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sage: f = attrcall('core', 3) sage: loads(dumps(f))
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sage: f = attrcall('core', 3); f
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def __init__(self, name, args, kwds): """ TESTS::
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121ccd216bc42a7590bf74ca68be4cffd080bd7c /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/121ccd216bc42a7590bf74ca68be4cffd080bd7c/misc.py
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- ``name`` - a string of the name of the method you want to call - ``args, kwds`` - arguments and keywords to be passed to the method
|
- ``name`` - a string of the name of the method you want to call - ``args, kwds`` - arguments and keywords to be passed to the method
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def attrcall(name, *args, **kwds): """ Returns a callable which takes in an object, gets the method named name from that object, and calls it with the specified arguments and keywords. INPUT: - ``name`` - a string of the name of the method you want to call - ``args, kwds`` - arguments and keywords to be passed to the method EXAMPLES:: sage: f = attrcall('core', 3); f *.core(3) sage: [f(p) for p in Partitions(5)] [[2], [1, 1], [1, 1], [3, 1, 1], [2], [2], [1, 1]] """ return AttrCallObject(name, args, kwds)
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121ccd216bc42a7590bf74ca68be4cffd080bd7c /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/121ccd216bc42a7590bf74ca68be4cffd080bd7c/misc.py
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Shafarevich-Tate group for the Elliptic Curve defined by y^2 + y = x^3 - x^2 - 10*x - 20 over Rational Field
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Tate-Shafarevich group for the Elliptic Curve defined by y^2 + y = x^3 - x^2 - 10*x - 20 over Rational Field
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def update(self): """ Updates some properties from ``curve``.
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f3e23fc9191f9fb680d3dd908b46a28ef81af033 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/f3e23fc9191f9fb680d3dd908b46a28ef81af033/BSD.py
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A curve for which 3 divides the order of the Shafarevich-Tate group::
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A curve for which 3 divides the order of the Tate-Shafarevich group::
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sage: def foo(use_database):
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f3e23fc9191f9fb680d3dd908b46a28ef81af033 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/f3e23fc9191f9fb680d3dd908b46a28ef81af033/BSD.py
|
- ``algorithm`` - string (default: 'recursive') specifying which algorithm to be used when computing the iterated palindromic closure. It must be one of the two following values: - ``'definition'`` means that the iterated right palindromic closure is computed using the definition. - ``'recursive'`` is based on an efficient formula that recursively computes the iterated right palindromic closure without having to recompute the longest `f`-palindromic suffix at each iteration [2].
|
- ``algorithm`` - string (default: ``'recursive'``) specifying which algorithm to be used when computing the iterated palindromic closure. It must be one of the two following values: - ``'definition'`` - computed using the definition - ``'recursive'`` - computation based on an efficient formula that recursively computes the iterated right palindromic closure without having to recompute the longest `f`-palindromic suffix at each iteration [2].
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def iterated_right_palindromic_closure(self, f=None, algorithm='recursive'): r""" Returns the iterated (`f`-)palindromic closure of self.
|
e980978296e16c6e63b477ce4f93e8427871483a /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/e980978296e16c6e63b477ce4f93e8427871483a/word.py
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l = len(sub)
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L = len(sub)
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def find(self, sub, start=0, end=None): r""" Returns the index of the first occurrence of sub in self, such that sub is contained within self[start:end]. Returns -1 on failure.
|
e980978296e16c6e63b477ce4f93e8427871483a /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/e980978296e16c6e63b477ce4f93e8427871483a/word.py
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i = len(self) - l
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i = len(self) - L
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def find(self, sub, start=0, end=None): r""" Returns the index of the first occurrence of sub in self, such that sub is contained within self[start:end]. Returns -1 on failure.
|
e980978296e16c6e63b477ce4f93e8427871483a /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/e980978296e16c6e63b477ce4f93e8427871483a/word.py
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i = start - l
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i = start - L
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def find(self, sub, start=0, end=None): r""" Returns the index of the first occurrence of sub in self, such that sub is contained within self[start:end]. Returns -1 on failure.
|
e980978296e16c6e63b477ce4f93e8427871483a /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/e980978296e16c6e63b477ce4f93e8427871483a/word.py
|
if self[i:i+l] == sub: return i
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if self[i:i+L] == sub: return i
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def find(self, sub, start=0, end=None): r""" Returns the index of the first occurrence of sub in self, such that sub is contained within self[start:end]. Returns -1 on failure.
|
e980978296e16c6e63b477ce4f93e8427871483a /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/e980978296e16c6e63b477ce4f93e8427871483a/word.py
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l = len(sub)
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L = len(sub)
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def rfind(self, sub, start=0, end=None): r""" Returns the index of the last occurrence of sub in self, such that sub is contained within self[start:end]. Returns -1 on failure.
|
e980978296e16c6e63b477ce4f93e8427871483a /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/e980978296e16c6e63b477ce4f93e8427871483a/word.py
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i = len(self) - l
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i = len(self) - L
|
def rfind(self, sub, start=0, end=None): r""" Returns the index of the last occurrence of sub in self, such that sub is contained within self[start:end]. Returns -1 on failure.
|
e980978296e16c6e63b477ce4f93e8427871483a /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/e980978296e16c6e63b477ce4f93e8427871483a/word.py
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i = end - l
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i = end - L
|
def rfind(self, sub, start=0, end=None): r""" Returns the index of the last occurrence of sub in self, such that sub is contained within self[start:end]. Returns -1 on failure.
|
e980978296e16c6e63b477ce4f93e8427871483a /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/e980978296e16c6e63b477ce4f93e8427871483a/word.py
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if self[i:i+l] == sub: return i
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if self[i:i+L] == sub: return i
|
def rfind(self, sub, start=0, end=None): r""" Returns the index of the last occurrence of sub in self, such that sub is contained within self[start:end]. Returns -1 on failure.
