummies = get_contraction_structure(expr)
+        else:
+            indices = []
+            dummies = {None: (expr,)}
+        openloop, closeloop = self._get_loop_opening_ending(indices)
+
+        # terms with no summations first
+        if None in dummies:
+            text = StrPrinter.doprint(self, Add(*dummies[None]))
+        else:
+            # If all terms have summations we must initialize array to Zero
+            text = StrPrinter.doprint(self, 0)
+
+        # skip redundant assignments (where lhs == rhs)
+        lhs_printed = self._print(assign_to)
+        lines = []
+        if text != lhs_printed:
+            lines.extend(openloop)
+            if assign_to is not None:
+                text = self._get_statement("%s = %s" % (lhs_printed, text))
+            lines.append(text)
+            lines.extend(closeloop)
+
+        # then terms with summations
+        for d in dummies:
+            if isinstance(d, tuple):
+                indices = self._sort_optimized(d, expr)
+                openloop_d, closeloop_d = self._get_loop_opening_ending(
+                    indices)
+
+                for term in dummies[d]:
+                    if term in dummies and not ([list(f.keys()) for f in dummies[term]]
+                            == [[None] for f in dummies[term]]):
+                        # If one factor in the term has it's own internal
+                        # contractions, those must be computed first.
+                        # (temporary variables?)
+                        raise NotImplementedError(
+                            "FIXME: no support for contractions in factor yet")
+                    else:
+
+                        # We need the lhs expression as an accumulator for
+                        # the loops, i.e
+                        #
+                        # for (int d=0; d < dim; d++){
+                        #    lhs[] = lhs[] + term[][d]
+                        # }           ^.................. the accumulator
+                        #
+                        # We check if the expression already contains the
+                        # lhs, and raise an exception if it does, as that
+                        # syntax is currently undefined.  FIXME: What would be
+                        # a good interpretation?
+                        if assign_to is None:
+                            raise AssignmentError(
+                                "need assignment variable for loops")
+                        if term.has(assign_to):
+                            raise ValueError("FIXME: lhs present in rhs,\
+                                this is undefined in CodePrinter")
+
+                        lines.extend(openloop)
+                        lines.extend(openloop_d)
+                        text = "%s = %s" % (lhs_printed, StrPrinter.doprint(
+                            self, assign_to + term))
+                        lines.append(self._get_statement(text))
+                        lines.extend(closeloop_d)
+                        lines.extend(closeloop)
+
+        return "\n".join(lines)
+
+    def _get_expression_indices(self, expr, assign_to):
+        from sympy.tensor import get_indices
+        rinds, junk = get_indices(expr)
+        linds, junk = get_indices(assign_to)
+
+        # support broadcast of scalar
+        if linds and not rinds:
+            rinds = linds
+        if rinds != linds:
+            raise ValueError("lhs indices must match non-dummy"
+                    " rhs indices in %s" % expr)
+
+        return self._sort_optimized(rinds, assign_to)
+
+    def _sort_optimized(self, indices, expr):
+
+        from sympy.tensor.indexed import Indexed
+
+        if not indices:
+            return []
+
+        # determine optimized loop order by giving a score to each index
+        # the index with the highest score are put in the innermost loop.
+        score_table = {}
+        for i in indices:
+            score_table[i] = 0
+
+        arrays = expr.atoms(Indexed)
+        for arr in arrays:
+            for p, ind in enumerate(arr.indices):
+                try:
+                    score_table[ind] += self._rate_index_position(p)
+                except KeyError:
+                    pass
+
+        return sorted(indices, key=lambda x: score_table[x])
+
+    def _rate_index_position(self, p):
+        """function to calculate score based on position among indices
+
+        This method is used to sort loops in an optimized order, see
+        CodePrinter._sort_optimized()
+        """
+        raise NotImplementedError("This function must be implemented by "
+                                  "subclass of CodePrinter.")
+
+    def _get_statement(self, codestring):
+        """Formats a codestring with the proper line ending."""
+        raise NotImplementedError("This function must be implemented by "
+                                  "subclass of CodePrinter.")
+
+    def _get_comment(self, text):
+        """Formats a text string as a comment."""
+        raise NotImplementedError("This function must be implemented by "
+                                  "subclass of CodePrinter.")
+
+    def _declare_number_const(self, name, value):
+        """Declare a numeric constant at the top of a function"""
+        raise NotImplementedError("This function must be implemented by "
+                                  "subclass of CodePrinter.")
+
+    def _format_code(self, lines):
+        """Take in a list of lines of code, and format them accordingly.
+
+        This may include indenting, wrapping long lines, etc..."""
+        raise NotImplementedError("This function must be implemented by "
+                                  "subclass of CodePrinter.")
+
+    def _get_loop_opening_ending(self, indices):
+        """Returns a tuple (open_lines, close_lines) containing lists
+        of codelines"""
+        raise NotImplementedError("This function must be implemented by "
+                                  "subclass of CodePrinter.")
+
+    def _print_Dummy(self, expr):
+        if expr.name.startswith('Dummy_'):
+            return '_' + expr.name
+        else:
+            return '%s_%d' % (expr.name, expr.dummy_index)
+
+    def _print_CodeBlock(self, expr):
+        return '\n'.join([self._print(i) for i in expr.args])
+
+    def _print_String(self, string):
+        return str(string)
+
+    def _print_QuotedString(self, arg):
+        return '"%s"' % arg.text
+
+    def _print_Comment(self, string):
+        return self._get_comment(str(string))
+
+    def _print_Assignment(self, expr):
+        from sympy.codegen.ast import Assignment
+        from sympy.functions.elementary.piecewise import Piecewise
+        from sympy.matrices.expressions.matexpr import MatrixSymbol
+        from sympy.tensor.indexed import IndexedBase
+        lhs = expr.lhs
+        rhs = expr.rhs
+        # We special case assignments that take multiple lines
+        if isinstance(expr.rhs, Piecewise):
+            # Here we modify Piecewise so each expression is now
+            # an Assignment, and then continue on the print.
+            expressions = []
+            conditions = []
+            for (e, c) in rhs.args:
+                expressions.append(Assignment(lhs, e))
+                conditions.append(c)
+            temp = Piecewise(*zip(expressions, conditions))
+            return self._print(temp)
+        elif isinstance(lhs, MatrixSymbol):
+            # Here we form an Assignment for each element in the array,
+            # printing each one.
+            lines = []
+            for (i, j) in self._traverse_matrix_indices(lhs):
+                temp = Assignment(lhs[i, j], rhs[i, j])
+                code0 = self._print(temp)
+                lines.append(code0)
+            return "\n".join(lines)
+        elif self._settings.get("contract", False) and (lhs.has(IndexedBase) or
+                rhs.has(IndexedBase)):
+            # Here we check if there is looping to be done, and if so
+            # print the required loops.
+            return self._doprint_loops(rhs, lhs)
+        else:
+            lhs_code = self._print(lhs)
+            rhs_code = self._print(rhs)
+            return self._get_statement("%s = %s" % (lhs_code, rhs_code))
+
+    def _print_AugmentedAssignment(self, expr):
+        lhs_code = self._print(expr.lhs)
+        rhs_code = self._print(expr.rhs)
+        return self._get_statement("{} {} {}".format(
+            *(self._print(arg) for arg in [lhs_code, expr.op, rhs_code])))
+
+    def _print_FunctionCall(self, expr):
+        return '%s(%s)' % (
+            expr.name,
+            ', '.join((self._print(arg) for arg in expr.function_args)))
+
+    def _print_Variable(self, expr):
+        return self._print(expr.symbol)
+
+    def _print_Symbol(self, expr):
+
+        name = super()._print_Symbol(expr)
+
+        if name in self.reserved_words:
+            if self._settings['error_on_reserved']:
+                msg = ('This expression includes the symbol "{}" which is a '
+                       'reserved keyword in this language.')
+                raise ValueError(msg.format(name))
+            return name + self._settings['reserved_word_suffix']
+        else:
+            return name
+
+    def _can_print(self, name):
+        """ Check if function ``name`` is either a known function or has its own
+            printing method. Used to check if rewriting is possible."""
+        return name in self.known_functions or getattr(self, '_print_{}'.format(name), False)
+
+    def _print_Function(self, expr):
+        if expr.func.__name__ in self.known_functions:
+            cond_func = self.known_functions[expr.func.__name__]
+            if isinstance(cond_func, str):
+                return "%s(%s)" % (cond_func, self.stringify(expr.args, ", "))
+            else:
+                for cond, func in cond_func:
+                    if cond(*expr.args):
+                        break
+                if func is not None:
+                    try:
+                        return func(*[self.parenthesize(item, 0) for item in expr.args])
+                    except TypeError:
+                        return "%s(%s)" % (func, self.stringify(expr.args, ", "))
+        elif hasattr(expr, '_imp_') and isinstance(expr._imp_, Lambda):
+            # inlined function
+            return self._print(expr._imp_(*expr.args))
+        elif expr.func.__name__ in self._rewriteable_functions:
+            # Simple rewrite to supported function possible
+            target_f, required_fs = self._rewriteable_functions[expr.func.__name__]
+            if self._can_print(target_f) and all(self._can_print(f) for f in required_fs):
+                return self._print(expr.rewrite(target_f))
+        if expr.is_Function and self._settings.get('allow_unknown_functions', False):
+            return '%s(%s)' % (self._print(expr.func), ', '.join(map(self._print, expr.args)))
+        else:
+            return self._print_not_supported(expr)
+
+    _print_Expr = _print_Function
+
+    # Don't inherit the str-printer method for Heaviside to the code printers
+    _print_Heaviside = None
+
+    def _print_NumberSymbol(self, expr):
+        if self._settings.get("inline", False):
+            return self._print(Float(expr.evalf(self._settings["precision"])))
+        else:
+            # A Number symbol that is not implemented here or with _printmethod
+            # is registered and evaluated
+            self._number_symbols.add((expr,
+                Float(expr.evalf(self._settings["precision"]))))
+            return str(expr)
+
+    def _print_Catalan(self, expr):
+        return self._print_NumberSymbol(expr)
+    def _print_EulerGamma(self, expr):
+        return self._print_NumberSymbol(expr)
+    def _print_GoldenRatio(self, expr):
+        return self._print_NumberSymbol(expr)
+    def _print_TribonacciConstant(self, expr):
+        return self._print_NumberSymbol(expr)
+    def _print_Exp1(self, expr):
+        return self._print_NumberSymbol(expr)
+    def _print_Pi(self, expr):
+        return self._print_NumberSymbol(expr)
+
+    def _print_And(self, expr):
+        PREC = precedence(expr)
+        return (" %s " % self._operators['and']).join(self.parenthesize(a, PREC)
+                for a in sorted(expr.args, key=default_sort_key))
+
+    def _print_Or(self, expr):
+        PREC = precedence(expr)
+        return (" %s " % self._operators['or']).join(self.parenthesize(a, PREC)
+                for a in sorted(expr.args, key=default_sort_key))
+
+    def _print_Xor(self, expr):
+        if self._operators.get('xor') is None:
+            return self._print(expr.to_nnf())
+        PREC = precedence(expr)
+        return (" %s " % self._operators['xor']).join(self.parenthesize(a, PREC)
+                for a in expr.args)
+
+    def _print_Equivalent(self, expr):
+        if self._operators.get('equivalent') is None:
+            return self._print(expr.to_nnf())
+        PREC = precedence(expr)
+        return (" %s " % self._operators['equivalent']).join(self.parenthesize(a, PREC)
+                for a in expr.args)
+
+    def _print_Not(self, expr):
+        PREC = precedence(expr)
+        return self._operators['not'] + self.parenthesize(expr.args[0], PREC)
+
+    def _print_BooleanFunction(self, expr):
+        return self._print(expr.to_nnf())
+
+    def _print_Mul(self, expr):
+
+        prec = precedence(expr)
+
+        c, e = expr.as_coeff_Mul()
+        if c < 0:
+            expr = _keep_coeff(-c, e)
+            sign = "-"
+        else:
+            sign = ""
+
+        a = []  # items in the numerator
+        b = []  # items that are in the denominator (if any)
+
+        pow_paren = []  # Will collect all pow with more than one base element and exp = -1
+
+        if self.order not in ('old', 'none'):
+            args = expr.as_ordered_factors()
+        else:
+            # use make_args in case expr was something like -x -> x
+            args = Mul.make_args(expr)
+
+        # Gather args for numerator/denominator
+        for item in args:
+            if item.is_commutative and item.is_Pow and item.exp.is_Rational and item.exp.is_negative:
+                if item.exp != -1:
+                    b.append(Pow(item.base, -item.exp, evaluate=False))
+                else:
+                    if len(item.args[0].args) != 1 and isinstance(item.base, Mul):   # To avoid situations like #14160
+                        pow_paren.append(item)
+                    b.append(Pow(item.base, -item.exp))
+            else:
+                a.append(item)
+
+        a = a or [S.One]
+
+        if len(a) == 1 and sign == "-":
+            # Unary minus does not have a SymPy class, and hence there's no
+            # precedence weight associated with it, Python's unary minus has
+            # an operator precedence between multiplication and exponentiation,
+            # so we use this to compute a weight.
+            a_str = [self.parenthesize(a[0], 0.5*(PRECEDENCE["Pow"]+PRECEDENCE["Mul"]))]
+        else:
+            a_str = [self.parenthesize(x, prec) for x in a]
+        b_str = [self.parenthesize(x, prec) for x in b]
+
+        # To parenthesize Pow with exp = -1 and having more than one Symbol
+        for item in pow_paren:
+            if item.base in b:
+                b_str[b.index(item.base)] = "(%s)" % b_str[b.index(item.base)]
+
+        if not b:
+            return sign + '*'.join(a_str)
+        elif len(b) == 1:
+            return sign + '*'.join(a_str) + "/" + b_str[0]
+        else:
+            return sign + '*'.join(a_str) + "/(%s)" % '*'.join(b_str)
+
+    def _print_not_supported(self, expr):
+        try:
+            self._not_supported.add(expr)
+        except TypeError:
+            # not hashable
+            pass
+        return self.emptyPrinter(expr)
+
+    # The following can not be simply translated into C or Fortran
+    _print_Basic = _print_not_supported
+    _print_ComplexInfinity = _print_not_supported
+    _print_Derivative = _print_not_supported
+    _print_ExprCondPair = _print_not_supported
+    _print_GeometryEntity = _print_not_supported
+    _print_Infinity = _print_not_supported
+    _print_Integral = _print_not_supported
+    _print_Interval = _print_not_supported
+    _print_AccumulationBounds = _print_not_supported
+    _print_Limit = _print_not_supported
+    _print_MatrixBase = _print_not_supported
+    _print_DeferredVector = _print_not_supported
+    _print_NaN = _print_not_supported
+    _print_NegativeInfinity = _print_not_supported
+    _print_Order = _print_not_supported
+    _print_RootOf = _print_not_supported
+    _print_RootsOf = _print_not_supported
+    _print_RootSum = _print_not_supported
+    _print_Uniform = _print_not_supported
+    _print_Unit = _print_not_supported
+    _print_Wild = _print_not_supported
+    _print_WildFunction = _print_not_supported
+    _print_Relational = _print_not_supported
+
+
+# Code printer functions. These are included in this file so that they can be
+# imported in the top-level __init__.py without importing the sympy.codegen
+# module.
+
+def ccode(expr, assign_to=None, standard='c99', **settings):
+    """Converts an expr to a string of c code
+
+    Parameters
+    ==========
+
+    expr : Expr
+        A SymPy expression to be converted.
+    assign_to : optional
+        When given, the argument is used as the name of the variable to which
+        the expression is assigned. Can be a string, ``Symbol``,
+        ``MatrixSymbol``, or ``Indexed`` type. This is helpful in case of
+        line-wrapping, or for expressions that generate multi-line statements.
+    standard : str, optional
+        String specifying the standard. If your compiler supports a more modern
+        standard you may set this to 'c99' to allow the printer to use more math
+        functions. [default='c89'].
+    precision : integer, optional
+        The precision for numbers such as pi [default=17].
+    user_functions : dict, optional
+        A dictionary where the keys are string representations of either
+        ``FunctionClass`` or ``UndefinedFunction`` instances and the values
+        are their desired C string representations. Alternatively, the
+        dictionary value can be a list of tuples i.e. [(argument_test,
+        cfunction_string)] or [(argument_test, cfunction_formater)]. See below
+        for examples.
+    dereference : iterable, optional
+        An iterable of symbols that should be dereferenced in the printed code
+        expression. These would be values passed by address to the function.
+        For example, if ``dereference=[a]``, the resulting code would print
+        ``(*a)`` instead of ``a``.
+    human : bool, optional
+        If True, the result is a single string that may contain some constant
+        declarations for the number symbols. If False, the same information is
+        returned in a tuple of (symbols_to_declare, not_supported_functions,
+        code_text). [default=True].
+    contract: bool, optional
+        If True, ``Indexed`` instances are assumed to obey tensor contraction
+        rules and the corresponding nested loops over indices are generated.
+        Setting contract=False will not generate loops, instead the user is
+        responsible to provide values for the indices in the code.
+        [default=True].
+
+    Examples
+    ========
+
+    >>> from sympy import ccode, symbols, Rational, sin, ceiling, Abs, Function
+    >>> x, tau = symbols("x, tau")
+    >>> expr = (2*tau)**Rational(7, 2)
+    >>> ccode(expr)
+    '8*M_SQRT2*pow(tau, 7.0/2.0)'
+    >>> ccode(expr, math_macros={})
+    '8*sqrt(2)*pow(tau, 7.0/2.0)'
+    >>> ccode(sin(x), assign_to="s")
+    's = sin(x);'
+    >>> from sympy.codegen.ast import real, float80
+    >>> ccode(expr, type_aliases={real: float80})
+    '8*M_SQRT2l*powl(tau, 7.0L/2.0L)'
+
+    Simple custom printing can be defined for certain types by passing a
+    dictionary of {"type" : "function"} to the ``user_functions`` kwarg.
+    Alternatively, the dictionary value can be a list of tuples i.e.
+    [(argument_test, cfunction_string)].
+
+    >>> custom_functions = {
+    ...   "ceiling": "CEIL",
+    ...   "Abs": [(lambda x: not x.is_integer, "fabs"),
+    ...           (lambda x: x.is_integer, "ABS")],
+    ...   "func": "f"
+    ... }
+    >>> func = Function('func')
+    >>> ccode(func(Abs(x) + ceiling(x)), standard='C89', user_functions=custom_functions)
+    'f(fabs(x) + CEIL(x))'
+
+    or if the C-function takes a subset of the original arguments:
+
+    >>> ccode(2**x + 3**x, standard='C99', user_functions={'Pow': [
+    ...   (lambda b, e: b == 2, lambda b, e: 'exp2(%s)' % e),
+    ...   (lambda b, e: b != 2, 'pow')]})
+    'exp2(x) + pow(3, x)'
+
+    ``Piecewise`` expressions are converted into conditionals. If an
+    ``assign_to`` variable is provided an if statement is created, otherwise
+    the ternary operator is used. Note that if the ``Piecewise`` lacks a
+    default term, represented by ``(expr, True)`` then an error will be thrown.
+    This is to prevent generating an expression that may not evaluate to
+    anything.
+
+    >>> from sympy import Piecewise
+    >>> expr = Piecewise((x + 1, x > 0), (x, True))
+    >>> print(ccode(expr, tau, standard='C89'))
+    if (x > 0) {
+    tau = x + 1;
+    }
+    else {
+    tau = x;
+    }
+
+    Support for loops is provided through ``Indexed`` types. With
+    ``contract=True`` these expressions will be turned into loops, whereas
+    ``contract=False`` will just print the assignment expression that should be
+    looped over:
+
+    >>> from sympy import Eq, IndexedBase, Idx
+    >>> len_y = 5
+    >>> y = IndexedBase('y', shape=(len_y,))
+    >>> t = IndexedBase('t', shape=(len_y,))
+    >>> Dy = IndexedBase('Dy', shape=(len_y-1,))
+    >>> i = Idx('i', len_y-1)
+    >>> e=Eq(Dy[i], (y[i+1]-y[i])/(t[i+1]-t[i]))
+    >>> ccode(e.rhs, assign_to=e.lhs, contract=False, standard='C89')
+    'Dy[i] = (y[i + 1] - y[i])/(t[i + 1] - t[i]);'
+
+    Matrices are also supported, but a ``MatrixSymbol`` of the same dimensions
+    must be provided to ``assign_to``. Note that any expression that can be
+    generated normally can also exist inside a Matrix:
+
+    >>> from sympy import Matrix, MatrixSymbol
+    >>> mat = Matrix([x**2, Piecewise((x + 1, x > 0), (x, True)), sin(x)])
+    >>> A = MatrixSymbol('A', 3, 1)
+    >>> print(ccode(mat, A, standard='C89'))
+    A[0] = pow(x, 2);
+    if (x > 0) {
+       A[1] = x + 1;
+    }
+    else {
+       A[1] = x;
+    }
+    A[2] = sin(x);
+    """
+    from sympy.printing.c import c_code_printers
+    return c_code_printers[standard.lower()](settings).doprint(expr, assign_to)
+
+def print_ccode(expr, **settings):
+    """Prints C representation of the given expression."""
+    print(ccode(expr, **settings))
+
+def fcode(expr, assign_to=None, **settings):
+    """Converts an expr to a string of fortran code
+
+    Parameters
+    ==========
+
+    expr : Expr
+        A SymPy expression to be converted.
+    assign_to : optional
+        When given, the argument is used as the name of the variable to which
+        the expression is assigned. Can be a string, ``Symbol``,
+        ``MatrixSymbol``, or ``Indexed`` type. This is helpful in case of
+        line-wrapping, or for expressions that generate multi-line statements.
+    precision : integer, optional
+        DEPRECATED. Use type_mappings instead. The precision for numbers such
+        as pi [default=17].
+    user_functions : dict, optional
+        A dictionary where keys are ``FunctionClass`` instances and values are
+        their string representations. Alternatively, the dictionary value can
+        be a list of tuples i.e. [(argument_test, cfunction_string)]. See below
+        for examples.
+    human : bool, optional
+        If True, the result is a single string that may contain some constant
+        declarations for the number symbols. If False, the same information is
+        returned in a tuple of (symbols_to_declare, not_supported_functions,
+        code_text). [default=True].
+    contract: bool, optional
+        If True, ``Indexed`` instances are assumed to obey tensor contraction
+        rules and the corresponding nested loops over indices are generated.
+        Setting contract=False will not generate loops, instead the user is
+        responsible to provide values for the indices in the code.
+        [default=True].
+    source_format : optional
+        The source format can be either 'fixed' or 'free'. [default='fixed']
+    standard : integer, optional
+        The Fortran standard to be followed. This is specified as an integer.
+        Acceptable standards are 66, 77, 90, 95, 2003, and 2008. Default is 77.
+        Note that currently the only distinction internally is between
+        standards before 95, and those 95 and after. This may change later as
+        more features are added.
+    name_mangling : bool, optional
+        If True, then the variables that would become identical in
+        case-insensitive Fortran are mangled by appending different number
+        of ``_`` at the end. If False, SymPy Will not interfere with naming of
+        variables. [default=True]
+
+    Examples
+    ========
+
+    >>> from sympy import fcode, symbols, Rational, sin, ceiling, floor
+    >>> x, tau = symbols("x, tau")
+    >>> fcode((2*tau)**Rational(7, 2))
+    '      8*sqrt(2.0d0)*tau**(7.0d0/2.0d0)'
+    >>> fcode(sin(x), assign_to="s")
+    '      s = sin(x)'
+
+    Custom printing can be defined for certain types by passing a dictionary of
+    "type" : "function" to the ``user_functions`` kwarg. Alternatively, the
+    dictionary value can be a list of tuples i.e. [(argument_test,
+    cfunction_string)].
+
+    >>> custom_functions = {
+    ...   "ceiling": "CEIL",
+    ...   "floor": [(lambda x: not x.is_integer, "FLOOR1"),
+    ...             (lambda x: x.is_integer, "FLOOR2")]
+    ... }
+    >>> fcode(floor(x) + ceiling(x), user_functions=custom_functions)
+    '      CEIL(x) + FLOOR1(x)'
+
+    ``Piecewise`` expressions are converted into conditionals. If an
+    ``assign_to`` variable is provided an if statement is created, otherwise
+    the ternary operator is used. Note that if the ``Piecewise`` lacks a
+    default term, represented by ``(expr, True)`` then an error will be thrown.
+    This is to prevent generating an expression that may not evaluate to
+    anything.
+
+    >>> from sympy import Piecewise
+    >>> expr = Piecewise((x + 1, x > 0), (x, True))
+    >>> print(fcode(expr, tau))
+          if (x > 0) then
+             tau = x + 1
+          else
+             tau = x
+          end if
+
+    Support for loops is provided through ``Indexed`` types. With
+    ``contract=True`` these expressions will be turned into loops, whereas
+    ``contract=False`` will just print the assignment expression that should be
+    looped over:
+
+    >>> from sympy import Eq, IndexedBase, Idx
+    >>> len_y = 5
+    >>> y = IndexedBase('y', shape=(len_y,))
+    >>> t = IndexedBase('t', shape=(len_y,))
+    >>> Dy = IndexedBase('Dy', shape=(len_y-1,))
+    >>> i = Idx('i', len_y-1)
+    >>> e=Eq(Dy[i], (y[i+1]-y[i])/(t[i+1]-t[i]))
+    >>> fcode(e.rhs, assign_to=e.lhs, contract=False)
+    '      Dy(i) = (y(i + 1) - y(i))/(t(i + 1) - t(i))'
+
+    Matrices are also supported, but a ``MatrixSymbol`` of the same dimensions
+    must be provided to ``assign_to``. Note that any expression that can be
+    generated normally can also exist inside a Matrix:
+
+    >>> from sympy import Matrix, MatrixSymbol
+    >>> mat = Matrix([x**2, Piecewise((x + 1, x > 0), (x, True)), sin(x)])
+    >>> A = MatrixSymbol('A', 3, 1)
+    >>> print(fcode(mat, A))
+          A(1, 1) = x**2
+             if (x > 0) then
+          A(2, 1) = x + 1
+             else
+          A(2, 1) = x
+             end if
+          A(3, 1) = sin(x)
+    """
+    from sympy.printing.fortran import FCodePrinter
+    return FCodePrinter(settings).doprint(expr, assign_to)
+
+
+def print_fcode(expr, **settings):
+    """Prints the Fortran representation of the given expression.
+
+       See fcode for the meaning of the optional arguments.
+    """
+    print(fcode(expr, **settings))
+
+def cxxcode(expr, assign_to=None, standard='c++11', **settings):
+    """ C++ equivalent of :func:`~.ccode`. """
+    from sympy.printing.cxx import cxx_code_printers
+    return cxx_code_printers[standard.lower()](settings).doprint(expr, assign_to)

venv/lib/python3.10/site-packages/sympy/printing/cxx.py

@@ -0,0 +1,169 @@
+"""
+C++ code printer
+"""
+
+from itertools import chain
+from sympy.codegen.ast import Type, none
+from .c import C89CodePrinter, C99CodePrinter
+
+# These are defined in the other file so we can avoid importing sympy.codegen
+# from the top-level 'import sympy'. Export them here as well.
+from sympy.printing.codeprinter import cxxcode # noqa:F401
+
+# from https://en.cppreference.com/w/cpp/keyword
+reserved = {
+    'C++98': [
+        'and', 'and_eq', 'asm', 'auto', 'bitand', 'bitor', 'bool', 'break',
+        'case', 'catch,', 'char', 'class', 'compl', 'const', 'const_cast',
+        'continue', 'default', 'delete', 'do', 'double', 'dynamic_cast',
+        'else', 'enum', 'explicit', 'export', 'extern', 'false', 'float',
+        'for', 'friend', 'goto', 'if', 'inline', 'int', 'long', 'mutable',
+        'namespace', 'new', 'not', 'not_eq', 'operator', 'or', 'or_eq',
+        'private', 'protected', 'public', 'register', 'reinterpret_cast',
+        'return', 'short', 'signed', 'sizeof', 'static', 'static_cast',
+        'struct', 'switch', 'template', 'this', 'throw', 'true', 'try',
+        'typedef', 'typeid', 'typename', 'union', 'unsigned', 'using',
+        'virtual', 'void', 'volatile', 'wchar_t', 'while', 'xor', 'xor_eq'
+    ]
+}
+
+reserved['C++11'] = reserved['C++98'][:] + [
+    'alignas', 'alignof', 'char16_t', 'char32_t', 'constexpr', 'decltype',
+    'noexcept', 'nullptr', 'static_assert', 'thread_local'
+]
+reserved['C++17'] = reserved['C++11'][:]
+reserved['C++17'].remove('register')
+# TM TS: atomic_cancel, atomic_commit, atomic_noexcept, synchronized
+# concepts TS: concept, requires
+# module TS: import, module
+
+
+_math_functions = {
+    'C++98': {
+        'Mod': 'fmod',
+        'ceiling': 'ceil',
+    },
+    'C++11': {
+        'gamma': 'tgamma',
+    },
+    'C++17': {
+        'beta': 'beta',
+        'Ei': 'expint',
+        'zeta': 'riemann_zeta',
+    }
+}
+
+# from https://en.cppreference.com/w/cpp/header/cmath
+for k in ('Abs', 'exp', 'log', 'log10', 'sqrt', 'sin', 'cos', 'tan',  # 'Pow'
+          'asin', 'acos', 'atan', 'atan2', 'sinh', 'cosh', 'tanh', 'floor'):
+    _math_functions['C++98'][k] = k.lower()
+
+
+for k in ('asinh', 'acosh', 'atanh', 'erf', 'erfc'):
+    _math_functions['C++11'][k] = k.lower()
+
+
+def _attach_print_method(cls, sympy_name, func_name):
+    meth_name = '_print_%s' % sympy_name
+    if hasattr(cls, meth_name):
+        raise ValueError("Edit method (or subclass) instead of overwriting.")
+    def _print_method(self, expr):
+        return '{}{}({})'.format(self._ns, func_name, ', '.join(map(self._print, expr.args)))
+    _print_method.__doc__ = "Prints code for %s" % k
+    setattr(cls, meth_name, _print_method)
+
+
+def _attach_print_methods(cls, cont):
+    for sympy_name, cxx_name in cont[cls.standard].items():
+        _attach_print_method(cls, sympy_name, cxx_name)
+
+
+class _CXXCodePrinterBase:
+    printmethod = "_cxxcode"
+    language = 'C++'
+    _ns = 'std::'  # namespace
+
+    def __init__(self, settings=None):
+        super().__init__(settings or {})
+
+    def _print_Max(self, expr):
+        from sympy.functions.elementary.miscellaneous import Max
+        if len(expr.args) == 1:
+            return self._print(expr.args[0])
+        return "%smax(%s, %s)" % (self._ns, self._print(expr.args[0]),
+                                  self._print(Max(*expr.args[1:])))
+
+    def _print_Min(self, expr):
+        from sympy.functions.elementary.miscellaneous import Min
+        if len(expr.args) == 1:
+            return self._print(expr.args[0])
+        return "%smin(%s, %s)" % (self._ns, self._print(expr.args[0]),
+                                  self._print(Min(*expr.args[1:])))
+
+    def _print_using(self, expr):
+        if expr.alias == none:
+            return 'using %s' % expr.type
+        else:
+            raise ValueError("C++98 does not support type aliases")
+
+
+class CXX98CodePrinter(_CXXCodePrinterBase, C89CodePrinter):
+    standard = 'C++98'
+    reserved_words = set(reserved['C++98'])
+
+
+# _attach_print_methods(CXX98CodePrinter, _math_functions)
+
+
+class CXX11CodePrinter(_CXXCodePrinterBase, C99CodePrinter):
+    standard = 'C++11'
+    reserved_words = set(reserved['C++11'])
+    type_mappings = dict(chain(
+        CXX98CodePrinter.type_mappings.items(),
+        {
+            Type('int8'): ('int8_t', {'cstdint'}),
+            Type('int16'): ('int16_t', {'cstdint'}),
+            Type('int32'): ('int32_t', {'cstdint'}),
+            Type('int64'): ('int64_t', {'cstdint'}),
+            Type('uint8'): ('uint8_t', {'cstdint'}),
+            Type('uint16'): ('uint16_t', {'cstdint'}),
+            Type('uint32'): ('uint32_t', {'cstdint'}),
+            Type('uint64'): ('uint64_t', {'cstdint'}),
+            Type('complex64'): ('std::complex<float>', {'complex'}),
+            Type('complex128'): ('std::complex<double>', {'complex'}),
+            Type('bool'): ('bool', None),
+        }.items()
+    ))
+
+    def _print_using(self, expr):
+        if expr.alias == none:
+            return super()._print_using(expr)
+        else:
+            return 'using %(alias)s = %(type)s' % expr.kwargs(apply=self._print)
+
+# _attach_print_methods(CXX11CodePrinter, _math_functions)
+
+
+class CXX17CodePrinter(_CXXCodePrinterBase, C99CodePrinter):
+    standard = 'C++17'
+    reserved_words = set(reserved['C++17'])
+
+    _kf = dict(C99CodePrinter._kf, **_math_functions['C++17'])
+
+    def _print_beta(self, expr):
+        return self._print_math_func(expr)
+
+    def _print_Ei(self, expr):
+        return self._print_math_func(expr)
+
+    def _print_zeta(self, expr):
+        return self._print_math_func(expr)
+
+
+# _attach_print_methods(CXX17CodePrinter, _math_functions)
+
+cxx_code_printers = {
+    'c++98': CXX98CodePrinter,
+    'c++11': CXX11CodePrinter,
+    'c++17': CXX17CodePrinter
+}

venv/lib/python3.10/site-packages/sympy/printing/dot.py

@@ -0,0 +1,294 @@
+from sympy.core.basic import Basic
+from sympy.core.expr import Expr
+from sympy.core.symbol import Symbol
+from sympy.core.numbers import Integer, Rational, Float
+from sympy.printing.repr import srepr
+
+__all__ = ['dotprint']
+
+default_styles = (
+    (Basic, {'color': 'blue', 'shape': 'ellipse'}),
+    (Expr,  {'color': 'black'})
+)
+
+slotClasses = (Symbol, Integer, Rational, Float)
+def purestr(x, with_args=False):
+    """A string that follows ```obj = type(obj)(*obj.args)``` exactly.
+
+    Parameters
+    ==========
+
+    with_args : boolean, optional
+        If ``True``, there will be a second argument for the return
+        value, which is a tuple containing ``purestr`` applied to each
+        of the subnodes.
+
+        If ``False``, there will not be a second argument for the
+        return.
+
+        Default is ``False``
+
+    Examples
+    ========
+
+    >>> from sympy import Float, Symbol, MatrixSymbol
+    >>> from sympy import Integer # noqa: F401
+    >>> from sympy.core.symbol import Str # noqa: F401
+    >>> from sympy.printing.dot import purestr
+
+    Applying ``purestr`` for basic symbolic object:
+    >>> code = purestr(Symbol('x'))
+    >>> code
+    "Symbol('x')"
+    >>> eval(code) == Symbol('x')
+    True
+
+    For basic numeric object:
+    >>> purestr(Float(2))
+    "Float('2.0', precision=53)"
+
+    For matrix symbol:
+    >>> code = purestr(MatrixSymbol('x', 2, 2))
+    >>> code
+    "MatrixSymbol(Str('x'), Integer(2), Integer(2))"
+    >>> eval(code) == MatrixSymbol('x', 2, 2)
+    True
+
+    With ``with_args=True``:
+    >>> purestr(Float(2), with_args=True)
+    ("Float('2.0', precision=53)", ())
+    >>> purestr(MatrixSymbol('x', 2, 2), with_args=True)
+    ("MatrixSymbol(Str('x'), Integer(2), Integer(2))",
+     ("Str('x')", 'Integer(2)', 'Integer(2)'))
+    """
+    sargs = ()
+    if not isinstance(x, Basic):
+        rv = str(x)
+    elif not x.args:
+        rv = srepr(x)
+    else:
+        args = x.args
+        sargs = tuple(map(purestr, args))
+        rv = "%s(%s)"%(type(x).__name__, ', '.join(sargs))
+    if with_args:
+        rv = rv, sargs
+    return rv
+
+
+def styleof(expr, styles=default_styles):
+    """ Merge style dictionaries in order
+
+    Examples
+    ========
+
+    >>> from sympy import Symbol, Basic, Expr, S
+    >>> from sympy.printing.dot import styleof
+    >>> styles = [(Basic, {'color': 'blue', 'shape': 'ellipse'}),
+    ...           (Expr,  {'color': 'black'})]
+
+    >>> styleof(Basic(S(1)), styles)
+    {'color': 'blue', 'shape': 'ellipse'}
+
+    >>> x = Symbol('x')
+    >>> styleof(x + 1, styles)  # this is an Expr
+    {'color': 'black', 'shape': 'ellipse'}
+    """
+    style = {}
+    for typ, sty in styles:
+        if isinstance(expr, typ):
+            style.update(sty)
+    return style
+
+
+def attrprint(d, delimiter=', '):
+    """ Print a dictionary of attributes
+
+    Examples
+    ========
+
+    >>> from sympy.printing.dot import attrprint
+    >>> print(attrprint({'color': 'blue', 'shape': 'ellipse'}))
+    "color"="blue", "shape"="ellipse"
+    """
+    return delimiter.join('"%s"="%s"'%item for item in sorted(d.items()))
+
+
+def dotnode(expr, styles=default_styles, labelfunc=str, pos=(), repeat=True):
+    """ String defining a node
+
+    Examples
+    ========
+
+    >>> from sympy.printing.dot import dotnode
+    >>> from sympy.abc import x
+    >>> print(dotnode(x))
+    "Symbol('x')_()" ["color"="black", "label"="x", "shape"="ellipse"];
+    """
+    style = styleof(expr, styles)
+
+    if isinstance(expr, Basic) and not expr.is_Atom:
+        label = str(expr.__class__.__name__)
+    else:
+        label = labelfunc(expr)
+    style['label'] = label
+    expr_str = purestr(expr)
+    if repeat:
+        expr_str += '_%s' % str(pos)
+    return '"%s" [%s];' % (expr_str, attrprint(style))
+
+
+def dotedges(expr, atom=lambda x: not isinstance(x, Basic), pos=(), repeat=True):
+    """ List of strings for all expr->expr.arg pairs
+
+    See the docstring of dotprint for explanations of the options.
+
+    Examples
+    ========
+
+    >>> from sympy.printing.dot import dotedges
+    >>> from sympy.abc import x
+    >>> for e in dotedges(x+2):
+    ...     print(e)
+    "Add(Integer(2), Symbol('x'))_()" -> "Integer(2)_(0,)";
+    "Add(Integer(2), Symbol('x'))_()" -> "Symbol('x')_(1,)";
+    """
+    if atom(expr):
+        return []
+    else:
+        expr_str, arg_strs = purestr(expr, with_args=True)
+        if repeat:
+            expr_str += '_%s' % str(pos)
+            arg_strs = ['%s_%s' % (a, str(pos + (i,)))
+                for i, a in enumerate(arg_strs)]
+        return ['"%s" -> "%s";' % (expr_str, a) for a in arg_strs]
+
+template = \
+"""digraph{
+
+# Graph style
+%(graphstyle)s
+
+#########
+# Nodes #
+#########
+
+%(nodes)s
+
+#########
+# Edges #
+#########
+
+%(edges)s
+}"""
+
+_graphstyle = {'rankdir': 'TD', 'ordering': 'out'}
+
+def dotprint(expr,
+    styles=default_styles, atom=lambda x: not isinstance(x, Basic),
+    maxdepth=None, repeat=True, labelfunc=str, **kwargs):
+    """DOT description of a SymPy expression tree
+
+    Parameters
+    ==========
+
+    styles : list of lists composed of (Class, mapping), optional
+        Styles for different classes.
+
+        The default is
+
+        .. code-block:: python
+
+            (
+                (Basic, {'color': 'blue', 'shape': 'ellipse'}),
+                (Expr,  {'color': 'black'})
+            )
+
+    atom : function, optional
+        Function used to determine if an arg is an atom.
+
+        A good choice is ``lambda x: not x.args``.
+
+        The default is ``lambda x: not isinstance(x, Basic)``.
+
+    maxdepth : integer, optional
+        The maximum depth.
+
+        The default is ``None``, meaning no limit.
+
+    repeat : boolean, optional
+        Whether to use different nodes for common subexpressions.
+
+        The default is ``True``.
+
+        For example, for ``x + x*y`` with ``repeat=True``, it will have
+        two nodes for ``x``; with ``repeat=False``, it will have one
+        node.
+
+        .. warning::
+            Even if a node appears twice in the same object like ``x`` in
+            ``Pow(x, x)``, it will still only appear once.
+            Hence, with ``repeat=False``, the number of arrows out of an
+            object might not equal the number of args it has.
+
+    labelfunc : function, optional
+        A function to create a label for a given leaf node.
+
+        The default is ``str``.
+
+        Another good option is ``srepr``.
+
+        For example with ``str``, the leaf nodes of ``x + 1`` are labeled,
+        ``x`` and ``1``.  With ``srepr``, they are labeled ``Symbol('x')``
+        and ``Integer(1)``.
+
+    **kwargs : optional
+        Additional keyword arguments are included as styles for the graph.
+
+    Examples
+    ========
+
+    >>> from sympy import dotprint
+    >>> from sympy.abc import x
+    >>> print(dotprint(x+2)) # doctest: +NORMALIZE_WHITESPACE
+    digraph{
+    <BLANKLINE>
+    # Graph style
+    "ordering"="out"
+    "rankdir"="TD"
+    <BLANKLINE>
+    #########
+    # Nodes #
+    #########
+    <BLANKLINE>
+    "Add(Integer(2), Symbol('x'))_()" ["color"="black", "label"="Add", "shape"="ellipse"];
+    "Integer(2)_(0,)" ["color"="black", "label"="2", "shape"="ellipse"];
+    "Symbol('x')_(1,)" ["color"="black", "label"="x", "shape"="ellipse"];
+    <BLANKLINE>
+    #########
+    # Edges #
+    #########
+    <BLANKLINE>
+    "Add(Integer(2), Symbol('x'))_()" -> "Integer(2)_(0,)";
+    "Add(Integer(2), Symbol('x'))_()" -> "Symbol('x')_(1,)";
+    }
+
+    """
+    # repeat works by adding a signature tuple to the end of each node for its
+    # position in the graph. For example, for expr = Add(x, Pow(x, 2)), the x in the
+    # Pow will have the tuple (1, 0), meaning it is expr.args[1].args[0].
+    graphstyle = _graphstyle.copy()
+    graphstyle.update(kwargs)
+
+    nodes = []
+    edges = []
+    def traverse(e, depth, pos=()):
+        nodes.append(dotnode(e, styles, labelfunc=labelfunc, pos=pos, repeat=repeat))
+        if maxdepth and depth >= maxdepth:
+            return
+        edges.extend(dotedges(e, atom=atom, pos=pos, repeat=repeat))
+        [traverse(arg, depth+1, pos + (i,)) for i, arg in enumerate(e.args) if not atom(arg)]
+    traverse(expr, 0)
+
+    return template%{'graphstyle': attrprint(graphstyle, delimiter='\n'),
+                     'nodes': '\n'.join(nodes),
+                     'edges': '\n'.join(edges)}