|
e980978296e16c6e63b477ce4f93e8427871483a /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/e980978296e16c6e63b477ce4f93e8427871483a/word.py
|
if order is Infinity:
|
if order == 1: if isinstance(w, (tuple,str,list)): length = 'finite' elif isinstance(w, FiniteWord_class): length = sum(self._morph[a].length() * b for (a,b) in w.evaluation_dict().iteritems()) elif hasattr(w, '__iter__'): length = Infinity datatype = 'iter' elif w in self._domain.alphabet(): return self._morph[w] else: raise TypeError, "Don't know how to handle an input (=%s) that is not iterable or not in the domain alphabet."%w return self.codomain()((x for y in w for x in self._morph[y]), length=length, datatype=datatype) elif order is Infinity:
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def __call__(self, w, order=1, datatype='iter'): r""" Returns the image of ``w`` under self to the given order.
|
504ba7b1455ea380dd159b2aa42179a48a8ef384 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/504ba7b1455ea380dd159b2aa42179a48a8ef384/morphism.py
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if not isinstance(order, (int,Integer)) or order < 0 : raise TypeError, "order (%s) must be a positive integer or plus Infinity" % order
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elif isinstance(order, (int,Integer)) and order > 1: return self(self(w, order-1),datatype=datatype)
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def __call__(self, w, order=1, datatype='iter'): r""" Returns the image of ``w`` under self to the given order.
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504ba7b1455ea380dd159b2aa42179a48a8ef384 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/504ba7b1455ea380dd159b2aa42179a48a8ef384/morphism.py
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elif order == 1: if isinstance(w, (tuple,str,list)): length = 'finite' elif isinstance(w, FiniteWord_class): length = sum(self._morph[a].length() * b for (a,b) in w.evaluation_dict().iteritems()) elif hasattr(w, '__iter__'): length = Infinity datatype = 'iter' elif w in self._domain.alphabet(): w = [w] length = 'finite' else: raise TypeError, "Don't know how to handle an input (=%s) that is not iterable or not in the domain alphabet."%w return self.codomain()((x for y in w for x in self._morph[y]), length=length, datatype=datatype) elif order > 1: return self(self(w, order-1),datatype=datatype)
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else: raise TypeError, "order (%s) must be a positive integer or plus Infinity" % order
|
def __call__(self, w, order=1, datatype='iter'): r""" Returns the image of ``w`` under self to the given order.
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504ba7b1455ea380dd159b2aa42179a48a8ef384 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/504ba7b1455ea380dd159b2aa42179a48a8ef384/morphism.py
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if not isinstance(self.codomain(),Words_all):
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if not isinstance(self.codomain(), Words_all):
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def is_prolongable(self, letter): r""" Returns ``True`` if ``self`` is prolongable on ``letter``.
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504ba7b1455ea380dd159b2aa42179a48a8ef384 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/504ba7b1455ea380dd159b2aa42179a48a8ef384/morphism.py
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image = self(letter)
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image = self.image(letter)
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def is_prolongable(self, letter): r""" Returns ``True`` if ``self`` is prolongable on ``letter``.
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504ba7b1455ea380dd159b2aa42179a48a8ef384 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/504ba7b1455ea380dd159b2aa42179a48a8ef384/morphism.py
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def letter_iterator(self, letter):
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def _fixed_point_iterator(self, letter):
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def letter_iterator(self, letter): r""" Returns an iterator of the letters of the fixed point of ``self`` starting with ``letter``.
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504ba7b1455ea380dd159b2aa42179a48a8ef384 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/504ba7b1455ea380dd159b2aa42179a48a8ef384/morphism.py
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sage: list(m.letter_iterator('b')) Traceback (most recent call last): ... TypeError: self must be prolongable on b sage: list(m.letter_iterator('a'))
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sage: list(m._fixed_point_iterator('a'))
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def letter_iterator(self, letter): r""" Returns an iterator of the letters of the fixed point of ``self`` starting with ``letter``.
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504ba7b1455ea380dd159b2aa42179a48a8ef384 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/504ba7b1455ea380dd159b2aa42179a48a8ef384/morphism.py
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sage: m = WordMorphism('a->aa,b->aac') sage: list(m.letter_iterator('a')) Traceback (most recent call last): ... TypeError: self (=WordMorphism: a->aa, b->aac) is not a endomorphism """ if not self.is_endomorphism(): raise TypeError, "self (=%s) is not a endomorphism"%self if not self.is_prolongable(letter=letter): raise TypeError, "self must be prolongable on %s"%letter w = list(self(letter))
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The morphism must be prolongable on the letter:: sage: list(m._fixed_point_iterator('b')) Traceback (most recent call last): ... IndexError: pop from empty list The morphism must be an endomorphism:: sage: m = WordMorphism('a->ac,b->aac') sage: list(m._fixed_point_iterator('a')) Traceback (most recent call last): ... KeyError: 'c' We check that sage: s = WordMorphism({('a', 1):[('a', 1), ('a', 2)], ('a', 2):[('a', 1)]}) sage: it = s._fixed_point_iterator(('a',1)) sage: it.next() ('a', 1) """ w = list(self.image(letter))
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def letter_iterator(self, letter): r""" Returns an iterator of the letters of the fixed point of ``self`` starting with ``letter``.
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504ba7b1455ea380dd159b2aa42179a48a8ef384 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/504ba7b1455ea380dd159b2aa42179a48a8ef384/morphism.py
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for a in self(w.pop(0)):
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for a in self.image(w.pop(0)):
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def letter_iterator(self, letter): r""" Returns an iterator of the letters of the fixed point of ``self`` starting with ``letter``.
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504ba7b1455ea380dd159b2aa42179a48a8ef384 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/504ba7b1455ea380dd159b2aa42179a48a8ef384/morphism.py
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w.extend(self(w[0]))
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w.extend(self.image(w[0]))
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def letter_iterator(self, letter): r""" Returns an iterator of the letters of the fixed point of ``self`` starting with ``letter``.
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504ba7b1455ea380dd159b2aa42179a48a8ef384 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/504ba7b1455ea380dd159b2aa42179a48a8ef384/morphism.py
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image = self(letter)
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image = self.image(letter)
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def fixed_point(self, letter): r""" Returns the fixed point of ``self`` beginning by the given ``letter``.
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504ba7b1455ea380dd159b2aa42179a48a8ef384 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/504ba7b1455ea380dd159b2aa42179a48a8ef384/morphism.py
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w = self.codomain()(self.letter_iterator(letter), datatype='iter')
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w = self.codomain()(self._fixed_point_iterator(letter), datatype='iter')
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def fixed_point(self, letter): r""" Returns the fixed point of ``self`` beginning by the given ``letter``.
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504ba7b1455ea380dd159b2aa42179a48a8ef384 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/504ba7b1455ea380dd159b2aa42179a48a8ef384/morphism.py
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def longest_path(self, s = None, t = None, weighted = False, algorithm = "MILP", solver = None, verbose = 0):
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def longest_path(self, s=None, t=None, weighted=False, algorithm="MILP", solver=None, verbose=0):
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def longest_path(self, s = None, t = None, weighted = False, algorithm = "MILP", solver = None, verbose = 0): r""" Returns a longest path of ``self``.
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fbdfc46fda1150428e37faef1f31cd5518ab4374 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/fbdfc46fda1150428e37faef1f31cd5518ab4374/generic_graph.py
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- ``weighted`` (boolean) -- whether the label on the edges are tobe considered as weights (a label set to ``None`` or
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- ``weighted`` (boolean) -- whether the labels on the edges are to be considered as weights (a label set to ``None`` or
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def longest_path(self, s = None, t = None, weighted = False, algorithm = "MILP", solver = None, verbose = 0): r""" Returns a longest path of ``self``.
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fbdfc46fda1150428e37faef1f31cd5518ab4374 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/fbdfc46fda1150428e37faef1f31cd5518ab4374/generic_graph.py
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``"backtrack"``. Two remarks on this respect :
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``"backtrack"``. Two remarks on this respect:
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def longest_path(self, s = None, t = None, weighted = False, algorithm = "MILP", solver = None, verbose = 0): r""" Returns a longest path of ``self``.
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fbdfc46fda1150428e37faef1f31cd5518ab4374 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/fbdfc46fda1150428e37faef1f31cd5518ab4374/generic_graph.py
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weighting, setting ``weighted`` to ``True`` will force
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weighting, setting ``weighted=True`` will force
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def longest_path(self, s = None, t = None, weighted = False, algorithm = "MILP", solver = None, verbose = 0): r""" Returns a longest path of ``self``.
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fbdfc46fda1150428e37faef1f31cd5518ab4374 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/fbdfc46fda1150428e37faef1f31cd5518ab4374/generic_graph.py
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- ``solver`` -- (default: ``None``) Specify a Linear Program (LP)
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- ``solver`` -- (default: ``None``) Specify the Linear Program (LP)
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def longest_path(self, s = None, t = None, weighted = False, algorithm = "MILP", solver = None, verbose = 0): r""" Returns a longest path of ``self``.
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fbdfc46fda1150428e37faef1f31cd5518ab4374 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/fbdfc46fda1150428e37faef1f31cd5518ab4374/generic_graph.py
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sage: g.longest_path(algorithm = "backtrack").edges()
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sage: g.longest_path(algorithm="backtrack").edges()
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def longest_path(self, s = None, t = None, weighted = False, algorithm = "MILP", solver = None, verbose = 0): r""" Returns a longest path of ``self``.
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fbdfc46fda1150428e37faef1f31cd5518ab4374 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/fbdfc46fda1150428e37faef1f31cd5518ab4374/generic_graph.py
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Let us compute longest path on random graphs with random weights. We each time ensure the given graph is indeed a
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Let us compute longest paths on random graphs with random weights. Each time, we ensure the resulting graph is indeed a
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def longest_path(self, s = None, t = None, weighted = False, algorithm = "MILP", solver = None, verbose = 0): r""" Returns a longest path of ``self``.
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fbdfc46fda1150428e37faef1f31cd5518ab4374 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/fbdfc46fda1150428e37faef1f31cd5518ab4374/generic_graph.py
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sage: for i in xrange(20): ... g = graphs.RandomGNP(15,.3) ... for u,v in g.edges(labels = False): ... g.set_edge_label(u,v,random())
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sage: for i in range(20): ... g = graphs.RandomGNP(15, 0.3) ... for u, v in g.edges(labels=False): ... g.set_edge_label(u, v, random())
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def longest_path(self, s = None, t = None, weighted = False, algorithm = "MILP", solver = None, verbose = 0): r""" Returns a longest path of ``self``.
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fbdfc46fda1150428e37faef1f31cd5518ab4374 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/fbdfc46fda1150428e37faef1f31cd5518ab4374/generic_graph.py
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... print "Error !"
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... print("Error!")
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def longest_path(self, s = None, t = None, weighted = False, algorithm = "MILP", solver = None, verbose = 0): r""" Returns a longest path of ``self``.
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fbdfc46fda1150428e37faef1f31cd5518ab4374 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/fbdfc46fda1150428e37faef1f31cd5518ab4374/generic_graph.py
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sage: print "Test finished !" Test finished ! TESTS::
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ValueError: algorithm must be either 'backtrack' or 'MILP'
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def longest_path(self, s = None, t = None, weighted = False, algorithm = "MILP", solver = None, verbose = 0): r""" Returns a longest path of ``self``.