venv/lib/python3.10/site-packages/sympy/printing/glsl.py

@@ -0,0 +1,557 @@
+from __future__ import annotations
+
+from sympy.core import Basic, S
+from sympy.core.function import Lambda
+from sympy.core.numbers import equal_valued
+from sympy.printing.codeprinter import CodePrinter
+from sympy.printing.precedence import precedence
+from functools import reduce
+
+known_functions = {
+    'Abs': 'abs',
+    'sin': 'sin',
+    'cos': 'cos',
+    'tan': 'tan',
+    'acos': 'acos',
+    'asin': 'asin',
+    'atan': 'atan',
+    'atan2': 'atan',
+    'ceiling': 'ceil',
+    'floor': 'floor',
+    'sign': 'sign',
+    'exp': 'exp',
+    'log': 'log',
+    'add': 'add',
+    'sub': 'sub',
+    'mul': 'mul',
+    'pow': 'pow'
+}
+
+class GLSLPrinter(CodePrinter):
+    """
+    Rudimentary, generic GLSL printing tools.
+
+    Additional settings:
+    'use_operators': Boolean (should the printer use operators for +,-,*, or functions?)
+    """
+    _not_supported: set[Basic] = set()
+    printmethod = "_glsl"
+    language = "GLSL"
+
+    _default_settings = {
+        'use_operators': True,
+        'zero': 0,
+        'mat_nested': False,
+        'mat_separator': ',\n',
+        'mat_transpose': False,
+        'array_type': 'float',
+        'glsl_types': True,
+
+        'order': None,
+        'full_prec': 'auto',
+        'precision': 9,
+        'user_functions': {},
+        'human': True,
+        'allow_unknown_functions': False,
+        'contract': True,
+        'error_on_reserved': False,
+        'reserved_word_suffix': '_',
+    }
+
+    def __init__(self, settings={}):
+        CodePrinter.__init__(self, settings)
+        self.known_functions = dict(known_functions)
+        userfuncs = settings.get('user_functions', {})
+        self.known_functions.update(userfuncs)
+
+    def _rate_index_position(self, p):
+        return p*5
+
+    def _get_statement(self, codestring):
+        return "%s;" % codestring
+
+    def _get_comment(self, text):
+        return "// {}".format(text)
+
+    def _declare_number_const(self, name, value):
+        return "float {} = {};".format(name, value)
+
+    def _format_code(self, lines):
+        return self.indent_code(lines)
+
+    def indent_code(self, code):
+        """Accepts a string of code or a list of code lines"""
+
+        if isinstance(code, str):
+            code_lines = self.indent_code(code.splitlines(True))
+            return ''.join(code_lines)
+
+        tab = "   "
+        inc_token = ('{', '(', '{\n', '(\n')
+        dec_token = ('}', ')')
+
+        code = [line.lstrip(' \t') for line in code]
+
+        increase = [int(any(map(line.endswith, inc_token))) for line in code]
+        decrease = [int(any(map(line.startswith, dec_token))) for line in code]
+
+        pretty = []
+        level = 0
+        for n, line in enumerate(code):
+            if line in ('', '\n'):
+                pretty.append(line)
+                continue
+            level -= decrease[n]
+            pretty.append("%s%s" % (tab*level, line))
+            level += increase[n]
+        return pretty
+
+    def _print_MatrixBase(self, mat):
+        mat_separator = self._settings['mat_separator']
+        mat_transpose = self._settings['mat_transpose']
+        column_vector = (mat.rows == 1) if mat_transpose else (mat.cols == 1)
+        A = mat.transpose() if mat_transpose != column_vector else mat
+
+        glsl_types = self._settings['glsl_types']
+        array_type = self._settings['array_type']
+        array_size = A.cols*A.rows
+        array_constructor = "{}[{}]".format(array_type, array_size)
+
+        if A.cols == 1:
+            return self._print(A[0]);
+        if A.rows <= 4 and A.cols <= 4 and glsl_types:
+            if A.rows == 1:
+                return "vec{}{}".format(
+                    A.cols, A.table(self,rowstart='(',rowend=')')
+                )
+            elif A.rows == A.cols:
+                return "mat{}({})".format(
+                    A.rows, A.table(self,rowsep=', ',
+                    rowstart='',rowend='')
+                )
+            else:
+                return "mat{}x{}({})".format(
+                    A.cols, A.rows,
+                    A.table(self,rowsep=', ',
+                    rowstart='',rowend='')
+                )
+        elif S.One in A.shape:
+            return "{}({})".format(
+                array_constructor,
+                A.table(self,rowsep=mat_separator,rowstart='',rowend='')
+            )
+        elif not self._settings['mat_nested']:
+            return "{}(\n{}\n) /* a {}x{} matrix */".format(
+                array_constructor,
+                A.table(self,rowsep=mat_separator,rowstart='',rowend=''),
+                A.rows, A.cols
+            )
+        elif self._settings['mat_nested']:
+            return "{}[{}][{}](\n{}\n)".format(
+                array_type, A.rows, A.cols,
+                A.table(self,rowsep=mat_separator,rowstart='float[](',rowend=')')
+            )
+
+    def _print_SparseRepMatrix(self, mat):
+        # do not allow sparse matrices to be made dense
+        return self._print_not_supported(mat)
+
+    def _traverse_matrix_indices(self, mat):
+        mat_transpose = self._settings['mat_transpose']
+        if mat_transpose:
+            rows,cols = mat.shape
+        else:
+            cols,rows = mat.shape
+        return ((i, j) for i in range(cols) for j in range(rows))
+
+    def _print_MatrixElement(self, expr):
+        # print('begin _print_MatrixElement')
+        nest = self._settings['mat_nested'];
+        glsl_types = self._settings['glsl_types'];
+        mat_transpose = self._settings['mat_transpose'];
+        if mat_transpose:
+            cols,rows = expr.parent.shape
+            i,j = expr.j,expr.i
+        else:
+            rows,cols = expr.parent.shape
+            i,j = expr.i,expr.j
+        pnt = self._print(expr.parent)
+        if glsl_types and ((rows <= 4 and cols <=4) or nest):
+            return "{}[{}][{}]".format(pnt, i, j)
+        else:
+            return "{}[{}]".format(pnt, i + j*rows)
+
+    def _print_list(self, expr):
+        l = ', '.join(self._print(item) for item in expr)
+        glsl_types = self._settings['glsl_types']
+        array_type = self._settings['array_type']
+        array_size = len(expr)
+        array_constructor = '{}[{}]'.format(array_type, array_size)
+
+        if array_size <= 4 and glsl_types:
+            return 'vec{}({})'.format(array_size, l)
+        else:
+            return '{}({})'.format(array_constructor, l)
+
+    _print_tuple = _print_list
+    _print_Tuple = _print_list
+
+    def _get_loop_opening_ending(self, indices):
+        open_lines = []
+        close_lines = []
+        loopstart = "for (int %(varble)s=%(start)s; %(varble)s<%(end)s; %(varble)s++){"
+        for i in indices:
+            # GLSL arrays start at 0 and end at dimension-1
+            open_lines.append(loopstart % {
+                'varble': self._print(i.label),
+                'start': self._print(i.lower),
+                'end': self._print(i.upper + 1)})
+            close_lines.append("}")
+        return open_lines, close_lines
+
+    def _print_Function_with_args(self, func, func_args):
+        if func in self.known_functions:
+            cond_func = self.known_functions[func]
+            func = None
+            if isinstance(cond_func, str):
+                func = cond_func
+            else:
+                for cond, func in cond_func:
+                    if cond(func_args):
+                        break
+            if func is not None:
+                try:
+                    return func(*[self.parenthesize(item, 0) for item in func_args])
+                except TypeError:
+                    return '{}({})'.format(func, self.stringify(func_args, ", "))
+        elif isinstance(func, Lambda):
+            # inlined function
+            return self._print(func(*func_args))
+        else:
+            return self._print_not_supported(func)
+
+    def _print_Piecewise(self, expr):
+        from sympy.codegen.ast import Assignment
+        if expr.args[-1].cond != True:
+            # We need the last conditional to be a True, otherwise the resulting
+            # function may not return a result.
+            raise ValueError("All Piecewise expressions must contain an "
+                             "(expr, True) statement to be used as a default "
+                             "condition. Without one, the generated "
+                             "expression may not evaluate to anything under "
+                             "some condition.")
+        lines = []
+        if expr.has(Assignment):
+            for i, (e, c) in enumerate(expr.args):
+                if i == 0:
+                    lines.append("if (%s) {" % self._print(c))
+                elif i == len(expr.args) - 1 and c == True:
+                    lines.append("else {")
+                else:
+                    lines.append("else if (%s) {" % self._print(c))
+                code0 = self._print(e)
+                lines.append(code0)
+                lines.append("}")
+            return "\n".join(lines)
+        else:
+            # The piecewise was used in an expression, need to do inline
+            # operators. This has the downside that inline operators will
+            # not work for statements that span multiple lines (Matrix or
+            # Indexed expressions).
+            ecpairs = ["((%s) ? (\n%s\n)\n" % (self._print(c),
+                                               self._print(e))
+                    for e, c in expr.args[:-1]]
+            last_line = ": (\n%s\n)" % self._print(expr.args[-1].expr)
+            return ": ".join(ecpairs) + last_line + " ".join([")"*len(ecpairs)])
+
+    def _print_Idx(self, expr):
+        return self._print(expr.label)
+
+    def _print_Indexed(self, expr):
+        # calculate index for 1d array
+        dims = expr.shape
+        elem = S.Zero
+        offset = S.One
+        for i in reversed(range(expr.rank)):
+            elem += expr.indices[i]*offset
+            offset *= dims[i]
+        return "{}[{}]".format(
+            self._print(expr.base.label),
+            self._print(elem)
+        )
+
+    def _print_Pow(self, expr):
+        PREC = precedence(expr)
+        if equal_valued(expr.exp, -1):
+            return '1.0/%s' % (self.parenthesize(expr.base, PREC))
+        elif equal_valued(expr.exp, 0.5):
+            return 'sqrt(%s)' % self._print(expr.base)
+        else:
+            try:
+                e = self._print(float(expr.exp))
+            except TypeError:
+                e = self._print(expr.exp)
+            return self._print_Function_with_args('pow', (
+                self._print(expr.base),
+                e
+            ))
+
+    def _print_int(self, expr):
+        return str(float(expr))
+
+    def _print_Rational(self, expr):
+        return "{}.0/{}.0".format(expr.p, expr.q)
+
+    def _print_Relational(self, expr):
+        lhs_code = self._print(expr.lhs)
+        rhs_code = self._print(expr.rhs)
+        op = expr.rel_op
+        return "{} {} {}".format(lhs_code, op, rhs_code)
+
+    def _print_Add(self, expr, order=None):
+        if self._settings['use_operators']:
+            return CodePrinter._print_Add(self, expr, order=order)
+
+        terms = expr.as_ordered_terms()
+
+        def partition(p,l):
+            return reduce(lambda x, y: (x[0]+[y], x[1]) if p(y) else (x[0], x[1]+[y]), l,  ([], []))
+        def add(a,b):
+            return self._print_Function_with_args('add', (a, b))
+            # return self.known_functions['add']+'(%s, %s)' % (a,b)
+        neg, pos = partition(lambda arg: arg.could_extract_minus_sign(), terms)
+        if pos:
+            s = pos = reduce(lambda a,b: add(a,b), (self._print(t) for t in pos))
+        else:
+            s = pos = self._print(self._settings['zero'])
+
+        if neg:
+            # sum the absolute values of the negative terms
+            neg = reduce(lambda a,b: add(a,b), (self._print(-n) for n in neg))
+            # then subtract them from the positive terms
+            s = self._print_Function_with_args('sub', (pos,neg))
+            # s = self.known_functions['sub']+'(%s, %s)' % (pos,neg)
+        return s
+
+    def _print_Mul(self, expr, **kwargs):
+        if self._settings['use_operators']:
+            return CodePrinter._print_Mul(self, expr, **kwargs)
+        terms = expr.as_ordered_factors()
+        def mul(a,b):
+            # return self.known_functions['mul']+'(%s, %s)' % (a,b)
+            return self._print_Function_with_args('mul', (a,b))
+
+        s = reduce(lambda a,b: mul(a,b), (self._print(t) for t in terms))
+        return s
+
+def glsl_code(expr,assign_to=None,**settings):
+    """Converts an expr to a string of GLSL code
+
+    Parameters
+    ==========
+
+    expr : Expr
+        A SymPy expression to be converted.
+    assign_to : optional
+        When given, the argument is used for naming the variable or variables
+        to which the expression is assigned. Can be a string, ``Symbol``,
+        ``MatrixSymbol`` or ``Indexed`` type object. In cases where ``expr``
+        would be printed as an array, a list of string or ``Symbol`` objects
+        can also be passed.
+
+        This is helpful in case of line-wrapping, or for expressions that
+        generate multi-line statements.  It can also be used to spread an array-like
+        expression into multiple assignments.
+    use_operators: bool, optional
+        If set to False, then *,/,+,- operators will be replaced with functions
+        mul, add, and sub, which must be implemented by the user, e.g. for
+        implementing non-standard rings or emulated quad/octal precision.
+        [default=True]
+    glsl_types: bool, optional
+        Set this argument to ``False`` in order to avoid using the ``vec`` and ``mat``
+        types.  The printer will instead use arrays (or nested arrays).
+        [default=True]
+    mat_nested: bool, optional
+        GLSL version 4.3 and above support nested arrays (arrays of arrays).  Set this to ``True``
+        to render matrices as nested arrays.
+        [default=False]
+    mat_separator: str, optional
+        By default, matrices are rendered with newlines using this separator,
+        making them easier to read, but less compact.  By removing the newline
+        this option can be used to make them more vertically compact.
+        [default=',\n']
+    mat_transpose: bool, optional
+        GLSL's matrix multiplication implementation assumes column-major indexing.
+        By default, this printer ignores that convention. Setting this option to
+        ``True`` transposes all matrix output.
+        [default=False]
+    array_type: str, optional
+        The GLSL array constructor type.
+        [default='float']
+    precision : integer, optional
+        The precision for numbers such as pi [default=15].
+    user_functions : dict, optional
+        A dictionary where keys are ``FunctionClass`` instances and values are
+        their string representations. Alternatively, the dictionary value can
+        be a list of tuples i.e. [(argument_test, js_function_string)]. See
+        below for examples.
+    human : bool, optional
+        If True, the result is a single string that may contain some constant
+        declarations for the number symbols. If False, the same information is
+        returned in a tuple of (symbols_to_declare, not_supported_functions,
+        code_text). [default=True].
+    contract: bool, optional
+        If True, ``Indexed`` instances are assumed to obey tensor contraction
+        rules and the corresponding nested loops over indices are generated.
+        Setting contract=False will not generate loops, instead the user is
+        responsible to provide values for the indices in the code.
+        [default=True].
+
+    Examples
+    ========
+
+    >>> from sympy import glsl_code, symbols, Rational, sin, ceiling, Abs
+    >>> x, tau = symbols("x, tau")
+    >>> glsl_code((2*tau)**Rational(7, 2))
+    '8*sqrt(2)*pow(tau, 3.5)'
+    >>> glsl_code(sin(x), assign_to="float y")
+    'float y = sin(x);'
+
+    Various GLSL types are supported:
+    >>> from sympy import Matrix, glsl_code
+    >>> glsl_code(Matrix([1,2,3]))
+    'vec3(1, 2, 3)'
+
+    >>> glsl_code(Matrix([[1, 2],[3, 4]]))
+    'mat2(1, 2, 3, 4)'
+
+    Pass ``mat_transpose = True`` to switch to column-major indexing:
+    >>> glsl_code(Matrix([[1, 2],[3, 4]]), mat_transpose = True)
+    'mat2(1, 3, 2, 4)'
+
+    By default, larger matrices get collapsed into float arrays:
+    >>> print(glsl_code( Matrix([[1,2,3,4,5],[6,7,8,9,10]]) ))
+    float[10](
+       1, 2, 3, 4,  5,
+       6, 7, 8, 9, 10
+    ) /* a 2x5 matrix */
+
+    The type of array constructor used to print GLSL arrays can be controlled
+    via the ``array_type`` parameter:
+    >>> glsl_code(Matrix([1,2,3,4,5]), array_type='int')
+    'int[5](1, 2, 3, 4, 5)'
+
+    Passing a list of strings or ``symbols`` to the ``assign_to`` parameter will yield
+    a multi-line assignment for each item in an array-like expression:
+    >>> x_struct_members = symbols('x.a x.b x.c x.d')
+    >>> print(glsl_code(Matrix([1,2,3,4]), assign_to=x_struct_members))
+    x.a = 1;
+    x.b = 2;
+    x.c = 3;
+    x.d = 4;
+
+    This could be useful in cases where it's desirable to modify members of a
+    GLSL ``Struct``.  It could also be used to spread items from an array-like
+    expression into various miscellaneous assignments:
+    >>> misc_assignments = ('x[0]', 'x[1]', 'float y', 'float z')
+    >>> print(glsl_code(Matrix([1,2,3,4]), assign_to=misc_assignments))
+    x[0] = 1;
+    x[1] = 2;
+    float y = 3;
+    float z = 4;
+
+    Passing ``mat_nested = True`` instead prints out nested float arrays, which are
+    supported in GLSL 4.3 and above.
+    >>> mat = Matrix([
+    ... [ 0,  1,  2],
+    ... [ 3,  4,  5],
+    ... [ 6,  7,  8],
+    ... [ 9, 10, 11],
+    ... [12, 13, 14]])
+    >>> print(glsl_code( mat, mat_nested = True ))
+    float[5][3](
+       float[]( 0,  1,  2),
+       float[]( 3,  4,  5),
+       float[]( 6,  7,  8),
+       float[]( 9, 10, 11),
+       float[](12, 13, 14)
+    )
+
+
+
+    Custom printing can be defined for certain types by passing a dictionary of
+    "type" : "function" to the ``user_functions`` kwarg. Alternatively, the
+    dictionary value can be a list of tuples i.e. [(argument_test,
+    js_function_string)].
+
+    >>> custom_functions = {
+    ...   "ceiling": "CEIL",
+    ...   "Abs": [(lambda x: not x.is_integer, "fabs"),
+    ...           (lambda x: x.is_integer, "ABS")]
+    ... }
+    >>> glsl_code(Abs(x) + ceiling(x), user_functions=custom_functions)
+    'fabs(x) + CEIL(x)'
+
+    If further control is needed, addition, subtraction, multiplication and
+    division operators can be replaced with ``add``, ``sub``, and ``mul``
+    functions.  This is done by passing ``use_operators = False``:
+
+    >>> x,y,z = symbols('x,y,z')
+    >>> glsl_code(x*(y+z), use_operators = False)
+    'mul(x, add(y, z))'
+    >>> glsl_code(x*(y+z*(x-y)**z), use_operators = False)
+    'mul(x, add(y, mul(z, pow(sub(x, y), z))))'
+
+    ``Piecewise`` expressions are converted into conditionals. If an
+    ``assign_to`` variable is provided an if statement is created, otherwise
+    the ternary operator is used. Note that if the ``Piecewise`` lacks a
+    default term, represented by ``(expr, True)`` then an error will be thrown.
+    This is to prevent generating an expression that may not evaluate to
+    anything.
+
+    >>> from sympy import Piecewise
+    >>> expr = Piecewise((x + 1, x > 0), (x, True))
+    >>> print(glsl_code(expr, tau))
+    if (x > 0) {
+       tau = x + 1;
+    }
+    else {
+       tau = x;
+    }
+
+    Support for loops is provided through ``Indexed`` types. With
+    ``contract=True`` these expressions will be turned into loops, whereas
+    ``contract=False`` will just print the assignment expression that should be
+    looped over:
+
+    >>> from sympy import Eq, IndexedBase, Idx
+    >>> len_y = 5
+    >>> y = IndexedBase('y', shape=(len_y,))
+    >>> t = IndexedBase('t', shape=(len_y,))
+    >>> Dy = IndexedBase('Dy', shape=(len_y-1,))
+    >>> i = Idx('i', len_y-1)
+    >>> e=Eq(Dy[i], (y[i+1]-y[i])/(t[i+1]-t[i]))
+    >>> glsl_code(e.rhs, assign_to=e.lhs, contract=False)
+    'Dy[i] = (y[i + 1] - y[i])/(t[i + 1] - t[i]);'
+
+    >>> from sympy import Matrix, MatrixSymbol
+    >>> mat = Matrix([x**2, Piecewise((x + 1, x > 0), (x, True)), sin(x)])
+    >>> A = MatrixSymbol('A', 3, 1)
+    >>> print(glsl_code(mat, A))
+    A[0][0] = pow(x, 2.0);
+    if (x > 0) {
+       A[1][0] = x + 1;
+    }
+    else {
+       A[1][0] = x;
+    }
+    A[2][0] = sin(x);
+    """
+    return GLSLPrinter(settings).doprint(expr,assign_to)
+
+def print_glsl(expr, **settings):
+    """Prints the GLSL representation of the given expression.
+
+       See GLSLPrinter init function for settings.
+    """
+    print(glsl_code(expr, **settings))

venv/lib/python3.10/site-packages/sympy/printing/gtk.py

@@ -0,0 +1,16 @@
+from sympy.printing.mathml import mathml
+from sympy.utilities.mathml import c2p
+import tempfile
+import subprocess
+
+
+def print_gtk(x, start_viewer=True):
+    """Print to Gtkmathview, a gtk widget capable of rendering MathML.
+
+    Needs libgtkmathview-bin"""
+    with tempfile.NamedTemporaryFile('w') as file:
+        file.write(c2p(mathml(x), simple=True))
+        file.flush()
+
+        if start_viewer:
+            subprocess.check_call(('mathmlviewer', file.name))

venv/lib/python3.10/site-packages/sympy/printing/julia.py

@@ -0,0 +1,658 @@
+"""
+Julia code printer
+
+The `JuliaCodePrinter` converts SymPy expressions into Julia expressions.
+
+A complete code generator, which uses `julia_code` extensively, can be found
+in `sympy.utilities.codegen`.  The `codegen` module can be used to generate
+complete source code files.
+
+"""
+
+from __future__ import annotations
+from typing import Any
+
+from sympy.core import Mul, Pow, S, Rational
+from sympy.core.mul import _keep_coeff
+from sympy.core.numbers import equal_valued
+from sympy.printing.codeprinter import CodePrinter
+from sympy.printing.precedence import precedence, PRECEDENCE
+from re import search
+
+# List of known functions.  First, those that have the same name in
+# SymPy and Julia. This is almost certainly incomplete!
+known_fcns_src1 = ["sin", "cos", "tan", "cot", "sec", "csc",
+                   "asin", "acos", "atan", "acot", "asec", "acsc",
+                   "sinh", "cosh", "tanh", "coth", "sech", "csch",
+                   "asinh", "acosh", "atanh", "acoth", "asech", "acsch",
+                   "sinc", "atan2", "sign", "floor", "log", "exp",
+                   "cbrt", "sqrt", "erf", "erfc", "erfi",
+                   "factorial", "gamma", "digamma", "trigamma",
+                   "polygamma", "beta",
+                   "airyai", "airyaiprime", "airybi", "airybiprime",
+                   "besselj", "bessely", "besseli", "besselk",
+                   "erfinv", "erfcinv"]
+# These functions have different names ("SymPy": "Julia"), more
+# generally a mapping to (argument_conditions, julia_function).
+known_fcns_src2 = {
+    "Abs": "abs",
+    "ceiling": "ceil",
+    "conjugate": "conj",
+    "hankel1": "hankelh1",
+    "hankel2": "hankelh2",
+    "im": "imag",
+    "re": "real"
+}
+
+
+class JuliaCodePrinter(CodePrinter):
+    """
+    A printer to convert expressions to strings of Julia code.
+    """
+    printmethod = "_julia"
+    language = "Julia"
+
+    _operators = {
+        'and': '&&',
+        'or': '||',
+        'not': '!',
+    }
+
+    _default_settings: dict[str, Any] = {
+        'order': None,
+        'full_prec': 'auto',
+        'precision': 17,
+        'user_functions': {},
+        'human': True,
+        'allow_unknown_functions': False,
+        'contract': True,
+        'inline': True,
+    }
+    # Note: contract is for expressing tensors as loops (if True), or just
+    # assignment (if False).  FIXME: this should be looked a more carefully
+    # for Julia.
+
+    def __init__(self, settings={}):
+        super().__init__(settings)
+        self.known_functions = dict(zip(known_fcns_src1, known_fcns_src1))
+        self.known_functions.update(dict(known_fcns_src2))
+        userfuncs = settings.get('user_functions', {})
+        self.known_functions.update(userfuncs)
+
+
+    def _rate_index_position(self, p):
+        return p*5
+
+
+    def _get_statement(self, codestring):
+        return "%s" % codestring
+
+
+    def _get_comment(self, text):
+        return "# {}".format(text)
+
+
+    def _declare_number_const(self, name, value):
+        return "const {} = {}".format(name, value)
+
+
+    def _format_code(self, lines):
+        return self.indent_code(lines)
+
+
+    def _traverse_matrix_indices(self, mat):
+        # Julia uses Fortran order (column-major)
+        rows, cols = mat.shape
+        return ((i, j) for j in range(cols) for i in range(rows))
+
+
+    def _get_loop_opening_ending(self, indices):
+        open_lines = []
+        close_lines = []
+        for i in indices:
+            # Julia arrays start at 1 and end at dimension
+            var, start, stop = map(self._print,
+                    [i.label, i.lower + 1, i.upper + 1])
+            open_lines.append("for %s = %s:%s" % (var, start, stop))
+            close_lines.append("end")
+        return open_lines, close_lines
+
+
+    def _print_Mul(self, expr):
+        # print complex numbers nicely in Julia
+        if (expr.is_number and expr.is_imaginary and
+                expr.as_coeff_Mul()[0].is_integer):
+            return "%sim" % self._print(-S.ImaginaryUnit*expr)
+
+        # cribbed from str.py
+        prec = precedence(expr)
+
+        c, e = expr.as_coeff_Mul()
+        if c < 0:
+            expr = _keep_coeff(-c, e)
+            sign = "-"
+        else:
+            sign = ""
+
+        a = []  # items in the numerator
+        b = []  # items that are in the denominator (if any)
+
+        pow_paren = []  # Will collect all pow with more than one base element and exp = -1
+
+        if self.order not in ('old', 'none'):
+            args = expr.as_ordered_factors()
+        else:
+            # use make_args in case expr was something like -x -> x
+            args = Mul.make_args(expr)
+
+        # Gather args for numerator/denominator
+        for item in args:
+            if (item.is_commutative and item.is_Pow and item.exp.is_Rational
+                    and item.exp.is_negative):
+                if item.exp != -1:
+                    b.append(Pow(item.base, -item.exp, evaluate=False))
+                else:
+                    if len(item.args[0].args) != 1 and isinstance(item.base, Mul):   # To avoid situations like #14160
+                        pow_paren.append(item)
+                    b.append(Pow(item.base, -item.exp))
+            elif item.is_Rational and item is not S.Infinity and item.p == 1:
+                # Save the Rational type in julia Unless the numerator is 1.
+                # For example:
+                # julia_code(Rational(3, 7)*x) --> (3 // 7) * x
+                # julia_code(x/3) --> x / 3 but not x * (1 // 3)
+                b.append(Rational(item.q))
+            else:
+                a.append(item)
+
+        a = a or [S.One]
+
+        a_str = [self.parenthesize(x, prec) for x in a]
+        b_str = [self.parenthesize(x, prec) for x in b]
+
+        # To parenthesize Pow with exp = -1 and having more than one Symbol
+        for item in pow_paren:
+            if item.base in b:
+                b_str[b.index(item.base)] = "(%s)" % b_str[b.index(item.base)]
+
+        # from here it differs from str.py to deal with "*" and ".*"
+        def multjoin(a, a_str):
+            # here we probably are assuming the constants will come first
+            r = a_str[0]
+            for i in range(1, len(a)):
+                mulsym = '*' if a[i-1].is_number else '.*'
+                r = "%s %s %s" % (r, mulsym, a_str[i])
+            return r
+
+        if not b:
+            return sign + multjoin(a, a_str)
+        elif len(b) == 1:
+            divsym = '/' if b[0].is_number else './'
+            return "%s %s %s" % (sign+multjoin(a, a_str), divsym, b_str[0])
+        else:
+            divsym = '/' if all(bi.is_number for bi in b) else './'
+            return "%s %s (%s)" % (sign + multjoin(a, a_str), divsym, multjoin(b, b_str))
+
+    def _print_Relational(self, expr):
+        lhs_code = self._print(expr.lhs)
+        rhs_code = self._print(expr.rhs)
+        op = expr.rel_op
+        return "{} {} {}".format(lhs_code, op, rhs_code)
+
+    def _print_Pow(self, expr):
+        powsymbol = '^' if all(x.is_number for x in expr.args) else '.^'
+
+        PREC = precedence(expr)
+
+        if equal_valued(expr.exp, 0.5):
+            return "sqrt(%s)" % self._print(expr.base)
+
+        if expr.is_commutative:
+            if equal_valued(expr.exp, -0.5):
+                sym = '/' if expr.base.is_number else './'
+                return "1 %s sqrt(%s)" % (sym, self._print(expr.base))
+            if equal_valued(expr.exp, -1):
+                sym = '/' if expr.base.is_number else './'
+                return  "1 %s %s" % (sym, self.parenthesize(expr.base, PREC))
+
+        return '%s %s %s' % (self.parenthesize(expr.base, PREC), powsymbol,
+                           self.parenthesize(expr.exp, PREC))
+
+
+    def _print_MatPow(self, expr):
+        PREC = precedence(expr)
+        return '%s ^ %s' % (self.parenthesize(expr.base, PREC),
+                          self.parenthesize(expr.exp, PREC))
+
+
+    def _print_Pi(self, expr):
+        if self._settings["inline"]:
+            return "pi"
+        else:
+            return super()._print_NumberSymbol(expr)
+
+
+    def _print_ImaginaryUnit(self, expr):
+        return "im"
+
+
+    def _print_Exp1(self, expr):
+        if self._settings["inline"]:
+            return "e"
+        else:
+            return super()._print_NumberSymbol(expr)
+
+
+    def _print_EulerGamma(self, expr):
+        if self._settings["inline"]:
+            return "eulergamma"
+        else:
+            return super()._print_NumberSymbol(expr)
+
+
+    def _print_Catalan(self, expr):
+        if self._settings["inline"]:
+            return "catalan"
+        else:
+            return super()._print_NumberSymbol(expr)
+
+
+    def _print_GoldenRatio(self, expr):
+        if self._settings["inline"]:
+            return "golden"
+        else:
+            return super()._print_NumberSymbol(expr)
+
+
+    def _print_Assignment(self, expr):
+        from sympy.codegen.ast import Assignment
+        from sympy.functions.elementary.piecewise import Piecewise
+        from sympy.tensor.indexed import IndexedBase
+        # Copied from codeprinter, but remove special MatrixSymbol treatment
+        lhs = expr.lhs
+        rhs = expr.rhs
+        # We special case assignments that take multiple lines
+        if not self._settings["inline"] and isinstance(expr.rhs, Piecewise):
+            # Here we modify Piecewise so each expression is now
+            # an Assignment, and then continue on the print.
+            expressions = []
+            conditions = []
+            for (e, c) in rhs.args:
+                expressions.append(Assignment(lhs, e))
+                conditions.append(c)
+            temp = Piecewise(*zip(expressions, conditions))
+            return self._print(temp)
+        if self._settings["contract"] and (lhs.has(IndexedBase) or
+                rhs.has(IndexedBase)):
+            # Here we check if there is looping to be done, and if so
+            # print the required loops.
+            return self._doprint_loops(rhs, lhs)
+        else:
+            lhs_code = self._print(lhs)
+            rhs_code = self._print(rhs)
+            return self._get_statement("%s = %s" % (lhs_code, rhs_code))
+
+
+    def _print_Infinity(self, expr):
+        return 'Inf'
+
+
+    def _print_NegativeInfinity(self, expr):
+        return '-Inf'
+
+
+    def _print_NaN(self, expr):
+        return 'NaN'
+
+
+    def _print_list(self, expr):
+        return 'Any[' + ', '.join(self._print(a) for a in expr) + ']'
+
+
+    def _print_tuple(self, expr):
+        if len(expr) == 1:
+            return "(%s,)" % self._print(expr[0])
+        else:
+            return "(%s)" % self.stringify(expr, ", ")
+    _print_Tuple = _print_tuple
+
+
+    def _print_BooleanTrue(self, expr):
+        return "true"
+
+
+    def _print_BooleanFalse(self, expr):
+        return "false"
+
+
+    def _print_bool(self, expr):
+        return str(expr).lower()
+
+
+    # Could generate quadrature code for definite Integrals?
+    #_print_Integral = _print_not_supported
+
+
+    def _print_MatrixBase(self, A):
+        # Handle zero dimensions:
+        if S.Zero in A.shape:
+            return 'zeros(%s, %s)' % (A.rows, A.cols)
+        elif (A.rows, A.cols) == (1, 1):
+            return "[%s]" % A[0, 0]
+        elif A.rows == 1:
+            return "[%s]" % A.table(self, rowstart='', rowend='', colsep=' ')
+        elif A.cols == 1:
+            # note .table would unnecessarily equispace the rows
+            return "[%s]" % ", ".join([self._print(a) for a in A])
+        return "[%s]" % A.table(self, rowstart='', rowend='',
+                                rowsep=';\n', colsep=' ')
+
+
+    def _print_SparseRepMatrix(self, A):
+        from sympy.matrices import Matrix
+        L = A.col_list();
+        # make row vectors of the indices and entries
+        I = Matrix([k[0] + 1 for k in L])
+        J = Matrix([k[1] + 1 for k in L])
+        AIJ = Matrix([k[2] for k in L])
+        return "sparse(%s, %s, %s, %s, %s)" % (self._print(I), self._print(J),
+                                            self._print(AIJ), A.rows, A.cols)
+
+
+    def _print_MatrixElement(self, expr):
+        return self.parenthesize(expr.parent, PRECEDENCE["Atom"], strict=True) \
+            + '[%s,%s]' % (expr.i + 1, expr.j + 1)
+
+
+    def _print_MatrixSlice(self, expr):
+        def strslice(x, lim):
+            l = x[0] + 1
+            h = x[1]
+            step = x[2]
+            lstr = self._print(l)
+            hstr = 'end' if h == lim else self._print(h)
+            if step == 1:
+                if l == 1 and h == lim:
+                    return ':'
+                if l == h:
+                    return lstr
+                else:
+                    return lstr + ':' + hstr
+            else:
+                return ':'.join((lstr, self._print(step), hstr))
+        return (self._print(expr.parent) + '[' +
+                strslice(expr.rowslice, expr.parent.shape[0]) + ',' +
+                strslice(expr.colslice, expr.parent.shape[1]) + ']')
+
+
+    def _print_Indexed(self, expr):
+        inds = [ self._print(i) for i in expr.indices ]
+        return "%s[%s]" % (self._print(expr.base.label), ",".join(inds))
+
+
+    def _print_Idx(self, expr):
+        return self._print(expr.label)
+
+
+    def _print_Identity(self, expr):
+        return "eye(%s)" % self._print(expr.shape[0])
+
+    def _print_HadamardProduct(self, expr):
+        return ' .* '.join([self.parenthesize(arg, precedence(expr))
+                          for arg in expr.args])
+
+    def _print_HadamardPower(self, expr):
+        PREC = precedence(expr)
+        return '.**'.join([
+            self.parenthesize(expr.base, PREC),
+            self.parenthesize(expr.exp, PREC)
+            ])
+
+    def _print_Rational(self, expr):
+        if expr.q == 1:
+            return str(expr.p)
+        return "%s // %s" % (expr.p, expr.q)
+
+    # Note: as of 2022, Julia doesn't have spherical Bessel functions
+    def _print_jn(self, expr):
+        from sympy.functions import sqrt, besselj
+        x = expr.argument
+        expr2 = sqrt(S.Pi/(2*x))*besselj(expr.order + S.Half, x)
+        return self._print(expr2)
+
+
+    def _print_yn(self, expr):
+        from sympy.functions import sqrt, bessely
+        x = expr.argument
+        expr2 = sqrt(S.Pi/(2*x))*bessely(expr.order + S.Half, x)
+        return self._print(expr2)
+
+
+    def _print_Piecewise(self, expr):
+        if expr.args[-1].cond != True:
+            # We need the last conditional to be a True, otherwise the resulting
+            # function may not return a result.
+            raise ValueError("All Piecewise expressions must contain an "
+                             "(expr, True) statement to be used as a default "
+                             "condition. Without one, the generated "
+                             "expression may not evaluate to anything under "
+                             "some condition.")
+        lines = []
+        if self._settings["inline"]:
+            # Express each (cond, expr) pair in a nested Horner form:
+            #   (condition) .* (expr) + (not cond) .* (<others>)
+            # Expressions that result in multiple statements won't work here.
+            ecpairs = ["({}) ? ({}) :".format
+                       (self._print(c), self._print(e))
+                       for e, c in expr.args[:-1]]
+            elast = " (%s)" % self._print(expr.args[-1].expr)
+            pw = "\n".join(ecpairs) + elast
+            # Note: current need these outer brackets for 2*pw.  Would be
+            # nicer to teach parenthesize() to do this for us when needed!
+            return "(" + pw + ")"
+        else:
+            for i, (e, c) in enumerate(expr.args):
+                if i == 0:
+                    lines.append("if (%s)" % self._print(c))
+                elif i == len(expr.args) - 1 and c == True:
+                    lines.append("else")
+                else:
+                    lines.append("elseif (%s)" % self._print(c))
+                code0 = self._print(e)
+                lines.append(code0)
+                if i == len(expr.args) - 1:
+                    lines.append("end")
+            return "\n".join(lines)
+
+    def _print_MatMul(self, expr):
+        c, m = expr.as_coeff_mmul()
+
+        sign = ""
+        if c.is_number:
+            re, im = c.as_real_imag()
+            if im.is_zero and re.is_negative:
+                expr = _keep_coeff(-c, m)
+                sign = "-"
+            elif re.is_zero and im.is_negative:
+                expr = _keep_coeff(-c, m)
+                sign = "-"
+
+        return sign + ' * '.join(
+            (self.parenthesize(arg, precedence(expr)) for arg in expr.args)
+        )
+
+
+    def indent_code(self, code):
+        """Accepts a string of code or a list of code lines"""
+
+        # code mostly copied from ccode
+        if isinstance(code, str):
+            code_lines = self.indent_code(code.splitlines(True))
+            return ''.join(code_lines)
+
+        tab = "    "
+        inc_regex = ('^function ', '^if ', '^elseif ', '^else$', '^for ')
+        dec_regex = ('^end$', '^elseif ', '^else$')
+
+        # pre-strip left-space from the code
+        code = [ line.lstrip(' \t') for line in code ]
+
+        increase = [ int(any(search(re, line) for re in inc_regex))
+                     for line in code ]
+        decrease = [ int(any(search(re, line) for re in dec_regex))
+                     for line in code ]
+
+        pretty = []
+        level = 0
+        for n, line in enumerate(code):
+            if line in ('', '\n'):
+                pretty.append(line)
+                continue
+            level -= decrease[n]
+            pretty.append("%s%s" % (tab*level, line))
+            level += increase[n]
+        return pretty
+
+
+def julia_code(expr, assign_to=None, **settings):
+    r"""Converts `expr` to a string of Julia code.
+
+    Parameters
+    ==========
+
+    expr : Expr
+        A SymPy expression to be converted.
+    assign_to : optional
+        When given, the argument is used as the name of the variable to which
+        the expression is assigned.  Can be a string, ``Symbol``,
+        ``MatrixSymbol``, or ``Indexed`` type.  This can be helpful for
+        expressions that generate multi-line statements.
+    precision : integer, optional
+        The precision for numbers such as pi  [default=16].
+    user_functions : dict, optional
+        A dictionary where keys are ``FunctionClass`` instances and values are
+        their string representations.  Alternatively, the dictionary value can
+        be a list of tuples i.e. [(argument_test, cfunction_string)].  See
+        below for examples.
+    human : bool, optional
+        If True, the result is a single string that may contain some constant
+        declarations for the number symbols.  If False, the same information is
+        returned in a tuple of (symbols_to_declare, not_supported_functions,
+        code_text).  [default=True].
+    contract: bool, optional
+        If True, ``Indexed`` instances are assumed to obey tensor contraction
+        rules and the corresponding nested loops over indices are generated.
+        Setting contract=False will not generate loops, instead the user is
+        responsible to provide values for the indices in the code.
+        [default=True].
+    inline: bool, optional
+        If True, we try to create single-statement code instead of multiple
+        statements.  [default=True].
+
+    Examples
+    ========
+
+    >>> from sympy import julia_code, symbols, sin, pi
+    >>> x = symbols('x')
+    >>> julia_code(sin(x).series(x).removeO())
+    'x .^ 5 / 120 - x .^ 3 / 6 + x'
+
+    >>> from sympy import Rational, ceiling
+    >>> x, y, tau = symbols("x, y, tau")
+    >>> julia_code((2*tau)**Rational(7, 2))
+    '8 * sqrt(2) * tau .^ (7 // 2)'
+
+    Note that element-wise (Hadamard) operations are used by default between
+    symbols.  This is because its possible in Julia to write "vectorized"
+    code.  It is harmless if the values are scalars.
+
+    >>> julia_code(sin(pi*x*y), assign_to="s")
+    's = sin(pi * x .* y)'
+
+    If you need a matrix product "*" or matrix power "^", you can specify the
+    symbol as a ``MatrixSymbol``.
+
+    >>> from sympy import Symbol, MatrixSymbol
+    >>> n = Symbol('n', integer=True, positive=True)
+    >>> A = MatrixSymbol('A', n, n)
+    >>> julia_code(3*pi*A**3)
+    '(3 * pi) * A ^ 3'
+
+    This class uses several rules to decide which symbol to use a product.
+    Pure numbers use "*", Symbols use ".*" and MatrixSymbols use "*".
+    A HadamardProduct can be used to specify componentwise multiplication ".*"
+    of two MatrixSymbols.  There is currently there is no easy way to specify
+    scalar symbols, so sometimes the code might have some minor cosmetic
+    issues.  For example, suppose x and y are scalars and A is a Matrix, then
+    while a human programmer might write "(x^2*y)*A^3", we generate:
+
+    >>> julia_code(x**2*y*A**3)
+    '(x .^ 2 .* y) * A ^ 3'
+
+    Matrices are supported using Julia inline notation.  When using
+    ``assign_to`` with matrices, the name can be specified either as a string
+    or as a ``MatrixSymbol``.  The dimensions must align in the latter case.
+
+    >>> from sympy import Matrix, MatrixSymbol
+    >>> mat = Matrix([[x**2, sin(x), ceiling(x)]])
+    >>> julia_code(mat, assign_to='A')
+    'A = [x .^ 2 sin(x) ceil(x)]'
+
+    ``Piecewise`` expressions are implemented with logical masking by default.
+    Alternatively, you can pass "inline=False" to use if-else conditionals.
+    Note that if the ``Piecewise`` lacks a default term, represented by
+    ``(expr, True)`` then an error will be thrown.  This is to prevent
+    generating an expression that may not evaluate to anything.
+
+    >>> from sympy import Piecewise
+    >>> pw = Piecewise((x + 1, x > 0), (x, True))
+    >>> julia_code(pw, assign_to=tau)
+    'tau = ((x > 0) ? (x + 1) : (x))'
+
+    Note that any expression that can be generated normally can also exist
+    inside a Matrix:
+
+    >>> mat = Matrix([[x**2, pw, sin(x)]])
+    >>> julia_code(mat, assign_to='A')
+    'A = [x .^ 2 ((x > 0) ? (x + 1) : (x)) sin(x)]'
+
+    Custom printing can be defined for certain types by passing a dictionary of
+    "type" : "function" to the ``user_functions`` kwarg.  Alternatively, the
+    dictionary value can be a list of tuples i.e., [(argument_test,
+    cfunction_string)].  This can be used to call a custom Julia function.
+
+    >>> from sympy import Function
+    >>> f = Function('f')
+    >>> g = Function('g')
+    >>> custom_functions = {
+    ...   "f": "existing_julia_fcn",
+    ...   "g": [(lambda x: x.is_Matrix, "my_mat_fcn"),
+    ...         (lambda x: not x.is_Matrix, "my_fcn")]
+    ... }
+    >>> mat = Matrix([[1, x]])
+    >>> julia_code(f(x) + g(x) + g(mat), user_functions=custom_functions)
+    'existing_julia_fcn(x) + my_fcn(x) + my_mat_fcn([1 x])'
+
+    Support for loops is provided through ``Indexed`` types. With
+    ``contract=True`` these expressions will be turned into loops, whereas
+    ``contract=False`` will just print the assignment expression that should be
+    looped over:
+
+    >>> from sympy import Eq, IndexedBase, Idx
+    >>> len_y = 5
+    >>> y = IndexedBase('y', shape=(len_y,))
+    >>> t = IndexedBase('t', shape=(len_y,))
+    >>> Dy = IndexedBase('Dy', shape=(len_y-1,))
+    >>> i = Idx('i', len_y-1)
+    >>> e = Eq(Dy[i], (y[i+1]-y[i])/(t[i+1]-t[i]))
+    >>> julia_code(e.rhs, assign_to=e.lhs, contract=False)
+    'Dy[i] = (y[i + 1] - y[i]) ./ (t[i + 1] - t[i])'
+    """
+    return JuliaCodePrinter(settings).doprint(expr, assign_to)
+
+
+def print_julia_code(expr, **settings):
+    """Prints the Julia representation of the given expression.
+
+    See `julia_code` for the meaning of the optional arguments.
+    """
+    print(julia_code(expr, **settings))