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fbdfc46fda1150428e37faef1f31cd5518ab4374 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/fbdfc46fda1150428e37faef1f31cd5518ab4374/generic_graph.py
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sage: for u,v in g.edges(labels = False): ... g.set_edge_label(u,v,random())
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sage: for u,v in g.edges(labels=False): ... g.set_edge_label(u, v, random())
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def longest_path(self, s = None, t = None, weighted = False, algorithm = "MILP", solver = None, verbose = 0): r""" Returns a longest path of ``self``.
|
fbdfc46fda1150428e37faef1f31cd5518ab4374 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/fbdfc46fda1150428e37faef1f31cd5518ab4374/generic_graph.py
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sage: lp1 = g1.longest_path(weighted = True) sage: lp2 = g2.longest_path(weighted = True)
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sage: lp1 = g1.longest_path(weighted=True) sage: lp2 = g2.longest_path(weighted=True)
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def longest_path(self, s = None, t = None, weighted = False, algorithm = "MILP", solver = None, verbose = 0): r""" Returns a longest path of ``self``.
|
fbdfc46fda1150428e37faef1f31cd5518ab4374 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/fbdfc46fda1150428e37faef1f31cd5518ab4374/generic_graph.py
|
sage: Graph().longest_path(weighted = True)
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sage: Graph().longest_path(weighted=True)
|
def longest_path(self, s = None, t = None, weighted = False, algorithm = "MILP", solver = None, verbose = 0): r""" Returns a longest path of ``self``.
|
fbdfc46fda1150428e37faef1f31cd5518ab4374 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/fbdfc46fda1150428e37faef1f31cd5518ab4374/generic_graph.py
|
sage: for i in xrange(20): ... g = digraphs.RandomDirectedGNP(15,.3) ... for u,v in g.edges(labels = False): ... g.set_edge_label(u,v,random())
|
sage: for i in range(20): ... g = digraphs.RandomDirectedGNP(15, 0.3) ... for u, v in g.edges(labels=False): ... g.set_edge_label(u, v, random())
|
def longest_path(self, s = None, t = None, weighted = False, algorithm = "MILP", solver = None, verbose = 0): r""" Returns a longest path of ``self``.
|
fbdfc46fda1150428e37faef1f31cd5518ab4374 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/fbdfc46fda1150428e37faef1f31cd5518ab4374/generic_graph.py
|
... print "Error !"
|
... print("Error!")
|
def longest_path(self, s = None, t = None, weighted = False, algorithm = "MILP", solver = None, verbose = 0): r""" Returns a longest path of ``self``.
|
fbdfc46fda1150428e37faef1f31cd5518ab4374 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/fbdfc46fda1150428e37faef1f31cd5518ab4374/generic_graph.py
|
... sage: print "Test finished !" Test finished !
|
def longest_path(self, s = None, t = None, weighted = False, algorithm = "MILP", solver = None, verbose = 0): r""" Returns a longest path of ``self``.
|
fbdfc46fda1150428e37faef1f31cd5518ab4374 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/fbdfc46fda1150428e37faef1f31cd5518ab4374/generic_graph.py
|
|
return max( g.longest_path(s = s, t = t, weighted = weighted, algorithm = algorithm) for g in self.connected_components_subgraphs() )
|
return max(g.longest_path(s=s, t=t, weighted=weighted, algorithm=algorithm) for g in self.connected_components_subgraphs())
|
def longest_path(self, s = None, t = None, weighted = False, algorithm = "MILP", solver = None, verbose = 0): r""" Returns a longest path of ``self``.
|
fbdfc46fda1150428e37faef1f31cd5518ab4374 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/fbdfc46fda1150428e37faef1f31cd5518ab4374/generic_graph.py
|
return max( (g.longest_path(s = s, t = t, weighted = weighted, algorithm = algorithm) for g in self.connected_components_subgraphs() ), key = lambda x : x.order() )
|
return max((g.longest_path(s=s, t=t, weighted=weighted, algorithm=algorithm) for g in self.connected_components_subgraphs()), key=lambda x: x.order())
|
def longest_path(self, s = None, t = None, weighted = False, algorithm = "MILP", solver = None, verbose = 0): r""" Returns a longest path of ``self``.
|
fbdfc46fda1150428e37faef1f31cd5518ab4374 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/fbdfc46fda1150428e37faef1f31cd5518ab4374/generic_graph.py
|
def longest_path(self, s = None, t = None, weighted = False, algorithm = "MILP", solver = None, verbose = 0): r""" Returns a longest path of ``self``.
|
fbdfc46fda1150428e37faef1f31cd5518ab4374 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/fbdfc46fda1150428e37faef1f31cd5518ab4374/generic_graph.py
|
||
def longest_path(self, s = None, t = None, weighted = False, algorithm = "MILP", solver = None, verbose = 0): r""" Returns a longest path of ``self``.
|
fbdfc46fda1150428e37faef1f31cd5518ab4374 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/fbdfc46fda1150428e37faef1f31cd5518ab4374/generic_graph.py
|
||
def longest_path(self, s = None, t = None, weighted = False, algorithm = "MILP", solver = None, verbose = 0): r""" Returns a longest path of ``self``.
|
fbdfc46fda1150428e37faef1f31cd5518ab4374 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/fbdfc46fda1150428e37faef1f31cd5518ab4374/generic_graph.py
|
||
def longest_path(self, s = None, t = None, weighted = False, algorithm = "MILP", solver = None, verbose = 0): r""" Returns a longest path of ``self``.
|
fbdfc46fda1150428e37faef1f31cd5518ab4374 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/fbdfc46fda1150428e37faef1f31cd5518ab4374/generic_graph.py
|
||
(s != None and (
|
(s is not None and (
|
def longest_path(self, s = None, t = None, weighted = False, algorithm = "MILP", solver = None, verbose = 0): r""" Returns a longest path of ``self``.
|
fbdfc46fda1150428e37faef1f31cd5518ab4374 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/fbdfc46fda1150428e37faef1f31cd5518ab4374/generic_graph.py
|
(t != None and (
|
(t is not None and (
|
def longest_path(self, s = None, t = None, weighted = False, algorithm = "MILP", solver = None, verbose = 0): r""" Returns a longest path of ``self``.
|
fbdfc46fda1150428e37faef1f31cd5518ab4374 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/fbdfc46fda1150428e37faef1f31cd5518ab4374/generic_graph.py
|
(self._directed and s != None and t != None and len(self.shortest_path(s,t) == 0))):
|
(self._directed and (s is not None) and (t is not None) and len(self.shortest_path(s, t) == 0))):
|
def longest_path(self, s = None, t = None, weighted = False, algorithm = "MILP", solver = None, verbose = 0): r""" Returns a longest path of ``self``.