venv/lib/python3.10/site-packages/sympy/printing/lambdarepr.py

@@ -0,0 +1,251 @@
+from .pycode import (
+    PythonCodePrinter,
+    MpmathPrinter,
+)
+from .numpy import NumPyPrinter  # NumPyPrinter is imported for backward compatibility
+from sympy.core.sorting import default_sort_key
+
+
+__all__ = [
+    'PythonCodePrinter',
+    'MpmathPrinter',  # MpmathPrinter is published for backward compatibility
+    'NumPyPrinter',
+    'LambdaPrinter',
+    'NumPyPrinter',
+    'IntervalPrinter',
+    'lambdarepr',
+]
+
+
+class LambdaPrinter(PythonCodePrinter):
+    """
+    This printer converts expressions into strings that can be used by
+    lambdify.
+    """
+    printmethod = "_lambdacode"
+
+
+    def _print_And(self, expr):
+        result = ['(']
+        for arg in sorted(expr.args, key=default_sort_key):
+            result.extend(['(', self._print(arg), ')'])
+            result.append(' and ')
+        result = result[:-1]
+        result.append(')')
+        return ''.join(result)
+
+    def _print_Or(self, expr):
+        result = ['(']
+        for arg in sorted(expr.args, key=default_sort_key):
+            result.extend(['(', self._print(arg), ')'])
+            result.append(' or ')
+        result = result[:-1]
+        result.append(')')
+        return ''.join(result)
+
+    def _print_Not(self, expr):
+        result = ['(', 'not (', self._print(expr.args[0]), '))']
+        return ''.join(result)
+
+    def _print_BooleanTrue(self, expr):
+        return "True"
+
+    def _print_BooleanFalse(self, expr):
+        return "False"
+
+    def _print_ITE(self, expr):
+        result = [
+            '((', self._print(expr.args[1]),
+            ') if (', self._print(expr.args[0]),
+            ') else (', self._print(expr.args[2]), '))'
+        ]
+        return ''.join(result)
+
+    def _print_NumberSymbol(self, expr):
+        return str(expr)
+
+    def _print_Pow(self, expr, **kwargs):
+        # XXX Temporary workaround. Should Python math printer be
+        # isolated from PythonCodePrinter?
+        return super(PythonCodePrinter, self)._print_Pow(expr, **kwargs)
+
+
+# numexpr works by altering the string passed to numexpr.evaluate
+# rather than by populating a namespace.  Thus a special printer...
+class NumExprPrinter(LambdaPrinter):
+    # key, value pairs correspond to SymPy name and numexpr name
+    # functions not appearing in this dict will raise a TypeError
+    printmethod = "_numexprcode"
+
+    _numexpr_functions = {
+        'sin' : 'sin',
+        'cos' : 'cos',
+        'tan' : 'tan',
+        'asin': 'arcsin',
+        'acos': 'arccos',
+        'atan': 'arctan',
+        'atan2' : 'arctan2',
+        'sinh' : 'sinh',
+        'cosh' : 'cosh',
+        'tanh' : 'tanh',
+        'asinh': 'arcsinh',
+        'acosh': 'arccosh',
+        'atanh': 'arctanh',
+        'ln' : 'log',
+        'log': 'log',
+        'exp': 'exp',
+        'sqrt' : 'sqrt',
+        'Abs' : 'abs',
+        'conjugate' : 'conj',
+        'im' : 'imag',
+        're' : 'real',
+        'where' : 'where',
+        'complex' : 'complex',
+        'contains' : 'contains',
+    }
+
+    module = 'numexpr'
+
+    def _print_ImaginaryUnit(self, expr):
+        return '1j'
+
+    def _print_seq(self, seq, delimiter=', '):
+        # simplified _print_seq taken from pretty.py
+        s = [self._print(item) for item in seq]
+        if s:
+            return delimiter.join(s)
+        else:
+            return ""
+
+    def _print_Function(self, e):
+        func_name = e.func.__name__
+
+        nstr = self._numexpr_functions.get(func_name, None)
+        if nstr is None:
+            # check for implemented_function
+            if hasattr(e, '_imp_'):
+                return "(%s)" % self._print(e._imp_(*e.args))
+            else:
+                raise TypeError("numexpr does not support function '%s'" %
+                                func_name)
+        return "%s(%s)" % (nstr, self._print_seq(e.args))
+
+    def _print_Piecewise(self, expr):
+        "Piecewise function printer"
+        exprs = [self._print(arg.expr) for arg in expr.args]
+        conds = [self._print(arg.cond) for arg in expr.args]
+        # If [default_value, True] is a (expr, cond) sequence in a Piecewise object
+        #     it will behave the same as passing the 'default' kwarg to select()
+        #     *as long as* it is the last element in expr.args.
+        # If this is not the case, it may be triggered prematurely.
+        ans = []
+        parenthesis_count = 0
+        is_last_cond_True = False
+        for cond, expr in zip(conds, exprs):
+            if cond == 'True':
+                ans.append(expr)
+                is_last_cond_True = True
+                break
+            else:
+                ans.append('where(%s, %s, ' % (cond, expr))
+                parenthesis_count += 1
+        if not is_last_cond_True:
+            # See https://github.com/pydata/numexpr/issues/298
+            #
+            # simplest way to put a nan but raises
+            # 'RuntimeWarning: invalid value encountered in log'
+            #
+            # There are other ways to do this such as
+            #
+            #   >>> import numexpr as ne
+            #   >>> nan = float('nan')
+            #   >>> ne.evaluate('where(x < 0, -1, nan)', {'x': [-1, 2, 3], 'nan':nan})
+            #   array([-1., nan, nan])
+            #
+            # That needs to be handled in the lambdified function though rather
+            # than here in the printer.
+            ans.append('log(-1)')
+        return ''.join(ans) + ')' * parenthesis_count
+
+    def _print_ITE(self, expr):
+        from sympy.functions.elementary.piecewise import Piecewise
+        return self._print(expr.rewrite(Piecewise))
+
+    def blacklisted(self, expr):
+        raise TypeError("numexpr cannot be used with %s" %
+                        expr.__class__.__name__)
+
+    # blacklist all Matrix printing
+    _print_SparseRepMatrix = \
+    _print_MutableSparseMatrix = \
+    _print_ImmutableSparseMatrix = \
+    _print_Matrix = \
+    _print_DenseMatrix = \
+    _print_MutableDenseMatrix = \
+    _print_ImmutableMatrix = \
+    _print_ImmutableDenseMatrix = \
+    blacklisted
+    # blacklist some Python expressions
+    _print_list = \
+    _print_tuple = \
+    _print_Tuple = \
+    _print_dict = \
+    _print_Dict = \
+    blacklisted
+
+    def _print_NumExprEvaluate(self, expr):
+        evaluate = self._module_format(self.module +".evaluate")
+        return "%s('%s', truediv=True)" % (evaluate, self._print(expr.expr))
+
+    def doprint(self, expr):
+        from sympy.codegen.ast import CodegenAST
+        from sympy.codegen.pynodes import NumExprEvaluate
+        if not isinstance(expr, CodegenAST):
+            expr = NumExprEvaluate(expr)
+        return super().doprint(expr)
+
+    def _print_Return(self, expr):
+        from sympy.codegen.pynodes import NumExprEvaluate
+        r, = expr.args
+        if not isinstance(r, NumExprEvaluate):
+            expr = expr.func(NumExprEvaluate(r))
+        return super()._print_Return(expr)
+
+    def _print_Assignment(self, expr):
+        from sympy.codegen.pynodes import NumExprEvaluate
+        lhs, rhs, *args = expr.args
+        if not isinstance(rhs, NumExprEvaluate):
+            expr = expr.func(lhs, NumExprEvaluate(rhs), *args)
+        return super()._print_Assignment(expr)
+
+    def _print_CodeBlock(self, expr):
+        from sympy.codegen.ast import CodegenAST
+        from sympy.codegen.pynodes import NumExprEvaluate
+        args = [ arg if isinstance(arg, CodegenAST) else NumExprEvaluate(arg) for arg in expr.args ]
+        return super()._print_CodeBlock(self, expr.func(*args))
+
+
+class IntervalPrinter(MpmathPrinter, LambdaPrinter):
+    """Use ``lambda`` printer but print numbers as ``mpi`` intervals. """
+
+    def _print_Integer(self, expr):
+        return "mpi('%s')" % super(PythonCodePrinter, self)._print_Integer(expr)
+
+    def _print_Rational(self, expr):
+        return "mpi('%s')" % super(PythonCodePrinter, self)._print_Rational(expr)
+
+    def _print_Half(self, expr):
+        return "mpi('%s')" % super(PythonCodePrinter, self)._print_Rational(expr)
+
+    def _print_Pow(self, expr):
+        return super(MpmathPrinter, self)._print_Pow(expr, rational=True)
+
+
+for k in NumExprPrinter._numexpr_functions:
+    setattr(NumExprPrinter, '_print_%s' % k, NumExprPrinter._print_Function)
+
+def lambdarepr(expr, **settings):
+    """
+    Returns a string usable for lambdifying.
+    """
+    return LambdaPrinter(settings).doprint(expr)

venv/lib/python3.10/site-packages/sympy/printing/llvmjitcode.py

@@ -0,0 +1,489 @@
+'''
+Use llvmlite to create executable functions from SymPy expressions
+
+This module requires llvmlite (https://github.com/numba/llvmlite).
+'''
+
+import ctypes
+
+from sympy.external import import_module
+from sympy.printing.printer import Printer
+from sympy.core.singleton import S
+from sympy.tensor.indexed import IndexedBase
+from sympy.utilities.decorator import doctest_depends_on
+
+llvmlite = import_module('llvmlite')
+if llvmlite:
+    ll = import_module('llvmlite.ir').ir
+    llvm = import_module('llvmlite.binding').binding
+    llvm.initialize()
+    llvm.initialize_native_target()
+    llvm.initialize_native_asmprinter()
+
+
+__doctest_requires__ = {('llvm_callable'): ['llvmlite']}
+
+
+class LLVMJitPrinter(Printer):
+    '''Convert expressions to LLVM IR'''
+    def __init__(self, module, builder, fn, *args, **kwargs):
+        self.func_arg_map = kwargs.pop("func_arg_map", {})
+        if not llvmlite:
+            raise ImportError("llvmlite is required for LLVMJITPrinter")
+        super().__init__(*args, **kwargs)
+        self.fp_type = ll.DoubleType()
+        self.module = module
+        self.builder = builder
+        self.fn = fn
+        self.ext_fn = {}  # keep track of wrappers to external functions
+        self.tmp_var = {}
+
+    def _add_tmp_var(self, name, value):
+        self.tmp_var[name] = value
+
+    def _print_Number(self, n):
+        return ll.Constant(self.fp_type, float(n))
+
+    def _print_Integer(self, expr):
+        return ll.Constant(self.fp_type, float(expr.p))
+
+    def _print_Symbol(self, s):
+        val = self.tmp_var.get(s)
+        if not val:
+            # look up parameter with name s
+            val = self.func_arg_map.get(s)
+        if not val:
+            raise LookupError("Symbol not found: %s" % s)
+        return val
+
+    def _print_Pow(self, expr):
+        base0 = self._print(expr.base)
+        if expr.exp == S.NegativeOne:
+            return self.builder.fdiv(ll.Constant(self.fp_type, 1.0), base0)
+        if expr.exp == S.Half:
+            fn = self.ext_fn.get("sqrt")
+            if not fn:
+                fn_type = ll.FunctionType(self.fp_type, [self.fp_type])
+                fn = ll.Function(self.module, fn_type, "sqrt")
+                self.ext_fn["sqrt"] = fn
+            return self.builder.call(fn, [base0], "sqrt")
+        if expr.exp == 2:
+            return self.builder.fmul(base0, base0)
+
+        exp0 = self._print(expr.exp)
+        fn = self.ext_fn.get("pow")
+        if not fn:
+            fn_type = ll.FunctionType(self.fp_type, [self.fp_type, self.fp_type])
+            fn = ll.Function(self.module, fn_type, "pow")
+            self.ext_fn["pow"] = fn
+        return self.builder.call(fn, [base0, exp0], "pow")
+
+    def _print_Mul(self, expr):
+        nodes = [self._print(a) for a in expr.args]
+        e = nodes[0]
+        for node in nodes[1:]:
+            e = self.builder.fmul(e, node)
+        return e
+
+    def _print_Add(self, expr):
+        nodes = [self._print(a) for a in expr.args]
+        e = nodes[0]
+        for node in nodes[1:]:
+            e = self.builder.fadd(e, node)
+        return e
+
+    # TODO - assumes all called functions take one double precision argument.
+    #        Should have a list of math library functions to validate this.
+    def _print_Function(self, expr):
+        name = expr.func.__name__
+        e0 = self._print(expr.args[0])
+        fn = self.ext_fn.get(name)
+        if not fn:
+            fn_type = ll.FunctionType(self.fp_type, [self.fp_type])
+            fn = ll.Function(self.module, fn_type, name)
+            self.ext_fn[name] = fn
+        return self.builder.call(fn, [e0], name)
+
+    def emptyPrinter(self, expr):
+        raise TypeError("Unsupported type for LLVM JIT conversion: %s"
+                        % type(expr))
+
+
+# Used when parameters are passed by array.  Often used in callbacks to
+# handle a variable number of parameters.
+class LLVMJitCallbackPrinter(LLVMJitPrinter):
+    def __init__(self, *args, **kwargs):
+        super().__init__(*args, **kwargs)
+
+    def _print_Indexed(self, expr):
+        array, idx = self.func_arg_map[expr.base]
+        offset = int(expr.indices[0].evalf())
+        array_ptr = self.builder.gep(array, [ll.Constant(ll.IntType(32), offset)])
+        fp_array_ptr = self.builder.bitcast(array_ptr, ll.PointerType(self.fp_type))
+        value = self.builder.load(fp_array_ptr)
+        return value
+
+    def _print_Symbol(self, s):
+        val = self.tmp_var.get(s)
+        if val:
+            return val
+
+        array, idx = self.func_arg_map.get(s, [None, 0])
+        if not array:
+            raise LookupError("Symbol not found: %s" % s)
+        array_ptr = self.builder.gep(array, [ll.Constant(ll.IntType(32), idx)])
+        fp_array_ptr = self.builder.bitcast(array_ptr,
+                                            ll.PointerType(self.fp_type))
+        value = self.builder.load(fp_array_ptr)
+        return value
+
+
+# ensure lifetime of the execution engine persists (else call to compiled
+#   function will seg fault)
+exe_engines = []
+
+# ensure names for generated functions are unique
+link_names = set()
+current_link_suffix = 0
+
+
+class LLVMJitCode:
+    def __init__(self, signature):
+        self.signature = signature
+        self.fp_type = ll.DoubleType()
+        self.module = ll.Module('mod1')
+        self.fn = None
+        self.llvm_arg_types = []
+        self.llvm_ret_type = self.fp_type
+        self.param_dict = {}  # map symbol name to LLVM function argument
+        self.link_name = ''
+
+    def _from_ctype(self, ctype):
+        if ctype == ctypes.c_int:
+            return ll.IntType(32)
+        if ctype == ctypes.c_double:
+            return self.fp_type
+        if ctype == ctypes.POINTER(ctypes.c_double):
+            return ll.PointerType(self.fp_type)
+        if ctype == ctypes.c_void_p:
+            return ll.PointerType(ll.IntType(32))
+        if ctype == ctypes.py_object:
+            return ll.PointerType(ll.IntType(32))
+
+        print("Unhandled ctype = %s" % str(ctype))
+
+    def _create_args(self, func_args):
+        """Create types for function arguments"""
+        self.llvm_ret_type = self._from_ctype(self.signature.ret_type)
+        self.llvm_arg_types = \
+            [self._from_ctype(a) for a in self.signature.arg_ctypes]
+
+    def _create_function_base(self):
+        """Create function with name and type signature"""
+        global link_names, current_link_suffix
+        default_link_name = 'jit_func'
+        current_link_suffix += 1
+        self.link_name = default_link_name + str(current_link_suffix)
+        link_names.add(self.link_name)
+
+        fn_type = ll.FunctionType(self.llvm_ret_type, self.llvm_arg_types)
+        self.fn = ll.Function(self.module, fn_type, name=self.link_name)
+
+    def _create_param_dict(self, func_args):
+        """Mapping of symbolic values to function arguments"""
+        for i, a in enumerate(func_args):
+            self.fn.args[i].name = str(a)
+            self.param_dict[a] = self.fn.args[i]
+
+    def _create_function(self, expr):
+        """Create function body and return LLVM IR"""
+        bb_entry = self.fn.append_basic_block('entry')
+        builder = ll.IRBuilder(bb_entry)
+
+        lj = LLVMJitPrinter(self.module, builder, self.fn,
+                            func_arg_map=self.param_dict)
+
+        ret = self._convert_expr(lj, expr)
+        lj.builder.ret(self._wrap_return(lj, ret))
+
+        strmod = str(self.module)
+        return strmod
+
+    def _wrap_return(self, lj, vals):
+        # Return a single double if there is one return value,
+        #  else return a tuple of doubles.
+
+        # Don't wrap return value in this case
+        if self.signature.ret_type == ctypes.c_double:
+            return vals[0]
+
+        # Use this instead of a real PyObject*
+        void_ptr = ll.PointerType(ll.IntType(32))
+
+        # Create a wrapped double: PyObject* PyFloat_FromDouble(double v)
+        wrap_type = ll.FunctionType(void_ptr, [self.fp_type])
+        wrap_fn = ll.Function(lj.module, wrap_type, "PyFloat_FromDouble")
+
+        wrapped_vals = [lj.builder.call(wrap_fn, [v]) for v in vals]
+        if len(vals) == 1:
+            final_val = wrapped_vals[0]
+        else:
+            # Create a tuple: PyObject* PyTuple_Pack(Py_ssize_t n, ...)
+
+            # This should be Py_ssize_t
+            tuple_arg_types = [ll.IntType(32)]
+
+            tuple_arg_types.extend([void_ptr]*len(vals))
+            tuple_type = ll.FunctionType(void_ptr, tuple_arg_types)
+            tuple_fn = ll.Function(lj.module, tuple_type, "PyTuple_Pack")
+
+            tuple_args = [ll.Constant(ll.IntType(32), len(wrapped_vals))]
+            tuple_args.extend(wrapped_vals)
+
+            final_val = lj.builder.call(tuple_fn, tuple_args)
+
+        return final_val
+
+    def _convert_expr(self, lj, expr):
+        try:
+            # Match CSE return data structure.
+            if len(expr) == 2:
+                tmp_exprs = expr[0]
+                final_exprs = expr[1]
+                if len(final_exprs) != 1 and self.signature.ret_type == ctypes.c_double:
+                    raise NotImplementedError("Return of multiple expressions not supported for this callback")
+                for name, e in tmp_exprs:
+                    val = lj._print(e)
+                    lj._add_tmp_var(name, val)
+        except TypeError:
+            final_exprs = [expr]
+
+        vals = [lj._print(e) for e in final_exprs]
+
+        return vals
+
+    def _compile_function(self, strmod):
+        global exe_engines
+        llmod = llvm.parse_assembly(strmod)
+
+        pmb = llvm.create_pass_manager_builder()
+        pmb.opt_level = 2
+        pass_manager = llvm.create_module_pass_manager()
+        pmb.populate(pass_manager)
+
+        pass_manager.run(llmod)
+
+        target_machine = \
+            llvm.Target.from_default_triple().create_target_machine()
+        exe_eng = llvm.create_mcjit_compiler(llmod, target_machine)
+        exe_eng.finalize_object()
+        exe_engines.append(exe_eng)
+
+        if False:
+            print("Assembly")
+            print(target_machine.emit_assembly(llmod))
+
+        fptr = exe_eng.get_function_address(self.link_name)
+
+        return fptr
+
+
+class LLVMJitCodeCallback(LLVMJitCode):
+    def __init__(self, signature):
+        super().__init__(signature)
+
+    def _create_param_dict(self, func_args):
+        for i, a in enumerate(func_args):
+            if isinstance(a, IndexedBase):
+                self.param_dict[a] = (self.fn.args[i], i)
+                self.fn.args[i].name = str(a)
+            else:
+                self.param_dict[a] = (self.fn.args[self.signature.input_arg],
+                                      i)
+
+    def _create_function(self, expr):
+        """Create function body and return LLVM IR"""
+        bb_entry = self.fn.append_basic_block('entry')
+        builder = ll.IRBuilder(bb_entry)
+
+        lj = LLVMJitCallbackPrinter(self.module, builder, self.fn,
+                                    func_arg_map=self.param_dict)
+
+        ret = self._convert_expr(lj, expr)
+
+        if self.signature.ret_arg:
+            output_fp_ptr = builder.bitcast(self.fn.args[self.signature.ret_arg],
+                                            ll.PointerType(self.fp_type))
+            for i, val in enumerate(ret):
+                index = ll.Constant(ll.IntType(32), i)
+                output_array_ptr = builder.gep(output_fp_ptr, [index])
+                builder.store(val, output_array_ptr)
+            builder.ret(ll.Constant(ll.IntType(32), 0))  # return success
+        else:
+            lj.builder.ret(self._wrap_return(lj, ret))
+
+        strmod = str(self.module)
+        return strmod
+
+
+class CodeSignature:
+    def __init__(self, ret_type):
+        self.ret_type = ret_type
+        self.arg_ctypes = []
+
+        # Input argument array element index
+        self.input_arg = 0
+
+        # For the case output value is referenced through a parameter rather
+        # than the return value
+        self.ret_arg = None
+
+
+def _llvm_jit_code(args, expr, signature, callback_type):
+    """Create a native code function from a SymPy expression"""
+    if callback_type is None:
+        jit = LLVMJitCode(signature)
+    else:
+        jit = LLVMJitCodeCallback(signature)
+
+    jit._create_args(args)
+    jit._create_function_base()
+    jit._create_param_dict(args)
+    strmod = jit._create_function(expr)
+    if False:
+        print("LLVM IR")
+        print(strmod)
+    fptr = jit._compile_function(strmod)
+    return fptr
+
+
+@doctest_depends_on(modules=('llvmlite', 'scipy'))
+def llvm_callable(args, expr, callback_type=None):
+    '''Compile function from a SymPy expression
+
+    Expressions are evaluated using double precision arithmetic.
+    Some single argument math functions (exp, sin, cos, etc.) are supported
+    in expressions.
+
+    Parameters
+    ==========
+
+    args : List of Symbol
+        Arguments to the generated function.  Usually the free symbols in
+        the expression.  Currently each one is assumed to convert to
+        a double precision scalar.
+    expr : Expr, or (Replacements, Expr) as returned from 'cse'
+        Expression to compile.
+    callback_type : string
+        Create function with signature appropriate to use as a callback.
+        Currently supported:
+           'scipy.integrate'
+           'scipy.integrate.test'
+           'cubature'
+
+    Returns
+    =======
+
+    Compiled function that can evaluate the expression.
+
+    Examples
+    ========
+
+    >>> import sympy.printing.llvmjitcode as jit
+    >>> from sympy.abc import a
+    >>> e = a*a + a + 1
+    >>> e1 = jit.llvm_callable([a], e)
+    >>> e.subs(a, 1.1)   # Evaluate via substitution
+    3.31000000000000
+    >>> e1(1.1)  # Evaluate using JIT-compiled code
+    3.3100000000000005
+
+
+    Callbacks for integration functions can be JIT compiled.
+    >>> import sympy.printing.llvmjitcode as jit
+    >>> from sympy.abc import a
+    >>> from sympy import integrate
+    >>> from scipy.integrate import quad
+    >>> e = a*a
+    >>> e1 = jit.llvm_callable([a], e, callback_type='scipy.integrate')
+    >>> integrate(e, (a, 0.0, 2.0))
+    2.66666666666667
+    >>> quad(e1, 0.0, 2.0)[0]
+    2.66666666666667
+
+    The 'cubature' callback is for the Python wrapper around the
+    cubature package ( https://github.com/saullocastro/cubature )
+    and ( http://ab-initio.mit.edu/wiki/index.php/Cubature )
+
+    There are two signatures for the SciPy integration callbacks.
+    The first ('scipy.integrate') is the function to be passed to the
+    integration routine, and will pass the signature checks.
+    The second ('scipy.integrate.test') is only useful for directly calling
+    the function using ctypes variables. It will not pass the signature checks
+    for scipy.integrate.
+
+    The return value from the cse module can also be compiled.  This
+    can improve the performance of the compiled function.  If multiple
+    expressions are given to cse, the compiled function returns a tuple.
+    The 'cubature' callback handles multiple expressions (set `fdim`
+    to match in the integration call.)
+    >>> import sympy.printing.llvmjitcode as jit
+    >>> from sympy import cse
+    >>> from sympy.abc import x,y
+    >>> e1 = x*x + y*y
+    >>> e2 = 4*(x*x + y*y) + 8.0
+    >>> after_cse = cse([e1,e2])
+    >>> after_cse
+    ([(x0, x**2), (x1, y**2)], [x0 + x1, 4*x0 + 4*x1 + 8.0])
+    >>> j1 = jit.llvm_callable([x,y], after_cse)
+    >>> j1(1.0, 2.0)
+    (5.0, 28.0)
+    '''
+
+    if not llvmlite:
+        raise ImportError("llvmlite is required for llvmjitcode")
+
+    signature = CodeSignature(ctypes.py_object)
+
+    arg_ctypes = []
+    if callback_type is None:
+        for _ in args:
+            arg_ctype = ctypes.c_double
+            arg_ctypes.append(arg_ctype)
+    elif callback_type in ('scipy.integrate', 'scipy.integrate.test'):
+        signature.ret_type = ctypes.c_double
+        arg_ctypes = [ctypes.c_int, ctypes.POINTER(ctypes.c_double)]
+        arg_ctypes_formal = [ctypes.c_int, ctypes.c_double]
+        signature.input_arg = 1
+    elif callback_type == 'cubature':
+        arg_ctypes = [ctypes.c_int,
+                      ctypes.POINTER(ctypes.c_double),
+                      ctypes.c_void_p,
+                      ctypes.c_int,
+                      ctypes.POINTER(ctypes.c_double)
+                      ]
+        signature.ret_type = ctypes.c_int
+        signature.input_arg = 1
+        signature.ret_arg = 4
+    else:
+        raise ValueError("Unknown callback type: %s" % callback_type)
+
+    signature.arg_ctypes = arg_ctypes
+
+    fptr = _llvm_jit_code(args, expr, signature, callback_type)
+
+    if callback_type and callback_type == 'scipy.integrate':
+        arg_ctypes = arg_ctypes_formal
+
+    # PYFUNCTYPE holds the GIL which is needed to prevent a segfault when
+    # calling PyFloat_FromDouble on Python 3.10. Probably it is better to use
+    # ctypes.c_double when returning a float rather than using ctypes.py_object
+    # and returning a PyFloat from inside the jitted function (i.e. let ctypes
+    # handle the conversion from double to PyFloat).
+    if signature.ret_type == ctypes.py_object:
+        FUNCTYPE = ctypes.PYFUNCTYPE
+    else:
+        FUNCTYPE = ctypes.CFUNCTYPE
+
+    cfunc = FUNCTYPE(signature.ret_type, *arg_ctypes)(fptr)
+    return cfunc

venv/lib/python3.10/site-packages/sympy/printing/mathematica.py

@@ -0,0 +1,354 @@
+"""
+Mathematica code printer
+"""
+
+from __future__ import annotations
+from typing import Any
+
+from sympy.core import Basic, Expr, Float
+from sympy.core.sorting import default_sort_key
+
+from sympy.printing.codeprinter import CodePrinter
+from sympy.printing.precedence import precedence
+
+# Used in MCodePrinter._print_Function(self)
+known_functions = {
+    "exp": [(lambda x: True, "Exp")],
+    "log": [(lambda x: True, "Log")],
+    "sin": [(lambda x: True, "Sin")],
+    "cos": [(lambda x: True, "Cos")],
+    "tan": [(lambda x: True, "Tan")],
+    "cot": [(lambda x: True, "Cot")],
+    "sec": [(lambda x: True, "Sec")],
+    "csc": [(lambda x: True, "Csc")],
+    "asin": [(lambda x: True, "ArcSin")],
+    "acos": [(lambda x: True, "ArcCos")],
+    "atan": [(lambda x: True, "ArcTan")],
+    "acot": [(lambda x: True, "ArcCot")],
+    "asec": [(lambda x: True, "ArcSec")],
+    "acsc": [(lambda x: True, "ArcCsc")],
+    "atan2": [(lambda *x: True, "ArcTan")],
+    "sinh": [(lambda x: True, "Sinh")],
+    "cosh": [(lambda x: True, "Cosh")],
+    "tanh": [(lambda x: True, "Tanh")],
+    "coth": [(lambda x: True, "Coth")],
+    "sech": [(lambda x: True, "Sech")],
+    "csch": [(lambda x: True, "Csch")],
+    "asinh": [(lambda x: True, "ArcSinh")],
+    "acosh": [(lambda x: True, "ArcCosh")],
+    "atanh": [(lambda x: True, "ArcTanh")],
+    "acoth": [(lambda x: True, "ArcCoth")],
+    "asech": [(lambda x: True, "ArcSech")],
+    "acsch": [(lambda x: True, "ArcCsch")],
+    "sinc": [(lambda x: True, "Sinc")],
+    "conjugate": [(lambda x: True, "Conjugate")],
+    "Max": [(lambda *x: True, "Max")],
+    "Min": [(lambda *x: True, "Min")],
+    "erf": [(lambda x: True, "Erf")],
+    "erf2": [(lambda *x: True, "Erf")],
+    "erfc": [(lambda x: True, "Erfc")],
+    "erfi": [(lambda x: True, "Erfi")],
+    "erfinv": [(lambda x: True, "InverseErf")],
+    "erfcinv": [(lambda x: True, "InverseErfc")],
+    "erf2inv": [(lambda *x: True, "InverseErf")],
+    "expint": [(lambda *x: True, "ExpIntegralE")],
+    "Ei": [(lambda x: True, "ExpIntegralEi")],
+    "fresnelc": [(lambda x: True, "FresnelC")],
+    "fresnels": [(lambda x: True, "FresnelS")],
+    "gamma": [(lambda x: True, "Gamma")],
+    "uppergamma": [(lambda *x: True, "Gamma")],
+    "polygamma": [(lambda *x: True, "PolyGamma")],
+    "loggamma": [(lambda x: True, "LogGamma")],
+    "beta": [(lambda *x: True, "Beta")],
+    "Ci": [(lambda x: True, "CosIntegral")],
+    "Si": [(lambda x: True, "SinIntegral")],
+    "Chi": [(lambda x: True, "CoshIntegral")],
+    "Shi": [(lambda x: True, "SinhIntegral")],
+    "li": [(lambda x: True, "LogIntegral")],
+    "factorial": [(lambda x: True, "Factorial")],
+    "factorial2": [(lambda x: True, "Factorial2")],
+    "subfactorial": [(lambda x: True, "Subfactorial")],
+    "catalan": [(lambda x: True, "CatalanNumber")],
+    "harmonic": [(lambda *x: True, "HarmonicNumber")],
+    "lucas": [(lambda x: True, "LucasL")],
+    "RisingFactorial": [(lambda *x: True, "Pochhammer")],
+    "FallingFactorial": [(lambda *x: True, "FactorialPower")],
+    "laguerre": [(lambda *x: True, "LaguerreL")],
+    "assoc_laguerre": [(lambda *x: True, "LaguerreL")],
+    "hermite": [(lambda *x: True, "HermiteH")],
+    "jacobi": [(lambda *x: True, "JacobiP")],
+    "gegenbauer": [(lambda *x: True, "GegenbauerC")],
+    "chebyshevt": [(lambda *x: True, "ChebyshevT")],
+    "chebyshevu": [(lambda *x: True, "ChebyshevU")],
+    "legendre": [(lambda *x: True, "LegendreP")],
+    "assoc_legendre": [(lambda *x: True, "LegendreP")],
+    "mathieuc": [(lambda *x: True, "MathieuC")],
+    "mathieus": [(lambda *x: True, "MathieuS")],
+    "mathieucprime": [(lambda *x: True, "MathieuCPrime")],
+    "mathieusprime": [(lambda *x: True, "MathieuSPrime")],
+    "stieltjes": [(lambda x: True, "StieltjesGamma")],
+    "elliptic_e": [(lambda *x: True, "EllipticE")],
+    "elliptic_f": [(lambda *x: True, "EllipticE")],
+    "elliptic_k": [(lambda x: True, "EllipticK")],
+    "elliptic_pi": [(lambda *x: True, "EllipticPi")],
+    "zeta": [(lambda *x: True, "Zeta")],
+    "dirichlet_eta": [(lambda x: True, "DirichletEta")],
+    "riemann_xi": [(lambda x: True, "RiemannXi")],
+    "besseli": [(lambda *x: True, "BesselI")],
+    "besselj": [(lambda *x: True, "BesselJ")],
+    "besselk": [(lambda *x: True, "BesselK")],
+    "bessely": [(lambda *x: True, "BesselY")],
+    "hankel1": [(lambda *x: True, "HankelH1")],
+    "hankel2": [(lambda *x: True, "HankelH2")],
+    "airyai": [(lambda x: True, "AiryAi")],
+    "airybi": [(lambda x: True, "AiryBi")],
+    "airyaiprime": [(lambda x: True, "AiryAiPrime")],
+    "airybiprime": [(lambda x: True, "AiryBiPrime")],
+    "polylog": [(lambda *x: True, "PolyLog")],
+    "lerchphi": [(lambda *x: True, "LerchPhi")],
+    "gcd": [(lambda *x: True, "GCD")],
+    "lcm": [(lambda *x: True, "LCM")],
+    "jn": [(lambda *x: True, "SphericalBesselJ")],
+    "yn": [(lambda *x: True, "SphericalBesselY")],
+    "hyper": [(lambda *x: True, "HypergeometricPFQ")],
+    "meijerg": [(lambda *x: True, "MeijerG")],
+    "appellf1": [(lambda *x: True, "AppellF1")],
+    "DiracDelta": [(lambda x: True, "DiracDelta")],
+    "Heaviside": [(lambda x: True, "HeavisideTheta")],
+    "KroneckerDelta": [(lambda *x: True, "KroneckerDelta")],
+    "sqrt": [(lambda x: True, "Sqrt")],  # For automatic rewrites
+}
+
+
+class MCodePrinter(CodePrinter):
+    """A printer to convert Python expressions to
+    strings of the Wolfram's Mathematica code
+    """
+    printmethod = "_mcode"
+    language = "Wolfram Language"
+
+    _default_settings: dict[str, Any] = {
+        'order': None,
+        'full_prec': 'auto',
+        'precision': 15,
+        'user_functions': {},
+        'human': True,
+        'allow_unknown_functions': False,
+    }
+
+    _number_symbols: set[tuple[Expr, Float]] = set()
+    _not_supported: set[Basic] = set()
+
+    def __init__(self, settings={}):
+        """Register function mappings supplied by user"""
+        CodePrinter.__init__(self, settings)
+        self.known_functions = dict(known_functions)
+        userfuncs = settings.get('user_functions', {}).copy()
+        for k, v in userfuncs.items():
+            if not isinstance(v, list):
+                userfuncs[k] = [(lambda *x: True, v)]
+        self.known_functions.update(userfuncs)
+
+    def _format_code(self, lines):
+        return lines
+
+    def _print_Pow(self, expr):
+        PREC = precedence(expr)
+        return '%s^%s' % (self.parenthesize(expr.base, PREC),
+                          self.parenthesize(expr.exp, PREC))
+
+    def _print_Mul(self, expr):
+        PREC = precedence(expr)
+        c, nc = expr.args_cnc()
+        res = super()._print_Mul(expr.func(*c))
+        if nc:
+            res += '*'
+            res += '**'.join(self.parenthesize(a, PREC) for a in nc)
+        return res
+
+    def _print_Relational(self, expr):
+        lhs_code = self._print(expr.lhs)
+        rhs_code = self._print(expr.rhs)
+        op = expr.rel_op
+        return "{} {} {}".format(lhs_code, op, rhs_code)
+
+    # Primitive numbers
+    def _print_Zero(self, expr):
+        return '0'
+
+    def _print_One(self, expr):
+        return '1'
+
+    def _print_NegativeOne(self, expr):
+        return '-1'
+
+    def _print_Half(self, expr):
+        return '1/2'
+
+    def _print_ImaginaryUnit(self, expr):
+        return 'I'
+
+
+    # Infinity and invalid numbers
+    def _print_Infinity(self, expr):
+        return 'Infinity'
+
+    def _print_NegativeInfinity(self, expr):
+        return '-Infinity'
+
+    def _print_ComplexInfinity(self, expr):
+        return 'ComplexInfinity'
+
+    def _print_NaN(self, expr):
+        return 'Indeterminate'
+
+
+    # Mathematical constants
+    def _print_Exp1(self, expr):
+        return 'E'
+
+    def _print_Pi(self, expr):
+        return 'Pi'
+
+    def _print_GoldenRatio(self, expr):
+        return 'GoldenRatio'
+
+    def _print_TribonacciConstant(self, expr):
+        expanded = expr.expand(func=True)
+        PREC = precedence(expr)
+        return self.parenthesize(expanded, PREC)
+
+    def _print_EulerGamma(self, expr):
+        return 'EulerGamma'
+
+    def _print_Catalan(self, expr):
+        return 'Catalan'
+
+
+    def _print_list(self, expr):
+        return '{' + ', '.join(self.doprint(a) for a in expr) + '}'
+    _print_tuple = _print_list
+    _print_Tuple = _print_list
+
+    def _print_ImmutableDenseMatrix(self, expr):
+        return self.doprint(expr.tolist())
+
+    def _print_ImmutableSparseMatrix(self, expr):
+
+        def print_rule(pos, val):
+            return '{} -> {}'.format(
+            self.doprint((pos[0]+1, pos[1]+1)), self.doprint(val))
+
+        def print_data():
+            items = sorted(expr.todok().items(), key=default_sort_key)
+            return '{' + \
+                ', '.join(print_rule(k, v) for k, v in items) + \
+                '}'
+
+        def print_dims():
+            return self.doprint(expr.shape)
+
+        return 'SparseArray[{}, {}]'.format(print_data(), print_dims())
+
+    def _print_ImmutableDenseNDimArray(self, expr):
+        return self.doprint(expr.tolist())
+
+    def _print_ImmutableSparseNDimArray(self, expr):
+        def print_string_list(string_list):
+            return '{' + ', '.join(a for a in string_list) + '}'
+
+        def to_mathematica_index(*args):
+            """Helper function to change Python style indexing to
+            Pathematica indexing.
+
+            Python indexing (0, 1 ... n-1)
+            -> Mathematica indexing (1, 2 ... n)
+            """
+            return tuple(i + 1 for i in args)
+
+        def print_rule(pos, val):
+            """Helper function to print a rule of Mathematica"""
+            return '{} -> {}'.format(self.doprint(pos), self.doprint(val))
+
+        def print_data():
+            """Helper function to print data part of Mathematica
+            sparse array.
+
+            It uses the fourth notation ``SparseArray[data,{d1,d2,...}]``
+            from
+            https://reference.wolfram.com/language/ref/SparseArray.html
+
+            ``data`` must be formatted with rule.
+            """
+            return print_string_list(
+                [print_rule(
+                    to_mathematica_index(*(expr._get_tuple_index(key))),
+                    value)
+                for key, value in sorted(expr._sparse_array.items())]
+            )
+
+        def print_dims():
+            """Helper function to print dimensions part of Mathematica
+            sparse array.
+
+            It uses the fourth notation ``SparseArray[data,{d1,d2,...}]``
+            from
+            https://reference.wolfram.com/language/ref/SparseArray.html
+            """
+            return self.doprint(expr.shape)
+
+        return 'SparseArray[{}, {}]'.format(print_data(), print_dims())
+
+    def _print_Function(self, expr):
+        if expr.func.__name__ in self.known_functions:
+            cond_mfunc = self.known_functions[expr.func.__name__]
+            for cond, mfunc in cond_mfunc:
+                if cond(*expr.args):
+                    return "%s[%s]" % (mfunc, self.stringify(expr.args, ", "))
+        elif expr.func.__name__ in self._rewriteable_functions:
+            # Simple rewrite to supported function possible
+            target_f, required_fs = self._rewriteable_functions[expr.func.__name__]
+            if self._can_print(target_f) and all(self._can_print(f) for f in required_fs):
+                return self._print(expr.rewrite(target_f))
+        return expr.func.__name__ + "[%s]" % self.stringify(expr.args, ", ")
+
+    _print_MinMaxBase = _print_Function
+
+    def _print_LambertW(self, expr):
+        if len(expr.args) == 1:
+            return "ProductLog[{}]".format(self._print(expr.args[0]))
+        return "ProductLog[{}, {}]".format(
+            self._print(expr.args[1]), self._print(expr.args[0]))
+
+    def _print_Integral(self, expr):
+        if len(expr.variables) == 1 and not expr.limits[0][1:]:
+            args = [expr.args[0], expr.variables[0]]
+        else:
+            args = expr.args
+        return "Hold[Integrate[" + ', '.join(self.doprint(a) for a in args) + "]]"
+
+    def _print_Sum(self, expr):
+        return "Hold[Sum[" + ', '.join(self.doprint(a) for a in expr.args) + "]]"
+
+    def _print_Derivative(self, expr):
+        dexpr = expr.expr
+        dvars = [i[0] if i[1] == 1 else i for i in expr.variable_count]
+        return "Hold[D[" + ', '.join(self.doprint(a) for a in [dexpr] + dvars) + "]]"
+
+
+    def _get_comment(self, text):
+        return "(* {} *)".format(text)
+
+
+def mathematica_code(expr, **settings):
+    r"""Converts an expr to a string of the Wolfram Mathematica code
+
+    Examples
+    ========
+
+    >>> from sympy import mathematica_code as mcode, symbols, sin
+    >>> x = symbols('x')
+    >>> mcode(sin(x).series(x).removeO())
+    '(1/120)*x^5 - 1/6*x^3 + x'
+    """
+    return MCodePrinter(settings).doprint(expr)

venv/lib/python3.10/site-packages/sympy/printing/octave.py

@@ -0,0 +1,719 @@
+"""
+Octave (and Matlab) code printer
+
+The `OctaveCodePrinter` converts SymPy expressions into Octave expressions.
+It uses a subset of the Octave language for Matlab compatibility.
+
+A complete code generator, which uses `octave_code` extensively, can be found
+in `sympy.utilities.codegen`.  The `codegen` module can be used to generate
+complete source code files.
+
+"""
+
+from __future__ import annotations
+from typing import Any
+
+from sympy.core import Mul, Pow, S, Rational
+from sympy.core.mul import _keep_coeff
+from sympy.core.numbers import equal_valued
+from sympy.printing.codeprinter import CodePrinter
+from sympy.printing.precedence import precedence, PRECEDENCE
+from re import search
+
+# List of known functions.  First, those that have the same name in
+# SymPy and Octave.   This is almost certainly incomplete!
+known_fcns_src1 = ["sin", "cos", "tan", "cot", "sec", "csc",
+                   "asin", "acos", "acot", "atan", "atan2", "asec", "acsc",
+                   "sinh", "cosh", "tanh", "coth", "csch", "sech",
+                   "asinh", "acosh", "atanh", "acoth", "asech", "acsch",
+                   "erfc", "erfi", "erf", "erfinv", "erfcinv",
+                   "besseli", "besselj", "besselk", "bessely",
+                   "bernoulli", "beta", "euler", "exp", "factorial", "floor",
+                   "fresnelc", "fresnels", "gamma", "harmonic", "log",
+                   "polylog", "sign", "zeta", "legendre"]
+
+# These functions have different names ("SymPy": "Octave"), more
+# generally a mapping to (argument_conditions, octave_function).
+known_fcns_src2 = {
+    "Abs": "abs",
+    "arg": "angle",  # arg/angle ok in Octave but only angle in Matlab
+    "binomial": "bincoeff",
+    "ceiling": "ceil",
+    "chebyshevu": "chebyshevU",
+    "chebyshevt": "chebyshevT",
+    "Chi": "coshint",
+    "Ci": "cosint",
+    "conjugate": "conj",
+    "DiracDelta": "dirac",
+    "Heaviside": "heaviside",
+    "im": "imag",
+    "laguerre": "laguerreL",
+    "LambertW": "lambertw",
+    "li": "logint",
+    "loggamma": "gammaln",
+    "Max": "max",
+    "Min": "min",
+    "Mod": "mod",
+    "polygamma": "psi",
+    "re": "real",
+    "RisingFactorial": "pochhammer",
+    "Shi": "sinhint",
+    "Si": "sinint",
+}
+
+
+class OctaveCodePrinter(CodePrinter):
+    """
+    A printer to convert expressions to strings of Octave/Matlab code.
+    """
+    printmethod = "_octave"
+    language = "Octave"
+
+    _operators = {
+        'and': '&',
+        'or': '|',
+        'not': '~',
+    }
+
+    _default_settings: dict[str, Any] = {
+        'order': None,
+        'full_prec': 'auto',
+        'precision': 17,
+        'user_functions': {},
+        'human': True,
+        'allow_unknown_functions': False,
+        'contract': True,
+        'inline': True,
+    }
+    # Note: contract is for expressing tensors as loops (if True), or just
+    # assignment (if False).  FIXME: this should be looked a more carefully
+    # for Octave.
+
+
+    def __init__(self, settings={}):
+        super().__init__(settings)
+        self.known_functions = dict(zip(known_fcns_src1, known_fcns_src1))
+        self.known_functions.update(dict(known_fcns_src2))
+        userfuncs = settings.get('user_functions', {})
+        self.known_functions.update(userfuncs)
+
+
+    def _rate_index_position(self, p):
+        return p*5
+
+
+    def _get_statement(self, codestring):
+        return "%s;" % codestring
+
+
+    def _get_comment(self, text):
+        return "% {}".format(text)
+
+
+    def _declare_number_const(self, name, value):
+        return "{} = {};".format(name, value)
+
+
+    def _format_code(self, lines):
+        return self.indent_code(lines)
+
+
+    def _traverse_matrix_indices(self, mat):
+        # Octave uses Fortran order (column-major)
+        rows, cols = mat.shape
+        return ((i, j) for j in range(cols) for i in range(rows))
+
+
+    def _get_loop_opening_ending(self, indices):
+        open_lines = []
+        close_lines = []
+        for i in indices:
+            # Octave arrays start at 1 and end at dimension
+            var, start, stop = map(self._print,
+                    [i.label, i.lower + 1, i.upper + 1])
+            open_lines.append("for %s = %s:%s" % (var, start, stop))
+            close_lines.append("end")
+        return open_lines, close_lines
+
+
+    def _print_Mul(self, expr):
+        # print complex numbers nicely in Octave
+        if (expr.is_number and expr.is_imaginary and
+                (S.ImaginaryUnit*expr).is_Integer):
+            return "%si" % self._print(-S.ImaginaryUnit*expr)
+
+        # cribbed from str.py
+        prec = precedence(expr)
+
+        c, e = expr.as_coeff_Mul()
+        if c < 0:
+            expr = _keep_coeff(-c, e)
+            sign = "-"
+        else:
+            sign = ""
+
+        a = []  # items in the numerator
+        b = []  # items that are in the denominator (if any)
+
+        pow_paren = []  # Will collect all pow with more than one base element and exp = -1
+
+        if self.order not in ('old', 'none'):
+            args = expr.as_ordered_factors()
+        else:
+            # use make_args in case expr was something like -x -> x
+            args = Mul.make_args(expr)
+
+        # Gather args for numerator/denominator
+        for item in args:
+            if (item.is_commutative and item.is_Pow and item.exp.is_Rational
+                    and item.exp.is_negative):
+                if item.exp != -1:
+                    b.append(Pow(item.base, -item.exp, evaluate=False))
+                else:
+                    if len(item.args[0].args) != 1 and isinstance(item.base, Mul):   # To avoid situations like #14160
+                        pow_paren.append(item)
+                    b.append(Pow(item.base, -item.exp))
+            elif item.is_Rational and item is not S.Infinity:
+                if item.p != 1:
+                    a.append(Rational(item.p))
+                if item.q != 1:
+                    b.append(Rational(item.q))
+            else:
+                a.append(item)
+
+        a = a or [S.One]
+
+        a_str = [self.parenthesize(x, prec) for x in a]
+        b_str = [self.parenthesize(x, prec) for x in b]
+
+        # To parenthesize Pow with exp = -1 and having more than one Symbol
+        for item in pow_paren:
+            if item.base in b:
+                b_str[b.index(item.base)] = "(%s)" % b_str[b.index(item.base)]
+
+        # from here it differs from str.py to deal with "*" and ".*"
+        def multjoin(a, a_str):
+            # here we probably are assuming the constants will come first
+            r = a_str[0]
+            for i in range(1, len(a)):
+                mulsym = '*' if a[i-1].is_number else '.*'
+                r = r + mulsym + a_str[i]
+            return r
+
+        if not b:
+            return sign + multjoin(a, a_str)
+        elif len(b) == 1:
+            divsym = '/' if b[0].is_number else './'
+            return sign + multjoin(a, a_str) + divsym + b_str[0]
+        else:
+            divsym = '/' if all(bi.is_number for bi in b) else './'
+            return (sign + multjoin(a, a_str) +
+                    divsym + "(%s)" % multjoin(b, b_str))
+
+    def _print_Relational(self, expr):
+        lhs_code = self._print(expr.lhs)
+        rhs_code = self._print(expr.rhs)
+        op = expr.rel_op
+        return "{} {} {}".format(lhs_code, op, rhs_code)
+
+    def _print_Pow(self, expr):
+        powsymbol = '^' if all(x.is_number for x in expr.args) else '.^'
+
+        PREC = precedence(expr)
+
+        if equal_valued(expr.exp, 0.5):
+            return "sqrt(%s)" % self._print(expr.base)
+
+        if expr.is_commutative:
+            if equal_valued(expr.exp, -0.5):
+                sym = '/' if expr.base.is_number else './'
+                return "1" + sym + "sqrt(%s)" % self._print(expr.base)
+            if equal_valued(expr.exp, -1):
+                sym = '/' if expr.base.is_number else './'
+                return "1" + sym + "%s" % self.parenthesize(expr.base, PREC)
+
+        return '%s%s%s' % (self.parenthesize(expr.base, PREC), powsymbol,
+                           self.parenthesize(expr.exp, PREC))
+
+
+    def _print_MatPow(self, expr):
+        PREC = precedence(expr)
+        return '%s^%s' % (self.parenthesize(expr.base, PREC),
+                          self.parenthesize(expr.exp, PREC))
+
+    def _print_MatrixSolve(self, expr):
+        PREC = precedence(expr)
+        return "%s \\ %s" % (self.parenthesize(expr.matrix, PREC),
+                             self.parenthesize(expr.vector, PREC))
+
+    def _print_Pi(self, expr):
+        return 'pi'
+
+
+    def _print_ImaginaryUnit(self, expr):
+        return "1i"
+
+
+    def _print_Exp1(self, expr):
+        return "exp(1)"
+
+
+    def _print_GoldenRatio(self, expr):
+        # FIXME: how to do better, e.g., for octave_code(2*GoldenRatio)?
+        #return self._print((1+sqrt(S(5)))/2)
+        return "(1+sqrt(5))/2"
+
+
+    def _print_Assignment(self, expr):
+        from sympy.codegen.ast import Assignment
+        from sympy.functions.elementary.piecewise import Piecewise
+        from sympy.tensor.indexed import IndexedBase
+        # Copied from codeprinter, but remove special MatrixSymbol treatment
+        lhs = expr.lhs
+        rhs = expr.rhs
+        # We special case assignments that take multiple lines
+        if not self._settings["inline"] and isinstance(expr.rhs, Piecewise):
+            # Here we modify Piecewise so each expression is now
+            # an Assignment, and then continue on the print.
+            expressions = []
+            conditions = []
+            for (e, c) in rhs.args:
+                expressions.append(Assignment(lhs, e))
+                conditions.append(c)
+            temp = Piecewise(*zip(expressions, conditions))
+            return self._print(temp)
+        if self._settings["contract"] and (lhs.has(IndexedBase) or
+                rhs.has(IndexedBase)):
+            # Here we check if there is looping to be done, and if so
+            # print the required loops.
+            return self._doprint_loops(rhs, lhs)
+        else:
+            lhs_code = self._print(lhs)
+            rhs_code = self._print(rhs)
+            return self._get_statement("%s = %s" % (lhs_code, rhs_code))
+
+
+    def _print_Infinity(self, expr):
+        return 'inf'
+
+
+    def _print_NegativeInfinity(self, expr):
+        return '-inf'
+
+
+    def _print_NaN(self, expr):
+        return 'NaN'
+
+
+    def _print_list(self, expr):
+        return '{' + ', '.join(self._print(a) for a in expr) + '}'
+    _print_tuple = _print_list
+    _print_Tuple = _print_list
+    _print_List = _print_list
+
+
+    def _print_BooleanTrue(self, expr):
+        return "true"
+
+
+    def _print_BooleanFalse(self, expr):
+        return "false"
+
+
+    def _print_bool(self, expr):
+        return str(expr).lower()
+
+
+    # Could generate quadrature code for definite Integrals?
+    #_print_Integral = _print_not_supported
+
+
+    def _print_MatrixBase(self, A):
+        # Handle zero dimensions:
+        if (A.rows, A.cols) == (0, 0):
+            return '[]'
+        elif S.Zero in A.shape:
+            return 'zeros(%s, %s)' % (A.rows, A.cols)
+        elif (A.rows, A.cols) == (1, 1):
+            # Octave does not distinguish between scalars and 1x1 matrices
+            return self._print(A[0, 0])
+        return "[%s]" % "; ".join(" ".join([self._print(a) for a in A[r, :]])
+                                  for r in range(A.rows))
+
+
+    def _print_SparseRepMatrix(self, A):
+        from sympy.matrices import Matrix
+        L = A.col_list();
+        # make row vectors of the indices and entries
+        I = Matrix([[k[0] + 1 for k in L]])
+        J = Matrix([[k[1] + 1 for k in L]])
+        AIJ = Matrix([[k[2] for k in L]])
+        return "sparse(%s, %s, %s, %s, %s)" % (self._print(I), self._print(J),
+                                            self._print(AIJ), A.rows, A.cols)
+
+
+    def _print_MatrixElement(self, expr):
+        return self.parenthesize(expr.parent, PRECEDENCE["Atom"], strict=True) \
+            + '(%s, %s)' % (expr.i + 1, expr.j + 1)
+
+
+    def _print_MatrixSlice(self, expr):
+        def strslice(x, lim):
+            l = x[0] + 1
+            h = x[1]
+            step = x[2]
+            lstr = self._print(l)
+            hstr = 'end' if h == lim else self._print(h)
+            if step == 1:
+                if l == 1 and h == lim:
+                    return ':'
+                if l == h:
+                    return lstr
+                else:
+                    return lstr + ':' + hstr
+            else:
+                return ':'.join((lstr, self._print(step), hstr))
+        return (self._print(expr.parent) + '(' +
+                strslice(expr.rowslice, expr.parent.shape[0]) + ', ' +
+                strslice(expr.colslice, expr.parent.shape[1]) + ')')
+
+
+    def _print_Indexed(self, expr):
+        inds = [ self._print(i) for i in expr.indices ]
+        return "%s(%s)" % (self._print(expr.base.label), ", ".join(inds))
+
+
+    def _print_Idx(self, expr):
+        return self._print(expr.label)
+
+
+    def _print_KroneckerDelta(self, expr):
+        prec = PRECEDENCE["Pow"]
+        return "double(%s == %s)" % tuple(self.parenthesize(x, prec)
+                                          for x in expr.args)
+
+    def _print_HadamardProduct(self, expr):
+        return '.*'.join([self.parenthesize(arg, precedence(expr))
+                          for arg in expr.args])
+
+    def _print_HadamardPower(self, expr):
+        PREC = precedence(expr)
+        return '.**'.join([
+            self.parenthesize(expr.base, PREC),
+            self.parenthesize(expr.exp, PREC)
+            ])
+
+    def _print_Identity(self, expr):
+        shape = expr.shape
+        if len(shape) == 2 and shape[0] == shape[1]:
+            shape = [shape[0]]
+        s = ", ".join(self._print(n) for n in shape)
+        return "eye(" + s + ")"
+
+    def _print_lowergamma(self, expr):
+        # Octave implements regularized incomplete gamma function
+        return "(gammainc({1}, {0}).*gamma({0}))".format(
+            self._print(expr.args[0]), self._print(expr.args[1]))
+
+
+    def _print_uppergamma(self, expr):
+        return "(gammainc({1}, {0}, 'upper').*gamma({0}))".format(
+            self._print(expr.args[0]), self._print(expr.args[1]))
+
+
+    def _print_sinc(self, expr):
+        #Note: Divide by pi because Octave implements normalized sinc function.
+        return "sinc(%s)" % self._print(expr.args[0]/S.Pi)
+
+
+    def _print_hankel1(self, expr):
+        return "besselh(%s, 1, %s)" % (self._print(expr.order),
+                                       self._print(expr.argument))
+
+
+    def _print_hankel2(self, expr):
+        return "besselh(%s, 2, %s)" % (self._print(expr.order),
+                                       self._print(expr.argument))
+
+
+    # Note: as of 2015, Octave doesn't have spherical Bessel functions
+    def _print_jn(self, expr):
+        from sympy.functions import sqrt, besselj
+        x = expr.argument
+        expr2 = sqrt(S.Pi/(2*x))*besselj(expr.order + S.Half, x)
+        return self._print(expr2)
+
+
+    def _print_yn(self, expr):
+        from sympy.functions import sqrt, bessely
+        x = expr.argument
+        expr2 = sqrt(S.Pi/(2*x))*bessely(expr.order + S.Half, x)
+        return self._print(expr2)
+
+
+    def _print_airyai(self, expr):
+        return "airy(0, %s)" % self._print(expr.args[0])
+
+
+    def _print_airyaiprime(self, expr):
+        return "airy(1, %s)" % self._print(expr.args[0])
+
+
+    def _print_airybi(self, expr):
+        return "airy(2, %s)" % self._print(expr.args[0])
+
+
+    def _print_airybiprime(self, expr):
+        return "airy(3, %s)" % self._print(expr.args[0])
+
+
+    def _print_expint(self, expr):
+        mu, x = expr.args
+        if mu != 1:
+            return self._print_not_supported(expr)
+        return "expint(%s)" % self._print(x)
+
+
+    def _one_or_two_reversed_args(self, expr):
+        assert len(expr.args) <= 2
+        return '{name}({args})'.format(
+            name=self.known_functions[expr.__class__.__name__],
+            args=", ".join([self._print(x) for x in reversed(expr.args)])
+        )
+
+
+    _print_DiracDelta = _print_LambertW = _one_or_two_reversed_args
+
+
+    def _nested_binary_math_func(self, expr):
+        return '{name}({arg1}, {arg2})'.format(
+            name=self.known_functions[expr.__class__.__name__],
+            arg1=self._print(expr.args[0]),
+            arg2=self._print(expr.func(*expr.args[1:]))
+            )
+
+    _print_Max = _print_Min = _nested_binary_math_func
+
+
+    def _print_Piecewise(self, expr):
+        if expr.args[-1].cond != True:
+            # We need the last conditional to be a True, otherwise the resulting
+            # function may not return a result.
+            raise ValueError("All Piecewise expressions must contain an "
+                             "(expr, True) statement to be used as a default "
+                             "condition. Without one, the generated "
+                             "expression may not evaluate to anything under "
+                             "some condition.")
+        lines = []
+        if self._settings["inline"]:
+            # Express each (cond, expr) pair in a nested Horner form:
+            #   (condition) .* (expr) + (not cond) .* (<others>)
+            # Expressions that result in multiple statements won't work here.
+            ecpairs = ["({0}).*({1}) + (~({0})).*(".format
+                       (self._print(c), self._print(e))
+                       for e, c in expr.args[:-1]]
+            elast = "%s" % self._print(expr.args[-1].expr)
+            pw = " ...\n".join(ecpairs) + elast + ")"*len(ecpairs)
+            # Note: current need these outer brackets for 2*pw.  Would be
+            # nicer to teach parenthesize() to do this for us when needed!
+            return "(" + pw + ")"
+        else:
+            for i, (e, c) in enumerate(expr.args):
+                if i == 0:
+                    lines.append("if (%s)" % self._print(c))
+                elif i == len(expr.args) - 1 and c == True:
+                    lines.append("else")
+                else:
+                    lines.append("elseif (%s)" % self._print(c))
+                code0 = self._print(e)
+                lines.append(code0)
+                if i == len(expr.args) - 1:
+                    lines.append("end")
+            return "\n".join(lines)
+
+
+    def _print_zeta(self, expr):
+        if len(expr.args) == 1:
+            return "zeta(%s)" % self._print(expr.args[0])
+        else:
+            # Matlab two argument zeta is not equivalent to SymPy's
+            return self._print_not_supported(expr)
+
+
+    def indent_code(self, code):
+        """Accepts a string of code or a list of code lines"""
+
+        # code mostly copied from ccode
+        if isinstance(code, str):
+            code_lines = self.indent_code(code.splitlines(True))
+            return ''.join(code_lines)
+
+        tab = "  "
+        inc_regex = ('^function ', '^if ', '^elseif ', '^else$', '^for ')
+        dec_regex = ('^end$', '^elseif ', '^else$')
+
+        # pre-strip left-space from the code
+        code = [ line.lstrip(' \t') for line in code ]
+
+        increase = [ int(any(search(re, line) for re in inc_regex))
+                     for line in code ]
+        decrease = [ int(any(search(re, line) for re in dec_regex))
+                     for line in code ]
+
+        pretty = []
+        level = 0
+        for n, line in enumerate(code):
+            if line in ('', '\n'):
+                pretty.append(line)
+                continue
+            level -= decrease[n]
+            pretty.append("%s%s" % (tab*level, line))
+            level += increase[n]
+        return pretty
+
+
+def octave_code(expr, assign_to=None, **settings):
+    r"""Converts `expr` to a string of Octave (or Matlab) code.
+
+    The string uses a subset of the Octave language for Matlab compatibility.
+
+    Parameters
+    ==========
+
+    expr : Expr
+        A SymPy expression to be converted.
+    assign_to : optional
+        When given, the argument is used as the name of the variable to which
+        the expression is assigned.  Can be a string, ``Symbol``,
+        ``MatrixSymbol``, or ``Indexed`` type.  This can be helpful for
+        expressions that generate multi-line statements.
+    precision : integer, optional
+        The precision for numbers such as pi  [default=16].
+    user_functions : dict, optional
+        A dictionary where keys are ``FunctionClass`` instances and values are
+        their string representations.  Alternatively, the dictionary value can
+        be a list of tuples i.e. [(argument_test, cfunction_string)].  See
+        below for examples.
+    human : bool, optional
+        If True, the result is a single string that may contain some constant
+        declarations for the number symbols.  If False, the same information is
+        returned in a tuple of (symbols_to_declare, not_supported_functions,
+        code_text).  [default=True].
+    contract: bool, optional
+        If True, ``Indexed`` instances are assumed to obey tensor contraction
+        rules and the corresponding nested loops over indices are generated.
+        Setting contract=False will not generate loops, instead the user is
+        responsible to provide values for the indices in the code.
+        [default=True].
+    inline: bool, optional
+        If True, we try to create single-statement code instead of multiple
+        statements.  [default=True].
+
+    Examples
+    ========
+
+    >>> from sympy import octave_code, symbols, sin, pi
+    >>> x = symbols('x')
+    >>> octave_code(sin(x).series(x).removeO())
+    'x.^5/120 - x.^3/6 + x'
+
+    >>> from sympy import Rational, ceiling
+    >>> x, y, tau = symbols("x, y, tau")
+    >>> octave_code((2*tau)**Rational(7, 2))
+    '8*sqrt(2)*tau.^(7/2)'
+
+    Note that element-wise (Hadamard) operations are used by default between
+    symbols.  This is because its very common in Octave to write "vectorized"
+    code.  It is harmless if the values are scalars.
+
+    >>> octave_code(sin(pi*x*y), assign_to="s")
+    's = sin(pi*x.*y);'
+
+    If you need a matrix product "*" or matrix power "^", you can specify the
+    symbol as a ``MatrixSymbol``.
+
+    >>> from sympy import Symbol, MatrixSymbol
+    >>> n = Symbol('n', integer=True, positive=True)
+    >>> A = MatrixSymbol('A', n, n)
+    >>> octave_code(3*pi*A**3)
+    '(3*pi)*A^3'
+
+    This class uses several rules to decide which symbol to use a product.
+    Pure numbers use "*", Symbols use ".*" and MatrixSymbols use "*".
+    A HadamardProduct can be used to specify componentwise multiplication ".*"
+    of two MatrixSymbols.  There is currently there is no easy way to specify
+    scalar symbols, so sometimes the code might have some minor cosmetic
+    issues.  For example, suppose x and y are scalars and A is a Matrix, then
+    while a human programmer might write "(x^2*y)*A^3", we generate:
+
+    >>> octave_code(x**2*y*A**3)
+    '(x.^2.*y)*A^3'
+
+    Matrices are supported using Octave inline notation.  When using
+    ``assign_to`` with matrices, the name can be specified either as a string
+    or as a ``MatrixSymbol``.  The dimensions must align in the latter case.
+
+    >>> from sympy import Matrix, MatrixSymbol
+    >>> mat = Matrix([[x**2, sin(x), ceiling(x)]])
+    >>> octave_code(mat, assign_to='A')
+    'A = [x.^2 sin(x) ceil(x)];'
+
+    ``Piecewise`` expressions are implemented with logical masking by default.
+    Alternatively, you can pass "inline=False" to use if-else conditionals.
+    Note that if the ``Piecewise`` lacks a default term, represented by
+    ``(expr, True)`` then an error will be thrown.  This is to prevent
+    generating an expression that may not evaluate to anything.
+
+    >>> from sympy import Piecewise
+    >>> pw = Piecewise((x + 1, x > 0), (x, True))
+    >>> octave_code(pw, assign_to=tau)
+    'tau = ((x > 0).*(x + 1) + (~(x > 0)).*(x));'
+
+    Note that any expression that can be generated normally can also exist
+    inside a Matrix:
+
+    >>> mat = Matrix([[x**2, pw, sin(x)]])
+    >>> octave_code(mat, assign_to='A')
+    'A = [x.^2 ((x > 0).*(x + 1) + (~(x > 0)).*(x)) sin(x)];'
+
+    Custom printing can be defined for certain types by passing a dictionary of
+    "type" : "function" to the ``user_functions`` kwarg.  Alternatively, the
+    dictionary value can be a list of tuples i.e., [(argument_test,
+    cfunction_string)].  This can be used to call a custom Octave function.
+
+    >>> from sympy import Function
+    >>> f = Function('f')
+    >>> g = Function('g')
+    >>> custom_functions = {
+    ...   "f": "existing_octave_fcn",
+    ...   "g": [(lambda x: x.is_Matrix, "my_mat_fcn"),
+    ...         (lambda x: not x.is_Matrix, "my_fcn")]
+    ... }
+    >>> mat = Matrix([[1, x]])
+    >>> octave_code(f(x) + g(x) + g(mat), user_functions=custom_functions)
+    'existing_octave_fcn(x) + my_fcn(x) + my_mat_fcn([1 x])'
+
+    Support for loops is provided through ``Indexed`` types. With
+    ``contract=True`` these expressions will be turned into loops, whereas
+    ``contract=False`` will just print the assignment expression that should be
+    looped over:
+
+    >>> from sympy import Eq, IndexedBase, Idx
+    >>> len_y = 5
+    >>> y = IndexedBase('y', shape=(len_y,))
+    >>> t = IndexedBase('t', shape=(len_y,))
+    >>> Dy = IndexedBase('Dy', shape=(len_y-1,))
+    >>> i = Idx('i', len_y-1)
+    >>> e = Eq(Dy[i], (y[i+1]-y[i])/(t[i+1]-t[i]))
+    >>> octave_code(e.rhs, assign_to=e.lhs, contract=False)
+    'Dy(i) = (y(i + 1) - y(i))./(t(i + 1) - t(i));'
+    """
+    return OctaveCodePrinter(settings).doprint(expr, assign_to)
+
+
+def print_octave_code(expr, **settings):
+    """Prints the Octave (or Matlab) representation of the given expression.
+
+    See `octave_code` for the meaning of the optional arguments.
+    """
+    print(octave_code(expr, **settings))

venv/lib/python3.10/site-packages/sympy/printing/precedence.py

@@ -0,0 +1,177 @@
+"""A module providing information about the necessity of brackets"""
+
+
+# Default precedence values for some basic types
+PRECEDENCE = {
+    "Lambda": 1,
+    "Xor": 10,
+    "Or": 20,
+    "And": 30,
+    "Relational": 35,
+    "Add": 40,
+    "Mul": 50,
+    "Pow": 60,
+    "Func": 70,
+    "Not": 100,
+    "Atom": 1000,
+    "BitwiseOr": 36,
+    "BitwiseXor": 37,
+    "BitwiseAnd": 38
+}
+
+# A dictionary assigning precedence values to certain classes. These values are
+# treated like they were inherited, so not every single class has to be named
+# here.
+# Do not use this with printers other than StrPrinter
+PRECEDENCE_VALUES = {
+    "Equivalent": PRECEDENCE["Xor"],
+    "Xor": PRECEDENCE["Xor"],
+    "Implies": PRECEDENCE["Xor"],
+    "Or": PRECEDENCE["Or"],
+    "And": PRECEDENCE["And"],
+    "Add": PRECEDENCE["Add"],
+    "Pow": PRECEDENCE["Pow"],
+    "Relational": PRECEDENCE["Relational"],
+    "Sub": PRECEDENCE["Add"],
+    "Not": PRECEDENCE["Not"],
+    "Function" : PRECEDENCE["Func"],
+    "NegativeInfinity": PRECEDENCE["Add"],
+    "MatAdd": PRECEDENCE["Add"],
+    "MatPow": PRECEDENCE["Pow"],
+    "MatrixSolve": PRECEDENCE["Mul"],
+    "Mod": PRECEDENCE["Mul"],
+    "TensAdd": PRECEDENCE["Add"],
+    # As soon as `TensMul` is a subclass of `Mul`, remove this:
+    "TensMul": PRECEDENCE["Mul"],
+    "HadamardProduct": PRECEDENCE["Mul"],
+    "HadamardPower": PRECEDENCE["Pow"],
+    "KroneckerProduct": PRECEDENCE["Mul"],
+    "Equality": PRECEDENCE["Mul"],
+    "Unequality": PRECEDENCE["Mul"],
+}
+
+# Sometimes it's not enough to assign a fixed precedence value to a
+# class. Then a function can be inserted in this dictionary that takes
+# an instance of this class as argument and returns the appropriate
+# precedence value.
+
+# Precedence functions
+
+
+def precedence_Mul(item):
+    if item.could_extract_minus_sign():
+        return PRECEDENCE["Add"]
+    return PRECEDENCE["Mul"]
+
+
+def precedence_Rational(item):
+    if item.p < 0:
+        return PRECEDENCE["Add"]
+    return PRECEDENCE["Mul"]
+
+
+def precedence_Integer(item):
+    if item.p < 0:
+        return PRECEDENCE["Add"]
+    return PRECEDENCE["Atom"]
+
+
+def precedence_Float(item):
+    if item < 0:
+        return PRECEDENCE["Add"]
+    return PRECEDENCE["Atom"]
+
+
+def precedence_PolyElement(item):
+    if item.is_generator:
+        return PRECEDENCE["Atom"]
+    elif item.is_ground:
+        return precedence(item.coeff(1))
+    elif item.is_term:
+        return PRECEDENCE["Mul"]
+    else:
+        return PRECEDENCE["Add"]
+
+
+def precedence_FracElement(item):
+    if item.denom == 1:
+        return precedence_PolyElement(item.numer)
+    else:
+        return PRECEDENCE["Mul"]
+
+
+def precedence_UnevaluatedExpr(item):
+    return precedence(item.args[0]) - 0.5
+
+
+PRECEDENCE_FUNCTIONS = {
+    "Integer": precedence_Integer,
+    "Mul": precedence_Mul,
+    "Rational": precedence_Rational,
+    "Float": precedence_Float,
+    "PolyElement": precedence_PolyElement,
+    "FracElement": precedence_FracElement,
+    "UnevaluatedExpr": precedence_UnevaluatedExpr,
+}
+
+
+def precedence(item):
+    """Returns the precedence of a given object.
+
+    This is the precedence for StrPrinter.
+    """
+    if hasattr(item, "precedence"):
+        return item.precedence
+    try:
+        mro = item.__class__.__mro__
+    except AttributeError:
+        return PRECEDENCE["Atom"]
+    for i in mro:
+        n = i.__name__
+        if n in PRECEDENCE_FUNCTIONS:
+            return PRECEDENCE_FUNCTIONS[n](item)
+        elif n in PRECEDENCE_VALUES:
+            return PRECEDENCE_VALUES[n]
+    return PRECEDENCE["Atom"]
+
+
+PRECEDENCE_TRADITIONAL = PRECEDENCE.copy()
+PRECEDENCE_TRADITIONAL['Integral'] = PRECEDENCE["Mul"]
+PRECEDENCE_TRADITIONAL['Sum'] = PRECEDENCE["Mul"]
+PRECEDENCE_TRADITIONAL['Product'] = PRECEDENCE["Mul"]
+PRECEDENCE_TRADITIONAL['Limit'] = PRECEDENCE["Mul"]
+PRECEDENCE_TRADITIONAL['Derivative'] = PRECEDENCE["Mul"]
+PRECEDENCE_TRADITIONAL['TensorProduct'] = PRECEDENCE["Mul"]
+PRECEDENCE_TRADITIONAL['Transpose'] = PRECEDENCE["Pow"]
+PRECEDENCE_TRADITIONAL['Adjoint'] = PRECEDENCE["Pow"]
+PRECEDENCE_TRADITIONAL['Dot'] = PRECEDENCE["Mul"] - 1
+PRECEDENCE_TRADITIONAL['Cross'] = PRECEDENCE["Mul"] - 1
+PRECEDENCE_TRADITIONAL['Gradient'] = PRECEDENCE["Mul"] - 1
+PRECEDENCE_TRADITIONAL['Divergence'] = PRECEDENCE["Mul"] - 1
+PRECEDENCE_TRADITIONAL['Curl'] = PRECEDENCE["Mul"] - 1
+PRECEDENCE_TRADITIONAL['Laplacian'] = PRECEDENCE["Mul"] - 1
+PRECEDENCE_TRADITIONAL['Union'] = PRECEDENCE['Xor']
+PRECEDENCE_TRADITIONAL['Intersection'] = PRECEDENCE['Xor']
+PRECEDENCE_TRADITIONAL['Complement'] = PRECEDENCE['Xor']
+PRECEDENCE_TRADITIONAL['SymmetricDifference'] = PRECEDENCE['Xor']
+PRECEDENCE_TRADITIONAL['ProductSet'] = PRECEDENCE['Xor']
+
+
+def precedence_traditional(item):
+    """Returns the precedence of a given object according to the
+    traditional rules of mathematics.
+
+    This is the precedence for the LaTeX and pretty printer.
+    """
+    # Integral, Sum, Product, Limit have the precedence of Mul in LaTeX,
+    # the precedence of Atom for other printers:
+    from sympy.core.expr import UnevaluatedExpr
+
+    if isinstance(item, UnevaluatedExpr):
+        return precedence_traditional(item.args[0])
+
+    n = item.__class__.__name__
+    if n in PRECEDENCE_TRADITIONAL:
+        return PRECEDENCE_TRADITIONAL[n]
+
+    return precedence(item)

venv/lib/python3.10/site-packages/sympy/printing/preview.py

@@ -0,0 +1,390 @@
+import os
+from os.path import join
+import shutil
+import tempfile
+
+try:
+    from subprocess import STDOUT, CalledProcessError, check_output
+except ImportError:
+    pass
+
+from sympy.utilities.decorator import doctest_depends_on
+from sympy.utilities.misc import debug
+from .latex import latex
+
+__doctest_requires__ = {('preview',): ['pyglet']}
+
+
+def _check_output_no_window(*args, **kwargs):
+    # Avoid showing a cmd.exe window when running this
+    # on Windows
+    if os.name == 'nt':
+        creation_flag = 0x08000000 # CREATE_NO_WINDOW
+    else:
+        creation_flag = 0 # Default value
+    return check_output(*args, creationflags=creation_flag, **kwargs)
+
+
+def system_default_viewer(fname, fmt):
+    """ Open fname with the default system viewer.
+
+    In practice, it is impossible for python to know when the system viewer is
+    done. For this reason, we ensure the passed file will not be deleted under
+    it, and this function does not attempt to block.
+    """
+    # copy to a new temporary file that will not be deleted
+    with tempfile.NamedTemporaryFile(prefix='sympy-preview-',
+                                     suffix=os.path.splitext(fname)[1],
+                                     delete=False) as temp_f:
+        with open(fname, 'rb') as f:
+            shutil.copyfileobj(f, temp_f)
+
+    import platform
+    if platform.system() == 'Darwin':
+        import subprocess
+        subprocess.call(('open', temp_f.name))
+    elif platform.system() == 'Windows':
+        os.startfile(temp_f.name)
+    else:
+        import subprocess
+        subprocess.call(('xdg-open', temp_f.name))
+
+
+def pyglet_viewer(fname, fmt):
+    try:
+        from pyglet import window, image, gl
+        from pyglet.window import key
+        from pyglet.image.codecs import ImageDecodeException
+    except ImportError:
+        raise ImportError("pyglet is required for preview.\n visit https://pyglet.org/")
+
+    try:
+        img = image.load(fname)
+    except ImageDecodeException:
+        raise ValueError("pyglet preview does not work for '{}' files.".format(fmt))
+
+    offset = 25
+
+    config = gl.Config(double_buffer=False)
+    win = window.Window(
+        width=img.width + 2*offset,
+        height=img.height + 2*offset,
+        caption="SymPy",
+        resizable=False,
+        config=config
+    )
+
+    win.set_vsync(False)
+
+    try:
+        def on_close():
+            win.has_exit = True
+
+        win.on_close = on_close
+
+        def on_key_press(symbol, modifiers):
+            if symbol in [key.Q, key.ESCAPE]:
+                on_close()
+
+        win.on_key_press = on_key_press
+
+        def on_expose():
+            gl.glClearColor(1.0, 1.0, 1.0, 1.0)
+            gl.glClear(gl.GL_COLOR_BUFFER_BIT)
+
+            img.blit(
+                (win.width - img.width) / 2,
+                (win.height - img.height) / 2
+            )
+
+        win.on_expose = on_expose
+
+        while not win.has_exit:
+            win.dispatch_events()
+            win.flip()
+    except KeyboardInterrupt:
+        pass
+
+    win.close()
+
+
+def _get_latex_main(expr, *, preamble=None, packages=(), extra_preamble=None,
+                    euler=True, fontsize=None, **latex_settings):
+    """
+    Generate string of a LaTeX document rendering ``expr``.
+    """
+    if preamble is None:
+        actual_packages = packages + ("amsmath", "amsfonts")
+        if euler:
+            actual_packages += ("euler",)
+        package_includes = "\n" + "\n".join(["\\usepackage{%s}" % p
+                                             for p in actual_packages])
+        if extra_preamble:
+            package_includes += extra_preamble
+
+        if not fontsize:
+            fontsize = "12pt"
+        elif isinstance(fontsize, int):
+            fontsize = "{}pt".format(fontsize)
+        preamble = r"""\documentclass[varwidth,%s]{standalone}
+%s
+
+\begin{document}
+""" % (fontsize, package_includes)
+    else:
+        if packages or extra_preamble:
+            raise ValueError("The \"packages\" or \"extra_preamble\" keywords"
+                             "must not be set if a "
+                             "custom LaTeX preamble was specified")
+
+    if isinstance(expr, str):
+        latex_string = expr
+    else:
+        latex_string = ('$\\displaystyle ' +
+                        latex(expr, mode='plain', **latex_settings) +
+                        '$')
+
+    return preamble + '\n' + latex_string + '\n\n' + r"\end{document}"
+
+
+@doctest_depends_on(exe=('latex', 'dvipng'), modules=('pyglet',),
+            disable_viewers=('evince', 'gimp', 'superior-dvi-viewer'))
+def preview(expr, output='png', viewer=None, euler=True, packages=(),
+            filename=None, outputbuffer=None, preamble=None, dvioptions=None,
+            outputTexFile=None, extra_preamble=None, fontsize=None,
+            **latex_settings):
+    r"""
+    View expression or LaTeX markup in PNG, DVI, PostScript or PDF form.
+
+    If the expr argument is an expression, it will be exported to LaTeX and
+    then compiled using the available TeX distribution.  The first argument,
+    'expr', may also be a LaTeX string.  The function will then run the
+    appropriate viewer for the given output format or use the user defined
+    one. By default png output is generated.
+
+    By default pretty Euler fonts are used for typesetting (they were used to
+    typeset the well known "Concrete Mathematics" book). For that to work, you
+    need the 'eulervm.sty' LaTeX style (in Debian/Ubuntu, install the
+    texlive-fonts-extra package). If you prefer default AMS fonts or your
+    system lacks 'eulervm' LaTeX package then unset the 'euler' keyword
+    argument.
+
+    To use viewer auto-detection, lets say for 'png' output, issue
+
+    >>> from sympy import symbols, preview, Symbol
+    >>> x, y = symbols("x,y")
+
+    >>> preview(x + y, output='png')
+
+    This will choose 'pyglet' by default. To select a different one, do
+
+    >>> preview(x + y, output='png', viewer='gimp')
+
+    The 'png' format is considered special. For all other formats the rules
+    are slightly different. As an example we will take 'dvi' output format. If
+    you would run
+
+    >>> preview(x + y, output='dvi')
+
+    then 'view' will look for available 'dvi' viewers on your system
+    (predefined in the function, so it will try evince, first, then kdvi and
+    xdvi). If nothing is found, it will fall back to using a system file
+    association (via ``open`` and ``xdg-open``). To always use your system file
+    association without searching for the above readers, use
+
+    >>> from sympy.printing.preview import system_default_viewer
+    >>> preview(x + y, output='dvi', viewer=system_default_viewer)
+
+    If this still does not find the viewer you want, it can be set explicitly.
+
+    >>> preview(x + y, output='dvi', viewer='superior-dvi-viewer')
+
+    This will skip auto-detection and will run user specified
+    'superior-dvi-viewer'. If ``view`` fails to find it on your system it will
+    gracefully raise an exception.
+
+    You may also enter ``'file'`` for the viewer argument. Doing so will cause
+    this function to return a file object in read-only mode, if ``filename``
+    is unset. However, if it was set, then 'preview' writes the generated
+    file to this filename instead.
+
+    There is also support for writing to a ``io.BytesIO`` like object, which
+    needs to be passed to the ``outputbuffer`` argument.
+
+    >>> from io import BytesIO
+    >>> obj = BytesIO()
+    >>> preview(x + y, output='png', viewer='BytesIO',
+    ...         outputbuffer=obj)
+
+    The LaTeX preamble can be customized by setting the 'preamble' keyword
+    argument. This can be used, e.g., to set a different font size, use a
+    custom documentclass or import certain set of LaTeX packages.
+
+    >>> preamble = "\\documentclass[10pt]{article}\n" \
+    ...            "\\usepackage{amsmath,amsfonts}\\begin{document}"
+    >>> preview(x + y, output='png', preamble=preamble)
+
+    It is also possible to use the standard preamble and provide additional
+    information to the preamble using the ``extra_preamble`` keyword argument.
+
+    >>> from sympy import sin
+    >>> extra_preamble = "\\renewcommand{\\sin}{\\cos}"
+    >>> preview(sin(x), output='png', extra_preamble=extra_preamble)
+
+    If the value of 'output' is different from 'dvi' then command line
+    options can be set ('dvioptions' argument) for the execution of the
+    'dvi'+output conversion tool. These options have to be in the form of a
+    list of strings (see ``subprocess.Popen``).
+
+    Additional keyword args will be passed to the :func:`~sympy.printing.latex.latex` call,
+    e.g., the ``symbol_names`` flag.
+
+    >>> phidd = Symbol('phidd')
+    >>> preview(phidd, symbol_names={phidd: r'\ddot{\varphi}'})
+
+    For post-processing the generated TeX File can be written to a file by
+    passing the desired filename to the 'outputTexFile' keyword
+    argument. To write the TeX code to a file named
+    ``"sample.tex"`` and run the default png viewer to display the resulting
+    bitmap, do
+
+    >>> preview(x + y, outputTexFile="sample.tex")
+
+
+    """
+    # pyglet is the default for png
+    if viewer is None and output == "png":
+        try:
+            import pyglet  # noqa: F401
+        except ImportError:
+            pass
+        else:
+            viewer = pyglet_viewer
+
+    # look up a known application
+    if viewer is None:
+        # sorted in order from most pretty to most ugly
+        # very discussable, but indeed 'gv' looks awful :)
+        candidates = {
+            "dvi": [ "evince", "okular", "kdvi", "xdvi" ],
+            "ps": [ "evince", "okular", "gsview", "gv" ],
+            "pdf": [ "evince", "okular", "kpdf", "acroread", "xpdf", "gv" ],
+        }
+
+        for candidate in candidates.get(output, []):
+            path = shutil.which(candidate)
+            if path is not None:
+                viewer = path
+                break
+
+    # otherwise, use the system default for file association
+    if viewer is None:
+        viewer = system_default_viewer
+
+    if viewer == "file":
+        if filename is None:
+            raise ValueError("filename has to be specified if viewer=\"file\"")
+    elif viewer == "BytesIO":
+        if outputbuffer is None:
+            raise ValueError("outputbuffer has to be a BytesIO "
+                             "compatible object if viewer=\"BytesIO\"")
+    elif not callable(viewer) and not shutil.which(viewer):
+        raise OSError("Unrecognized viewer: %s" % viewer)
+
+    latex_main = _get_latex_main(expr, preamble=preamble, packages=packages,
+                                 euler=euler, extra_preamble=extra_preamble,
+                                 fontsize=fontsize, **latex_settings)
+
+    debug("Latex code:")
+    debug(latex_main)
+    with tempfile.TemporaryDirectory() as workdir:
+        with open(join(workdir, 'texput.tex'), 'w', encoding='utf-8') as fh:
+            fh.write(latex_main)
+
+        if outputTexFile is not None:
+            shutil.copyfile(join(workdir, 'texput.tex'), outputTexFile)
+
+        if not shutil.which('latex'):
+            raise RuntimeError("latex program is not installed")
+
+        try:
+            _check_output_no_window(
+                ['latex', '-halt-on-error', '-interaction=nonstopmode',
+                 'texput.tex'],
+                cwd=workdir,
+                stderr=STDOUT)
+        except CalledProcessError as e:
+            raise RuntimeError(
+                "'latex' exited abnormally with the following output:\n%s" %
+                e.output)
+
+        src = "texput.%s" % (output)
+
+        if output != "dvi":
+            # in order of preference
+            commandnames = {
+                "ps": ["dvips"],
+                "pdf": ["dvipdfmx", "dvipdfm", "dvipdf"],
+                "png": ["dvipng"],
+                "svg": ["dvisvgm"],
+            }
+            try:
+                cmd_variants = commandnames[output]
+            except KeyError:
+                raise ValueError("Invalid output format: %s" % output) from None
+
+            # find an appropriate command
+            for cmd_variant in cmd_variants:
+                cmd_path = shutil.which(cmd_variant)
+                if cmd_path:
+                    cmd = [cmd_path]
+                    break
+            else:
+                if len(cmd_variants) > 1:
+                    raise RuntimeError("None of %s are installed" % ", ".join(cmd_variants))
+                else:
+                    raise RuntimeError("%s is not installed" % cmd_variants[0])
+
+            defaultoptions = {
+                "dvipng": ["-T", "tight", "-z", "9", "--truecolor"],
+                "dvisvgm": ["--no-fonts"],
+            }
+
+            commandend = {
+                "dvips": ["-o", src, "texput.dvi"],
+                "dvipdf": ["texput.dvi", src],
+                "dvipdfm": ["-o", src, "texput.dvi"],
+                "dvipdfmx": ["-o", src, "texput.dvi"],
+                "dvipng": ["-o", src, "texput.dvi"],
+                "dvisvgm": ["-o", src, "texput.dvi"],
+            }
+
+            if dvioptions is not None:
+                cmd.extend(dvioptions)
+            else:
+                cmd.extend(defaultoptions.get(cmd_variant, []))
+            cmd.extend(commandend[cmd_variant])
+
+            try:
+                _check_output_no_window(cmd, cwd=workdir, stderr=STDOUT)
+            except CalledProcessError as e:
+                raise RuntimeError(
+                    "'%s' exited abnormally with the following output:\n%s" %
+                    (' '.join(cmd), e.output))
+
+
+        if viewer == "file":
+            shutil.move(join(workdir, src), filename)
+        elif viewer == "BytesIO":
+            with open(join(workdir, src), 'rb') as fh:
+                outputbuffer.write(fh.read())
+        elif callable(viewer):
+            viewer(join(workdir, src), fmt=output)
+        else:
+            try:
+                _check_output_no_window(
+                    [viewer, src], cwd=workdir, stderr=STDOUT)
+            except CalledProcessError as e:
+                raise RuntimeError(
+                    "'%s %s' exited abnormally with the following output:\n%s" %
+                    (viewer, src, e.output))