|
fbdfc46fda1150428e37faef1f31cd5518ab4374 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/fbdfc46fda1150428e37faef1f31cd5518ab4374/generic_graph.py
|
else: from sage.graphs.all import Graph return [0, Graph()] if weighted else Graph()
|
from sage.graphs.all import Graph return [0, Graph()] if weighted else Graph()
|
def longest_path(self, s = None, t = None, weighted = False, algorithm = "MILP", solver = None, verbose = 0): r""" Returns a longest path of ``self``.
|
fbdfc46fda1150428e37faef1f31cd5518ab4374 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/fbdfc46fda1150428e37faef1f31cd5518ab4374/generic_graph.py
|
x = fh( self, find_path = True )[1] return self.subgraph(vertices = x, edges = zip(x[:-1], x[1:]))
|
x = fh(self, find_path=True)[1] return self.subgraph(vertices=x, edges=zip(x[:-1], x[1:]))
|
def longest_path(self, s = None, t = None, weighted = False, algorithm = "MILP", solver = None, verbose = 0): r""" Returns a longest path of ``self``.
|
fbdfc46fda1150428e37faef1f31cd5518ab4374 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/fbdfc46fda1150428e37faef1f31cd5518ab4374/generic_graph.py
|
weight = lambda x : x if (x is not None and x != {}) else 1
|
weight = lambda x: x if (x is not None and x != {}) else 1
|
def longest_path(self, s = None, t = None, weighted = False, algorithm = "MILP", solver = None, verbose = 0): r""" Returns a longest path of ``self``.
|
fbdfc46fda1150428e37faef1f31cd5518ab4374 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/fbdfc46fda1150428e37faef1f31cd5518ab4374/generic_graph.py
|
weight = lambda x : 1
|
weight = lambda x: 1
|
def longest_path(self, s = None, t = None, weighted = False, algorithm = "MILP", solver = None, verbose = 0): r""" Returns a longest path of ``self``.
|
fbdfc46fda1150428e37faef1f31cd5518ab4374 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/fbdfc46fda1150428e37faef1f31cd5518ab4374/generic_graph.py
|
def longest_path(self, s = None, t = None, weighted = False, algorithm = "MILP", solver = None, verbose = 0): r""" Returns a longest path of ``self``.
|
fbdfc46fda1150428e37faef1f31cd5518ab4374 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/fbdfc46fda1150428e37faef1f31cd5518ab4374/generic_graph.py
|
||
edge_used = p.new_variable(binary = True)
|
edge_used = p.new_variable(binary=True)
|
def longest_path(self, s = None, t = None, weighted = False, algorithm = "MILP", solver = None, verbose = 0): r""" Returns a longest path of ``self``.
|
fbdfc46fda1150428e37faef1f31cd5518ab4374 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/fbdfc46fda1150428e37faef1f31cd5518ab4374/generic_graph.py
|
vertex_used = p.new_variable(binary = True)
|
vertex_used = p.new_variable(binary=True)
|
def longest_path(self, s = None, t = None, weighted = False, algorithm = "MILP", solver = None, verbose = 0): r""" Returns a longest path of ``self``.
|
fbdfc46fda1150428e37faef1f31cd5518ab4374 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/fbdfc46fda1150428e37faef1f31cd5518ab4374/generic_graph.py
|
def longest_path(self, s = None, t = None, weighted = False, algorithm = "MILP", solver = None, verbose = 0): r""" Returns a longest path of ``self``.
|
fbdfc46fda1150428e37faef1f31cd5518ab4374 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/fbdfc46fda1150428e37faef1f31cd5518ab4374/generic_graph.py
|
||
for u,v in self.edges(labels = False): if self.has_edge(v,u): p.add_constraint(edge_used[(u,v)] + edge_used[(v,u)], max = 1)
|
for u, v in self.edges(labels=False): if self.has_edge(v, u): p.add_constraint(edge_used[(u,v)] + edge_used[(v,u)], max=1)
|
def longest_path(self, s = None, t = None, weighted = False, algorithm = "MILP", solver = None, verbose = 0): r""" Returns a longest path of ``self``.
|
fbdfc46fda1150428e37faef1f31cd5518ab4374 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/fbdfc46fda1150428e37faef1f31cd5518ab4374/generic_graph.py
|
for e in self.incoming_edges(labels = False): p.add_constraint(vertex_used[v] - edge_used[e], min = 0) for e in self.outgoing_edges(labels = False): p.add_constraint(vertex_used[v] - edge_used[e], min = 0)
|
for e in self.incoming_edges(labels=False): p.add_constraint(vertex_used[v] - edge_used[e], min=0) for e in self.outgoing_edges(labels=False): p.add_constraint(vertex_used[v] - edge_used[e], min=0)
|
def longest_path(self, s = None, t = None, weighted = False, algorithm = "MILP", solver = None, verbose = 0): r""" Returns a longest path of ``self``.
|
fbdfc46fda1150428e37faef1f31cd5518ab4374 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/fbdfc46fda1150428e37faef1f31cd5518ab4374/generic_graph.py
|
p.add_constraint(Sum( vertex_used[v] for v in self) - Sum( edge_used[e] for e in self.edges(labels = False)), min = 1, max = 1)
|
p.add_constraint( Sum(vertex_used[v] for v in self) - Sum(edge_used[e] for e in self.edges(labels=False)), min=1, max=1)
|
def longest_path(self, s = None, t = None, weighted = False, algorithm = "MILP", solver = None, verbose = 0): r""" Returns a longest path of ``self``.
|
fbdfc46fda1150428e37faef1f31cd5518ab4374 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/fbdfc46fda1150428e37faef1f31cd5518ab4374/generic_graph.py
|
p.add_constraint( Sum( edge_used[(u,v)] for u in self.neighbors_in(v) ), max = 1) p.add_constraint( Sum( edge_used[(v,u)] for u in self.neighbors_out(v) ), max = 1)
|
p.add_constraint( Sum(edge_used[(u,v)] for u in self.neighbors_in(v)), max=1) p.add_constraint( Sum(edge_used[(v,u)] for u in self.neighbors_out(v)), max=1)
|
def longest_path(self, s = None, t = None, weighted = False, algorithm = "MILP", solver = None, verbose = 0): r""" Returns a longest path of ``self``.