venv/lib/python3.10/site-packages/sympy/printing/printer.py

@@ -0,0 +1,396 @@
+"""Printing subsystem driver
+
+SymPy's printing system works the following way: Any expression can be
+passed to a designated Printer who then is responsible to return an
+adequate representation of that expression.
+
+**The basic concept is the following:**
+
+1.  Let the object print itself if it knows how.
+2.  Take the best fitting method defined in the printer.
+3.  As fall-back use the emptyPrinter method for the printer.
+
+Which Method is Responsible for Printing?
+^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+
+The whole printing process is started by calling ``.doprint(expr)`` on the printer
+which you want to use. This method looks for an appropriate method which can
+print the given expression in the given style that the printer defines.
+While looking for the method, it follows these steps:
+
+1.  **Let the object print itself if it knows how.**
+
+    The printer looks for a specific method in every object. The name of that method
+    depends on the specific printer and is defined under ``Printer.printmethod``.
+    For example, StrPrinter calls ``_sympystr`` and LatexPrinter calls ``_latex``.
+    Look at the documentation of the printer that you want to use.
+    The name of the method is specified there.
+
+    This was the original way of doing printing in sympy. Every class had
+    its own latex, mathml, str and repr methods, but it turned out that it
+    is hard to produce a high quality printer, if all the methods are spread
+    out that far. Therefore all printing code was combined into the different
+    printers, which works great for built-in SymPy objects, but not that
+    good for user defined classes where it is inconvenient to patch the
+    printers.
+
+2.  **Take the best fitting method defined in the printer.**
+
+    The printer loops through expr classes (class + its bases), and tries
+    to dispatch the work to ``_print_<EXPR_CLASS>``
+
+    e.g., suppose we have the following class hierarchy::
+
+            Basic
+            |
+            Atom
+            |
+            Number
+            |
+        Rational
+
+    then, for ``expr=Rational(...)``, the Printer will try
+    to call printer methods in the order as shown in the figure below::
+
+        p._print(expr)
+        |
+        |-- p._print_Rational(expr)
+        |
+        |-- p._print_Number(expr)
+        |
+        |-- p._print_Atom(expr)
+        |
+        `-- p._print_Basic(expr)
+
+    if ``._print_Rational`` method exists in the printer, then it is called,
+    and the result is returned back. Otherwise, the printer tries to call
+    ``._print_Number`` and so on.
+
+3.  **As a fall-back use the emptyPrinter method for the printer.**
+
+    As fall-back ``self.emptyPrinter`` will be called with the expression. If
+    not defined in the Printer subclass this will be the same as ``str(expr)``.
+
+.. _printer_example:
+
+Example of Custom Printer
+^^^^^^^^^^^^^^^^^^^^^^^^^
+
+In the example below, we have a printer which prints the derivative of a function
+in a shorter form.
+
+.. code-block:: python
+
+    from sympy.core.symbol import Symbol
+    from sympy.printing.latex import LatexPrinter, print_latex
+    from sympy.core.function import UndefinedFunction, Function
+
+
+    class MyLatexPrinter(LatexPrinter):
+        \"\"\"Print derivative of a function of symbols in a shorter form.
+        \"\"\"
+        def _print_Derivative(self, expr):
+            function, *vars = expr.args
+            if not isinstance(type(function), UndefinedFunction) or \\
+               not all(isinstance(i, Symbol) for i in vars):
+                return super()._print_Derivative(expr)
+
+            # If you want the printer to work correctly for nested
+            # expressions then use self._print() instead of str() or latex().
+            # See the example of nested modulo below in the custom printing
+            # method section.
+            return "{}_{{{}}}".format(
+                self._print(Symbol(function.func.__name__)),
+                            ''.join(self._print(i) for i in vars))
+
+
+    def print_my_latex(expr):
+        \"\"\" Most of the printers define their own wrappers for print().
+        These wrappers usually take printer settings. Our printer does not have
+        any settings.
+        \"\"\"
+        print(MyLatexPrinter().doprint(expr))
+
+
+    y = Symbol("y")
+    x = Symbol("x")
+    f = Function("f")
+    expr = f(x, y).diff(x, y)
+
+    # Print the expression using the normal latex printer and our custom
+    # printer.
+    print_latex(expr)
+    print_my_latex(expr)
+
+The output of the code above is::
+
+    \\frac{\\partial^{2}}{\\partial x\\partial y}  f{\\left(x,y \\right)}
+    f_{xy}
+
+.. _printer_method_example:
+
+Example of Custom Printing Method
+^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+
+In the example below, the latex printing of the modulo operator is modified.
+This is done by overriding the method ``_latex`` of ``Mod``.
+
+>>> from sympy import Symbol, Mod, Integer, print_latex
+
+>>> # Always use printer._print()
+>>> class ModOp(Mod):
+...     def _latex(self, printer):
+...         a, b = [printer._print(i) for i in self.args]
+...         return r"\\operatorname{Mod}{\\left(%s, %s\\right)}" % (a, b)
+
+Comparing the output of our custom operator to the builtin one:
+
+>>> x = Symbol('x')
+>>> m = Symbol('m')
+>>> print_latex(Mod(x, m))
+x \\bmod m
+>>> print_latex(ModOp(x, m))
+\\operatorname{Mod}{\\left(x, m\\right)}
+
+Common mistakes
+~~~~~~~~~~~~~~~
+It's important to always use ``self._print(obj)`` to print subcomponents of
+an expression when customizing a printer. Mistakes include:
+
+1.  Using ``self.doprint(obj)`` instead:
+
+    >>> # This example does not work properly, as only the outermost call may use
+    >>> # doprint.
+    >>> class ModOpModeWrong(Mod):
+    ...     def _latex(self, printer):
+    ...         a, b = [printer.doprint(i) for i in self.args]
+    ...         return r"\\operatorname{Mod}{\\left(%s, %s\\right)}" % (a, b)
+
+    This fails when the ``mode`` argument is passed to the printer:
+
+    >>> print_latex(ModOp(x, m), mode='inline')  # ok
+    $\\operatorname{Mod}{\\left(x, m\\right)}$
+    >>> print_latex(ModOpModeWrong(x, m), mode='inline')  # bad
+    $\\operatorname{Mod}{\\left($x$, $m$\\right)}$
+
+2.  Using ``str(obj)`` instead:
+
+    >>> class ModOpNestedWrong(Mod):
+    ...     def _latex(self, printer):
+    ...         a, b = [str(i) for i in self.args]
+    ...         return r"\\operatorname{Mod}{\\left(%s, %s\\right)}" % (a, b)
+
+    This fails on nested objects:
+
+    >>> # Nested modulo.
+    >>> print_latex(ModOp(ModOp(x, m), Integer(7)))  # ok
+    \\operatorname{Mod}{\\left(\\operatorname{Mod}{\\left(x, m\\right)}, 7\\right)}
+    >>> print_latex(ModOpNestedWrong(ModOpNestedWrong(x, m), Integer(7)))  # bad
+    \\operatorname{Mod}{\\left(ModOpNestedWrong(x, m), 7\\right)}
+
+3.  Using ``LatexPrinter()._print(obj)`` instead.
+
+    >>> from sympy.printing.latex import LatexPrinter
+    >>> class ModOpSettingsWrong(Mod):
+    ...     def _latex(self, printer):
+    ...         a, b = [LatexPrinter()._print(i) for i in self.args]
+    ...         return r"\\operatorname{Mod}{\\left(%s, %s\\right)}" % (a, b)
+
+    This causes all the settings to be discarded in the subobjects. As an
+    example, the ``full_prec`` setting which shows floats to full precision is
+    ignored:
+
+    >>> from sympy import Float
+    >>> print_latex(ModOp(Float(1) * x, m), full_prec=True)  # ok
+    \\operatorname{Mod}{\\left(1.00000000000000 x, m\\right)}
+    >>> print_latex(ModOpSettingsWrong(Float(1) * x, m), full_prec=True)  # bad
+    \\operatorname{Mod}{\\left(1.0 x, m\\right)}
+
+"""
+
+from __future__ import annotations
+import sys
+from typing import Any, Type
+import inspect
+from contextlib import contextmanager
+from functools import cmp_to_key, update_wrapper
+
+from sympy.core.add import Add
+from sympy.core.basic import Basic
+
+from sympy.core.function import AppliedUndef, UndefinedFunction, Function
+
+
+
+@contextmanager
+def printer_context(printer, **kwargs):
+    original = printer._context.copy()
+    try:
+        printer._context.update(kwargs)
+        yield
+    finally:
+        printer._context = original
+
+
+class Printer:
+    """ Generic printer
+
+    Its job is to provide infrastructure for implementing new printers easily.
+
+    If you want to define your custom Printer or your custom printing method
+    for your custom class then see the example above: printer_example_ .
+    """
+
+    _global_settings: dict[str, Any] = {}
+
+    _default_settings: dict[str, Any] = {}
+
+    printmethod = None  # type: str
+
+    @classmethod
+    def _get_initial_settings(cls):
+        settings = cls._default_settings.copy()
+        for key, val in cls._global_settings.items():
+            if key in cls._default_settings:
+                settings[key] = val
+        return settings
+
+    def __init__(self, settings=None):
+        self._str = str
+
+        self._settings = self._get_initial_settings()
+        self._context = {}  # mutable during printing
+
+        if settings is not None:
+            self._settings.update(settings)
+
+            if len(self._settings) > len(self._default_settings):
+                for key in self._settings:
+                    if key not in self._default_settings:
+                        raise TypeError("Unknown setting '%s'." % key)
+
+        # _print_level is the number of times self._print() was recursively
+        # called. See StrPrinter._print_Float() for an example of usage
+        self._print_level = 0
+
+    @classmethod
+    def set_global_settings(cls, **settings):
+        """Set system-wide printing settings. """
+        for key, val in settings.items():
+            if val is not None:
+                cls._global_settings[key] = val
+
+    @property
+    def order(self):
+        if 'order' in self._settings:
+            return self._settings['order']
+        else:
+            raise AttributeError("No order defined.")
+
+    def doprint(self, expr):
+        """Returns printer's representation for expr (as a string)"""
+        return self._str(self._print(expr))
+
+    def _print(self, expr, **kwargs) -> str:
+        """Internal dispatcher
+
+        Tries the following concepts to print an expression:
+            1. Let the object print itself if it knows how.
+            2. Take the best fitting method defined in the printer.
+            3. As fall-back use the emptyPrinter method for the printer.
+        """
+        self._print_level += 1
+        try:
+            # If the printer defines a name for a printing method
+            # (Printer.printmethod) and the object knows for itself how it
+            # should be printed, use that method.
+            if self.printmethod and hasattr(expr, self.printmethod):
+                if not (isinstance(expr, type) and issubclass(expr, Basic)):
+                    return getattr(expr, self.printmethod)(self, **kwargs)
+
+            # See if the class of expr is known, or if one of its super
+            # classes is known, and use that print function
+            # Exception: ignore the subclasses of Undefined, so that, e.g.,
+            # Function('gamma') does not get dispatched to _print_gamma
+            classes = type(expr).__mro__
+            if AppliedUndef in classes:
+                classes = classes[classes.index(AppliedUndef):]
+            if UndefinedFunction in classes:
+                classes = classes[classes.index(UndefinedFunction):]
+            # Another exception: if someone subclasses a known function, e.g.,
+            # gamma, and changes the name, then ignore _print_gamma
+            if Function in classes:
+                i = classes.index(Function)
+                classes = tuple(c for c in classes[:i] if \
+                    c.__name__ == classes[0].__name__ or \
+                    c.__name__.endswith("Base")) + classes[i:]
+            for cls in classes:
+                printmethodname = '_print_' + cls.__name__
+                printmethod = getattr(self, printmethodname, None)
+                if printmethod is not None:
+                    return printmethod(expr, **kwargs)
+            # Unknown object, fall back to the emptyPrinter.
+            return self.emptyPrinter(expr)
+        finally:
+            self._print_level -= 1
+
+    def emptyPrinter(self, expr):
+        return str(expr)
+
+    def _as_ordered_terms(self, expr, order=None):
+        """A compatibility function for ordering terms in Add. """
+        order = order or self.order
+
+        if order == 'old':
+            return sorted(Add.make_args(expr), key=cmp_to_key(Basic._compare_pretty))
+        elif order == 'none':
+            return list(expr.args)
+        else:
+            return expr.as_ordered_terms(order=order)
+
+
+class _PrintFunction:
+    """
+    Function wrapper to replace ``**settings`` in the signature with printer defaults
+    """
+    def __init__(self, f, print_cls: Type[Printer]):
+        # find all the non-setting arguments
+        params = list(inspect.signature(f).parameters.values())
+        assert params.pop(-1).kind == inspect.Parameter.VAR_KEYWORD
+        self.__other_params = params
+
+        self.__print_cls = print_cls
+        update_wrapper(self, f)
+
+    def __reduce__(self):
+        # Since this is used as a decorator, it replaces the original function.
+        # The default pickling will try to pickle self.__wrapped__ and fail
+        # because the wrapped function can't be retrieved by name.
+        return self.__wrapped__.__qualname__
+
+    def __call__(self, *args, **kwargs):
+        return self.__wrapped__(*args, **kwargs)
+
+    @property
+    def __signature__(self) -> inspect.Signature:
+        settings = self.__print_cls._get_initial_settings()
+        return inspect.Signature(
+            parameters=self.__other_params + [
+                inspect.Parameter(k, inspect.Parameter.KEYWORD_ONLY, default=v)
+                for k, v in settings.items()
+            ],
+            return_annotation=self.__wrapped__.__annotations__.get('return', inspect.Signature.empty)  # type:ignore
+        )
+
+
+def print_function(print_cls):
+    """ A decorator to replace kwargs with the printer settings in __signature__ """
+    def decorator(f):
+        if sys.version_info < (3, 9):
+            # We have to create a subclass so that `help` actually shows the docstring in older Python versions.
+            # IPython and Sphinx do not need this, only a raw Python console.
+            cls = type(f'{f.__qualname__}_PrintFunction', (_PrintFunction,), {"__doc__": f.__doc__})
+        else:
+            cls = _PrintFunction
+        return cls(f, print_cls)
+    return decorator

venv/lib/python3.10/site-packages/sympy/printing/pycode.py

@@ -0,0 +1,750 @@
+"""
+Python code printers
+
+This module contains Python code printers for plain Python as well as NumPy & SciPy enabled code.
+"""
+from collections import defaultdict
+from itertools import chain
+from sympy.core import S
+from sympy.core.mod import Mod
+from .precedence import precedence
+from .codeprinter import CodePrinter
+
+_kw = {
+    'and', 'as', 'assert', 'break', 'class', 'continue', 'def', 'del', 'elif',
+    'else', 'except', 'finally', 'for', 'from', 'global', 'if', 'import', 'in',
+    'is', 'lambda', 'not', 'or', 'pass', 'raise', 'return', 'try', 'while',
+    'with', 'yield', 'None', 'False', 'nonlocal', 'True'
+}
+
+_known_functions = {
+    'Abs': 'abs',
+    'Min': 'min',
+    'Max': 'max',
+}
+_known_functions_math = {
+    'acos': 'acos',
+    'acosh': 'acosh',
+    'asin': 'asin',
+    'asinh': 'asinh',
+    'atan': 'atan',
+    'atan2': 'atan2',
+    'atanh': 'atanh',
+    'ceiling': 'ceil',
+    'cos': 'cos',
+    'cosh': 'cosh',
+    'erf': 'erf',
+    'erfc': 'erfc',
+    'exp': 'exp',
+    'expm1': 'expm1',
+    'factorial': 'factorial',
+    'floor': 'floor',
+    'gamma': 'gamma',
+    'hypot': 'hypot',
+    'loggamma': 'lgamma',
+    'log': 'log',
+    'ln': 'log',
+    'log10': 'log10',
+    'log1p': 'log1p',
+    'log2': 'log2',
+    'sin': 'sin',
+    'sinh': 'sinh',
+    'Sqrt': 'sqrt',
+    'tan': 'tan',
+    'tanh': 'tanh'
+}  # Not used from ``math``: [copysign isclose isfinite isinf isnan ldexp frexp pow modf
+# radians trunc fmod fsum gcd degrees fabs]
+_known_constants_math = {
+    'Exp1': 'e',
+    'Pi': 'pi',
+    'E': 'e',
+    'Infinity': 'inf',
+    'NaN': 'nan',
+    'ComplexInfinity': 'nan'
+}
+
+def _print_known_func(self, expr):
+    known = self.known_functions[expr.__class__.__name__]
+    return '{name}({args})'.format(name=self._module_format(known),
+                                   args=', '.join((self._print(arg) for arg in expr.args)))
+
+
+def _print_known_const(self, expr):
+    known = self.known_constants[expr.__class__.__name__]
+    return self._module_format(known)
+
+
+class AbstractPythonCodePrinter(CodePrinter):
+    printmethod = "_pythoncode"
+    language = "Python"
+    reserved_words = _kw
+    modules = None  # initialized to a set in __init__
+    tab = '    '
+    _kf = dict(chain(
+        _known_functions.items(),
+        [(k, 'math.' + v) for k, v in _known_functions_math.items()]
+    ))
+    _kc = {k: 'math.'+v for k, v in _known_constants_math.items()}
+    _operators = {'and': 'and', 'or': 'or', 'not': 'not'}
+    _default_settings = dict(
+        CodePrinter._default_settings,
+        user_functions={},
+        precision=17,
+        inline=True,
+        fully_qualified_modules=True,
+        contract=False,
+        standard='python3',
+    )
+
+    def __init__(self, settings=None):
+        super().__init__(settings)
+
+        # Python standard handler
+        std = self._settings['standard']
+        if std is None:
+            import sys
+            std = 'python{}'.format(sys.version_info.major)
+        if std != 'python3':
+            raise ValueError('Only Python 3 is supported.')
+        self.standard = std
+
+        self.module_imports = defaultdict(set)
+
+        # Known functions and constants handler
+        self.known_functions = dict(self._kf, **(settings or {}).get(
+            'user_functions', {}))
+        self.known_constants = dict(self._kc, **(settings or {}).get(
+            'user_constants', {}))
+
+    def _declare_number_const(self, name, value):
+        return "%s = %s" % (name, value)
+
+    def _module_format(self, fqn, register=True):
+        parts = fqn.split('.')
+        if register and len(parts) > 1:
+            self.module_imports['.'.join(parts[:-1])].add(parts[-1])
+
+        if self._settings['fully_qualified_modules']:
+            return fqn
+        else:
+            return fqn.split('(')[0].split('[')[0].split('.')[-1]
+
+    def _format_code(self, lines):
+        return lines
+
+    def _get_statement(self, codestring):
+        return "{}".format(codestring)
+
+    def _get_comment(self, text):
+        return "  # {}".format(text)
+
+    def _expand_fold_binary_op(self, op, args):
+        """
+        This method expands a fold on binary operations.
+
+        ``functools.reduce`` is an example of a folded operation.
+
+        For example, the expression
+
+        `A + B + C + D`
+
+        is folded into
+
+        `((A + B) + C) + D`
+        """
+        if len(args) == 1:
+            return self._print(args[0])
+        else:
+            return "%s(%s, %s)" % (
+                self._module_format(op),
+                self._expand_fold_binary_op(op, args[:-1]),
+                self._print(args[-1]),
+            )
+
+    def _expand_reduce_binary_op(self, op, args):
+        """
+        This method expands a reductin on binary operations.
+
+        Notice: this is NOT the same as ``functools.reduce``.
+
+        For example, the expression
+
+        `A + B + C + D`
+
+        is reduced into:
+
+        `(A + B) + (C + D)`
+        """
+        if len(args) == 1:
+            return self._print(args[0])
+        else:
+            N = len(args)
+            Nhalf = N // 2
+            return "%s(%s, %s)" % (
+                self._module_format(op),
+                self._expand_reduce_binary_op(args[:Nhalf]),
+                self._expand_reduce_binary_op(args[Nhalf:]),
+            )
+
+    def _print_NaN(self, expr):
+        return "float('nan')"
+
+    def _print_Infinity(self, expr):
+        return "float('inf')"
+
+    def _print_NegativeInfinity(self, expr):
+        return "float('-inf')"
+
+    def _print_ComplexInfinity(self, expr):
+        return self._print_NaN(expr)
+
+    def _print_Mod(self, expr):
+        PREC = precedence(expr)
+        return ('{} % {}'.format(*(self.parenthesize(x, PREC) for x in expr.args)))
+
+    def _print_Piecewise(self, expr):
+        result = []
+        i = 0
+        for arg in expr.args:
+            e = arg.expr
+            c = arg.cond
+            if i == 0:
+                result.append('(')
+            result.append('(')
+            result.append(self._print(e))
+            result.append(')')
+            result.append(' if ')
+            result.append(self._print(c))
+            result.append(' else ')
+            i += 1
+        result = result[:-1]
+        if result[-1] == 'True':
+            result = result[:-2]
+            result.append(')')
+        else:
+            result.append(' else None)')
+        return ''.join(result)
+
+    def _print_Relational(self, expr):
+        "Relational printer for Equality and Unequality"
+        op = {
+            '==' :'equal',
+            '!=' :'not_equal',
+            '<'  :'less',
+            '<=' :'less_equal',
+            '>'  :'greater',
+            '>=' :'greater_equal',
+        }
+        if expr.rel_op in op:
+            lhs = self._print(expr.lhs)
+            rhs = self._print(expr.rhs)
+            return '({lhs} {op} {rhs})'.format(op=expr.rel_op, lhs=lhs, rhs=rhs)
+        return super()._print_Relational(expr)
+
+    def _print_ITE(self, expr):
+        from sympy.functions.elementary.piecewise import Piecewise
+        return self._print(expr.rewrite(Piecewise))
+
+    def _print_Sum(self, expr):
+        loops = (
+            'for {i} in range({a}, {b}+1)'.format(
+                i=self._print(i),
+                a=self._print(a),
+                b=self._print(b))
+            for i, a, b in expr.limits)
+        return '(builtins.sum({function} {loops}))'.format(
+            function=self._print(expr.function),
+            loops=' '.join(loops))
+
+    def _print_ImaginaryUnit(self, expr):
+        return '1j'
+
+    def _print_KroneckerDelta(self, expr):
+        a, b = expr.args
+
+        return '(1 if {a} == {b} else 0)'.format(
+            a = self._print(a),
+            b = self._print(b)
+        )
+
+    def _print_MatrixBase(self, expr):
+        name = expr.__class__.__name__
+        func = self.known_functions.get(name, name)
+        return "%s(%s)" % (func, self._print(expr.tolist()))
+
+    _print_SparseRepMatrix = \
+        _print_MutableSparseMatrix = \
+        _print_ImmutableSparseMatrix = \
+        _print_Matrix = \
+        _print_DenseMatrix = \
+        _print_MutableDenseMatrix = \
+        _print_ImmutableMatrix = \
+        _print_ImmutableDenseMatrix = \
+        lambda self, expr: self._print_MatrixBase(expr)
+
+    def _indent_codestring(self, codestring):
+        return '\n'.join([self.tab + line for line in codestring.split('\n')])
+
+    def _print_FunctionDefinition(self, fd):
+        body = '\n'.join((self._print(arg) for arg in fd.body))
+        return "def {name}({parameters}):\n{body}".format(
+            name=self._print(fd.name),
+            parameters=', '.join([self._print(var.symbol) for var in fd.parameters]),
+            body=self._indent_codestring(body)
+        )
+
+    def _print_While(self, whl):
+        body = '\n'.join((self._print(arg) for arg in whl.body))
+        return "while {cond}:\n{body}".format(
+            cond=self._print(whl.condition),
+            body=self._indent_codestring(body)
+        )
+
+    def _print_Declaration(self, decl):
+        return '%s = %s' % (
+            self._print(decl.variable.symbol),
+            self._print(decl.variable.value)
+        )
+
+    def _print_Return(self, ret):
+        arg, = ret.args
+        return 'return %s' % self._print(arg)
+
+    def _print_Print(self, prnt):
+        print_args = ', '.join((self._print(arg) for arg in prnt.print_args))
+        if prnt.format_string != None: # Must be '!= None', cannot be 'is not None'
+            print_args = '{} % ({})'.format(
+                self._print(prnt.format_string), print_args)
+        if prnt.file != None: # Must be '!= None', cannot be 'is not None'
+            print_args += ', file=%s' % self._print(prnt.file)
+
+        return 'print(%s)' % print_args
+
+    def _print_Stream(self, strm):
+        if str(strm.name) == 'stdout':
+            return self._module_format('sys.stdout')
+        elif str(strm.name) == 'stderr':
+            return self._module_format('sys.stderr')
+        else:
+            return self._print(strm.name)
+
+    def _print_NoneToken(self, arg):
+        return 'None'
+
+    def _hprint_Pow(self, expr, rational=False, sqrt='math.sqrt'):
+        """Printing helper function for ``Pow``
+
+        Notes
+        =====
+
+        This preprocesses the ``sqrt`` as math formatter and prints division
+
+        Examples
+        ========
+
+        >>> from sympy import sqrt
+        >>> from sympy.printing.pycode import PythonCodePrinter
+        >>> from sympy.abc import x
+
+        Python code printer automatically looks up ``math.sqrt``.
+
+        >>> printer = PythonCodePrinter()
+        >>> printer._hprint_Pow(sqrt(x), rational=True)
+        'x**(1/2)'
+        >>> printer._hprint_Pow(sqrt(x), rational=False)
+        'math.sqrt(x)'
+        >>> printer._hprint_Pow(1/sqrt(x), rational=True)
+        'x**(-1/2)'
+        >>> printer._hprint_Pow(1/sqrt(x), rational=False)
+        '1/math.sqrt(x)'
+        >>> printer._hprint_Pow(1/x, rational=False)
+        '1/x'
+        >>> printer._hprint_Pow(1/x, rational=True)
+        'x**(-1)'
+
+        Using sqrt from numpy or mpmath
+
+        >>> printer._hprint_Pow(sqrt(x), sqrt='numpy.sqrt')
+        'numpy.sqrt(x)'
+        >>> printer._hprint_Pow(sqrt(x), sqrt='mpmath.sqrt')
+        'mpmath.sqrt(x)'
+
+        See Also
+        ========
+
+        sympy.printing.str.StrPrinter._print_Pow
+        """
+        PREC = precedence(expr)
+
+        if expr.exp == S.Half and not rational:
+            func = self._module_format(sqrt)
+            arg = self._print(expr.base)
+            return '{func}({arg})'.format(func=func, arg=arg)
+
+        if expr.is_commutative and not rational:
+            if -expr.exp is S.Half:
+                func = self._module_format(sqrt)
+                num = self._print(S.One)
+                arg = self._print(expr.base)
+                return f"{num}/{func}({arg})"
+            if expr.exp is S.NegativeOne:
+                num = self._print(S.One)
+                arg = self.parenthesize(expr.base, PREC, strict=False)
+                return f"{num}/{arg}"
+
+
+        base_str = self.parenthesize(expr.base, PREC, strict=False)
+        exp_str = self.parenthesize(expr.exp, PREC, strict=False)
+        return "{}**{}".format(base_str, exp_str)
+
+
+class ArrayPrinter:
+
+    def _arrayify(self, indexed):
+        from sympy.tensor.array.expressions.from_indexed_to_array import convert_indexed_to_array
+        try:
+            return convert_indexed_to_array(indexed)
+        except Exception:
+            return indexed
+
+    def _get_einsum_string(self, subranks, contraction_indices):
+        letters = self._get_letter_generator_for_einsum()
+        contraction_string = ""
+        counter = 0
+        d = {j: min(i) for i in contraction_indices for j in i}
+        indices = []
+        for rank_arg in subranks:
+            lindices = []
+            for i in range(rank_arg):
+                if counter in d:
+                    lindices.append(d[counter])
+                else:
+                    lindices.append(counter)
+                counter += 1
+            indices.append(lindices)
+        mapping = {}
+        letters_free = []
+        letters_dum = []
+        for i in indices:
+            for j in i:
+                if j not in mapping:
+                    l = next(letters)
+                    mapping[j] = l
+                else:
+                    l = mapping[j]
+                contraction_string += l
+                if j in d:
+                    if l not in letters_dum:
+                        letters_dum.append(l)
+                else:
+                    letters_free.append(l)
+            contraction_string += ","
+        contraction_string = contraction_string[:-1]
+        return contraction_string, letters_free, letters_dum
+
+    def _get_letter_generator_for_einsum(self):
+        for i in range(97, 123):
+            yield chr(i)
+        for i in range(65, 91):
+            yield chr(i)
+        raise ValueError("out of letters")
+
+    def _print_ArrayTensorProduct(self, expr):
+        letters = self._get_letter_generator_for_einsum()
+        contraction_string = ",".join(["".join([next(letters) for j in range(i)]) for i in expr.subranks])
+        return '%s("%s", %s)' % (
+                self._module_format(self._module + "." + self._einsum),
+                contraction_string,
+                ", ".join([self._print(arg) for arg in expr.args])
+        )
+
+    def _print_ArrayContraction(self, expr):
+        from sympy.tensor.array.expressions.array_expressions import ArrayTensorProduct
+        base = expr.expr
+        contraction_indices = expr.contraction_indices
+
+        if isinstance(base, ArrayTensorProduct):
+            elems = ",".join(["%s" % (self._print(arg)) for arg in base.args])
+            ranks = base.subranks
+        else:
+            elems = self._print(base)
+            ranks = [len(base.shape)]
+
+        contraction_string, letters_free, letters_dum = self._get_einsum_string(ranks, contraction_indices)
+
+        if not contraction_indices:
+            return self._print(base)
+        if isinstance(base, ArrayTensorProduct):
+            elems = ",".join(["%s" % (self._print(arg)) for arg in base.args])
+        else:
+            elems = self._print(base)
+        return "%s(\"%s\", %s)" % (
+            self._module_format(self._module + "." + self._einsum),
+            "{}->{}".format(contraction_string, "".join(sorted(letters_free))),
+            elems,
+        )
+
+    def _print_ArrayDiagonal(self, expr):
+        from sympy.tensor.array.expressions.array_expressions import ArrayTensorProduct
+        diagonal_indices = list(expr.diagonal_indices)
+        if isinstance(expr.expr, ArrayTensorProduct):
+            subranks = expr.expr.subranks
+            elems = expr.expr.args
+        else:
+            subranks = expr.subranks
+            elems = [expr.expr]
+        diagonal_string, letters_free, letters_dum = self._get_einsum_string(subranks, diagonal_indices)
+        elems = [self._print(i) for i in elems]
+        return '%s("%s", %s)' % (
+            self._module_format(self._module + "." + self._einsum),
+            "{}->{}".format(diagonal_string, "".join(letters_free+letters_dum)),
+            ", ".join(elems)
+        )
+
+    def _print_PermuteDims(self, expr):
+        return "%s(%s, %s)" % (
+            self._module_format(self._module + "." + self._transpose),
+            self._print(expr.expr),
+            self._print(expr.permutation.array_form),
+        )
+
+    def _print_ArrayAdd(self, expr):
+        return self._expand_fold_binary_op(self._module + "." + self._add, expr.args)
+
+    def _print_OneArray(self, expr):
+        return "%s((%s,))" % (
+            self._module_format(self._module+ "." + self._ones),
+            ','.join(map(self._print,expr.args))
+        )
+
+    def _print_ZeroArray(self, expr):
+        return "%s((%s,))" % (
+            self._module_format(self._module+ "." + self._zeros),
+            ','.join(map(self._print,expr.args))
+        )
+
+    def _print_Assignment(self, expr):
+        #XXX: maybe this needs to happen at a higher level e.g. at _print or
+        #doprint?
+        lhs = self._print(self._arrayify(expr.lhs))
+        rhs = self._print(self._arrayify(expr.rhs))
+        return "%s = %s" % ( lhs, rhs )
+
+    def _print_IndexedBase(self, expr):
+        return self._print_ArraySymbol(expr)
+
+
+class PythonCodePrinter(AbstractPythonCodePrinter):
+
+    def _print_sign(self, e):
+        return '(0.0 if {e} == 0 else {f}(1, {e}))'.format(
+            f=self._module_format('math.copysign'), e=self._print(e.args[0]))
+
+    def _print_Not(self, expr):
+        PREC = precedence(expr)
+        return self._operators['not'] + self.parenthesize(expr.args[0], PREC)
+
+    def _print_Indexed(self, expr):
+        base = expr.args[0]
+        index = expr.args[1:]
+        return "{}[{}]".format(str(base), ", ".join([self._print(ind) for ind in index]))
+
+    def _print_Pow(self, expr, rational=False):
+        return self._hprint_Pow(expr, rational=rational)
+
+    def _print_Rational(self, expr):
+        return '{}/{}'.format(expr.p, expr.q)
+
+    def _print_Half(self, expr):
+        return self._print_Rational(expr)
+
+    def _print_frac(self, expr):
+        return self._print_Mod(Mod(expr.args[0], 1))
+
+    def _print_Symbol(self, expr):
+
+        name = super()._print_Symbol(expr)
+
+        if name in self.reserved_words:
+            if self._settings['error_on_reserved']:
+                msg = ('This expression includes the symbol "{}" which is a '
+                       'reserved keyword in this language.')
+                raise ValueError(msg.format(name))
+            return name + self._settings['reserved_word_suffix']
+        elif '{' in name:   # Remove curly braces from subscripted variables
+            return name.replace('{', '').replace('}', '')
+        else:
+            return name
+
+    _print_lowergamma = CodePrinter._print_not_supported
+    _print_uppergamma = CodePrinter._print_not_supported
+    _print_fresnelc = CodePrinter._print_not_supported
+    _print_fresnels = CodePrinter._print_not_supported
+
+
+for k in PythonCodePrinter._kf:
+    setattr(PythonCodePrinter, '_print_%s' % k, _print_known_func)
+
+for k in _known_constants_math:
+    setattr(PythonCodePrinter, '_print_%s' % k, _print_known_const)
+
+
+def pycode(expr, **settings):
+    """ Converts an expr to a string of Python code
+
+    Parameters
+    ==========
+
+    expr : Expr
+        A SymPy expression.
+    fully_qualified_modules : bool
+        Whether or not to write out full module names of functions
+        (``math.sin`` vs. ``sin``). default: ``True``.
+    standard : str or None, optional
+        Only 'python3' (default) is supported.
+        This parameter may be removed in the future.
+
+    Examples
+    ========
+
+    >>> from sympy import pycode, tan, Symbol
+    >>> pycode(tan(Symbol('x')) + 1)
+    'math.tan(x) + 1'
+
+    """
+    return PythonCodePrinter(settings).doprint(expr)
+
+
+_not_in_mpmath = 'log1p log2'.split()
+_in_mpmath = [(k, v) for k, v in _known_functions_math.items() if k not in _not_in_mpmath]
+_known_functions_mpmath = dict(_in_mpmath, **{
+    'beta': 'beta',
+    'frac': 'frac',
+    'fresnelc': 'fresnelc',
+    'fresnels': 'fresnels',
+    'sign': 'sign',
+    'loggamma': 'loggamma',
+    'hyper': 'hyper',
+    'meijerg': 'meijerg',
+    'besselj': 'besselj',
+    'bessely': 'bessely',
+    'besseli': 'besseli',
+    'besselk': 'besselk',
+})
+_known_constants_mpmath = {
+    'Exp1': 'e',
+    'Pi': 'pi',
+    'GoldenRatio': 'phi',
+    'EulerGamma': 'euler',
+    'Catalan': 'catalan',
+    'NaN': 'nan',
+    'Infinity': 'inf',
+    'NegativeInfinity': 'ninf'
+}
+
+
+def _unpack_integral_limits(integral_expr):
+    """ helper function for _print_Integral that
+        - accepts an Integral expression
+        - returns a tuple of
+           - a list variables of integration
+           - a list of tuples of the upper and lower limits of integration
+    """
+    integration_vars = []
+    limits = []
+    for integration_range in integral_expr.limits:
+        if len(integration_range) == 3:
+            integration_var, lower_limit, upper_limit = integration_range
+        else:
+            raise NotImplementedError("Only definite integrals are supported")
+        integration_vars.append(integration_var)
+        limits.append((lower_limit, upper_limit))
+    return integration_vars, limits
+
+
+class MpmathPrinter(PythonCodePrinter):
+    """
+    Lambda printer for mpmath which maintains precision for floats
+    """
+    printmethod = "_mpmathcode"
+
+    language = "Python with mpmath"
+
+    _kf = dict(chain(
+        _known_functions.items(),
+        [(k, 'mpmath.' + v) for k, v in _known_functions_mpmath.items()]
+    ))
+    _kc = {k: 'mpmath.'+v for k, v in _known_constants_mpmath.items()}
+
+    def _print_Float(self, e):
+        # XXX: This does not handle setting mpmath.mp.dps. It is assumed that
+        # the caller of the lambdified function will have set it to sufficient
+        # precision to match the Floats in the expression.
+
+        # Remove 'mpz' if gmpy is installed.
+        args = str(tuple(map(int, e._mpf_)))
+        return '{func}({args})'.format(func=self._module_format('mpmath.mpf'), args=args)
+
+
+    def _print_Rational(self, e):
+        return "{func}({p})/{func}({q})".format(
+            func=self._module_format('mpmath.mpf'),
+            q=self._print(e.q),
+            p=self._print(e.p)
+        )
+
+    def _print_Half(self, e):
+        return self._print_Rational(e)
+
+    def _print_uppergamma(self, e):
+        return "{}({}, {}, {})".format(
+            self._module_format('mpmath.gammainc'),
+            self._print(e.args[0]),
+            self._print(e.args[1]),
+            self._module_format('mpmath.inf'))
+
+    def _print_lowergamma(self, e):
+        return "{}({}, 0, {})".format(
+            self._module_format('mpmath.gammainc'),
+            self._print(e.args[0]),
+            self._print(e.args[1]))
+
+    def _print_log2(self, e):
+        return '{0}({1})/{0}(2)'.format(
+            self._module_format('mpmath.log'), self._print(e.args[0]))
+
+    def _print_log1p(self, e):
+        return '{}({})'.format(
+            self._module_format('mpmath.log1p'), self._print(e.args[0]))
+
+    def _print_Pow(self, expr, rational=False):
+        return self._hprint_Pow(expr, rational=rational, sqrt='mpmath.sqrt')
+
+    def _print_Integral(self, e):
+        integration_vars, limits = _unpack_integral_limits(e)
+
+        return "{}(lambda {}: {}, {})".format(
+                self._module_format("mpmath.quad"),
+                ", ".join(map(self._print, integration_vars)),
+                self._print(e.args[0]),
+                ", ".join("(%s, %s)" % tuple(map(self._print, l)) for l in limits))
+
+
+for k in MpmathPrinter._kf:
+    setattr(MpmathPrinter, '_print_%s' % k, _print_known_func)
+
+for k in _known_constants_mpmath:
+    setattr(MpmathPrinter, '_print_%s' % k, _print_known_const)
+
+
+class SymPyPrinter(AbstractPythonCodePrinter):
+
+    language = "Python with SymPy"
+
+    def _print_Function(self, expr):
+        mod = expr.func.__module__ or ''
+        return '%s(%s)' % (self._module_format(mod + ('.' if mod else '') + expr.func.__name__),
+                           ', '.join((self._print(arg) for arg in expr.args)))
+
+    def _print_Pow(self, expr, rational=False):
+        return self._hprint_Pow(expr, rational=rational, sqrt='sympy.sqrt')

venv/lib/python3.10/site-packages/sympy/printing/python.py

@@ -0,0 +1,93 @@
+import keyword as kw
+import sympy
+from .repr import ReprPrinter
+from .str import StrPrinter
+
+# A list of classes that should be printed using StrPrinter
+STRPRINT = ("Add", "Infinity", "Integer", "Mul", "NegativeInfinity",
+            "Pow", "Zero")
+
+
+class PythonPrinter(ReprPrinter, StrPrinter):
+    """A printer which converts an expression into its Python interpretation."""
+
+    def __init__(self, settings=None):
+        super().__init__(settings)
+        self.symbols = []
+        self.functions = []
+
+        # Create print methods for classes that should use StrPrinter instead
+        # of ReprPrinter.
+        for name in STRPRINT:
+            f_name = "_print_%s" % name
+            f = getattr(StrPrinter, f_name)
+            setattr(PythonPrinter, f_name, f)
+
+    def _print_Function(self, expr):
+        func = expr.func.__name__
+        if not hasattr(sympy, func) and func not in self.functions:
+            self.functions.append(func)
+        return StrPrinter._print_Function(self, expr)
+
+    # procedure (!) for defining symbols which have be defined in print_python()
+    def _print_Symbol(self, expr):
+        symbol = self._str(expr)
+        if symbol not in self.symbols:
+            self.symbols.append(symbol)
+        return StrPrinter._print_Symbol(self, expr)
+
+    def _print_module(self, expr):
+        raise ValueError('Modules in the expression are unacceptable')
+
+
+def python(expr, **settings):
+    """Return Python interpretation of passed expression
+    (can be passed to the exec() function without any modifications)"""
+
+    printer = PythonPrinter(settings)
+    exprp = printer.doprint(expr)
+
+    result = ''
+    # Returning found symbols and functions
+    renamings = {}
+    for symbolname in printer.symbols:
+        # Remove curly braces from subscripted variables
+        if '{' in symbolname:
+            newsymbolname = symbolname.replace('{', '').replace('}', '')
+            renamings[sympy.Symbol(symbolname)] = newsymbolname
+        else:
+            newsymbolname = symbolname
+
+        # Escape symbol names that are reserved Python keywords
+        if kw.iskeyword(newsymbolname):
+            while True:
+                newsymbolname += "_"
+                if (newsymbolname not in printer.symbols and
+                        newsymbolname not in printer.functions):
+                    renamings[sympy.Symbol(
+                        symbolname)] = sympy.Symbol(newsymbolname)
+                    break
+        result += newsymbolname + ' = Symbol(\'' + symbolname + '\')\n'
+
+    for functionname in printer.functions:
+        newfunctionname = functionname
+        # Escape function names that are reserved Python keywords
+        if kw.iskeyword(newfunctionname):
+            while True:
+                newfunctionname += "_"
+                if (newfunctionname not in printer.symbols and
+                        newfunctionname not in printer.functions):
+                    renamings[sympy.Function(
+                        functionname)] = sympy.Function(newfunctionname)
+                    break
+        result += newfunctionname + ' = Function(\'' + functionname + '\')\n'
+
+    if renamings:
+        exprp = expr.subs(renamings)
+    result += 'e = ' + printer._str(exprp)
+    return result
+
+
+def print_python(expr, **settings):
+    """Print output of python() function"""
+    print(python(expr, **settings))

venv/lib/python3.10/site-packages/sympy/printing/rcode.py

@@ -0,0 +1,410 @@
+"""
+R code printer
+
+The RCodePrinter converts single SymPy expressions into single R expressions,
+using the functions defined in math.h where possible.
+
+
+
+"""
+
+from __future__ import annotations
+from typing import Any
+
+from sympy.core.numbers import equal_valued
+from sympy.printing.codeprinter import CodePrinter
+from sympy.printing.precedence import precedence, PRECEDENCE
+from sympy.sets.fancysets import Range
+
+# dictionary mapping SymPy function to (argument_conditions, C_function).
+# Used in RCodePrinter._print_Function(self)
+known_functions = {
+    #"Abs": [(lambda x: not x.is_integer, "fabs")],
+    "Abs": "abs",
+    "sin": "sin",
+    "cos": "cos",
+    "tan": "tan",
+    "asin": "asin",
+    "acos": "acos",
+    "atan": "atan",
+    "atan2": "atan2",
+    "exp": "exp",
+    "log": "log",
+    "erf": "erf",
+    "sinh": "sinh",
+    "cosh": "cosh",
+    "tanh": "tanh",
+    "asinh": "asinh",
+    "acosh": "acosh",
+    "atanh": "atanh",
+    "floor": "floor",
+    "ceiling": "ceiling",
+    "sign": "sign",
+    "Max": "max",
+    "Min": "min",
+    "factorial": "factorial",
+    "gamma": "gamma",
+    "digamma": "digamma",
+    "trigamma": "trigamma",
+    "beta": "beta",
+    "sqrt": "sqrt",  # To enable automatic rewrite
+}
+
+# These are the core reserved words in the R language. Taken from:
+# https://cran.r-project.org/doc/manuals/r-release/R-lang.html#Reserved-words
+
+reserved_words = ['if',
+                  'else',
+                  'repeat',
+                  'while',
+                  'function',
+                  'for',
+                  'in',
+                  'next',
+                  'break',
+                  'TRUE',
+                  'FALSE',
+                  'NULL',
+                  'Inf',
+                  'NaN',
+                  'NA',
+                  'NA_integer_',
+                  'NA_real_',
+                  'NA_complex_',
+                  'NA_character_',
+                  'volatile']
+
+
+class RCodePrinter(CodePrinter):
+    """A printer to convert SymPy expressions to strings of R code"""
+    printmethod = "_rcode"
+    language = "R"
+
+    _default_settings: dict[str, Any] = {
+        'order': None,
+        'full_prec': 'auto',
+        'precision': 15,
+        'user_functions': {},
+        'human': True,
+        'contract': True,
+        'dereference': set(),
+        'error_on_reserved': False,
+        'reserved_word_suffix': '_',
+    }
+    _operators = {
+       'and': '&',
+        'or': '|',
+       'not': '!',
+    }
+
+    _relationals: dict[str, str] = {}
+
+    def __init__(self, settings={}):
+        CodePrinter.__init__(self, settings)
+        self.known_functions = dict(known_functions)
+        userfuncs = settings.get('user_functions', {})
+        self.known_functions.update(userfuncs)
+        self._dereference = set(settings.get('dereference', []))
+        self.reserved_words = set(reserved_words)
+
+    def _rate_index_position(self, p):
+        return p*5
+
+    def _get_statement(self, codestring):
+        return "%s;" % codestring
+
+    def _get_comment(self, text):
+        return "// {}".format(text)
+
+    def _declare_number_const(self, name, value):
+        return "{} = {};".format(name, value)
+
+    def _format_code(self, lines):
+        return self.indent_code(lines)
+
+    def _traverse_matrix_indices(self, mat):
+        rows, cols = mat.shape
+        return ((i, j) for i in range(rows) for j in range(cols))
+
+    def _get_loop_opening_ending(self, indices):
+        """Returns a tuple (open_lines, close_lines) containing lists of codelines
+        """
+        open_lines = []
+        close_lines = []
+        loopstart = "for (%(var)s in %(start)s:%(end)s){"
+        for i in indices:
+            # R arrays start at 1 and end at dimension
+            open_lines.append(loopstart % {
+                'var': self._print(i.label),
+                'start': self._print(i.lower+1),
+                'end': self._print(i.upper + 1)})
+            close_lines.append("}")
+        return open_lines, close_lines
+
+    def _print_Pow(self, expr):
+        if "Pow" in self.known_functions:
+            return self._print_Function(expr)
+        PREC = precedence(expr)
+        if equal_valued(expr.exp, -1):
+            return '1.0/%s' % (self.parenthesize(expr.base, PREC))
+        elif equal_valued(expr.exp, 0.5):
+            return 'sqrt(%s)' % self._print(expr.base)
+        else:
+            return '%s^%s' % (self.parenthesize(expr.base, PREC),
+                                 self.parenthesize(expr.exp, PREC))
+
+
+    def _print_Rational(self, expr):
+        p, q = int(expr.p), int(expr.q)
+        return '%d.0/%d.0' % (p, q)
+
+    def _print_Indexed(self, expr):
+        inds = [ self._print(i) for i in expr.indices ]
+        return "%s[%s]" % (self._print(expr.base.label), ", ".join(inds))
+
+    def _print_Idx(self, expr):
+        return self._print(expr.label)
+
+    def _print_Exp1(self, expr):
+        return "exp(1)"
+
+    def _print_Pi(self, expr):
+        return 'pi'
+
+    def _print_Infinity(self, expr):
+        return 'Inf'
+
+    def _print_NegativeInfinity(self, expr):
+        return '-Inf'
+
+    def _print_Assignment(self, expr):
+        from sympy.codegen.ast import Assignment
+
+        from sympy.matrices.expressions.matexpr import MatrixSymbol
+        from sympy.tensor.indexed import IndexedBase
+        lhs = expr.lhs
+        rhs = expr.rhs
+        # We special case assignments that take multiple lines
+        #if isinstance(expr.rhs, Piecewise):
+        #    from sympy.functions.elementary.piecewise import Piecewise
+        #    # Here we modify Piecewise so each expression is now
+        #    # an Assignment, and then continue on the print.
+        #    expressions = []
+        #    conditions = []
+        #    for (e, c) in rhs.args:
+        #        expressions.append(Assignment(lhs, e))
+        #        conditions.append(c)
+        #    temp = Piecewise(*zip(expressions, conditions))
+        #    return self._print(temp)
+        #elif isinstance(lhs, MatrixSymbol):
+        if isinstance(lhs, MatrixSymbol):
+            # Here we form an Assignment for each element in the array,
+            # printing each one.
+            lines = []
+            for (i, j) in self._traverse_matrix_indices(lhs):
+                temp = Assignment(lhs[i, j], rhs[i, j])
+                code0 = self._print(temp)
+                lines.append(code0)
+            return "\n".join(lines)
+        elif self._settings["contract"] and (lhs.has(IndexedBase) or
+                rhs.has(IndexedBase)):
+            # Here we check if there is looping to be done, and if so
+            # print the required loops.
+            return self._doprint_loops(rhs, lhs)
+        else:
+            lhs_code = self._print(lhs)
+            rhs_code = self._print(rhs)
+            return self._get_statement("%s = %s" % (lhs_code, rhs_code))
+
+    def _print_Piecewise(self, expr):
+        # This method is called only for inline if constructs
+        # Top level piecewise is handled in doprint()
+        if expr.args[-1].cond == True:
+            last_line = "%s" % self._print(expr.args[-1].expr)
+        else:
+            last_line = "ifelse(%s,%s,NA)" % (self._print(expr.args[-1].cond), self._print(expr.args[-1].expr))
+        code=last_line
+        for e, c in reversed(expr.args[:-1]):
+            code= "ifelse(%s,%s," % (self._print(c), self._print(e))+code+")"
+        return(code)
+
+    def _print_ITE(self, expr):
+        from sympy.functions import Piecewise
+        return self._print(expr.rewrite(Piecewise))
+
+    def _print_MatrixElement(self, expr):
+        return "{}[{}]".format(self.parenthesize(expr.parent, PRECEDENCE["Atom"],
+            strict=True), expr.j + expr.i*expr.parent.shape[1])
+
+    def _print_Symbol(self, expr):
+        name = super()._print_Symbol(expr)
+        if expr in self._dereference:
+            return '(*{})'.format(name)
+        else:
+            return name
+
+    def _print_Relational(self, expr):
+        lhs_code = self._print(expr.lhs)
+        rhs_code = self._print(expr.rhs)
+        op = expr.rel_op
+        return "{} {} {}".format(lhs_code, op, rhs_code)
+
+    def _print_AugmentedAssignment(self, expr):
+        lhs_code = self._print(expr.lhs)
+        op = expr.op
+        rhs_code = self._print(expr.rhs)
+        return "{} {} {};".format(lhs_code, op, rhs_code)
+
+    def _print_For(self, expr):
+        target = self._print(expr.target)
+        if isinstance(expr.iterable, Range):
+            start, stop, step = expr.iterable.args
+        else:
+            raise NotImplementedError("Only iterable currently supported is Range")
+        body = self._print(expr.body)
+        return 'for({target} in seq(from={start}, to={stop}, by={step}){{\n{body}\n}}'.format(target=target, start=start,
+                stop=stop-1, step=step, body=body)
+
+
+    def indent_code(self, code):
+        """Accepts a string of code or a list of code lines"""
+
+        if isinstance(code, str):
+            code_lines = self.indent_code(code.splitlines(True))
+            return ''.join(code_lines)
+
+        tab = "   "
+        inc_token = ('{', '(', '{\n', '(\n')
+        dec_token = ('}', ')')
+
+        code = [ line.lstrip(' \t') for line in code ]
+
+        increase = [ int(any(map(line.endswith, inc_token))) for line in code ]
+        decrease = [ int(any(map(line.startswith, dec_token)))
+                     for line in code ]
+
+        pretty = []
+        level = 0
+        for n, line in enumerate(code):
+            if line in ('', '\n'):
+                pretty.append(line)
+                continue
+            level -= decrease[n]
+            pretty.append("%s%s" % (tab*level, line))
+            level += increase[n]
+        return pretty
+
+
+def rcode(expr, assign_to=None, **settings):
+    """Converts an expr to a string of r code
+
+    Parameters
+    ==========
+
+    expr : Expr
+        A SymPy expression to be converted.
+    assign_to : optional
+        When given, the argument is used as the name of the variable to which
+        the expression is assigned. Can be a string, ``Symbol``,
+        ``MatrixSymbol``, or ``Indexed`` type. This is helpful in case of
+        line-wrapping, or for expressions that generate multi-line statements.
+    precision : integer, optional
+        The precision for numbers such as pi [default=15].
+    user_functions : dict, optional
+        A dictionary where the keys are string representations of either
+        ``FunctionClass`` or ``UndefinedFunction`` instances and the values
+        are their desired R string representations. Alternatively, the
+        dictionary value can be a list of tuples i.e. [(argument_test,
+        rfunction_string)] or [(argument_test, rfunction_formater)]. See below
+        for examples.
+    human : bool, optional
+        If True, the result is a single string that may contain some constant
+        declarations for the number symbols. If False, the same information is
+        returned in a tuple of (symbols_to_declare, not_supported_functions,
+        code_text). [default=True].
+    contract: bool, optional
+        If True, ``Indexed`` instances are assumed to obey tensor contraction
+        rules and the corresponding nested loops over indices are generated.
+        Setting contract=False will not generate loops, instead the user is
+        responsible to provide values for the indices in the code.
+        [default=True].
+
+    Examples
+    ========
+
+    >>> from sympy import rcode, symbols, Rational, sin, ceiling, Abs, Function
+    >>> x, tau = symbols("x, tau")
+    >>> rcode((2*tau)**Rational(7, 2))
+    '8*sqrt(2)*tau^(7.0/2.0)'
+    >>> rcode(sin(x), assign_to="s")
+    's = sin(x);'
+
+    Simple custom printing can be defined for certain types by passing a
+    dictionary of {"type" : "function"} to the ``user_functions`` kwarg.
+    Alternatively, the dictionary value can be a list of tuples i.e.
+    [(argument_test, cfunction_string)].
+
+    >>> custom_functions = {
+    ...   "ceiling": "CEIL",
+    ...   "Abs": [(lambda x: not x.is_integer, "fabs"),
+    ...           (lambda x: x.is_integer, "ABS")],
+    ...   "func": "f"
+    ... }
+    >>> func = Function('func')
+    >>> rcode(func(Abs(x) + ceiling(x)), user_functions=custom_functions)
+    'f(fabs(x) + CEIL(x))'
+
+    or if the R-function takes a subset of the original arguments:
+
+    >>> rcode(2**x + 3**x, user_functions={'Pow': [
+    ...   (lambda b, e: b == 2, lambda b, e: 'exp2(%s)' % e),
+    ...   (lambda b, e: b != 2, 'pow')]})
+    'exp2(x) + pow(3, x)'
+
+    ``Piecewise`` expressions are converted into conditionals. If an
+    ``assign_to`` variable is provided an if statement is created, otherwise
+    the ternary operator is used. Note that if the ``Piecewise`` lacks a
+    default term, represented by ``(expr, True)`` then an error will be thrown.
+    This is to prevent generating an expression that may not evaluate to
+    anything.
+
+    >>> from sympy import Piecewise
+    >>> expr = Piecewise((x + 1, x > 0), (x, True))
+    >>> print(rcode(expr, assign_to=tau))
+    tau = ifelse(x > 0,x + 1,x);
+
+    Support for loops is provided through ``Indexed`` types. With
+    ``contract=True`` these expressions will be turned into loops, whereas
+    ``contract=False`` will just print the assignment expression that should be
+    looped over:
+
+    >>> from sympy import Eq, IndexedBase, Idx
+    >>> len_y = 5
+    >>> y = IndexedBase('y', shape=(len_y,))
+    >>> t = IndexedBase('t', shape=(len_y,))
+    >>> Dy = IndexedBase('Dy', shape=(len_y-1,))
+    >>> i = Idx('i', len_y-1)
+    >>> e=Eq(Dy[i], (y[i+1]-y[i])/(t[i+1]-t[i]))
+    >>> rcode(e.rhs, assign_to=e.lhs, contract=False)
+    'Dy[i] = (y[i + 1] - y[i])/(t[i + 1] - t[i]);'
+
+    Matrices are also supported, but a ``MatrixSymbol`` of the same dimensions
+    must be provided to ``assign_to``. Note that any expression that can be
+    generated normally can also exist inside a Matrix:
+
+    >>> from sympy import Matrix, MatrixSymbol
+    >>> mat = Matrix([x**2, Piecewise((x + 1, x > 0), (x, True)), sin(x)])
+    >>> A = MatrixSymbol('A', 3, 1)
+    >>> print(rcode(mat, A))
+    A[0] = x^2;
+    A[1] = ifelse(x > 0,x + 1,x);
+    A[2] = sin(x);
+
+    """
+
+    return RCodePrinter(settings).doprint(expr, assign_to)
+
+
+def print_rcode(expr, **settings):
+    """Prints R representation of the given expression."""
+    print(rcode(expr, **settings))