|
fbdfc46fda1150428e37faef1f31cd5518ab4374 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/fbdfc46fda1150428e37faef1f31cd5518ab4374/generic_graph.py
|
for u,v in self.edges(labels = False): p.add_constraint( r_edge_used[(u,v)]
|
for u, v in self.edges(labels=False): p.add_constraint(r_edge_used[(u,v)]
|
def longest_path(self, s = None, t = None, weighted = False, algorithm = "MILP", solver = None, verbose = 0): r""" Returns a longest path of ``self``.
|
fbdfc46fda1150428e37faef1f31cd5518ab4374 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/fbdfc46fda1150428e37faef1f31cd5518ab4374/generic_graph.py
|
min = 0)
|
min=0)
|
def longest_path(self, s = None, t = None, weighted = False, algorithm = "MILP", solver = None, verbose = 0): r""" Returns a longest path of ``self``.
|
fbdfc46fda1150428e37faef1f31cd5518ab4374 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/fbdfc46fda1150428e37faef1f31cd5518ab4374/generic_graph.py
|
p.add_constraint( Sum( r_edge_used[(u,v)] for u in self.neighbors(v)), max = 1-epsilon)
|
p.add_constraint( Sum(r_edge_used[(u,v)] for u in self.neighbors(v)), max=1-epsilon)
|
def longest_path(self, s = None, t = None, weighted = False, algorithm = "MILP", solver = None, verbose = 0): r""" Returns a longest path of ``self``.
|
fbdfc46fda1150428e37faef1f31cd5518ab4374 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/fbdfc46fda1150428e37faef1f31cd5518ab4374/generic_graph.py
|
if s!=None: p.add_constraint( Sum( edge_used[(u,s)] for u in self.neighbors_in(s)), max = 0, min = 0) p.add_constraint( Sum( edge_used[(s,u)] for u in self.neighbors_out(s)), min = 1, max = 1)
|
if s is not None: p.add_constraint( Sum(edge_used[(u,s)] for u in self.neighbors_in(s)), max=0, min=0) p.add_constraint( Sum(edge_used[(s,u)] for u in self.neighbors_out(s)), min=1, max=1)
|
def longest_path(self, s = None, t = None, weighted = False, algorithm = "MILP", solver = None, verbose = 0): r""" Returns a longest path of ``self``.
|
fbdfc46fda1150428e37faef1f31cd5518ab4374 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/fbdfc46fda1150428e37faef1f31cd5518ab4374/generic_graph.py
|
if t!=None: p.add_constraint( Sum( edge_used[(u,t)] for u in self.neighbors_in(t)), min = 1, max = 1) p.add_constraint( Sum( edge_used[(t,u)] for u in self.neighbors_out(t)), max = 0, min = 0)
|
if t is not None: p.add_constraint( Sum(edge_used[(u,t)] for u in self.neighbors_in(t)), min=1, max=1) p.add_constraint( Sum(edge_used[(t,u)] for u in self.neighbors_out(t)), max=0, min=0)
|
def longest_path(self, s = None, t = None, weighted = False, algorithm = "MILP", solver = None, verbose = 0): r""" Returns a longest path of ``self``.
|
fbdfc46fda1150428e37faef1f31cd5518ab4374 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/fbdfc46fda1150428e37faef1f31cd5518ab4374/generic_graph.py
|
p.set_objective( Sum( weight(l) * edge_used[(u,v)] for u,v,l in self.edges() ) )
|
p.set_objective( Sum(weight(l) * edge_used[(u,v)] for u, v, l in self.edges()))
|
def longest_path(self, s = None, t = None, weighted = False, algorithm = "MILP", solver = None, verbose = 0): r""" Returns a longest path of ``self``.
|
fbdfc46fda1150428e37faef1f31cd5518ab4374 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/fbdfc46fda1150428e37faef1f31cd5518ab4374/generic_graph.py
|
def longest_path(self, s = None, t = None, weighted = False, algorithm = "MILP", solver = None, verbose = 0): r""" Returns a longest path of ``self``.
|
fbdfc46fda1150428e37faef1f31cd5518ab4374 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/fbdfc46fda1150428e37faef1f31cd5518ab4374/generic_graph.py
|
||
f_edge_used = lambda u,v : edge_used[ (u,v) if hash(u) < hash(v) else (v,u) ]
|
f_edge_used = lambda u, v: edge_used[ (u,v) if hash(u) < hash(v) else (v,u)]
|
def longest_path(self, s = None, t = None, weighted = False, algorithm = "MILP", solver = None, verbose = 0): r""" Returns a longest path of ``self``.
|
fbdfc46fda1150428e37faef1f31cd5518ab4374 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/fbdfc46fda1150428e37faef1f31cd5518ab4374/generic_graph.py
|
p.add_constraint(vertex_used[v] - f_edge_used(u,v), min = 0)
|
p.add_constraint(vertex_used[v] - f_edge_used(u,v), min=0)
|
def longest_path(self, s = None, t = None, weighted = False, algorithm = "MILP", solver = None, verbose = 0): r""" Returns a longest path of ``self``.
|
fbdfc46fda1150428e37faef1f31cd5518ab4374 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/fbdfc46fda1150428e37faef1f31cd5518ab4374/generic_graph.py
|
p.add_constraint( Sum( vertex_used[v] for v in self) - Sum( f_edge_used(u,v) for u,v in self.edges(labels = False)), min = 1, max = 1)
|
p.add_constraint( Sum(vertex_used[v] for v in self) - Sum(f_edge_used(u,v) for u, v in self.edges(labels=False)), min=1, max=1)
|
def longest_path(self, s = None, t = None, weighted = False, algorithm = "MILP", solver = None, verbose = 0): r""" Returns a longest path of ``self``.