venv/lib/python3.10/site-packages/sympy/printing/repr.py

@@ -0,0 +1,342 @@
+"""
+A Printer for generating executable code.
+
+The most important function here is srepr that returns a string so that the
+relation eval(srepr(expr))=expr holds in an appropriate environment.
+"""
+
+from __future__ import annotations
+from typing import Any
+
+from sympy.core.function import AppliedUndef
+from sympy.core.mul import Mul
+from mpmath.libmp import repr_dps, to_str as mlib_to_str
+
+from .printer import Printer, print_function
+
+
+class ReprPrinter(Printer):
+    printmethod = "_sympyrepr"
+
+    _default_settings: dict[str, Any] = {
+        "order": None,
+        "perm_cyclic" : True,
+    }
+
+    def reprify(self, args, sep):
+        """
+        Prints each item in `args` and joins them with `sep`.
+        """
+        return sep.join([self.doprint(item) for item in args])
+
+    def emptyPrinter(self, expr):
+        """
+        The fallback printer.
+        """
+        if isinstance(expr, str):
+            return expr
+        elif hasattr(expr, "__srepr__"):
+            return expr.__srepr__()
+        elif hasattr(expr, "args") and hasattr(expr.args, "__iter__"):
+            l = []
+            for o in expr.args:
+                l.append(self._print(o))
+            return expr.__class__.__name__ + '(%s)' % ', '.join(l)
+        elif hasattr(expr, "__module__") and hasattr(expr, "__name__"):
+            return "<'%s.%s'>" % (expr.__module__, expr.__name__)
+        else:
+            return str(expr)
+
+    def _print_Add(self, expr, order=None):
+        args = self._as_ordered_terms(expr, order=order)
+        args = map(self._print, args)
+        clsname = type(expr).__name__
+        return clsname + "(%s)" % ", ".join(args)
+
+    def _print_Cycle(self, expr):
+        return expr.__repr__()
+
+    def _print_Permutation(self, expr):
+        from sympy.combinatorics.permutations import Permutation, Cycle
+        from sympy.utilities.exceptions import sympy_deprecation_warning
+
+        perm_cyclic = Permutation.print_cyclic
+        if perm_cyclic is not None:
+            sympy_deprecation_warning(
+                f"""
+                Setting Permutation.print_cyclic is deprecated. Instead use
+                init_printing(perm_cyclic={perm_cyclic}).
+                """,
+                deprecated_since_version="1.6",
+                active_deprecations_target="deprecated-permutation-print_cyclic",
+                stacklevel=7,
+            )
+        else:
+            perm_cyclic = self._settings.get("perm_cyclic", True)
+
+        if perm_cyclic:
+            if not expr.size:
+                return 'Permutation()'
+            # before taking Cycle notation, see if the last element is
+            # a singleton and move it to the head of the string
+            s = Cycle(expr)(expr.size - 1).__repr__()[len('Cycle'):]
+            last = s.rfind('(')
+            if not last == 0 and ',' not in s[last:]:
+                s = s[last:] + s[:last]
+            return 'Permutation%s' %s
+        else:
+            s = expr.support()
+            if not s:
+                if expr.size < 5:
+                    return 'Permutation(%s)' % str(expr.array_form)
+                return 'Permutation([], size=%s)' % expr.size
+            trim = str(expr.array_form[:s[-1] + 1]) + ', size=%s' % expr.size
+            use = full = str(expr.array_form)
+            if len(trim) < len(full):
+                use = trim
+            return 'Permutation(%s)' % use
+
+    def _print_Function(self, expr):
+        r = self._print(expr.func)
+        r += '(%s)' % ', '.join([self._print(a) for a in expr.args])
+        return r
+
+    def _print_Heaviside(self, expr):
+        # Same as _print_Function but uses pargs to suppress default value for
+        # 2nd arg.
+        r = self._print(expr.func)
+        r += '(%s)' % ', '.join([self._print(a) for a in expr.pargs])
+        return r
+
+    def _print_FunctionClass(self, expr):
+        if issubclass(expr, AppliedUndef):
+            return 'Function(%r)' % (expr.__name__)
+        else:
+            return expr.__name__
+
+    def _print_Half(self, expr):
+        return 'Rational(1, 2)'
+
+    def _print_RationalConstant(self, expr):
+        return str(expr)
+
+    def _print_AtomicExpr(self, expr):
+        return str(expr)
+
+    def _print_NumberSymbol(self, expr):
+        return str(expr)
+
+    def _print_Integer(self, expr):
+        return 'Integer(%i)' % expr.p
+
+    def _print_Complexes(self, expr):
+        return 'Complexes'
+
+    def _print_Integers(self, expr):
+        return 'Integers'
+
+    def _print_Naturals(self, expr):
+        return 'Naturals'
+
+    def _print_Naturals0(self, expr):
+        return 'Naturals0'
+
+    def _print_Rationals(self, expr):
+        return 'Rationals'
+
+    def _print_Reals(self, expr):
+        return 'Reals'
+
+    def _print_EmptySet(self, expr):
+        return 'EmptySet'
+
+    def _print_UniversalSet(self, expr):
+        return 'UniversalSet'
+
+    def _print_EmptySequence(self, expr):
+        return 'EmptySequence'
+
+    def _print_list(self, expr):
+        return "[%s]" % self.reprify(expr, ", ")
+
+    def _print_dict(self, expr):
+        sep = ", "
+        dict_kvs = ["%s: %s" % (self.doprint(key), self.doprint(value)) for key, value in expr.items()]
+        return "{%s}" % sep.join(dict_kvs)
+
+    def _print_set(self, expr):
+        if not expr:
+            return "set()"
+        return "{%s}" % self.reprify(expr, ", ")
+
+    def _print_MatrixBase(self, expr):
+        # special case for some empty matrices
+        if (expr.rows == 0) ^ (expr.cols == 0):
+            return '%s(%s, %s, %s)' % (expr.__class__.__name__,
+                                       self._print(expr.rows),
+                                       self._print(expr.cols),
+                                       self._print([]))
+        l = []
+        for i in range(expr.rows):
+            l.append([])
+            for j in range(expr.cols):
+                l[-1].append(expr[i, j])
+        return '%s(%s)' % (expr.__class__.__name__, self._print(l))
+
+    def _print_BooleanTrue(self, expr):
+        return "true"
+
+    def _print_BooleanFalse(self, expr):
+        return "false"
+
+    def _print_NaN(self, expr):
+        return "nan"
+
+    def _print_Mul(self, expr, order=None):
+        if self.order not in ('old', 'none'):
+            args = expr.as_ordered_factors()
+        else:
+            # use make_args in case expr was something like -x -> x
+            args = Mul.make_args(expr)
+
+        args = map(self._print, args)
+        clsname = type(expr).__name__
+        return clsname + "(%s)" % ", ".join(args)
+
+    def _print_Rational(self, expr):
+        return 'Rational(%s, %s)' % (self._print(expr.p), self._print(expr.q))
+
+    def _print_PythonRational(self, expr):
+        return "%s(%d, %d)" % (expr.__class__.__name__, expr.p, expr.q)
+
+    def _print_Fraction(self, expr):
+        return 'Fraction(%s, %s)' % (self._print(expr.numerator), self._print(expr.denominator))
+
+    def _print_Float(self, expr):
+        r = mlib_to_str(expr._mpf_, repr_dps(expr._prec))
+        return "%s('%s', precision=%i)" % (expr.__class__.__name__, r, expr._prec)
+
+    def _print_Sum2(self, expr):
+        return "Sum2(%s, (%s, %s, %s))" % (self._print(expr.f), self._print(expr.i),
+                                           self._print(expr.a), self._print(expr.b))
+
+    def _print_Str(self, s):
+        return "%s(%s)" % (s.__class__.__name__, self._print(s.name))
+
+    def _print_Symbol(self, expr):
+        d = expr._assumptions_orig
+        # print the dummy_index like it was an assumption
+        if expr.is_Dummy:
+            d['dummy_index'] = expr.dummy_index
+
+        if d == {}:
+            return "%s(%s)" % (expr.__class__.__name__, self._print(expr.name))
+        else:
+            attr = ['%s=%s' % (k, v) for k, v in d.items()]
+            return "%s(%s, %s)" % (expr.__class__.__name__,
+                                   self._print(expr.name), ', '.join(attr))
+
+    def _print_CoordinateSymbol(self, expr):
+        d = expr._assumptions.generator
+
+        if d == {}:
+            return "%s(%s, %s)" % (
+                expr.__class__.__name__,
+                self._print(expr.coord_sys),
+                self._print(expr.index)
+            )
+        else:
+            attr = ['%s=%s' % (k, v) for k, v in d.items()]
+            return "%s(%s, %s, %s)" % (
+                expr.__class__.__name__,
+                self._print(expr.coord_sys),
+                self._print(expr.index),
+                ', '.join(attr)
+            )
+
+    def _print_Predicate(self, expr):
+        return "Q.%s" % expr.name
+
+    def _print_AppliedPredicate(self, expr):
+        # will be changed to just expr.args when args overriding is removed
+        args = expr._args
+        return "%s(%s)" % (expr.__class__.__name__, self.reprify(args, ", "))
+
+    def _print_str(self, expr):
+        return repr(expr)
+
+    def _print_tuple(self, expr):
+        if len(expr) == 1:
+            return "(%s,)" % self._print(expr[0])
+        else:
+            return "(%s)" % self.reprify(expr, ", ")
+
+    def _print_WildFunction(self, expr):
+        return "%s('%s')" % (expr.__class__.__name__, expr.name)
+
+    def _print_AlgebraicNumber(self, expr):
+        return "%s(%s, %s)" % (expr.__class__.__name__,
+            self._print(expr.root), self._print(expr.coeffs()))
+
+    def _print_PolyRing(self, ring):
+        return "%s(%s, %s, %s)" % (ring.__class__.__name__,
+            self._print(ring.symbols), self._print(ring.domain), self._print(ring.order))
+
+    def _print_FracField(self, field):
+        return "%s(%s, %s, %s)" % (field.__class__.__name__,
+            self._print(field.symbols), self._print(field.domain), self._print(field.order))
+
+    def _print_PolyElement(self, poly):
+        terms = list(poly.terms())
+        terms.sort(key=poly.ring.order, reverse=True)
+        return "%s(%s, %s)" % (poly.__class__.__name__, self._print(poly.ring), self._print(terms))
+
+    def _print_FracElement(self, frac):
+        numer_terms = list(frac.numer.terms())
+        numer_terms.sort(key=frac.field.order, reverse=True)
+        denom_terms = list(frac.denom.terms())
+        denom_terms.sort(key=frac.field.order, reverse=True)
+        numer = self._print(numer_terms)
+        denom = self._print(denom_terms)
+        return "%s(%s, %s, %s)" % (frac.__class__.__name__, self._print(frac.field), numer, denom)
+
+    def _print_FractionField(self, domain):
+        cls = domain.__class__.__name__
+        field = self._print(domain.field)
+        return "%s(%s)" % (cls, field)
+
+    def _print_PolynomialRingBase(self, ring):
+        cls = ring.__class__.__name__
+        dom = self._print(ring.domain)
+        gens = ', '.join(map(self._print, ring.gens))
+        order = str(ring.order)
+        if order != ring.default_order:
+            orderstr = ", order=" + order
+        else:
+            orderstr = ""
+        return "%s(%s, %s%s)" % (cls, dom, gens, orderstr)
+
+    def _print_DMP(self, p):
+        cls = p.__class__.__name__
+        rep = self._print(p.rep)
+        dom = self._print(p.dom)
+        if p.ring is not None:
+            ringstr = ", ring=" + self._print(p.ring)
+        else:
+            ringstr = ""
+        return "%s(%s, %s%s)" % (cls, rep, dom, ringstr)
+
+    def _print_MonogenicFiniteExtension(self, ext):
+        # The expanded tree shown by srepr(ext.modulus)
+        # is not practical.
+        return "FiniteExtension(%s)" % str(ext.modulus)
+
+    def _print_ExtensionElement(self, f):
+        rep = self._print(f.rep)
+        ext = self._print(f.ext)
+        return "ExtElem(%s, %s)" % (rep, ext)
+
+@print_function(ReprPrinter)
+def srepr(expr, **settings):
+    """return expr in repr form"""
+    return ReprPrinter(settings).doprint(expr)

venv/lib/python3.10/site-packages/sympy/printing/rust.py

@@ -0,0 +1,625 @@
+"""
+Rust code printer
+
+The `RustCodePrinter` converts SymPy expressions into Rust expressions.
+
+A complete code generator, which uses `rust_code` extensively, can be found
+in `sympy.utilities.codegen`. The `codegen` module can be used to generate
+complete source code files.
+
+"""
+
+# Possible Improvement
+#
+# * make sure we follow Rust Style Guidelines_
+# * make use of pattern matching
+# * better support for reference
+# * generate generic code and use trait to make sure they have specific methods
+# * use crates_ to get more math support
+#     - num_
+#         + BigInt_, BigUint_
+#         + Complex_
+#         + Rational64_, Rational32_, BigRational_
+#
+# .. _crates: https://crates.io/
+# .. _Guidelines: https://github.com/rust-lang/rust/tree/master/src/doc/style
+# .. _num: http://rust-num.github.io/num/num/
+# .. _BigInt: http://rust-num.github.io/num/num/bigint/struct.BigInt.html
+# .. _BigUint: http://rust-num.github.io/num/num/bigint/struct.BigUint.html
+# .. _Complex: http://rust-num.github.io/num/num/complex/struct.Complex.html
+# .. _Rational32: http://rust-num.github.io/num/num/rational/type.Rational32.html
+# .. _Rational64: http://rust-num.github.io/num/num/rational/type.Rational64.html
+# .. _BigRational: http://rust-num.github.io/num/num/rational/type.BigRational.html
+
+from __future__ import annotations
+from typing import Any
+
+from sympy.core import S, Rational, Float, Lambda
+from sympy.core.numbers import equal_valued
+from sympy.printing.codeprinter import CodePrinter
+
+# Rust's methods for integer and float can be found at here :
+#
+# * `Rust - Primitive Type f64 <https://doc.rust-lang.org/std/primitive.f64.html>`_
+# * `Rust - Primitive Type i64 <https://doc.rust-lang.org/std/primitive.i64.html>`_
+#
+# Function Style :
+#
+# 1. args[0].func(args[1:]), method with arguments
+# 2. args[0].func(), method without arguments
+# 3. args[1].func(), method without arguments (e.g. (e, x) => x.exp())
+# 4. func(args), function with arguments
+
+# dictionary mapping SymPy function to (argument_conditions, Rust_function).
+# Used in RustCodePrinter._print_Function(self)
+
+# f64 method in Rust
+known_functions = {
+    # "": "is_nan",
+    # "": "is_infinite",
+    # "": "is_finite",
+    # "": "is_normal",
+    # "": "classify",
+    "floor": "floor",
+    "ceiling": "ceil",
+    # "": "round",
+    # "": "trunc",
+    # "": "fract",
+    "Abs": "abs",
+    "sign": "signum",
+    # "": "is_sign_positive",
+    # "": "is_sign_negative",
+    # "": "mul_add",
+    "Pow": [(lambda base, exp: equal_valued(exp, -1), "recip", 2),   # 1.0/x
+            (lambda base, exp: equal_valued(exp, 0.5), "sqrt", 2),   # x ** 0.5
+            (lambda base, exp: equal_valued(exp, -0.5), "sqrt().recip", 2),   # 1/(x ** 0.5)
+            (lambda base, exp: exp == Rational(1, 3), "cbrt", 2),    # x ** (1/3)
+            (lambda base, exp: equal_valued(base, 2), "exp2", 3),    # 2 ** x
+            (lambda base, exp: exp.is_integer, "powi", 1),           # x ** y, for i32
+            (lambda base, exp: not exp.is_integer, "powf", 1)],      # x ** y, for f64
+    "exp": [(lambda exp: True, "exp", 2)],   # e ** x
+    "log": "ln",
+    # "": "log",          # number.log(base)
+    # "": "log2",
+    # "": "log10",
+    # "": "to_degrees",
+    # "": "to_radians",
+    "Max": "max",
+    "Min": "min",
+    # "": "hypot",        # (x**2 + y**2) ** 0.5
+    "sin": "sin",
+    "cos": "cos",
+    "tan": "tan",
+    "asin": "asin",
+    "acos": "acos",
+    "atan": "atan",
+    "atan2": "atan2",
+    # "": "sin_cos",
+    # "": "exp_m1",       # e ** x - 1
+    # "": "ln_1p",        # ln(1 + x)
+    "sinh": "sinh",
+    "cosh": "cosh",
+    "tanh": "tanh",
+    "asinh": "asinh",
+    "acosh": "acosh",
+    "atanh": "atanh",
+    "sqrt": "sqrt",  # To enable automatic rewrites
+}
+
+# i64 method in Rust
+# known_functions_i64 = {
+#     "": "min_value",
+#     "": "max_value",
+#     "": "from_str_radix",
+#     "": "count_ones",
+#     "": "count_zeros",
+#     "": "leading_zeros",
+#     "": "trainling_zeros",
+#     "": "rotate_left",
+#     "": "rotate_right",
+#     "": "swap_bytes",
+#     "": "from_be",
+#     "": "from_le",
+#     "": "to_be",    # to big endian
+#     "": "to_le",    # to little endian
+#     "": "checked_add",
+#     "": "checked_sub",
+#     "": "checked_mul",
+#     "": "checked_div",
+#     "": "checked_rem",
+#     "": "checked_neg",
+#     "": "checked_shl",
+#     "": "checked_shr",
+#     "": "checked_abs",
+#     "": "saturating_add",
+#     "": "saturating_sub",
+#     "": "saturating_mul",
+#     "": "wrapping_add",
+#     "": "wrapping_sub",
+#     "": "wrapping_mul",
+#     "": "wrapping_div",
+#     "": "wrapping_rem",
+#     "": "wrapping_neg",
+#     "": "wrapping_shl",
+#     "": "wrapping_shr",
+#     "": "wrapping_abs",
+#     "": "overflowing_add",
+#     "": "overflowing_sub",
+#     "": "overflowing_mul",
+#     "": "overflowing_div",
+#     "": "overflowing_rem",
+#     "": "overflowing_neg",
+#     "": "overflowing_shl",
+#     "": "overflowing_shr",
+#     "": "overflowing_abs",
+#     "Pow": "pow",
+#     "Abs": "abs",
+#     "sign": "signum",
+#     "": "is_positive",
+#     "": "is_negnative",
+# }
+
+# These are the core reserved words in the Rust language. Taken from:
+# http://doc.rust-lang.org/grammar.html#keywords
+
+reserved_words = ['abstract',
+                  'alignof',
+                  'as',
+                  'become',
+                  'box',
+                  'break',
+                  'const',
+                  'continue',
+                  'crate',
+                  'do',
+                  'else',
+                  'enum',
+                  'extern',
+                  'false',
+                  'final',
+                  'fn',
+                  'for',
+                  'if',
+                  'impl',
+                  'in',
+                  'let',
+                  'loop',
+                  'macro',
+                  'match',
+                  'mod',
+                  'move',
+                  'mut',
+                  'offsetof',
+                  'override',
+                  'priv',
+                  'proc',
+                  'pub',
+                  'pure',
+                  'ref',
+                  'return',
+                  'Self',
+                  'self',
+                  'sizeof',
+                  'static',
+                  'struct',
+                  'super',
+                  'trait',
+                  'true',
+                  'type',
+                  'typeof',
+                  'unsafe',
+                  'unsized',
+                  'use',
+                  'virtual',
+                  'where',
+                  'while',
+                  'yield']
+
+
+class RustCodePrinter(CodePrinter):
+    """A printer to convert SymPy expressions to strings of Rust code"""
+    printmethod = "_rust_code"
+    language = "Rust"
+
+    _default_settings: dict[str, Any] = {
+        'order': None,
+        'full_prec': 'auto',
+        'precision': 17,
+        'user_functions': {},
+        'human': True,
+        'contract': True,
+        'dereference': set(),
+        'error_on_reserved': False,
+        'reserved_word_suffix': '_',
+        'inline': False,
+    }
+
+    def __init__(self, settings={}):
+        CodePrinter.__init__(self, settings)
+        self.known_functions = dict(known_functions)
+        userfuncs = settings.get('user_functions', {})
+        self.known_functions.update(userfuncs)
+        self._dereference = set(settings.get('dereference', []))
+        self.reserved_words = set(reserved_words)
+
+    def _rate_index_position(self, p):
+        return p*5
+
+    def _get_statement(self, codestring):
+        return "%s;" % codestring
+
+    def _get_comment(self, text):
+        return "// %s" % text
+
+    def _declare_number_const(self, name, value):
+        return "const %s: f64 = %s;" % (name, value)
+
+    def _format_code(self, lines):
+        return self.indent_code(lines)
+
+    def _traverse_matrix_indices(self, mat):
+        rows, cols = mat.shape
+        return ((i, j) for i in range(rows) for j in range(cols))
+
+    def _get_loop_opening_ending(self, indices):
+        open_lines = []
+        close_lines = []
+        loopstart = "for %(var)s in %(start)s..%(end)s {"
+        for i in indices:
+            # Rust arrays start at 0 and end at dimension-1
+            open_lines.append(loopstart % {
+                'var': self._print(i),
+                'start': self._print(i.lower),
+                'end': self._print(i.upper + 1)})
+            close_lines.append("}")
+        return open_lines, close_lines
+
+    def _print_caller_var(self, expr):
+        if len(expr.args) > 1:
+            # for something like `sin(x + y + z)`,
+            # make sure we can get '(x + y + z).sin()'
+            # instead of 'x + y + z.sin()'
+            return '(' + self._print(expr) + ')'
+        elif expr.is_number:
+            return self._print(expr, _type=True)
+        else:
+            return self._print(expr)
+
+    def _print_Function(self, expr):
+        """
+        basic function for printing `Function`
+
+        Function Style :
+
+        1. args[0].func(args[1:]), method with arguments
+        2. args[0].func(), method without arguments
+        3. args[1].func(), method without arguments (e.g. (e, x) => x.exp())
+        4. func(args), function with arguments
+        """
+
+        if expr.func.__name__ in self.known_functions:
+            cond_func = self.known_functions[expr.func.__name__]
+            func = None
+            style = 1
+            if isinstance(cond_func, str):
+                func = cond_func
+            else:
+                for cond, func, style in cond_func:
+                    if cond(*expr.args):
+                        break
+            if func is not None:
+                if style == 1:
+                    ret = "%(var)s.%(method)s(%(args)s)" % {
+                        'var': self._print_caller_var(expr.args[0]),
+                        'method': func,
+                        'args': self.stringify(expr.args[1:], ", ") if len(expr.args) > 1 else ''
+                    }
+                elif style == 2:
+                    ret = "%(var)s.%(method)s()" % {
+                        'var': self._print_caller_var(expr.args[0]),
+                        'method': func,
+                    }
+                elif style == 3:
+                    ret = "%(var)s.%(method)s()" % {
+                        'var': self._print_caller_var(expr.args[1]),
+                        'method': func,
+                    }
+                else:
+                    ret = "%(func)s(%(args)s)" % {
+                        'func': func,
+                        'args': self.stringify(expr.args, ", "),
+                    }
+                return ret
+        elif hasattr(expr, '_imp_') and isinstance(expr._imp_, Lambda):
+            # inlined function
+            return self._print(expr._imp_(*expr.args))
+        elif expr.func.__name__ in self._rewriteable_functions:
+            # Simple rewrite to supported function possible
+            target_f, required_fs = self._rewriteable_functions[expr.func.__name__]
+            if self._can_print(target_f) and all(self._can_print(f) for f in required_fs):
+                return self._print(expr.rewrite(target_f))
+        else:
+            return self._print_not_supported(expr)
+
+    def _print_Pow(self, expr):
+        if expr.base.is_integer and not expr.exp.is_integer:
+            expr = type(expr)(Float(expr.base), expr.exp)
+            return self._print(expr)
+        return self._print_Function(expr)
+
+    def _print_Float(self, expr, _type=False):
+        ret = super()._print_Float(expr)
+        if _type:
+            return ret + '_f64'
+        else:
+            return ret
+
+    def _print_Integer(self, expr, _type=False):
+        ret = super()._print_Integer(expr)
+        if _type:
+            return ret + '_i32'
+        else:
+            return ret
+
+    def _print_Rational(self, expr):
+        p, q = int(expr.p), int(expr.q)
+        return '%d_f64/%d.0' % (p, q)
+
+    def _print_Relational(self, expr):
+        lhs_code = self._print(expr.lhs)
+        rhs_code = self._print(expr.rhs)
+        op = expr.rel_op
+        return "{} {} {}".format(lhs_code, op, rhs_code)
+
+    def _print_Indexed(self, expr):
+        # calculate index for 1d array
+        dims = expr.shape
+        elem = S.Zero
+        offset = S.One
+        for i in reversed(range(expr.rank)):
+            elem += expr.indices[i]*offset
+            offset *= dims[i]
+        return "%s[%s]" % (self._print(expr.base.label), self._print(elem))
+
+    def _print_Idx(self, expr):
+        return expr.label.name
+
+    def _print_Dummy(self, expr):
+        return expr.name
+
+    def _print_Exp1(self, expr, _type=False):
+        return "E"
+
+    def _print_Pi(self, expr, _type=False):
+        return 'PI'
+
+    def _print_Infinity(self, expr, _type=False):
+        return 'INFINITY'
+
+    def _print_NegativeInfinity(self, expr, _type=False):
+        return 'NEG_INFINITY'
+
+    def _print_BooleanTrue(self, expr, _type=False):
+        return "true"
+
+    def _print_BooleanFalse(self, expr, _type=False):
+        return "false"
+
+    def _print_bool(self, expr, _type=False):
+        return str(expr).lower()
+
+    def _print_NaN(self, expr, _type=False):
+        return "NAN"
+
+    def _print_Piecewise(self, expr):
+        if expr.args[-1].cond != True:
+            # We need the last conditional to be a True, otherwise the resulting
+            # function may not return a result.
+            raise ValueError("All Piecewise expressions must contain an "
+                             "(expr, True) statement to be used as a default "
+                             "condition. Without one, the generated "
+                             "expression may not evaluate to anything under "
+                             "some condition.")
+        lines = []
+
+        for i, (e, c) in enumerate(expr.args):
+            if i == 0:
+                lines.append("if (%s) {" % self._print(c))
+            elif i == len(expr.args) - 1 and c == True:
+                lines[-1] += " else {"
+            else:
+                lines[-1] += " else if (%s) {" % self._print(c)
+            code0 = self._print(e)
+            lines.append(code0)
+            lines.append("}")
+
+        if self._settings['inline']:
+            return " ".join(lines)
+        else:
+            return "\n".join(lines)
+
+    def _print_ITE(self, expr):
+        from sympy.functions import Piecewise
+        return self._print(expr.rewrite(Piecewise, deep=False))
+
+    def _print_MatrixBase(self, A):
+        if A.cols == 1:
+            return "[%s]" % ", ".join(self._print(a) for a in A)
+        else:
+            raise ValueError("Full Matrix Support in Rust need Crates (https://crates.io/keywords/matrix).")
+
+    def _print_SparseRepMatrix(self, mat):
+        # do not allow sparse matrices to be made dense
+        return self._print_not_supported(mat)
+
+    def _print_MatrixElement(self, expr):
+        return "%s[%s]" % (expr.parent,
+                           expr.j + expr.i*expr.parent.shape[1])
+
+    def _print_Symbol(self, expr):
+
+        name = super()._print_Symbol(expr)
+
+        if expr in self._dereference:
+            return '(*%s)' % name
+        else:
+            return name
+
+    def _print_Assignment(self, expr):
+        from sympy.tensor.indexed import IndexedBase
+        lhs = expr.lhs
+        rhs = expr.rhs
+        if self._settings["contract"] and (lhs.has(IndexedBase) or
+                rhs.has(IndexedBase)):
+            # Here we check if there is looping to be done, and if so
+            # print the required loops.
+            return self._doprint_loops(rhs, lhs)
+        else:
+            lhs_code = self._print(lhs)
+            rhs_code = self._print(rhs)
+            return self._get_statement("%s = %s" % (lhs_code, rhs_code))
+
+    def indent_code(self, code):
+        """Accepts a string of code or a list of code lines"""
+
+        if isinstance(code, str):
+            code_lines = self.indent_code(code.splitlines(True))
+            return ''.join(code_lines)
+
+        tab = "    "
+        inc_token = ('{', '(', '{\n', '(\n')
+        dec_token = ('}', ')')
+
+        code = [ line.lstrip(' \t') for line in code ]
+
+        increase = [ int(any(map(line.endswith, inc_token))) for line in code ]
+        decrease = [ int(any(map(line.startswith, dec_token)))
+                     for line in code ]
+
+        pretty = []
+        level = 0
+        for n, line in enumerate(code):
+            if line in ('', '\n'):
+                pretty.append(line)
+                continue
+            level -= decrease[n]
+            pretty.append("%s%s" % (tab*level, line))
+            level += increase[n]
+        return pretty
+
+
+def rust_code(expr, assign_to=None, **settings):
+    """Converts an expr to a string of Rust code
+
+    Parameters
+    ==========
+
+    expr : Expr
+        A SymPy expression to be converted.
+    assign_to : optional
+        When given, the argument is used as the name of the variable to which
+        the expression is assigned. Can be a string, ``Symbol``,
+        ``MatrixSymbol``, or ``Indexed`` type. This is helpful in case of
+        line-wrapping, or for expressions that generate multi-line statements.
+    precision : integer, optional
+        The precision for numbers such as pi [default=15].
+    user_functions : dict, optional
+        A dictionary where the keys are string representations of either
+        ``FunctionClass`` or ``UndefinedFunction`` instances and the values
+        are their desired C string representations. Alternatively, the
+        dictionary value can be a list of tuples i.e. [(argument_test,
+        cfunction_string)].  See below for examples.
+    dereference : iterable, optional
+        An iterable of symbols that should be dereferenced in the printed code
+        expression. These would be values passed by address to the function.
+        For example, if ``dereference=[a]``, the resulting code would print
+        ``(*a)`` instead of ``a``.
+    human : bool, optional
+        If True, the result is a single string that may contain some constant
+        declarations for the number symbols. If False, the same information is
+        returned in a tuple of (symbols_to_declare, not_supported_functions,
+        code_text). [default=True].
+    contract: bool, optional
+        If True, ``Indexed`` instances are assumed to obey tensor contraction
+        rules and the corresponding nested loops over indices are generated.
+        Setting contract=False will not generate loops, instead the user is
+        responsible to provide values for the indices in the code.
+        [default=True].
+
+    Examples
+    ========
+
+    >>> from sympy import rust_code, symbols, Rational, sin, ceiling, Abs, Function
+    >>> x, tau = symbols("x, tau")
+    >>> rust_code((2*tau)**Rational(7, 2))
+    '8*1.4142135623731*tau.powf(7_f64/2.0)'
+    >>> rust_code(sin(x), assign_to="s")
+    's = x.sin();'
+
+    Simple custom printing can be defined for certain types by passing a
+    dictionary of {"type" : "function"} to the ``user_functions`` kwarg.
+    Alternatively, the dictionary value can be a list of tuples i.e.
+    [(argument_test, cfunction_string)].
+
+    >>> custom_functions = {
+    ...   "ceiling": "CEIL",
+    ...   "Abs": [(lambda x: not x.is_integer, "fabs", 4),
+    ...           (lambda x: x.is_integer, "ABS", 4)],
+    ...   "func": "f"
+    ... }
+    >>> func = Function('func')
+    >>> rust_code(func(Abs(x) + ceiling(x)), user_functions=custom_functions)
+    '(fabs(x) + x.CEIL()).f()'
+
+    ``Piecewise`` expressions are converted into conditionals. If an
+    ``assign_to`` variable is provided an if statement is created, otherwise
+    the ternary operator is used. Note that if the ``Piecewise`` lacks a
+    default term, represented by ``(expr, True)`` then an error will be thrown.
+    This is to prevent generating an expression that may not evaluate to
+    anything.
+
+    >>> from sympy import Piecewise
+    >>> expr = Piecewise((x + 1, x > 0), (x, True))
+    >>> print(rust_code(expr, tau))
+    tau = if (x > 0) {
+        x + 1
+    } else {
+        x
+    };
+
+    Support for loops is provided through ``Indexed`` types. With
+    ``contract=True`` these expressions will be turned into loops, whereas
+    ``contract=False`` will just print the assignment expression that should be
+    looped over:
+
+    >>> from sympy import Eq, IndexedBase, Idx
+    >>> len_y = 5
+    >>> y = IndexedBase('y', shape=(len_y,))
+    >>> t = IndexedBase('t', shape=(len_y,))
+    >>> Dy = IndexedBase('Dy', shape=(len_y-1,))
+    >>> i = Idx('i', len_y-1)
+    >>> e=Eq(Dy[i], (y[i+1]-y[i])/(t[i+1]-t[i]))
+    >>> rust_code(e.rhs, assign_to=e.lhs, contract=False)
+    'Dy[i] = (y[i + 1] - y[i])/(t[i + 1] - t[i]);'
+
+    Matrices are also supported, but a ``MatrixSymbol`` of the same dimensions
+    must be provided to ``assign_to``. Note that any expression that can be
+    generated normally can also exist inside a Matrix:
+
+    >>> from sympy import Matrix, MatrixSymbol
+    >>> mat = Matrix([x**2, Piecewise((x + 1, x > 0), (x, True)), sin(x)])
+    >>> A = MatrixSymbol('A', 3, 1)
+    >>> print(rust_code(mat, A))
+    A = [x.powi(2), if (x > 0) {
+        x + 1
+    } else {
+        x
+    }, x.sin()];
+    """
+
+    return RustCodePrinter(settings).doprint(expr, assign_to)
+
+
+def print_rust_code(expr, **settings):
+    """Prints Rust representation of the given expression."""
+    print(rust_code(expr, **settings))