|
fbdfc46fda1150428e37faef1f31cd5518ab4374 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/fbdfc46fda1150428e37faef1f31cd5518ab4374/generic_graph.py
|
p.add_constraint( Sum( f_edge_used(u,v) for u in self.neighbors(v) ), max = 2)
|
p.add_constraint( Sum(f_edge_used(u,v) for u in self.neighbors(v)), max=2)
|
def longest_path(self, s = None, t = None, weighted = False, algorithm = "MILP", solver = None, verbose = 0): r""" Returns a longest path of ``self``.
|
fbdfc46fda1150428e37faef1f31cd5518ab4374 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/fbdfc46fda1150428e37faef1f31cd5518ab4374/generic_graph.py
|
for u,v in self.edges(labels = False): p.add_constraint( r_edge_used[(u,v)]
|
for u, v in self.edges(labels=False): p.add_constraint(r_edge_used[(u,v)]
|
def longest_path(self, s = None, t = None, weighted = False, algorithm = "MILP", solver = None, verbose = 0): r""" Returns a longest path of ``self``.
|
fbdfc46fda1150428e37faef1f31cd5518ab4374 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/fbdfc46fda1150428e37faef1f31cd5518ab4374/generic_graph.py
|
min = 0)
|
min=0)
|
def longest_path(self, s = None, t = None, weighted = False, algorithm = "MILP", solver = None, verbose = 0): r""" Returns a longest path of ``self``.
|
fbdfc46fda1150428e37faef1f31cd5518ab4374 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/fbdfc46fda1150428e37faef1f31cd5518ab4374/generic_graph.py
|
p.add_constraint( Sum( r_edge_used[(u,v)] for u in self.neighbors(v)), max = 1-epsilon)
|
p.add_constraint( Sum(r_edge_used[(u,v)] for u in self.neighbors(v)), max=1-epsilon)
|
def longest_path(self, s = None, t = None, weighted = False, algorithm = "MILP", solver = None, verbose = 0): r""" Returns a longest path of ``self``.
|
fbdfc46fda1150428e37faef1f31cd5518ab4374 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/fbdfc46fda1150428e37faef1f31cd5518ab4374/generic_graph.py
|
if s != None: p.add_constraint( Sum( f_edge_used(s,u) for u in self.neighbors(s) ), max = 1, min = 1) if t != None: p.add_constraint( Sum( f_edge_used(t,u) for u in self.neighbors(t) ), max = 1, min = 1)
|
if s is not None: p.add_constraint( Sum(f_edge_used(s,u) for u in self.neighbors(s)), max=1, min=1) if t is not None: p.add_constraint( Sum(f_edge_used(t,u) for u in self.neighbors(t)), max=1, min=1)
|
def longest_path(self, s = None, t = None, weighted = False, algorithm = "MILP", solver = None, verbose = 0): r""" Returns a longest path of ``self``.
|
fbdfc46fda1150428e37faef1f31cd5518ab4374 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/fbdfc46fda1150428e37faef1f31cd5518ab4374/generic_graph.py
|
p.set_objective( Sum( weight(l) * f_edge_used(u,v) for u,v,l in self.edges() ) )
|
p.set_objective(Sum(weight(l) * f_edge_used(u,v) for u, v, l in self.edges()))
|
def longest_path(self, s = None, t = None, weighted = False, algorithm = "MILP", solver = None, verbose = 0): r""" Returns a longest path of ``self``.
|
fbdfc46fda1150428e37faef1f31cd5518ab4374 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/fbdfc46fda1150428e37faef1f31cd5518ab4374/generic_graph.py
|
p.solve(solver = solver, log = verbose)
|
p.solve(solver=solver, log=verbose)
|
def longest_path(self, s = None, t = None, weighted = False, algorithm = "MILP", solver = None, verbose = 0): r""" Returns a longest path of ``self``.
|
fbdfc46fda1150428e37faef1f31cd5518ab4374 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/fbdfc46fda1150428e37faef1f31cd5518ab4374/generic_graph.py
|
def longest_path(self, s = None, t = None, weighted = False, algorithm = "MILP", solver = None, verbose = 0): r""" Returns a longest path of ``self``.
|
fbdfc46fda1150428e37faef1f31cd5518ab4374 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/fbdfc46fda1150428e37faef1f31cd5518ab4374/generic_graph.py
|
||
g = self.subgraph( vertices = (v for v in self if vertex_used[v] >= .5), edges = ( (u,v,l) for u,v,l in self.edges() if edge_used[(u,v)] >= .5 ))
|
g = self.subgraph( vertices=(v for v in self if vertex_used[v] >= 0.5), edges=((u,v,l) for u, v, l in self.edges() if edge_used[(u,v)] >= 0.5))
|
def longest_path(self, s = None, t = None, weighted = False, algorithm = "MILP", solver = None, verbose = 0): r""" Returns a longest path of ``self``.
|
fbdfc46fda1150428e37faef1f31cd5518ab4374 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/fbdfc46fda1150428e37faef1f31cd5518ab4374/generic_graph.py
|
g = self.subgraph( vertices = (v for v in self if vertex_used[v] >= .5), edges = ( (u,v,l) for u,v,l in self.edges() if f_edge_used(u,v) >= .5 ))
|
g = self.subgraph( vertices=(v for v in self if vertex_used[v] >= 0.5), edges=((u,v,l) for u, v, l in self.edges() if f_edge_used(u,v) >= 0.5))
|
def longest_path(self, s = None, t = None, weighted = False, algorithm = "MILP", solver = None, verbose = 0): r""" Returns a longest path of ``self``.
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fbdfc46fda1150428e37faef1f31cd5518ab4374 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/fbdfc46fda1150428e37faef1f31cd5518ab4374/generic_graph.py
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return sum(map(weight,g.edge_labels())), g
|
return sum(map(weight, g.edge_labels())), g
|
def longest_path(self, s = None, t = None, weighted = False, algorithm = "MILP", solver = None, verbose = 0): r""" Returns a longest path of ``self``.
|
fbdfc46fda1150428e37faef1f31cd5518ab4374 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/fbdfc46fda1150428e37faef1f31cd5518ab4374/generic_graph.py
|
return sage_eval(x, self.gens_dict())
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return self(sage_eval(x, self.gens_dict()))
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def __call__(self, x, check=True): """ Convert ``x`` to an element of this multivariate polynomial ring, possibly non-canonically.