venv/lib/python3.10/site-packages/sympy/printing/smtlib.py

@@ -0,0 +1,526 @@
+import typing
+
+import sympy
+from sympy.core import Add, Mul
+from sympy.core import Symbol, Expr, Float, Rational, Integer, Basic
+from sympy.core.function import UndefinedFunction, Function
+from sympy.core.relational import Relational, Unequality, Equality, LessThan, GreaterThan, StrictLessThan, StrictGreaterThan
+from sympy.functions.elementary.complexes import Abs
+from sympy.functions.elementary.exponential import exp, log, Pow
+from sympy.functions.elementary.hyperbolic import sinh, cosh, tanh
+from sympy.functions.elementary.miscellaneous import Min, Max
+from sympy.functions.elementary.piecewise import Piecewise
+from sympy.functions.elementary.trigonometric import sin, cos, tan, asin, acos, atan, atan2
+from sympy.logic.boolalg import And, Or, Xor, Implies, Boolean
+from sympy.logic.boolalg import BooleanTrue, BooleanFalse, BooleanFunction, Not, ITE
+from sympy.printing.printer import Printer
+from sympy.sets import Interval
+
+
+class SMTLibPrinter(Printer):
+    printmethod = "_smtlib"
+
+    # based on dReal, an automated reasoning tool for solving problems that can be encoded as first-order logic formulas over the real numbers.
+    # dReal's special strength is in handling problems that involve a wide range of nonlinear real functions.
+    _default_settings: dict = {
+        'precision': None,
+        'known_types': {
+            bool: 'Bool',
+            int: 'Int',
+            float: 'Real'
+        },
+        'known_constants': {
+            # pi: 'MY_VARIABLE_PI_DECLARED_ELSEWHERE',
+        },
+        'known_functions': {
+            Add: '+',
+            Mul: '*',
+
+            Equality: '=',
+            LessThan: '<=',
+            GreaterThan: '>=',
+            StrictLessThan: '<',
+            StrictGreaterThan: '>',
+
+            exp: 'exp',
+            log: 'log',
+            Abs: 'abs',
+            sin: 'sin',
+            cos: 'cos',
+            tan: 'tan',
+            asin: 'arcsin',
+            acos: 'arccos',
+            atan: 'arctan',
+            atan2: 'arctan2',
+            sinh: 'sinh',
+            cosh: 'cosh',
+            tanh: 'tanh',
+            Min: 'min',
+            Max: 'max',
+            Pow: 'pow',
+
+            And: 'and',
+            Or: 'or',
+            Xor: 'xor',
+            Not: 'not',
+            ITE: 'ite',
+            Implies: '=>',
+        }
+    }
+
+    symbol_table: dict
+
+    def __init__(self, settings: typing.Optional[dict] = None,
+                 symbol_table=None):
+        settings = settings or {}
+        self.symbol_table = symbol_table or {}
+        Printer.__init__(self, settings)
+        self._precision = self._settings['precision']
+        self._known_types = dict(self._settings['known_types'])
+        self._known_constants = dict(self._settings['known_constants'])
+        self._known_functions = dict(self._settings['known_functions'])
+
+        for _ in self._known_types.values(): assert self._is_legal_name(_)
+        for _ in self._known_constants.values(): assert self._is_legal_name(_)
+        # for _ in self._known_functions.values(): assert self._is_legal_name(_)  # +, *, <, >, etc.
+
+    def _is_legal_name(self, s: str):
+        if not s: return False
+        if s[0].isnumeric(): return False
+        return all(_.isalnum() or _ == '_' for _ in s)
+
+    def _s_expr(self, op: str, args: typing.Union[list, tuple]) -> str:
+        args_str = ' '.join(
+            a if isinstance(a, str)
+            else self._print(a)
+            for a in args
+        )
+        return f'({op} {args_str})'
+
+    def _print_Function(self, e):
+        if e in self._known_functions:
+            op = self._known_functions[e]
+        elif type(e) in self._known_functions:
+            op = self._known_functions[type(e)]
+        elif type(type(e)) == UndefinedFunction:
+            op = e.name
+        else:
+            op = self._known_functions[e]  # throw KeyError
+
+        return self._s_expr(op, e.args)
+
+    def _print_Relational(self, e: Relational):
+        return self._print_Function(e)
+
+    def _print_BooleanFunction(self, e: BooleanFunction):
+        return self._print_Function(e)
+
+    def _print_Expr(self, e: Expr):
+        return self._print_Function(e)
+
+    def _print_Unequality(self, e: Unequality):
+        if type(e) in self._known_functions:
+            return self._print_Relational(e)  # default
+        else:
+            eq_op = self._known_functions[Equality]
+            not_op = self._known_functions[Not]
+            return self._s_expr(not_op, [self._s_expr(eq_op, e.args)])
+
+    def _print_Piecewise(self, e: Piecewise):
+        def _print_Piecewise_recursive(args: typing.Union[list, tuple]):
+            e, c = args[0]
+            if len(args) == 1:
+                assert (c is True) or isinstance(c, BooleanTrue)
+                return self._print(e)
+            else:
+                ite = self._known_functions[ITE]
+                return self._s_expr(ite, [
+                    c, e, _print_Piecewise_recursive(args[1:])
+                ])
+
+        return _print_Piecewise_recursive(e.args)
+
+    def _print_Interval(self, e: Interval):
+        if e.start.is_infinite and e.end.is_infinite:
+            return ''
+        elif e.start.is_infinite != e.end.is_infinite:
+            raise ValueError(f'One-sided intervals (`{e}`) are not supported in SMT.')
+        else:
+            return f'[{e.start}, {e.end}]'
+
+    # todo: Sympy does not support quantifiers yet as of 2022, but quantifiers can be handy in SMT.
+    # For now, users can extend this class and build in their own quantifier support.
+    # See `test_quantifier_extensions()` in test_smtlib.py for an example of how this might look.
+
+    # def _print_ForAll(self, e: ForAll):
+    #     return self._s('forall', [
+    #         self._s('', [
+    #             self._s(sym.name, [self._type_name(sym), Interval(start, end)])
+    #             for sym, start, end in e.limits
+    #         ]),
+    #         e.function
+    #     ])
+
+    def _print_BooleanTrue(self, x: BooleanTrue):
+        return 'true'
+
+    def _print_BooleanFalse(self, x: BooleanFalse):
+        return 'false'
+
+    def _print_Float(self, x: Float):
+        f = x.evalf(self._precision) if self._precision else x.evalf()
+        return str(f).rstrip('0')
+
+    def _print_float(self, x: float):
+        return str(x)
+
+    def _print_Rational(self, x: Rational):
+        return self._s_expr('/', [x.p, x.q])
+
+    def _print_Integer(self, x: Integer):
+        assert x.q == 1
+        return str(x.p)
+
+    def _print_int(self, x: int):
+        return str(x)
+
+    def _print_Symbol(self, x: Symbol):
+        assert self._is_legal_name(x.name)
+        return x.name
+
+    def _print_NumberSymbol(self, x):
+        name = self._known_constants.get(x)
+        return name if name else self._print_Float(x)
+
+    def _print_UndefinedFunction(self, x):
+        assert self._is_legal_name(x.name)
+        return x.name
+
+    def _print_Exp1(self, x):
+        return (
+            self._print_Function(exp(1, evaluate=False))
+            if exp in self._known_functions else
+            self._print_NumberSymbol(x)
+        )
+
+    def emptyPrinter(self, expr):
+        raise NotImplementedError(f'Cannot convert `{repr(expr)}` of type `{type(expr)}` to SMT.')
+
+
+def smtlib_code(
+    expr,
+    auto_assert=True, auto_declare=True,
+    precision=None,
+    symbol_table=None,
+    known_types=None, known_constants=None, known_functions=None,
+    prefix_expressions=None, suffix_expressions=None,
+    log_warn=None
+):
+    r"""Converts ``expr`` to a string of smtlib code.
+
+    Parameters
+    ==========
+
+    expr : Expr | List[Expr]
+        A SymPy expression or system to be converted.
+    auto_assert : bool, optional
+        If false, do not modify expr and produce only the S-Expression equivalent of expr.
+        If true, assume expr is a system and assert each boolean element.
+    auto_declare : bool, optional
+        If false, do not produce declarations for the symbols used in expr.
+        If true, prepend all necessary declarations for variables used in expr based on symbol_table.
+    precision : integer, optional
+        The ``evalf(..)`` precision for numbers such as pi.
+    symbol_table : dict, optional
+        A dictionary where keys are ``Symbol`` or ``Function`` instances and values are their Python type i.e. ``bool``, ``int``, ``float``, or ``Callable[...]``.
+        If incomplete, an attempt will be made to infer types from ``expr``.
+    known_types: dict, optional
+        A dictionary where keys are ``bool``, ``int``, ``float`` etc. and values are their corresponding SMT type names.
+        If not given, a partial listing compatible with several solvers will be used.
+    known_functions : dict, optional
+        A dictionary where keys are ``Function``, ``Relational``, ``BooleanFunction``, or ``Expr`` instances and values are their SMT string representations.
+        If not given, a partial listing optimized for dReal solver (but compatible with others) will be used.
+    known_constants: dict, optional
+        A dictionary where keys are ``NumberSymbol`` instances and values are their SMT variable names.
+        When using this feature, extra caution must be taken to avoid naming collisions between user symbols and listed constants.
+        If not given, constants will be expanded inline i.e. ``3.14159`` instead of ``MY_SMT_VARIABLE_FOR_PI``.
+    prefix_expressions: list, optional
+        A list of lists of ``str`` and/or expressions to convert into SMTLib and prefix to the output.
+    suffix_expressions: list, optional
+        A list of lists of ``str`` and/or expressions to convert into SMTLib and postfix to the output.
+    log_warn: lambda function, optional
+        A function to record all warnings during potentially risky operations.
+        Soundness is a core value in SMT solving, so it is good to log all assumptions made.
+
+    Examples
+    ========
+    >>> from sympy import smtlib_code, symbols, sin, Eq
+    >>> x = symbols('x')
+    >>> smtlib_code(sin(x).series(x).removeO(), log_warn=print)
+    Could not infer type of `x`. Defaulting to float.
+    Non-Boolean expression `x**5/120 - x**3/6 + x` will not be asserted. Converting to SMTLib verbatim.
+    '(declare-const x Real)\n(+ x (* (/ -1 6) (pow x 3)) (* (/ 1 120) (pow x 5)))'
+
+    >>> from sympy import Rational
+    >>> x, y, tau = symbols("x, y, tau")
+    >>> smtlib_code((2*tau)**Rational(7, 2), log_warn=print)
+    Could not infer type of `tau`. Defaulting to float.
+    Non-Boolean expression `8*sqrt(2)*tau**(7/2)` will not be asserted. Converting to SMTLib verbatim.
+    '(declare-const tau Real)\n(* 8 (pow 2 (/ 1 2)) (pow tau (/ 7 2)))'
+
+    ``Piecewise`` expressions are implemented with ``ite`` expressions by default.
+    Note that if the ``Piecewise`` lacks a default term, represented by
+    ``(expr, True)`` then an error will be thrown.  This is to prevent
+    generating an expression that may not evaluate to anything.
+
+    >>> from sympy import Piecewise
+    >>> pw = Piecewise((x + 1, x > 0), (x, True))
+    >>> smtlib_code(Eq(pw, 3), symbol_table={x: float}, log_warn=print)
+    '(declare-const x Real)\n(assert (= (ite (> x 0) (+ 1 x) x) 3))'
+
+    Custom printing can be defined for certain types by passing a dictionary of
+    PythonType : "SMT Name" to the ``known_types``, ``known_constants``, and ``known_functions`` kwargs.
+
+    >>> from typing import Callable
+    >>> from sympy import Function, Add
+    >>> f = Function('f')
+    >>> g = Function('g')
+    >>> smt_builtin_funcs = {  # functions our SMT solver will understand
+    ...   f: "existing_smtlib_fcn",
+    ...   Add: "sum",
+    ... }
+    >>> user_def_funcs = {  # functions defined by the user must have their types specified explicitly
+    ...   g: Callable[[int], float],
+    ... }
+    >>> smtlib_code(f(x) + g(x), symbol_table=user_def_funcs, known_functions=smt_builtin_funcs, log_warn=print)
+    Non-Boolean expression `f(x) + g(x)` will not be asserted. Converting to SMTLib verbatim.
+    '(declare-const x Int)\n(declare-fun g (Int) Real)\n(sum (existing_smtlib_fcn x) (g x))'
+    """
+    log_warn = log_warn or (lambda _: None)
+
+    if not isinstance(expr, list): expr = [expr]
+    expr = [
+        sympy.sympify(_, strict=True, evaluate=False, convert_xor=False)
+        for _ in expr
+    ]
+
+    if not symbol_table: symbol_table = {}
+    symbol_table = _auto_infer_smtlib_types(
+        *expr, symbol_table=symbol_table
+    )
+    # See [FALLBACK RULES]
+    # Need SMTLibPrinter to populate known_functions and known_constants first.
+
+    settings = {}
+    if precision: settings['precision'] = precision
+    del precision
+
+    if known_types: settings['known_types'] = known_types
+    del known_types
+
+    if known_functions: settings['known_functions'] = known_functions
+    del known_functions
+
+    if known_constants: settings['known_constants'] = known_constants
+    del known_constants
+
+    if not prefix_expressions: prefix_expressions = []
+    if not suffix_expressions: suffix_expressions = []
+
+    p = SMTLibPrinter(settings, symbol_table)
+    del symbol_table
+
+    # [FALLBACK RULES]
+    for e in expr:
+        for sym in e.atoms(Symbol, Function):
+            if (
+                sym.is_Symbol and
+                sym not in p._known_constants and
+                sym not in p.symbol_table
+            ):
+                log_warn(f"Could not infer type of `{sym}`. Defaulting to float.")
+                p.symbol_table[sym] = float
+            if (
+                sym.is_Function and
+                type(sym) not in p._known_functions and
+                type(sym) not in p.symbol_table and
+                not sym.is_Piecewise
+            ): raise TypeError(
+                f"Unknown type of undefined function `{sym}`. "
+                f"Must be mapped to ``str`` in known_functions or mapped to ``Callable[..]`` in symbol_table."
+            )
+
+    declarations = []
+    if auto_declare:
+        constants = {sym.name: sym for e in expr for sym in e.free_symbols
+                     if sym not in p._known_constants}
+        functions = {fnc.name: fnc for e in expr for fnc in e.atoms(Function)
+                     if type(fnc) not in p._known_functions and not fnc.is_Piecewise}
+        declarations = \
+            [
+                _auto_declare_smtlib(sym, p, log_warn)
+                for sym in constants.values()
+            ] + [
+                _auto_declare_smtlib(fnc, p, log_warn)
+                for fnc in functions.values()
+            ]
+        declarations = [decl for decl in declarations if decl]
+
+    if auto_assert:
+        expr = [_auto_assert_smtlib(e, p, log_warn) for e in expr]
+
+    # return SMTLibPrinter().doprint(expr)
+    return '\n'.join([
+        # ';; PREFIX EXPRESSIONS',
+        *[
+            e if isinstance(e, str) else p.doprint(e)
+            for e in prefix_expressions
+        ],
+
+        # ';; DECLARATIONS',
+        *sorted(e for e in declarations),
+
+        # ';; EXPRESSIONS',
+        *[
+            e if isinstance(e, str) else p.doprint(e)
+            for e in expr
+        ],
+
+        # ';; SUFFIX EXPRESSIONS',
+        *[
+            e if isinstance(e, str) else p.doprint(e)
+            for e in suffix_expressions
+        ],
+    ])
+
+
+def _auto_declare_smtlib(sym: typing.Union[Symbol, Function], p: SMTLibPrinter, log_warn: typing.Callable[[str], None]):
+    if sym.is_Symbol:
+        type_signature = p.symbol_table[sym]
+        assert isinstance(type_signature, type)
+        type_signature = p._known_types[type_signature]
+        return p._s_expr('declare-const', [sym, type_signature])
+
+    elif sym.is_Function:
+        type_signature = p.symbol_table[type(sym)]
+        assert callable(type_signature)
+        type_signature = [p._known_types[_] for _ in type_signature.__args__]
+        assert len(type_signature) > 0
+        params_signature = f"({' '.join(type_signature[:-1])})"
+        return_signature = type_signature[-1]
+        return p._s_expr('declare-fun', [type(sym), params_signature, return_signature])
+
+    else:
+        log_warn(f"Non-Symbol/Function `{sym}` will not be declared.")
+        return None
+
+
+def _auto_assert_smtlib(e: Expr, p: SMTLibPrinter, log_warn: typing.Callable[[str], None]):
+    if isinstance(e, Boolean) or (
+        e in p.symbol_table and p.symbol_table[e] == bool
+    ) or (
+        e.is_Function and
+        type(e) in p.symbol_table and
+        p.symbol_table[type(e)].__args__[-1] == bool
+    ):
+        return p._s_expr('assert', [e])
+    else:
+        log_warn(f"Non-Boolean expression `{e}` will not be asserted. Converting to SMTLib verbatim.")
+        return e
+
+
+def _auto_infer_smtlib_types(
+    *exprs: Basic,
+    symbol_table: typing.Optional[dict] = None
+) -> dict:
+    # [TYPE INFERENCE RULES]
+    # X is alone in an expr => X is bool
+    # X in BooleanFunction.args => X is bool
+    # X matches to a bool param of a symbol_table function => X is bool
+    # X matches to an int param of a symbol_table function => X is int
+    # X.is_integer => X is int
+    # X == Y, where X is T => Y is T
+
+    # [FALLBACK RULES]
+    # see _auto_declare_smtlib(..)
+    # X is not bool and X is not int and X is Symbol => X is float
+    # else (e.g. X is Function) => error. must be specified explicitly.
+
+    _symbols = dict(symbol_table) if symbol_table else {}
+
+    def safe_update(syms: set, inf):
+        for s in syms:
+            assert s.is_Symbol
+            if (old_type := _symbols.setdefault(s, inf)) != inf:
+                raise TypeError(f"Could not infer type of `{s}`. Apparently both `{old_type}` and `{inf}`?")
+
+    # EXPLICIT TYPES
+    safe_update({
+        e
+        for e in exprs
+        if e.is_Symbol
+    }, bool)
+
+    safe_update({
+        symbol
+        for e in exprs
+        for boolfunc in e.atoms(BooleanFunction)
+        for symbol in boolfunc.args
+        if symbol.is_Symbol
+    }, bool)
+
+    safe_update({
+        symbol
+        for e in exprs
+        for boolfunc in e.atoms(Function)
+        if type(boolfunc) in _symbols
+        for symbol, param in zip(boolfunc.args, _symbols[type(boolfunc)].__args__)
+        if symbol.is_Symbol and param == bool
+    }, bool)
+
+    safe_update({
+        symbol
+        for e in exprs
+        for intfunc in e.atoms(Function)
+        if type(intfunc) in _symbols
+        for symbol, param in zip(intfunc.args, _symbols[type(intfunc)].__args__)
+        if symbol.is_Symbol and param == int
+    }, int)
+
+    safe_update({
+        symbol
+        for e in exprs
+        for symbol in e.atoms(Symbol)
+        if symbol.is_integer
+    }, int)
+
+    safe_update({
+        symbol
+        for e in exprs
+        for symbol in e.atoms(Symbol)
+        if symbol.is_real and not symbol.is_integer
+    }, float)
+
+    # EQUALITY RELATION RULE
+    rels = [rel for expr in exprs for rel in expr.atoms(Equality)]
+    rels = [
+               (rel.lhs, rel.rhs) for rel in rels if rel.lhs.is_Symbol
+           ] + [
+               (rel.rhs, rel.lhs) for rel in rels if rel.rhs.is_Symbol
+           ]
+    for infer, reltd in rels:
+        inference = (
+            _symbols[infer] if infer in _symbols else
+            _symbols[reltd] if reltd in _symbols else
+
+            _symbols[type(reltd)].__args__[-1]
+            if reltd.is_Function and type(reltd) in _symbols else
+
+            bool if reltd.is_Boolean else
+            int if reltd.is_integer or reltd.is_Integer else
+            float if reltd.is_real else
+            None
+        )
+        if inference: safe_update({infer}, inference)
+
+    return _symbols

venv/lib/python3.10/site-packages/sympy/printing/str.py

@@ -0,0 +1,1027 @@
+"""
+A Printer for generating readable representation of most SymPy classes.
+"""
+
+from __future__ import annotations
+from typing import Any
+
+from sympy.core import S, Rational, Pow, Basic, Mul, Number
+from sympy.core.mul import _keep_coeff
+from sympy.core.relational import Relational
+from sympy.core.sorting import default_sort_key
+from sympy.core.sympify import SympifyError
+from sympy.utilities.iterables import sift
+from .precedence import precedence, PRECEDENCE
+from .printer import Printer, print_function
+
+from mpmath.libmp import prec_to_dps, to_str as mlib_to_str
+
+
+class StrPrinter(Printer):
+    printmethod = "_sympystr"
+    _default_settings: dict[str, Any] = {
+        "order": None,
+        "full_prec": "auto",
+        "sympy_integers": False,
+        "abbrev": False,
+        "perm_cyclic": True,
+        "min": None,
+        "max": None,
+    }
+
+    _relationals: dict[str, str] = {}
+
+    def parenthesize(self, item, level, strict=False):
+        if (precedence(item) < level) or ((not strict) and precedence(item) <= level):
+            return "(%s)" % self._print(item)
+        else:
+            return self._print(item)
+
+    def stringify(self, args, sep, level=0):
+        return sep.join([self.parenthesize(item, level) for item in args])
+
+    def emptyPrinter(self, expr):
+        if isinstance(expr, str):
+            return expr
+        elif isinstance(expr, Basic):
+            return repr(expr)
+        else:
+            return str(expr)
+
+    def _print_Add(self, expr, order=None):
+        terms = self._as_ordered_terms(expr, order=order)
+
+        prec = precedence(expr)
+        l = []
+        for term in terms:
+            t = self._print(term)
+            if t.startswith('-') and not term.is_Add:
+                sign = "-"
+                t = t[1:]
+            else:
+                sign = "+"
+            if precedence(term) < prec or term.is_Add:
+                l.extend([sign, "(%s)" % t])
+            else:
+                l.extend([sign, t])
+        sign = l.pop(0)
+        if sign == '+':
+            sign = ""
+        return sign + ' '.join(l)
+
+    def _print_BooleanTrue(self, expr):
+        return "True"
+
+    def _print_BooleanFalse(self, expr):
+        return "False"
+
+    def _print_Not(self, expr):
+        return '~%s' %(self.parenthesize(expr.args[0],PRECEDENCE["Not"]))
+
+    def _print_And(self, expr):
+        args = list(expr.args)
+        for j, i in enumerate(args):
+            if isinstance(i, Relational) and (
+                    i.canonical.rhs is S.NegativeInfinity):
+                args.insert(0, args.pop(j))
+        return self.stringify(args, " & ", PRECEDENCE["BitwiseAnd"])
+
+    def _print_Or(self, expr):
+        return self.stringify(expr.args, " | ", PRECEDENCE["BitwiseOr"])
+
+    def _print_Xor(self, expr):
+        return self.stringify(expr.args, " ^ ", PRECEDENCE["BitwiseXor"])
+
+    def _print_AppliedPredicate(self, expr):
+        return '%s(%s)' % (
+            self._print(expr.function), self.stringify(expr.arguments, ", "))
+
+    def _print_Basic(self, expr):
+        l = [self._print(o) for o in expr.args]
+        return expr.__class__.__name__ + "(%s)" % ", ".join(l)
+
+    def _print_BlockMatrix(self, B):
+        if B.blocks.shape == (1, 1):
+            self._print(B.blocks[0, 0])
+        return self._print(B.blocks)
+
+    def _print_Catalan(self, expr):
+        return 'Catalan'
+
+    def _print_ComplexInfinity(self, expr):
+        return 'zoo'
+
+    def _print_ConditionSet(self, s):
+        args = tuple([self._print(i) for i in (s.sym, s.condition)])
+        if s.base_set is S.UniversalSet:
+            return 'ConditionSet(%s, %s)' % args
+        args += (self._print(s.base_set),)
+        return 'ConditionSet(%s, %s, %s)' % args
+
+    def _print_Derivative(self, expr):
+        dexpr = expr.expr
+        dvars = [i[0] if i[1] == 1 else i for i in expr.variable_count]
+        return 'Derivative(%s)' % ", ".join((self._print(arg) for arg in [dexpr] + dvars))
+
+    def _print_dict(self, d):
+        keys = sorted(d.keys(), key=default_sort_key)
+        items = []
+
+        for key in keys:
+            item = "%s: %s" % (self._print(key), self._print(d[key]))
+            items.append(item)
+
+        return "{%s}" % ", ".join(items)
+
+    def _print_Dict(self, expr):
+        return self._print_dict(expr)
+
+    def _print_RandomDomain(self, d):
+        if hasattr(d, 'as_boolean'):
+            return 'Domain: ' + self._print(d.as_boolean())
+        elif hasattr(d, 'set'):
+            return ('Domain: ' + self._print(d.symbols) + ' in ' +
+                    self._print(d.set))
+        else:
+            return 'Domain on ' + self._print(d.symbols)
+
+    def _print_Dummy(self, expr):
+        return '_' + expr.name
+
+    def _print_EulerGamma(self, expr):
+        return 'EulerGamma'
+
+    def _print_Exp1(self, expr):
+        return 'E'
+
+    def _print_ExprCondPair(self, expr):
+        return '(%s, %s)' % (self._print(expr.expr), self._print(expr.cond))
+
+    def _print_Function(self, expr):
+        return expr.func.__name__ + "(%s)" % self.stringify(expr.args, ", ")
+
+    def _print_GoldenRatio(self, expr):
+        return 'GoldenRatio'
+
+    def _print_Heaviside(self, expr):
+        # Same as _print_Function but uses pargs to suppress default 1/2 for
+        # 2nd args
+        return expr.func.__name__ + "(%s)" % self.stringify(expr.pargs, ", ")
+
+    def _print_TribonacciConstant(self, expr):
+        return 'TribonacciConstant'
+
+    def _print_ImaginaryUnit(self, expr):
+        return 'I'
+
+    def _print_Infinity(self, expr):
+        return 'oo'
+
+    def _print_Integral(self, expr):
+        def _xab_tostr(xab):
+            if len(xab) == 1:
+                return self._print(xab[0])
+            else:
+                return self._print((xab[0],) + tuple(xab[1:]))
+        L = ', '.join([_xab_tostr(l) for l in expr.limits])
+        return 'Integral(%s, %s)' % (self._print(expr.function), L)
+
+    def _print_Interval(self, i):
+        fin =  'Interval{m}({a}, {b})'
+        a, b, l, r = i.args
+        if a.is_infinite and b.is_infinite:
+            m = ''
+        elif a.is_infinite and not r:
+            m = ''
+        elif b.is_infinite and not l:
+            m = ''
+        elif not l and not r:
+            m = ''
+        elif l and r:
+            m = '.open'
+        elif l:
+            m = '.Lopen'
+        else:
+            m = '.Ropen'
+        return fin.format(**{'a': a, 'b': b, 'm': m})
+
+    def _print_AccumulationBounds(self, i):
+        return "AccumBounds(%s, %s)" % (self._print(i.min),
+                                        self._print(i.max))
+
+    def _print_Inverse(self, I):
+        return "%s**(-1)" % self.parenthesize(I.arg, PRECEDENCE["Pow"])
+
+    def _print_Lambda(self, obj):
+        expr = obj.expr
+        sig = obj.signature
+        if len(sig) == 1 and sig[0].is_symbol:
+            sig = sig[0]
+        return "Lambda(%s, %s)" % (self._print(sig), self._print(expr))
+
+    def _print_LatticeOp(self, expr):
+        args = sorted(expr.args, key=default_sort_key)
+        return expr.func.__name__ + "(%s)" % ", ".join(self._print(arg) for arg in args)
+
+    def _print_Limit(self, expr):
+        e, z, z0, dir = expr.args
+        return "Limit(%s, %s, %s, dir='%s')" % tuple(map(self._print, (e, z, z0, dir)))
+
+
+    def _print_list(self, expr):
+        return "[%s]" % self.stringify(expr, ", ")
+
+    def _print_List(self, expr):
+        return self._print_list(expr)
+
+    def _print_MatrixBase(self, expr):
+        return expr._format_str(self)
+
+    def _print_MatrixElement(self, expr):
+        return self.parenthesize(expr.parent, PRECEDENCE["Atom"], strict=True) \
+            + '[%s, %s]' % (self._print(expr.i), self._print(expr.j))
+
+    def _print_MatrixSlice(self, expr):
+        def strslice(x, dim):
+            x = list(x)
+            if x[2] == 1:
+                del x[2]
+            if x[0] == 0:
+                x[0] = ''
+            if x[1] == dim:
+                x[1] = ''
+            return ':'.join((self._print(arg) for arg in x))
+        return (self.parenthesize(expr.parent, PRECEDENCE["Atom"], strict=True) + '[' +
+                strslice(expr.rowslice, expr.parent.rows) + ', ' +
+                strslice(expr.colslice, expr.parent.cols) + ']')
+
+    def _print_DeferredVector(self, expr):
+        return expr.name
+
+    def _print_Mul(self, expr):
+
+        prec = precedence(expr)
+
+        # Check for unevaluated Mul. In this case we need to make sure the
+        # identities are visible, multiple Rational factors are not combined
+        # etc so we display in a straight-forward form that fully preserves all
+        # args and their order.
+        args = expr.args
+        if args[0] is S.One or any(
+                isinstance(a, Number) or
+                a.is_Pow and all(ai.is_Integer for ai in a.args)
+                for a in args[1:]):
+            d, n = sift(args, lambda x:
+                isinstance(x, Pow) and bool(x.exp.as_coeff_Mul()[0] < 0),
+                binary=True)
+            for i, di in enumerate(d):
+                if di.exp.is_Number:
+                    e = -di.exp
+                else:
+                    dargs = list(di.exp.args)
+                    dargs[0] = -dargs[0]
+                    e = Mul._from_args(dargs)
+                d[i] = Pow(di.base, e, evaluate=False) if e - 1 else di.base
+
+            pre = []
+            # don't parenthesize first factor if negative
+            if n and not n[0].is_Add and n[0].could_extract_minus_sign():
+                pre = [self._print(n.pop(0))]
+
+            nfactors = pre + [self.parenthesize(a, prec, strict=False)
+                for a in n]
+            if not nfactors:
+                nfactors = ['1']
+
+            # don't parenthesize first of denominator unless singleton
+            if len(d) > 1 and d[0].could_extract_minus_sign():
+                pre = [self._print(d.pop(0))]
+            else:
+                pre = []
+            dfactors = pre + [self.parenthesize(a, prec, strict=False)
+                for a in d]
+
+            n = '*'.join(nfactors)
+            d = '*'.join(dfactors)
+            if len(dfactors) > 1:
+                return '%s/(%s)' % (n, d)
+            elif dfactors:
+                return '%s/%s' % (n, d)
+            return n
+
+        c, e = expr.as_coeff_Mul()
+        if c < 0:
+            expr = _keep_coeff(-c, e)
+            sign = "-"
+        else:
+            sign = ""
+
+        a = []  # items in the numerator
+        b = []  # items that are in the denominator (if any)
+
+        pow_paren = []  # Will collect all pow with more than one base element and exp = -1
+
+        if self.order not in ('old', 'none'):
+            args = expr.as_ordered_factors()
+        else:
+            # use make_args in case expr was something like -x -> x
+            args = Mul.make_args(expr)
+
+        # Gather args for numerator/denominator
+        def apow(i):
+            b, e = i.as_base_exp()
+            eargs = list(Mul.make_args(e))
+            if eargs[0] is S.NegativeOne:
+                eargs = eargs[1:]
+            else:
+                eargs[0] = -eargs[0]
+            e = Mul._from_args(eargs)
+            if isinstance(i, Pow):
+                return i.func(b, e, evaluate=False)
+            return i.func(e, evaluate=False)
+        for item in args:
+            if (item.is_commutative and
+                    isinstance(item, Pow) and
+                    bool(item.exp.as_coeff_Mul()[0] < 0)):
+                if item.exp is not S.NegativeOne:
+                    b.append(apow(item))
+                else:
+                    if (len(item.args[0].args) != 1 and
+                            isinstance(item.base, (Mul, Pow))):
+                        # To avoid situations like #14160
+                        pow_paren.append(item)
+                    b.append(item.base)
+            elif item.is_Rational and item is not S.Infinity:
+                if item.p != 1:
+                    a.append(Rational(item.p))
+                if item.q != 1:
+                    b.append(Rational(item.q))
+            else:
+                a.append(item)
+
+        a = a or [S.One]
+
+        a_str = [self.parenthesize(x, prec, strict=False) for x in a]
+        b_str = [self.parenthesize(x, prec, strict=False) for x in b]
+
+        # To parenthesize Pow with exp = -1 and having more than one Symbol
+        for item in pow_paren:
+            if item.base in b:
+                b_str[b.index(item.base)] = "(%s)" % b_str[b.index(item.base)]
+
+        if not b:
+            return sign + '*'.join(a_str)
+        elif len(b) == 1:
+            return sign + '*'.join(a_str) + "/" + b_str[0]
+        else:
+            return sign + '*'.join(a_str) + "/(%s)" % '*'.join(b_str)
+
+    def _print_MatMul(self, expr):
+        c, m = expr.as_coeff_mmul()
+
+        sign = ""
+        if c.is_number:
+            re, im = c.as_real_imag()
+            if im.is_zero and re.is_negative:
+                expr = _keep_coeff(-c, m)
+                sign = "-"
+            elif re.is_zero and im.is_negative:
+                expr = _keep_coeff(-c, m)
+                sign = "-"
+
+        return sign + '*'.join(
+            [self.parenthesize(arg, precedence(expr)) for arg in expr.args]
+        )
+
+    def _print_ElementwiseApplyFunction(self, expr):
+        return "{}.({})".format(
+            expr.function,
+            self._print(expr.expr),
+        )
+
+    def _print_NaN(self, expr):
+        return 'nan'
+
+    def _print_NegativeInfinity(self, expr):
+        return '-oo'
+
+    def _print_Order(self, expr):
+        if not expr.variables or all(p is S.Zero for p in expr.point):
+            if len(expr.variables) <= 1:
+                return 'O(%s)' % self._print(expr.expr)
+            else:
+                return 'O(%s)' % self.stringify((expr.expr,) + expr.variables, ', ', 0)
+        else:
+            return 'O(%s)' % self.stringify(expr.args, ', ', 0)
+
+    def _print_Ordinal(self, expr):
+        return expr.__str__()
+
+    def _print_Cycle(self, expr):
+        return expr.__str__()
+
+    def _print_Permutation(self, expr):
+        from sympy.combinatorics.permutations import Permutation, Cycle
+        from sympy.utilities.exceptions import sympy_deprecation_warning
+
+        perm_cyclic = Permutation.print_cyclic
+        if perm_cyclic is not None:
+            sympy_deprecation_warning(
+                f"""
+                Setting Permutation.print_cyclic is deprecated. Instead use
+                init_printing(perm_cyclic={perm_cyclic}).
+                """,
+                deprecated_since_version="1.6",
+                active_deprecations_target="deprecated-permutation-print_cyclic",
+                stacklevel=7,
+            )
+        else:
+            perm_cyclic = self._settings.get("perm_cyclic", True)
+
+        if perm_cyclic:
+            if not expr.size:
+                return '()'
+            # before taking Cycle notation, see if the last element is
+            # a singleton and move it to the head of the string
+            s = Cycle(expr)(expr.size - 1).__repr__()[len('Cycle'):]
+            last = s.rfind('(')
+            if not last == 0 and ',' not in s[last:]:
+                s = s[last:] + s[:last]
+            s = s.replace(',', '')
+            return s
+        else:
+            s = expr.support()
+            if not s:
+                if expr.size < 5:
+                    return 'Permutation(%s)' % self._print(expr.array_form)
+                return 'Permutation([], size=%s)' % self._print(expr.size)
+            trim = self._print(expr.array_form[:s[-1] + 1]) + ', size=%s' % self._print(expr.size)
+            use = full = self._print(expr.array_form)
+            if len(trim) < len(full):
+                use = trim
+            return 'Permutation(%s)' % use
+
+    def _print_Subs(self, obj):
+        expr, old, new = obj.args
+        if len(obj.point) == 1:
+            old = old[0]
+            new = new[0]
+        return "Subs(%s, %s, %s)" % (
+            self._print(expr), self._print(old), self._print(new))
+
+    def _print_TensorIndex(self, expr):
+        return expr._print()
+
+    def _print_TensorHead(self, expr):
+        return expr._print()
+
+    def _print_Tensor(self, expr):
+        return expr._print()
+
+    def _print_TensMul(self, expr):
+        # prints expressions like "A(a)", "3*A(a)", "(1+x)*A(a)"
+        sign, args = expr._get_args_for_traditional_printer()
+        return sign + "*".join(
+            [self.parenthesize(arg, precedence(expr)) for arg in args]
+        )
+
+    def _print_TensAdd(self, expr):
+        return expr._print()
+
+    def _print_ArraySymbol(self, expr):
+        return self._print(expr.name)
+
+    def _print_ArrayElement(self, expr):
+        return "%s[%s]" % (
+            self.parenthesize(expr.name, PRECEDENCE["Func"], True), ", ".join([self._print(i) for i in expr.indices]))
+
+    def _print_PermutationGroup(self, expr):
+        p = ['    %s' % self._print(a) for a in expr.args]
+        return 'PermutationGroup([\n%s])' % ',\n'.join(p)
+
+    def _print_Pi(self, expr):
+        return 'pi'
+
+    def _print_PolyRing(self, ring):
+        return "Polynomial ring in %s over %s with %s order" % \
+            (", ".join((self._print(rs) for rs in ring.symbols)),
+            self._print(ring.domain), self._print(ring.order))
+
+    def _print_FracField(self, field):
+        return "Rational function field in %s over %s with %s order" % \
+            (", ".join((self._print(fs) for fs in field.symbols)),
+            self._print(field.domain), self._print(field.order))
+
+    def _print_FreeGroupElement(self, elm):
+        return elm.__str__()
+
+    def _print_GaussianElement(self, poly):
+        return "(%s + %s*I)" % (poly.x, poly.y)
+
+    def _print_PolyElement(self, poly):
+        return poly.str(self, PRECEDENCE, "%s**%s", "*")
+
+    def _print_FracElement(self, frac):
+        if frac.denom == 1:
+            return self._print(frac.numer)
+        else:
+            numer = self.parenthesize(frac.numer, PRECEDENCE["Mul"], strict=True)
+            denom = self.parenthesize(frac.denom, PRECEDENCE["Atom"], strict=True)
+            return numer + "/" + denom
+
+    def _print_Poly(self, expr):
+        ATOM_PREC = PRECEDENCE["Atom"] - 1
+        terms, gens = [], [ self.parenthesize(s, ATOM_PREC) for s in expr.gens ]
+
+        for monom, coeff in expr.terms():
+            s_monom = []
+
+            for i, e in enumerate(monom):
+                if e > 0:
+                    if e == 1:
+                        s_monom.append(gens[i])
+                    else:
+                        s_monom.append(gens[i] + "**%d" % e)
+
+            s_monom = "*".join(s_monom)
+
+            if coeff.is_Add:
+                if s_monom:
+                    s_coeff = "(" + self._print(coeff) + ")"
+                else:
+                    s_coeff = self._print(coeff)
+            else:
+                if s_monom:
+                    if coeff is S.One:
+                        terms.extend(['+', s_monom])
+                        continue
+
+                    if coeff is S.NegativeOne:
+                        terms.extend(['-', s_monom])
+                        continue
+
+                s_coeff = self._print(coeff)
+
+            if not s_monom:
+                s_term = s_coeff
+            else:
+                s_term = s_coeff + "*" + s_monom
+
+            if s_term.startswith('-'):
+                terms.extend(['-', s_term[1:]])
+            else:
+                terms.extend(['+', s_term])
+
+        if terms[0] in ('-', '+'):
+            modifier = terms.pop(0)
+
+            if modifier == '-':
+                terms[0] = '-' + terms[0]
+
+        format = expr.__class__.__name__ + "(%s, %s"
+
+        from sympy.polys.polyerrors import PolynomialError
+
+        try:
+            format += ", modulus=%s" % expr.get_modulus()
+        except PolynomialError:
+            format += ", domain='%s'" % expr.get_domain()
+
+        format += ")"
+
+        for index, item in enumerate(gens):
+            if len(item) > 2 and (item[:1] == "(" and item[len(item) - 1:] == ")"):
+                gens[index] = item[1:len(item) - 1]
+
+        return format % (' '.join(terms), ', '.join(gens))
+
+    def _print_UniversalSet(self, p):
+        return 'UniversalSet'
+
+    def _print_AlgebraicNumber(self, expr):
+        if expr.is_aliased:
+            return self._print(expr.as_poly().as_expr())
+        else:
+            return self._print(expr.as_expr())
+
+    def _print_Pow(self, expr, rational=False):
+        """Printing helper function for ``Pow``
+
+        Parameters
+        ==========
+
+        rational : bool, optional
+            If ``True``, it will not attempt printing ``sqrt(x)`` or
+            ``x**S.Half`` as ``sqrt``, and will use ``x**(1/2)``
+            instead.
+
+            See examples for additional details
+
+        Examples
+        ========
+
+        >>> from sympy import sqrt, StrPrinter
+        >>> from sympy.abc import x
+
+        How ``rational`` keyword works with ``sqrt``:
+
+        >>> printer = StrPrinter()
+        >>> printer._print_Pow(sqrt(x), rational=True)
+        'x**(1/2)'
+        >>> printer._print_Pow(sqrt(x), rational=False)
+        'sqrt(x)'
+        >>> printer._print_Pow(1/sqrt(x), rational=True)
+        'x**(-1/2)'
+        >>> printer._print_Pow(1/sqrt(x), rational=False)
+        '1/sqrt(x)'
+
+        Notes
+        =====
+
+        ``sqrt(x)`` is canonicalized as ``Pow(x, S.Half)`` in SymPy,
+        so there is no need of defining a separate printer for ``sqrt``.
+        Instead, it should be handled here as well.
+        """
+        PREC = precedence(expr)
+
+        if expr.exp is S.Half and not rational:
+            return "sqrt(%s)" % self._print(expr.base)
+
+        if expr.is_commutative:
+            if -expr.exp is S.Half and not rational:
+                # Note: Don't test "expr.exp == -S.Half" here, because that will
+                # match -0.5, which we don't want.
+                return "%s/sqrt(%s)" % tuple((self._print(arg) for arg in (S.One, expr.base)))
+            if expr.exp is -S.One:
+                # Similarly to the S.Half case, don't test with "==" here.
+                return '%s/%s' % (self._print(S.One),
+                                  self.parenthesize(expr.base, PREC, strict=False))
+
+        e = self.parenthesize(expr.exp, PREC, strict=False)
+        if self.printmethod == '_sympyrepr' and expr.exp.is_Rational and expr.exp.q != 1:
+            # the parenthesized exp should be '(Rational(a, b))' so strip parens,
+            # but just check to be sure.
+            if e.startswith('(Rational'):
+                return '%s**%s' % (self.parenthesize(expr.base, PREC, strict=False), e[1:-1])
+        return '%s**%s' % (self.parenthesize(expr.base, PREC, strict=False), e)
+
+    def _print_UnevaluatedExpr(self, expr):
+        return self._print(expr.args[0])
+
+    def _print_MatPow(self, expr):
+        PREC = precedence(expr)
+        return '%s**%s' % (self.parenthesize(expr.base, PREC, strict=False),
+                         self.parenthesize(expr.exp, PREC, strict=False))
+
+    def _print_Integer(self, expr):
+        if self._settings.get("sympy_integers", False):
+            return "S(%s)" % (expr)
+        return str(expr.p)
+
+    def _print_Integers(self, expr):
+        return 'Integers'
+
+    def _print_Naturals(self, expr):
+        return 'Naturals'
+
+    def _print_Naturals0(self, expr):
+        return 'Naturals0'
+
+    def _print_Rationals(self, expr):
+        return 'Rationals'
+
+    def _print_Reals(self, expr):
+        return 'Reals'
+
+    def _print_Complexes(self, expr):
+        return 'Complexes'
+
+    def _print_EmptySet(self, expr):
+        return 'EmptySet'
+
+    def _print_EmptySequence(self, expr):
+        return 'EmptySequence'
+
+    def _print_int(self, expr):
+        return str(expr)
+
+    def _print_mpz(self, expr):
+        return str(expr)
+
+    def _print_Rational(self, expr):
+        if expr.q == 1:
+            return str(expr.p)
+        else:
+            if self._settings.get("sympy_integers", False):
+                return "S(%s)/%s" % (expr.p, expr.q)
+            return "%s/%s" % (expr.p, expr.q)
+
+    def _print_PythonRational(self, expr):
+        if expr.q == 1:
+            return str(expr.p)
+        else:
+            return "%d/%d" % (expr.p, expr.q)
+
+    def _print_Fraction(self, expr):
+        if expr.denominator == 1:
+            return str(expr.numerator)
+        else:
+            return "%s/%s" % (expr.numerator, expr.denominator)
+
+    def _print_mpq(self, expr):
+        if expr.denominator == 1:
+            return str(expr.numerator)
+        else:
+            return "%s/%s" % (expr.numerator, expr.denominator)
+
+    def _print_Float(self, expr):
+        prec = expr._prec
+        if prec < 5:
+            dps = 0
+        else:
+            dps = prec_to_dps(expr._prec)
+        if self._settings["full_prec"] is True:
+            strip = False
+        elif self._settings["full_prec"] is False:
+            strip = True
+        elif self._settings["full_prec"] == "auto":
+            strip = self._print_level > 1
+        low = self._settings["min"] if "min" in self._settings else None
+        high = self._settings["max"] if "max" in self._settings else None
+        rv = mlib_to_str(expr._mpf_, dps, strip_zeros=strip, min_fixed=low, max_fixed=high)
+        if rv.startswith('-.0'):
+            rv = '-0.' + rv[3:]
+        elif rv.startswith('.0'):
+            rv = '0.' + rv[2:]
+        if rv.startswith('+'):
+            # e.g., +inf -> inf
+            rv = rv[1:]
+        return rv
+
+    def _print_Relational(self, expr):
+
+        charmap = {
+            "==": "Eq",
+            "!=": "Ne",
+            ":=": "Assignment",
+            '+=': "AddAugmentedAssignment",
+            "-=": "SubAugmentedAssignment",
+            "*=": "MulAugmentedAssignment",
+            "/=": "DivAugmentedAssignment",
+            "%=": "ModAugmentedAssignment",
+        }
+
+        if expr.rel_op in charmap:
+            return '%s(%s, %s)' % (charmap[expr.rel_op], self._print(expr.lhs),
+                                   self._print(expr.rhs))
+
+        return '%s %s %s' % (self.parenthesize(expr.lhs, precedence(expr)),
+                           self._relationals.get(expr.rel_op) or expr.rel_op,
+                           self.parenthesize(expr.rhs, precedence(expr)))
+
+    def _print_ComplexRootOf(self, expr):
+        return "CRootOf(%s, %d)" % (self._print_Add(expr.expr,  order='lex'),
+                                    expr.index)
+
+    def _print_RootSum(self, expr):
+        args = [self._print_Add(expr.expr, order='lex')]
+
+        if expr.fun is not S.IdentityFunction:
+            args.append(self._print(expr.fun))
+
+        return "RootSum(%s)" % ", ".join(args)
+
+    def _print_GroebnerBasis(self, basis):
+        cls = basis.__class__.__name__
+
+        exprs = [self._print_Add(arg, order=basis.order) for arg in basis.exprs]
+        exprs = "[%s]" % ", ".join(exprs)
+
+        gens = [ self._print(gen) for gen in basis.gens ]
+        domain = "domain='%s'" % self._print(basis.domain)
+        order = "order='%s'" % self._print(basis.order)
+
+        args = [exprs] + gens + [domain, order]
+
+        return "%s(%s)" % (cls, ", ".join(args))
+
+    def _print_set(self, s):
+        items = sorted(s, key=default_sort_key)
+
+        args = ', '.join(self._print(item) for item in items)
+        if not args:
+            return "set()"
+        return '{%s}' % args
+
+    def _print_FiniteSet(self, s):
+        from sympy.sets.sets import FiniteSet
+        items = sorted(s, key=default_sort_key)
+
+        args = ', '.join(self._print(item) for item in items)
+        if any(item.has(FiniteSet) for item in items):
+            return 'FiniteSet({})'.format(args)
+        return '{{{}}}'.format(args)
+
+    def _print_Partition(self, s):
+        items = sorted(s, key=default_sort_key)
+
+        args = ', '.join(self._print(arg) for arg in items)
+        return 'Partition({})'.format(args)
+
+    def _print_frozenset(self, s):
+        if not s:
+            return "frozenset()"
+        return "frozenset(%s)" % self._print_set(s)
+
+    def _print_Sum(self, expr):
+        def _xab_tostr(xab):
+            if len(xab) == 1:
+                return self._print(xab[0])
+            else:
+                return self._print((xab[0],) + tuple(xab[1:]))
+        L = ', '.join([_xab_tostr(l) for l in expr.limits])
+        return 'Sum(%s, %s)' % (self._print(expr.function), L)
+
+    def _print_Symbol(self, expr):
+        return expr.name
+    _print_MatrixSymbol = _print_Symbol
+    _print_RandomSymbol = _print_Symbol
+
+    def _print_Identity(self, expr):
+        return "I"
+
+    def _print_ZeroMatrix(self, expr):
+        return "0"
+
+    def _print_OneMatrix(self, expr):
+        return "1"
+
+    def _print_Predicate(self, expr):
+        return "Q.%s" % expr.name
+
+    def _print_str(self, expr):
+        return str(expr)
+
+    def _print_tuple(self, expr):
+        if len(expr) == 1:
+            return "(%s,)" % self._print(expr[0])
+        else:
+            return "(%s)" % self.stringify(expr, ", ")
+
+    def _print_Tuple(self, expr):
+        return self._print_tuple(expr)
+
+    def _print_Transpose(self, T):
+        return "%s.T" % self.parenthesize(T.arg, PRECEDENCE["Pow"])
+
+    def _print_Uniform(self, expr):
+        return "Uniform(%s, %s)" % (self._print(expr.a), self._print(expr.b))
+
+    def _print_Quantity(self, expr):
+        if self._settings.get("abbrev", False):
+            return "%s" % expr.abbrev
+        return "%s" % expr.name
+
+    def _print_Quaternion(self, expr):
+        s = [self.parenthesize(i, PRECEDENCE["Mul"], strict=True) for i in expr.args]
+        a = [s[0]] + [i+"*"+j for i, j in zip(s[1:], "ijk")]
+        return " + ".join(a)
+
+    def _print_Dimension(self, expr):
+        return str(expr)
+
+    def _print_Wild(self, expr):
+        return expr.name + '_'
+
+    def _print_WildFunction(self, expr):
+        return expr.name + '_'
+
+    def _print_WildDot(self, expr):
+        return expr.name
+
+    def _print_WildPlus(self, expr):
+        return expr.name
+
+    def _print_WildStar(self, expr):
+        return expr.name
+
+    def _print_Zero(self, expr):
+        if self._settings.get("sympy_integers", False):
+            return "S(0)"
+        return "0"
+
+    def _print_DMP(self, p):
+        try:
+            if p.ring is not None:
+                # TODO incorporate order
+                return self._print(p.ring.to_sympy(p))
+        except SympifyError:
+            pass
+
+        cls = p.__class__.__name__
+        rep = self._print(p.rep)
+        dom = self._print(p.dom)
+        ring = self._print(p.ring)
+
+        return "%s(%s, %s, %s)" % (cls, rep, dom, ring)
+
+    def _print_DMF(self, expr):
+        return self._print_DMP(expr)
+
+    def _print_Object(self, obj):
+        return 'Object("%s")' % obj.name
+
+    def _print_IdentityMorphism(self, morphism):
+        return 'IdentityMorphism(%s)' % morphism.domain
+
+    def _print_NamedMorphism(self, morphism):
+        return 'NamedMorphism(%s, %s, "%s")' % \
+               (morphism.domain, morphism.codomain, morphism.name)
+
+    def _print_Category(self, category):
+        return 'Category("%s")' % category.name
+
+    def _print_Manifold(self, manifold):
+        return manifold.name.name
+
+    def _print_Patch(self, patch):
+        return patch.name.name
+
+    def _print_CoordSystem(self, coords):
+        return coords.name.name
+
+    def _print_BaseScalarField(self, field):
+        return field._coord_sys.symbols[field._index].name
+
+    def _print_BaseVectorField(self, field):
+        return 'e_%s' % field._coord_sys.symbols[field._index].name
+
+    def _print_Differential(self, diff):
+        field = diff._form_field
+        if hasattr(field, '_coord_sys'):
+            return 'd%s' % field._coord_sys.symbols[field._index].name
+        else:
+            return 'd(%s)' % self._print(field)
+
+    def _print_Tr(self, expr):
+        #TODO : Handle indices
+        return "%s(%s)" % ("Tr", self._print(expr.args[0]))
+
+    def _print_Str(self, s):
+        return self._print(s.name)
+
+    def _print_AppliedBinaryRelation(self, expr):
+        rel = expr.function
+        return '%s(%s, %s)' % (self._print(rel),
+                               self._print(expr.lhs),
+                               self._print(expr.rhs))
+
+
+@print_function(StrPrinter)
+def sstr(expr, **settings):
+    """Returns the expression as a string.
+
+    For large expressions where speed is a concern, use the setting
+    order='none'. If abbrev=True setting is used then units are printed in
+    abbreviated form.
+
+    Examples
+    ========
+
+    >>> from sympy import symbols, Eq, sstr
+    >>> a, b = symbols('a b')
+    >>> sstr(Eq(a + b, 0))
+    'Eq(a + b, 0)'
+    """
+
+    p = StrPrinter(settings)
+    s = p.doprint(expr)
+
+    return s
+
+
+class StrReprPrinter(StrPrinter):
+    """(internal) -- see sstrrepr"""
+
+    def _print_str(self, s):
+        return repr(s)
+
+    def _print_Str(self, s):
+        # Str does not to be printed same as str here
+        return "%s(%s)" % (s.__class__.__name__, self._print(s.name))
+
+
+@print_function(StrReprPrinter)
+def sstrrepr(expr, **settings):
+    """return expr in mixed str/repr form
+
+       i.e. strings are returned in repr form with quotes, and everything else
+       is returned in str form.
+
+       This function could be useful for hooking into sys.displayhook
+    """
+
+    p = StrReprPrinter(settings)
+    s = p.doprint(expr)
+
+    return s

venv/lib/python3.10/site-packages/sympy/printing/tableform.py

@@ -0,0 +1,366 @@
+from sympy.core.containers import Tuple
+from sympy.core.singleton import S
+from sympy.core.symbol import Symbol
+from sympy.core.sympify import SympifyError
+
+from types import FunctionType
+
+
+class TableForm:
+    r"""
+    Create a nice table representation of data.
+
+    Examples
+    ========
+
+    >>> from sympy import TableForm
+    >>> t = TableForm([[5, 7], [4, 2], [10, 3]])
+    >>> print(t)
+    5  7
+    4  2
+    10 3
+
+    You can use the SymPy's printing system to produce tables in any
+    format (ascii, latex, html, ...).
+
+    >>> print(t.as_latex())
+    \begin{tabular}{l l}
+    $5$ & $7$ \\
+    $4$ & $2$ \\
+    $10$ & $3$ \\
+    \end{tabular}
+
+    """
+
+    def __init__(self, data, **kwarg):
+        """
+        Creates a TableForm.
+
+        Parameters:
+
+            data ...
+                            2D data to be put into the table; data can be
+                            given as a Matrix
+
+            headings ...
+                            gives the labels for rows and columns:
+
+                            Can be a single argument that applies to both
+                            dimensions:
+
+                                - None ... no labels
+                                - "automatic" ... labels are 1, 2, 3, ...
+
+                            Can be a list of labels for rows and columns:
+                            The labels for each dimension can be given
+                            as None, "automatic", or [l1, l2, ...] e.g.
+                            ["automatic", None] will number the rows
+
+                            [default: None]
+
+            alignments ...
+                            alignment of the columns with:
+
+                                - "left" or "<"
+                                - "center" or "^"
+                                - "right" or ">"
+
+                            When given as a single value, the value is used for
+                            all columns. The row headings (if given) will be
+                            right justified unless an explicit alignment is
+                            given for it and all other columns.
+
+                            [default: "left"]
+
+            formats ...
+                            a list of format strings or functions that accept
+                            3 arguments (entry, row number, col number) and
+                            return a string for the table entry. (If a function
+                            returns None then the _print method will be used.)
+
+            wipe_zeros ...
+                            Do not show zeros in the table.
+
+                            [default: True]
+
+            pad ...
+                            the string to use to indicate a missing value (e.g.
+                            elements that are None or those that are missing
+                            from the end of a row (i.e. any row that is shorter
+                            than the rest is assumed to have missing values).
+                            When None, nothing will be shown for values that
+                            are missing from the end of a row; values that are
+                            None, however, will be shown.
+
+                            [default: None]
+
+        Examples
+        ========
+
+        >>> from sympy import TableForm, Symbol
+        >>> TableForm([[5, 7], [4, 2], [10, 3]])
+        5  7
+        4  2
+        10 3
+        >>> TableForm([list('.'*i) for i in range(1, 4)], headings='automatic')
+          | 1 2 3
+        ---------
+        1 | .
+        2 | . .
+        3 | . . .
+        >>> TableForm([[Symbol('.'*(j if not i%2 else 1)) for i in range(3)]
+        ...            for j in range(4)], alignments='rcl')
+            .
+          . . .
+         .. . ..
+        ... . ...
+        """
+        from sympy.matrices.dense import Matrix
+
+        # We only support 2D data. Check the consistency:
+        if isinstance(data, Matrix):
+            data = data.tolist()
+        _h = len(data)
+
+        # fill out any short lines
+        pad = kwarg.get('pad', None)
+        ok_None = False
+        if pad is None:
+            pad = " "
+            ok_None = True
+        pad = Symbol(pad)
+        _w = max(len(line) for line in data)
+        for i, line in enumerate(data):
+            if len(line) != _w:
+                line.extend([pad]*(_w - len(line)))
+            for j, lj in enumerate(line):
+                if lj is None:
+                    if not ok_None:
+                        lj = pad
+                else:
+                    try:
+                        lj = S(lj)
+                    except SympifyError:
+                        lj = Symbol(str(lj))
+                line[j] = lj
+            data[i] = line
+        _lines = Tuple(*[Tuple(*d) for d in data])
+
+        headings = kwarg.get("headings", [None, None])
+        if headings == "automatic":
+            _headings = [range(1, _h + 1), range(1, _w + 1)]
+        else:
+            h1, h2 = headings
+            if h1 == "automatic":
+                h1 = range(1, _h + 1)
+            if h2 == "automatic":
+                h2 = range(1, _w + 1)
+            _headings = [h1, h2]
+
+        allow = ('l', 'r', 'c')
+        alignments = kwarg.get("alignments", "l")
+
+        def _std_align(a):
+            a = a.strip().lower()
+            if len(a) > 1:
+                return {'left': 'l', 'right': 'r', 'center': 'c'}.get(a, a)
+            else:
+                return {'<': 'l', '>': 'r', '^': 'c'}.get(a, a)
+        std_align = _std_align(alignments)
+        if std_align in allow:
+            _alignments = [std_align]*_w
+        else:
+            _alignments = []
+            for a in alignments:
+                std_align = _std_align(a)
+                _alignments.append(std_align)
+                if std_align not in ('l', 'r', 'c'):
+                    raise ValueError('alignment "%s" unrecognized' %
+                        alignments)
+        if _headings[0] and len(_alignments) == _w + 1:
+            _head_align = _alignments[0]
+            _alignments = _alignments[1:]
+        else:
+            _head_align = 'r'
+        if len(_alignments) != _w:
+            raise ValueError(
+                'wrong number of alignments: expected %s but got %s' %
+                (_w, len(_alignments)))
+
+        _column_formats = kwarg.get("formats", [None]*_w)
+
+        _wipe_zeros = kwarg.get("wipe_zeros", True)
+
+        self._w = _w
+        self._h = _h
+        self._lines = _lines
+        self._headings = _headings
+        self._head_align = _head_align
+        self._alignments = _alignments
+        self._column_formats = _column_formats
+        self._wipe_zeros = _wipe_zeros
+
+    def __repr__(self):
+        from .str import sstr
+        return sstr(self, order=None)
+
+    def __str__(self):
+        from .str import sstr
+        return sstr(self, order=None)
+
+    def as_matrix(self):
+        """Returns the data of the table in Matrix form.
+
+        Examples
+        ========
+
+        >>> from sympy import TableForm
+        >>> t = TableForm([[5, 7], [4, 2], [10, 3]], headings='automatic')
+        >>> t
+          | 1  2
+        --------
+        1 | 5  7
+        2 | 4  2
+        3 | 10 3
+        >>> t.as_matrix()
+        Matrix([
+        [ 5, 7],
+        [ 4, 2],
+        [10, 3]])
+        """
+        from sympy.matrices.dense import Matrix
+        return Matrix(self._lines)
+
+    def as_str(self):
+        # XXX obsolete ?
+        return str(self)
+
+    def as_latex(self):
+        from .latex import latex
+        return latex(self)
+
+    def _sympystr(self, p):
+        """
+        Returns the string representation of 'self'.
+
+        Examples
+        ========
+
+        >>> from sympy import TableForm
+        >>> t = TableForm([[5, 7], [4, 2], [10, 3]])
+        >>> s = t.as_str()
+
+        """
+        column_widths = [0] * self._w
+        lines = []
+        for line in self._lines:
+            new_line = []
+            for i in range(self._w):
+                # Format the item somehow if needed:
+                s = str(line[i])
+                if self._wipe_zeros and (s == "0"):
+                    s = " "
+                w = len(s)
+                if w > column_widths[i]:
+                    column_widths[i] = w
+                new_line.append(s)
+            lines.append(new_line)
+
+        # Check heading:
+        if self._headings[0]:
+            self._headings[0] = [str(x) for x in self._headings[0]]
+            _head_width = max([len(x) for x in self._headings[0]])
+
+        if self._headings[1]:
+            new_line = []
+            for i in range(self._w):
+                # Format the item somehow if needed:
+                s = str(self._headings[1][i])
+                w = len(s)
+                if w > column_widths[i]:
+                    column_widths[i] = w
+                new_line.append(s)
+            self._headings[1] = new_line
+
+        format_str = []
+
+        def _align(align, w):
+            return '%%%s%ss' % (
+                ("-" if align == "l" else ""),
+                str(w))
+        format_str = [_align(align, w) for align, w in
+                      zip(self._alignments, column_widths)]
+        if self._headings[0]:
+            format_str.insert(0, _align(self._head_align, _head_width))
+            format_str.insert(1, '|')
+        format_str = ' '.join(format_str) + '\n'
+
+        s = []
+        if self._headings[1]:
+            d = self._headings[1]
+            if self._headings[0]:
+                d = [""] + d
+            first_line = format_str % tuple(d)
+            s.append(first_line)
+            s.append("-" * (len(first_line) - 1) + "\n")
+        for i, line in enumerate(lines):
+            d = [l if self._alignments[j] != 'c' else
+                 l.center(column_widths[j]) for j, l in enumerate(line)]
+            if self._headings[0]:
+                l = self._headings[0][i]
+                l = (l if self._head_align != 'c' else
+                     l.center(_head_width))
+                d = [l] + d
+            s.append(format_str % tuple(d))
+        return ''.join(s)[:-1]  # don't include trailing newline
+
+    def _latex(self, printer):
+        """
+        Returns the string representation of 'self'.
+        """
+        # Check heading:
+        if self._headings[1]:
+            new_line = []
+            for i in range(self._w):
+                # Format the item somehow if needed:
+                new_line.append(str(self._headings[1][i]))
+            self._headings[1] = new_line
+
+        alignments = []
+        if self._headings[0]:
+            self._headings[0] = [str(x) for x in self._headings[0]]
+            alignments = [self._head_align]
+        alignments.extend(self._alignments)
+
+        s = r"\begin{tabular}{" + " ".join(alignments) + "}\n"
+
+        if self._headings[1]:
+            d = self._headings[1]
+            if self._headings[0]:
+                d = [""] + d
+            first_line = " & ".join(d) + r" \\" + "\n"
+            s += first_line
+            s += r"\hline" + "\n"
+        for i, line in enumerate(self._lines):
+            d = []
+            for j, x in enumerate(line):
+                if self._wipe_zeros and (x in (0, "0")):
+                    d.append(" ")
+                    continue
+                f = self._column_formats[j]
+                if f:
+                    if isinstance(f, FunctionType):
+                        v = f(x, i, j)
+                        if v is None:
+                            v = printer._print(x)
+                    else:
+                        v = f % x
+                    d.append(v)
+                else:
+                    v = printer._print(x)
+                    d.append("$%s$" % v)
+            if self._headings[0]:
+                d = [self._headings[0][i]] + d
+            s += " & ".join(d) + r" \\" + "\n"
+        s += r"\end{tabular}"
+        return s

venv/lib/python3.10/site-packages/sympy/printing/tensorflow.py

@@ -0,0 +1,216 @@
+from sympy.external.importtools import version_tuple
+from collections.abc import Iterable
+
+from sympy.core.mul import Mul
+from sympy.core.singleton import S
+from sympy.codegen.cfunctions import Sqrt
+from sympy.external import import_module
+from sympy.printing.precedence import PRECEDENCE
+from sympy.printing.pycode import AbstractPythonCodePrinter, ArrayPrinter
+import sympy
+
+tensorflow = import_module('tensorflow')
+
+class TensorflowPrinter(ArrayPrinter, AbstractPythonCodePrinter):
+    """
+    Tensorflow printer which handles vectorized piecewise functions,
+    logical operators, max/min, and relational operators.
+    """
+    printmethod = "_tensorflowcode"
+
+    mapping = {
+        sympy.Abs: "tensorflow.math.abs",
+        sympy.sign: "tensorflow.math.sign",
+
+        # XXX May raise error for ints.
+        sympy.ceiling: "tensorflow.math.ceil",
+        sympy.floor: "tensorflow.math.floor",
+        sympy.log: "tensorflow.math.log",
+        sympy.exp: "tensorflow.math.exp",
+        Sqrt: "tensorflow.math.sqrt",
+        sympy.cos: "tensorflow.math.cos",
+        sympy.acos: "tensorflow.math.acos",
+        sympy.sin: "tensorflow.math.sin",
+        sympy.asin: "tensorflow.math.asin",
+        sympy.tan: "tensorflow.math.tan",
+        sympy.atan: "tensorflow.math.atan",
+        sympy.atan2: "tensorflow.math.atan2",
+        # XXX Also may give NaN for complex results.
+        sympy.cosh: "tensorflow.math.cosh",
+        sympy.acosh: "tensorflow.math.acosh",
+        sympy.sinh: "tensorflow.math.sinh",
+        sympy.asinh: "tensorflow.math.asinh",
+        sympy.tanh: "tensorflow.math.tanh",
+        sympy.atanh: "tensorflow.math.atanh",
+
+        sympy.re: "tensorflow.math.real",
+        sympy.im: "tensorflow.math.imag",
+        sympy.arg: "tensorflow.math.angle",
+
+        # XXX May raise error for ints and complexes
+        sympy.erf: "tensorflow.math.erf",
+        sympy.loggamma: "tensorflow.math.lgamma",
+
+        sympy.Eq: "tensorflow.math.equal",
+        sympy.Ne: "tensorflow.math.not_equal",
+        sympy.StrictGreaterThan: "tensorflow.math.greater",
+        sympy.StrictLessThan: "tensorflow.math.less",
+        sympy.LessThan: "tensorflow.math.less_equal",
+        sympy.GreaterThan: "tensorflow.math.greater_equal",
+
+        sympy.And: "tensorflow.math.logical_and",
+        sympy.Or: "tensorflow.math.logical_or",
+        sympy.Not: "tensorflow.math.logical_not",
+        sympy.Max: "tensorflow.math.maximum",
+        sympy.Min: "tensorflow.math.minimum",
+
+        # Matrices
+        sympy.MatAdd: "tensorflow.math.add",
+        sympy.HadamardProduct: "tensorflow.math.multiply",
+        sympy.Trace: "tensorflow.linalg.trace",
+
+        # XXX May raise error for integer matrices.
+        sympy.Determinant : "tensorflow.linalg.det",
+    }
+
+    _default_settings = dict(
+        AbstractPythonCodePrinter._default_settings,
+        tensorflow_version=None
+    )
+
+    def __init__(self, settings=None):
+        super().__init__(settings)
+
+        version = self._settings['tensorflow_version']
+        if version is None and tensorflow:
+            version = tensorflow.__version__
+        self.tensorflow_version = version
+
+    def _print_Function(self, expr):
+        op = self.mapping.get(type(expr), None)
+        if op is None:
+            return super()._print_Basic(expr)
+        children = [self._print(arg) for arg in expr.args]
+        if len(children) == 1:
+            return "%s(%s)" % (
+                self._module_format(op),
+                children[0]
+            )
+        else:
+            return self._expand_fold_binary_op(op, children)
+
+    _print_Expr = _print_Function
+    _print_Application = _print_Function
+    _print_MatrixExpr = _print_Function
+    # TODO: a better class structure would avoid this mess:
+    _print_Relational = _print_Function
+    _print_Not = _print_Function
+    _print_And = _print_Function
+    _print_Or = _print_Function
+    _print_HadamardProduct = _print_Function
+    _print_Trace = _print_Function
+    _print_Determinant = _print_Function
+
+    def _print_Inverse(self, expr):
+        op = self._module_format('tensorflow.linalg.inv')
+        return "{}({})".format(op, self._print(expr.arg))
+
+    def _print_Transpose(self, expr):
+        version = self.tensorflow_version
+        if version and version_tuple(version) < version_tuple('1.14'):
+            op = self._module_format('tensorflow.matrix_transpose')
+        else:
+            op = self._module_format('tensorflow.linalg.matrix_transpose')
+        return "{}({})".format(op, self._print(expr.arg))
+
+    def _print_Derivative(self, expr):
+        variables = expr.variables
+        if any(isinstance(i, Iterable) for i in variables):
+            raise NotImplementedError("derivation by multiple variables is not supported")
+        def unfold(expr, args):
+            if not args:
+                return self._print(expr)
+            return "%s(%s, %s)[0]" % (
+                    self._module_format("tensorflow.gradients"),
+                    unfold(expr, args[:-1]),
+                    self._print(args[-1]),
+                )
+        return unfold(expr.expr, variables)
+
+    def _print_Piecewise(self, expr):
+        version = self.tensorflow_version
+        if version and version_tuple(version) < version_tuple('1.0'):
+            tensorflow_piecewise = "tensorflow.select"
+        else:
+            tensorflow_piecewise = "tensorflow.where"
+
+        from sympy.functions.elementary.piecewise import Piecewise
+        e, cond = expr.args[0].args
+        if len(expr.args) == 1:
+            return '{}({}, {}, {})'.format(
+                self._module_format(tensorflow_piecewise),
+                self._print(cond),
+                self._print(e),
+                0)
+
+        return '{}({}, {}, {})'.format(
+            self._module_format(tensorflow_piecewise),
+            self._print(cond),
+            self._print(e),
+            self._print(Piecewise(*expr.args[1:])))
+
+    def _print_Pow(self, expr):
+        # XXX May raise error for
+        # int**float or int**complex or float**complex
+        base, exp = expr.args
+        if expr.exp == S.Half:
+            return "{}({})".format(
+                self._module_format("tensorflow.math.sqrt"), self._print(base))
+        return "{}({}, {})".format(
+            self._module_format("tensorflow.math.pow"),
+            self._print(base), self._print(exp))
+
+    def _print_MatrixBase(self, expr):
+        tensorflow_f = "tensorflow.Variable" if expr.free_symbols else "tensorflow.constant"
+        data = "["+", ".join(["["+", ".join([self._print(j) for j in i])+"]" for i in expr.tolist()])+"]"
+        return "%s(%s)" % (
+            self._module_format(tensorflow_f),
+            data,
+        )
+
+    def _print_MatMul(self, expr):
+        from sympy.matrices.expressions import MatrixExpr
+        mat_args = [arg for arg in expr.args if isinstance(arg, MatrixExpr)]
+        args = [arg for arg in expr.args if arg not in mat_args]
+        if args:
+            return "%s*%s" % (
+                self.parenthesize(Mul.fromiter(args), PRECEDENCE["Mul"]),
+                self._expand_fold_binary_op(
+                    "tensorflow.linalg.matmul", mat_args)
+            )
+        else:
+            return self._expand_fold_binary_op(
+                "tensorflow.linalg.matmul", mat_args)
+
+    def _print_MatPow(self, expr):
+        return self._expand_fold_binary_op(
+            "tensorflow.linalg.matmul", [expr.base]*expr.exp)
+
+    def _print_CodeBlock(self, expr):
+        # TODO: is this necessary?
+        ret = []
+        for subexpr in expr.args:
+            ret.append(self._print(subexpr))
+        return "\n".join(ret)
+
+    _module = "tensorflow"
+    _einsum = "linalg.einsum"
+    _add = "math.add"
+    _transpose = "transpose"
+    _ones = "ones"
+    _zeros = "zeros"
+
+
+def tensorflow_code(expr, **settings):
+    printer = TensorflowPrinter(settings)
+    return printer.doprint(expr)

venv/lib/python3.10/site-packages/sympy/printing/theanocode.py

@@ -0,0 +1,565 @@
+"""
+.. deprecated:: 1.8
+
+  ``sympy.printing.theanocode`` is deprecated. Theano has been renamed to
+  Aesara. Use ``sympy.printing.aesaracode`` instead. See
+  :ref:`theanocode-deprecated` for more information.
+
+"""
+from __future__ import annotations
+from typing import Any
+
+from sympy.external import import_module
+from sympy.printing.printer import Printer
+from sympy.utilities.iterables import is_sequence
+import sympy
+from functools import partial
+
+from sympy.utilities.decorator import doctest_depends_on
+from sympy.utilities.exceptions import sympy_deprecation_warning
+
+theano = import_module('theano')
+
+if theano:
+    ts = theano.scalar
+    tt = theano.tensor
+    from theano.sandbox import linalg as tlinalg
+
+    mapping = {
+            sympy.Add: tt.add,
+            sympy.Mul: tt.mul,
+            sympy.Abs: tt.abs_,
+            sympy.sign: tt.sgn,
+            sympy.ceiling: tt.ceil,
+            sympy.floor: tt.floor,
+            sympy.log: tt.log,
+            sympy.exp: tt.exp,
+            sympy.sqrt: tt.sqrt,
+            sympy.cos: tt.cos,
+            sympy.acos: tt.arccos,
+            sympy.sin: tt.sin,
+            sympy.asin: tt.arcsin,
+            sympy.tan: tt.tan,
+            sympy.atan: tt.arctan,
+            sympy.atan2: tt.arctan2,
+            sympy.cosh: tt.cosh,
+            sympy.acosh: tt.arccosh,
+            sympy.sinh: tt.sinh,
+            sympy.asinh: tt.arcsinh,
+            sympy.tanh: tt.tanh,
+            sympy.atanh: tt.arctanh,
+            sympy.re: tt.real,
+            sympy.im: tt.imag,
+            sympy.arg: tt.angle,
+            sympy.erf: tt.erf,
+            sympy.gamma: tt.gamma,
+            sympy.loggamma: tt.gammaln,
+            sympy.Pow: tt.pow,
+            sympy.Eq: tt.eq,
+            sympy.StrictGreaterThan: tt.gt,
+            sympy.StrictLessThan: tt.lt,
+            sympy.LessThan: tt.le,
+            sympy.GreaterThan: tt.ge,
+            sympy.And: tt.and_,
+            sympy.Or: tt.or_,
+            sympy.Max: tt.maximum,  # SymPy accept >2 inputs, Theano only 2
+            sympy.Min: tt.minimum,  # SymPy accept >2 inputs, Theano only 2
+            sympy.conjugate: tt.conj,
+            sympy.core.numbers.ImaginaryUnit: lambda:tt.complex(0,1),
+            # Matrices
+            sympy.MatAdd: tt.Elemwise(ts.add),
+            sympy.HadamardProduct: tt.Elemwise(ts.mul),
+            sympy.Trace: tlinalg.trace,
+            sympy.Determinant : tlinalg.det,
+            sympy.Inverse: tlinalg.matrix_inverse,
+            sympy.Transpose: tt.DimShuffle((False, False), [1, 0]),
+    }
+
+
+class TheanoPrinter(Printer):
+    """ Code printer which creates Theano symbolic expression graphs.
+
+    Parameters
+    ==========
+
+    cache : dict
+        Cache dictionary to use. If None (default) will use
+        the global cache. To create a printer which does not depend on or alter
+        global state pass an empty dictionary. Note: the dictionary is not
+        copied on initialization of the printer and will be updated in-place,
+        so using the same dict object when creating multiple printers or making
+        multiple calls to :func:`.theano_code` or :func:`.theano_function` means
+        the cache is shared between all these applications.
+
+    Attributes
+    ==========
+
+    cache : dict
+        A cache of Theano variables which have been created for SymPy
+        symbol-like objects (e.g. :class:`sympy.core.symbol.Symbol` or
+        :class:`sympy.matrices.expressions.MatrixSymbol`). This is used to
+        ensure that all references to a given symbol in an expression (or
+        multiple expressions) are printed as the same Theano variable, which is
+        created only once. Symbols are differentiated only by name and type. The
+        format of the cache's contents should be considered opaque to the user.
+    """
+    printmethod = "_theano"
+
+    def __init__(self, *args, **kwargs):
+        self.cache = kwargs.pop('cache', {})
+        super().__init__(*args, **kwargs)
+
+    def _get_key(self, s, name=None, dtype=None, broadcastable=None):
+        """ Get the cache key for a SymPy object.
+
+        Parameters
+        ==========
+
+        s : sympy.core.basic.Basic
+            SymPy object to get key for.
+
+        name : str
+            Name of object, if it does not have a ``name`` attribute.
+        """
+
+        if name is None:
+            name = s.name
+
+        return (name, type(s), s.args, dtype, broadcastable)
+
+    def _get_or_create(self, s, name=None, dtype=None, broadcastable=None):
+        """
+        Get the Theano variable for a SymPy symbol from the cache, or create it
+        if it does not exist.
+        """
+
+        # Defaults
+        if name is None:
+            name = s.name
+        if dtype is None:
+            dtype = 'floatX'
+        if broadcastable is None:
+            broadcastable = ()
+
+        key = self._get_key(s, name, dtype=dtype, broadcastable=broadcastable)
+
+        if key in self.cache:
+            return self.cache[key]
+
+        value = tt.tensor(name=name, dtype=dtype, broadcastable=broadcastable)
+        self.cache[key] = value
+        return value
+
+    def _print_Symbol(self, s, **kwargs):
+        dtype = kwargs.get('dtypes', {}).get(s)
+        bc = kwargs.get('broadcastables', {}).get(s)
+        return self._get_or_create(s, dtype=dtype, broadcastable=bc)
+
+    def _print_AppliedUndef(self, s, **kwargs):
+        name = str(type(s)) + '_' + str(s.args[0])
+        dtype = kwargs.get('dtypes', {}).get(s)
+        bc = kwargs.get('broadcastables', {}).get(s)
+        return self._get_or_create(s, name=name, dtype=dtype, broadcastable=bc)
+
+    def _print_Basic(self, expr, **kwargs):
+        op = mapping[type(expr)]
+        children = [self._print(arg, **kwargs) for arg in expr.args]
+        return op(*children)
+
+    def _print_Number(self, n, **kwargs):
+        # Integers already taken care of below, interpret as float
+        return float(n.evalf())
+
+    def _print_MatrixSymbol(self, X, **kwargs):
+        dtype = kwargs.get('dtypes', {}).get(X)
+        return self._get_or_create(X, dtype=dtype, broadcastable=(None, None))
+
+    def _print_DenseMatrix(self, X, **kwargs):
+        if not hasattr(tt, 'stacklists'):
+            raise NotImplementedError(
+               "Matrix translation not yet supported in this version of Theano")
+
+        return tt.stacklists([
+            [self._print(arg, **kwargs) for arg in L]
+            for L in X.tolist()
+        ])
+
+    _print_ImmutableMatrix = _print_ImmutableDenseMatrix = _print_DenseMatrix
+
+    def _print_MatMul(self, expr, **kwargs):
+        children = [self._print(arg, **kwargs) for arg in expr.args]
+        result = children[0]
+        for child in children[1:]:
+            result = tt.dot(result, child)
+        return result
+
+    def _print_MatPow(self, expr, **kwargs):
+        children = [self._print(arg, **kwargs) for arg in expr.args]
+        result = 1
+        if isinstance(children[1], int) and children[1] > 0:
+            for i in range(children[1]):
+                result = tt.dot(result, children[0])
+        else:
+            raise NotImplementedError('''Only non-negative integer
+           powers of matrices can be handled by Theano at the moment''')
+        return result
+
+    def _print_MatrixSlice(self, expr, **kwargs):
+        parent = self._print(expr.parent, **kwargs)
+        rowslice = self._print(slice(*expr.rowslice), **kwargs)
+        colslice = self._print(slice(*expr.colslice), **kwargs)
+        return parent[rowslice, colslice]
+
+    def _print_BlockMatrix(self, expr, **kwargs):
+        nrows, ncols = expr.blocks.shape
+        blocks = [[self._print(expr.blocks[r, c], **kwargs)
+                        for c in range(ncols)]
+                        for r in range(nrows)]
+        return tt.join(0, *[tt.join(1, *row) for row in blocks])
+
+
+    def _print_slice(self, expr, **kwargs):
+        return slice(*[self._print(i, **kwargs)
+                        if isinstance(i, sympy.Basic) else i
+                        for i in (expr.start, expr.stop, expr.step)])
+
+    def _print_Pi(self, expr, **kwargs):
+        return 3.141592653589793
+
+    def _print_Exp1(self, expr, **kwargs):
+        return ts.exp(1)
+
+    def _print_Piecewise(self, expr, **kwargs):
+        import numpy as np
+        e, cond = expr.args[0].args  # First condition and corresponding value
+
+        # Print conditional expression and value for first condition
+        p_cond = self._print(cond, **kwargs)
+        p_e = self._print(e, **kwargs)
+
+        # One condition only
+        if len(expr.args) == 1:
+            # Return value if condition else NaN
+            return tt.switch(p_cond, p_e, np.nan)
+
+        # Return value_1 if condition_1 else evaluate remaining conditions
+        p_remaining = self._print(sympy.Piecewise(*expr.args[1:]), **kwargs)
+        return tt.switch(p_cond, p_e, p_remaining)
+
+    def _print_Rational(self, expr, **kwargs):
+        return tt.true_div(self._print(expr.p, **kwargs),
+                           self._print(expr.q, **kwargs))
+
+    def _print_Integer(self, expr, **kwargs):
+        return expr.p
+
+    def _print_factorial(self, expr, **kwargs):
+        return self._print(sympy.gamma(expr.args[0] + 1), **kwargs)
+
+    def _print_Derivative(self, deriv, **kwargs):
+        rv = self._print(deriv.expr, **kwargs)
+        for var in deriv.variables:
+            var = self._print(var, **kwargs)
+            rv = tt.Rop(rv, var, tt.ones_like(var))
+        return rv
+
+    def emptyPrinter(self, expr):
+        return expr
+
+    def doprint(self, expr, dtypes=None, broadcastables=None):
+        """ Convert a SymPy expression to a Theano graph variable.
+
+        The ``dtypes`` and ``broadcastables`` arguments are used to specify the
+        data type, dimension, and broadcasting behavior of the Theano variables
+        corresponding to the free symbols in ``expr``. Each is a mapping from
+        SymPy symbols to the value of the corresponding argument to
+        ``theano.tensor.Tensor``.
+
+        See the corresponding `documentation page`__ for more information on
+        broadcasting in Theano.
+
+        .. __: http://deeplearning.net/software/theano/tutorial/broadcasting.html
+
+        Parameters
+        ==========
+
+        expr : sympy.core.expr.Expr
+            SymPy expression to print.
+
+        dtypes : dict
+            Mapping from SymPy symbols to Theano datatypes to use when creating
+            new Theano variables for those symbols. Corresponds to the ``dtype``
+            argument to ``theano.tensor.Tensor``. Defaults to ``'floatX'``
+            for symbols not included in the mapping.
+
+        broadcastables : dict
+            Mapping from SymPy symbols to the value of the ``broadcastable``
+            argument to ``theano.tensor.Tensor`` to use when creating Theano
+            variables for those symbols. Defaults to the empty tuple for symbols
+            not included in the mapping (resulting in a scalar).
+
+        Returns
+        =======
+
+        theano.gof.graph.Variable
+            A variable corresponding to the expression's value in a Theano
+            symbolic expression graph.
+
+        """
+        if dtypes is None:
+            dtypes = {}
+        if broadcastables is None:
+            broadcastables = {}
+
+        return self._print(expr, dtypes=dtypes, broadcastables=broadcastables)
+
+
+global_cache: dict[Any, Any] = {}
+
+
+def theano_code(expr, cache=None, **kwargs):
+    """
+    Convert a SymPy expression into a Theano graph variable.
+
+    .. deprecated:: 1.8
+
+      ``sympy.printing.theanocode`` is deprecated. Theano has been renamed to
+      Aesara. Use ``sympy.printing.aesaracode`` instead. See
+      :ref:`theanocode-deprecated` for more information.
+
+    Parameters
+    ==========
+
+    expr : sympy.core.expr.Expr
+        SymPy expression object to convert.
+
+    cache : dict
+        Cached Theano variables (see :class:`TheanoPrinter.cache
+        <TheanoPrinter>`). Defaults to the module-level global cache.
+
+    dtypes : dict
+        Passed to :meth:`.TheanoPrinter.doprint`.
+
+    broadcastables : dict
+        Passed to :meth:`.TheanoPrinter.doprint`.
+
+    Returns
+    =======
+
+    theano.gof.graph.Variable
+        A variable corresponding to the expression's value in a Theano symbolic
+        expression graph.
+
+    """
+    sympy_deprecation_warning(
+        """
+        sympy.printing.theanocode is deprecated. Theano has been renamed to
+        Aesara. Use sympy.printing.aesaracode instead.""",
+        deprecated_since_version="1.8",
+    active_deprecations_target='theanocode-deprecated')
+
+    if not theano:
+        raise ImportError("theano is required for theano_code")
+
+    if cache is None:
+        cache = global_cache
+
+    return TheanoPrinter(cache=cache, settings={}).doprint(expr, **kwargs)
+
+
+def dim_handling(inputs, dim=None, dims=None, broadcastables=None):
+    r"""
+    Get value of ``broadcastables`` argument to :func:`.theano_code` from
+    keyword arguments to :func:`.theano_function`.
+
+    Included for backwards compatibility.
+
+    Parameters
+    ==========
+
+    inputs
+        Sequence of input symbols.
+
+    dim : int
+        Common number of dimensions for all inputs. Overrides other arguments
+        if given.
+
+    dims : dict
+        Mapping from input symbols to number of dimensions. Overrides
+        ``broadcastables`` argument if given.
+
+    broadcastables : dict
+        Explicit value of ``broadcastables`` argument to
+        :meth:`.TheanoPrinter.doprint`. If not None function will return this value unchanged.
+
+    Returns
+    =======
+    dict
+        Dictionary mapping elements of ``inputs`` to their "broadcastable"
+        values (tuple of ``bool``\ s).
+    """
+    if dim is not None:
+        return {s: (False,) * dim for s in inputs}
+
+    if dims is not None:
+        maxdim = max(dims.values())
+        return {
+            s: (False,) * d + (True,) * (maxdim - d)
+            for s, d in dims.items()
+        }
+
+    if broadcastables is not None:
+        return broadcastables
+
+    return {}
+
+
+@doctest_depends_on(modules=('theano',))
+def theano_function(inputs, outputs, scalar=False, *,
+        dim=None, dims=None, broadcastables=None, **kwargs):
+    """
+    Create a Theano function from SymPy expressions.
+
+    .. deprecated:: 1.8
+
+      ``sympy.printing.theanocode`` is deprecated. Theano has been renamed to
+      Aesara. Use ``sympy.printing.aesaracode`` instead. See
+      :ref:`theanocode-deprecated` for more information.
+
+    The inputs and outputs are converted to Theano variables using
+    :func:`.theano_code` and then passed to ``theano.function``.
+
+    Parameters
+    ==========
+
+    inputs
+        Sequence of symbols which constitute the inputs of the function.
+
+    outputs
+        Sequence of expressions which constitute the outputs(s) of the
+        function. The free symbols of each expression must be a subset of
+        ``inputs``.
+
+    scalar : bool
+        Convert 0-dimensional arrays in output to scalars. This will return a
+        Python wrapper function around the Theano function object.
+
+    cache : dict
+        Cached Theano variables (see :class:`TheanoPrinter.cache
+        <TheanoPrinter>`). Defaults to the module-level global cache.
+
+    dtypes : dict
+        Passed to :meth:`.TheanoPrinter.doprint`.
+
+    broadcastables : dict
+        Passed to :meth:`.TheanoPrinter.doprint`.
+
+    dims : dict
+        Alternative to ``broadcastables`` argument. Mapping from elements of
+        ``inputs`` to integers indicating the dimension of their associated
+        arrays/tensors. Overrides ``broadcastables`` argument if given.
+
+    dim : int
+        Another alternative to the ``broadcastables`` argument. Common number of
+        dimensions to use for all arrays/tensors.
+        ``theano_function([x, y], [...], dim=2)`` is equivalent to using
+        ``broadcastables={x: (False, False), y: (False, False)}``.
+
+    Returns
+    =======
+    callable
+        A callable object which takes values of ``inputs`` as positional
+        arguments and returns an output array for each of the expressions
+        in ``outputs``. If ``outputs`` is a single expression the function will
+        return a Numpy array, if it is a list of multiple expressions the
+        function will return a list of arrays. See description of the ``squeeze``
+        argument above for the behavior when a single output is passed in a list.
+        The returned object will either be an instance of
+        ``theano.compile.function_module.Function`` or a Python wrapper
+        function around one. In both cases, the returned value will have a
+        ``theano_function`` attribute which points to the return value of
+        ``theano.function``.
+
+    Examples
+    ========
+
+    >>> from sympy.abc import x, y, z
+    >>> from sympy.printing.theanocode import theano_function
+
+    A simple function with one input and one output:
+
+    >>> f1 = theano_function([x], [x**2 - 1], scalar=True)
+    >>> f1(3)
+    8.0
+
+    A function with multiple inputs and one output:
+
+    >>> f2 = theano_function([x, y, z], [(x**z + y**z)**(1/z)], scalar=True)
+    >>> f2(3, 4, 2)
+    5.0
+
+    A function with multiple inputs and multiple outputs:
+
+    >>> f3 = theano_function([x, y], [x**2 + y**2, x**2 - y**2], scalar=True)
+    >>> f3(2, 3)
+    [13.0, -5.0]
+
+    See also
+    ========
+
+    dim_handling
+
+    """
+    sympy_deprecation_warning(
+        """
+        sympy.printing.theanocode is deprecated. Theano has been renamed to Aesara. Use sympy.printing.aesaracode instead""",
+        deprecated_since_version="1.8",
+    active_deprecations_target='theanocode-deprecated')
+
+    if not theano:
+        raise ImportError("theano is required for theano_function")
+
+    # Pop off non-theano keyword args
+    cache = kwargs.pop('cache', {})
+    dtypes = kwargs.pop('dtypes', {})
+
+    broadcastables = dim_handling(
+        inputs, dim=dim, dims=dims, broadcastables=broadcastables,
+    )
+
+    # Print inputs/outputs
+    code = partial(theano_code, cache=cache, dtypes=dtypes,
+                   broadcastables=broadcastables)
+    tinputs = list(map(code, inputs))
+    toutputs = list(map(code, outputs))
+
+    #fix constant expressions as variables
+    toutputs = [output if isinstance(output, theano.Variable) else tt.as_tensor_variable(output) for output in toutputs]
+
+    if len(toutputs) == 1:
+        toutputs = toutputs[0]
+
+    # Compile theano func
+    func = theano.function(tinputs, toutputs, **kwargs)
+
+    is_0d = [len(o.variable.broadcastable) == 0 for o in func.outputs]
+
+    # No wrapper required
+    if not scalar or not any(is_0d):
+        func.theano_function = func
+        return func
+
+    # Create wrapper to convert 0-dimensional outputs to scalars
+    def wrapper(*args):
+        out = func(*args)
+        # out can be array(1.0) or [array(1.0), array(2.0)]
+
+        if is_sequence(out):
+            return [o[()] if is_0d[i] else o for i, o in enumerate(out)]
+        else:
+            return out[()]
+
+    wrapper.__wrapped__ = func
+    wrapper.__doc__ = func.__doc__
+    wrapper.theano_function = func
+    return wrapper

venv/lib/python3.10/site-packages/sympy/printing/tree.py

@@ -0,0 +1,175 @@
+def pprint_nodes(subtrees):
+    """
+    Prettyprints systems of nodes.
+
+    Examples
+    ========
+
+    >>> from sympy.printing.tree import pprint_nodes
+    >>> print(pprint_nodes(["a", "b1\\nb2", "c"]))
+    +-a
+    +-b1
+    | b2
+    +-c
+
+    """
+    def indent(s, type=1):
+        x = s.split("\n")
+        r = "+-%s\n" % x[0]
+        for a in x[1:]:
+            if a == "":
+                continue
+            if type == 1:
+                r += "| %s\n" % a
+            else:
+                r += "  %s\n" % a
+        return r
+    if not subtrees:
+        return ""
+    f = ""
+    for a in subtrees[:-1]:
+        f += indent(a)
+    f += indent(subtrees[-1], 2)
+    return f
+
+
+def print_node(node, assumptions=True):
+    """
+    Returns information about the "node".
+
+    This includes class name, string representation and assumptions.
+
+    Parameters
+    ==========
+
+    assumptions : bool, optional
+        See the ``assumptions`` keyword in ``tree``
+    """
+    s = "%s: %s\n" % (node.__class__.__name__, str(node))
+
+    if assumptions:
+        d = node._assumptions
+    else:
+        d = None
+
+    if d:
+        for a in sorted(d):
+            v = d[a]
+            if v is None:
+                continue
+            s += "%s: %s\n" % (a, v)
+
+    return s
+
+
+def tree(node, assumptions=True):
+    """
+    Returns a tree representation of "node" as a string.
+
+    It uses print_node() together with pprint_nodes() on node.args recursively.
+
+    Parameters
+    ==========
+
+    asssumptions : bool, optional
+        The flag to decide whether to print out all the assumption data
+        (such as ``is_integer`, ``is_real``) associated with the
+        expression or not.
+
+        Enabling the flag makes the result verbose, and the printed
+        result may not be determinisitic because of the randomness used
+        in backtracing the assumptions.
+
+    See Also
+    ========
+
+    print_tree
+
+    """
+    subtrees = []
+    for arg in node.args:
+        subtrees.append(tree(arg, assumptions=assumptions))
+    s = print_node(node, assumptions=assumptions) + pprint_nodes(subtrees)
+    return s
+
+
+def print_tree(node, assumptions=True):
+    """
+    Prints a tree representation of "node".
+
+    Parameters
+    ==========
+
+    asssumptions : bool, optional
+        The flag to decide whether to print out all the assumption data
+        (such as ``is_integer`, ``is_real``) associated with the
+        expression or not.
+
+        Enabling the flag makes the result verbose, and the printed
+        result may not be determinisitic because of the randomness used
+        in backtracing the assumptions.
+
+    Examples
+    ========
+
+    >>> from sympy.printing import print_tree
+    >>> from sympy import Symbol
+    >>> x = Symbol('x', odd=True)
+    >>> y = Symbol('y', even=True)
+
+    Printing with full assumptions information:
+
+    >>> print_tree(y**x)
+    Pow: y**x
+    +-Symbol: y
+    | algebraic: True
+    | commutative: True
+    | complex: True
+    | even: True
+    | extended_real: True
+    | finite: True
+    | hermitian: True
+    | imaginary: False
+    | infinite: False
+    | integer: True
+    | irrational: False
+    | noninteger: False
+    | odd: False
+    | rational: True
+    | real: True
+    | transcendental: False
+    +-Symbol: x
+      algebraic: True
+      commutative: True
+      complex: True
+      even: False
+      extended_nonzero: True
+      extended_real: True
+      finite: True
+      hermitian: True
+      imaginary: False
+      infinite: False
+      integer: True
+      irrational: False
+      noninteger: False
+      nonzero: True
+      odd: True
+      rational: True
+      real: True
+      transcendental: False
+      zero: False
+
+    Hiding the assumptions:
+
+    >>> print_tree(y**x, assumptions=False)
+    Pow: y**x
+    +-Symbol: y
+    +-Symbol: x
+
+    See Also
+    ========
+
+    tree
+
+    """
+    print(tree(node, assumptions=assumptions))

venv/lib/python3.10/site-packages/sympy/vector/__init__.py

@@ -0,0 +1,47 @@
+from sympy.vector.coordsysrect import CoordSys3D
+from sympy.vector.vector import (Vector, VectorAdd, VectorMul,
+                                 BaseVector, VectorZero, Cross, Dot, cross, dot)
+from sympy.vector.dyadic import (Dyadic, DyadicAdd, DyadicMul,
+                                 BaseDyadic, DyadicZero)
+from sympy.vector.scalar import BaseScalar
+from sympy.vector.deloperator import Del
+from sympy.vector.functions import (express, matrix_to_vector,
+                                    laplacian, is_conservative,
+                                    is_solenoidal, scalar_potential,
+                                    directional_derivative,
+                                    scalar_potential_difference)
+from sympy.vector.point import Point
+from sympy.vector.orienters import (AxisOrienter, BodyOrienter,
+                                    SpaceOrienter, QuaternionOrienter)
+from sympy.vector.operators import Gradient, Divergence, Curl, Laplacian, gradient, curl, divergence
+from sympy.vector.implicitregion import ImplicitRegion
+from sympy.vector.parametricregion import (ParametricRegion, parametric_region_list)
+from sympy.vector.integrals import (ParametricIntegral, vector_integrate)
+
+__all__ = [
+    'Vector', 'VectorAdd', 'VectorMul', 'BaseVector', 'VectorZero', 'Cross',
+    'Dot', 'cross', 'dot',
+
+    'Dyadic', 'DyadicAdd', 'DyadicMul', 'BaseDyadic', 'DyadicZero',
+
+    'BaseScalar',
+
+    'Del',
+
+    'CoordSys3D',
+
+    'express', 'matrix_to_vector', 'laplacian', 'is_conservative',
+    'is_solenoidal', 'scalar_potential', 'directional_derivative',
+    'scalar_potential_difference',
+
+    'Point',
+
+    'AxisOrienter', 'BodyOrienter', 'SpaceOrienter', 'QuaternionOrienter',
+
+    'Gradient', 'Divergence', 'Curl', 'Laplacian', 'gradient', 'curl',
+    'divergence',
+
+    'ParametricRegion', 'parametric_region_list', 'ImplicitRegion',
+
+    'ParametricIntegral', 'vector_integrate',
+]