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26de6f39c201638104460eca07a2caffa277ff58 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/26de6f39c201638104460eca07a2caffa277ff58/multi_polynomial_ring.py
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.. warning:: This function calls a Singular function that appears to be very buggy and should not be trusted.
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def riemann_roch_basis(self, D): r""" Return a basis for the Riemann-Roch space corresponding to `D`.
|
45f8022bf1ce8a03a200902d10a41e0e02d6cbbd /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/45f8022bf1ce8a03a200902d10a41e0e02d6cbbd/projective_curve.py
|
|
- ``sort`` - bool (default: True), if True return the point list sorted. If False, returns the points in the order computed by Singular.
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- ``D`` - a divisor OUTPUT: A list of function field elements that form a basis of the Riemann-Roch space
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def riemann_roch_basis(self, D): r""" Return a basis for the Riemann-Roch space corresponding to `D`.
|
45f8022bf1ce8a03a200902d10a41e0e02d6cbbd /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/45f8022bf1ce8a03a200902d10a41e0e02d6cbbd/projective_curve.py
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sage: D = C.divisor([ (4, pts[0]), (0,pts[1]), (4, pts[2]) ])
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sage: D = C.divisor([ (4, pts[0]), (4, pts[2]) ])
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def riemann_roch_basis(self, D): r""" Return a basis for the Riemann-Roch space corresponding to `D`.
|
45f8022bf1ce8a03a200902d10a41e0e02d6cbbd /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/45f8022bf1ce8a03a200902d10a41e0e02d6cbbd/projective_curve.py
|
The following example illustrates that the Riemann-Roch space function in Singular doesn't *not* work correctly.
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def riemann_roch_basis(self, D): r""" Return a basis for the Riemann-Roch space corresponding to `D`.
|
45f8022bf1ce8a03a200902d10a41e0e02d6cbbd /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/45f8022bf1ce8a03a200902d10a41e0e02d6cbbd/projective_curve.py
|
|
sage: C.riemann_roch_basis(D) [x/(y + x), (z + y)/(y + x)] The answer has dimension 2 (confirmed via Magma). But it varies between 1 and quite large with Singular.
|
sage: C.riemann_roch_basis(D) [(-2*x + y)/(x + y), (-x + z)/(x + y)] .. NOTE:: Currently this only works over prime field and divisors supported on rational points.
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def riemann_roch_basis(self, D): r""" Return a basis for the Riemann-Roch space corresponding to `D`.
|
45f8022bf1ce8a03a200902d10a41e0e02d6cbbd /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/45f8022bf1ce8a03a200902d10a41e0e02d6cbbd/projective_curve.py
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def riemann_roch_basis(self, D): r""" Return a basis for the Riemann-Roch space corresponding to `D`.
|
45f8022bf1ce8a03a200902d10a41e0e02d6cbbd /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/45f8022bf1ce8a03a200902d10a41e0e02d6cbbd/projective_curve.py
|
||
X3 = singular.extcurve(1, X2) R = X3[1][5]
|
v = X2[3].sage_flattened_str_list() v = [ v[i].partition(',') for i in range(len(v)) ] pnts = [ ( int(v[i][0]), int(v[i][2])-1 ) for i in range(len(v))] R = X2[5][1][1]
|
def riemann_roch_basis(self, D): r""" Return a basis for the Riemann-Roch space corresponding to `D`.
|
45f8022bf1ce8a03a200902d10a41e0e02d6cbbd /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/45f8022bf1ce8a03a200902d10a41e0e02d6cbbd/projective_curve.py
|
def riemann_roch_basis(self, D): r""" Return a basis for the Riemann-Roch space corresponding to `D`.
|
45f8022bf1ce8a03a200902d10a41e0e02d6cbbd /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/45f8022bf1ce8a03a200902d10a41e0e02d6cbbd/projective_curve.py
|
||
pnts = [self(int(v[3*i]), int(v[3*i+1]), int(v[3*i+2])) for i in range(len(v)/3)]
|
coords = [self(int(v[3*i]), int(v[3*i+1]), int(v[3*i+2])) for i in range(len(v)/3)]
|
def riemann_roch_basis(self, D): r""" Return a basis for the Riemann-Roch space corresponding to `D`.
|
45f8022bf1ce8a03a200902d10a41e0e02d6cbbd /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/45f8022bf1ce8a03a200902d10a41e0e02d6cbbd/projective_curve.py
|
Dcoeffs.append(D.coefficient(x))
|
if x[0] == 1: Dcoeffs.append(D.coefficient(coords[x[1]])) else: Dcoeffs.append(0)
|
def riemann_roch_basis(self, D): r""" Return a basis for the Riemann-Roch space corresponding to `D`.
|
45f8022bf1ce8a03a200902d10a41e0e02d6cbbd /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/45f8022bf1ce8a03a200902d10a41e0e02d6cbbd/projective_curve.py
|
def is_prime(n, flag=0):
|
def is_prime(n):
|
def is_prime(n, flag=0): r""" Returns True if `x` is prime, and False otherwise. The result is proven correct - *this is NOT a pseudo-primality test!*. INPUT: - ``flag`` - int - ``0`` (default) - use a combination of algorithms. - ``1`` - certify primality using the Pocklington-Lehmer Test. - ``2`` - certify primality using the APRCL test. OUTPUT: - ``bool`` - True or False .. note:: We do not consider negatives of prime numbers as prime. EXAMPLES:: sage: is_prime(389) True sage: is_prime(2000) False sage: is_prime(2) True sage: is_prime(-1) False sage: factor(-6) -1 * 2 * 3 sage: is_prime(1) False sage: is_prime(-2) False IMPLEMENTATION: Calls the PARI isprime function. """ n = ZZ(n) return pari(n).isprime()
|
bd4a8cfafce1ad06ab866905b52f8bdaee588220 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/bd4a8cfafce1ad06ab866905b52f8bdaee588220/arith.py
|
Returns True if `x` is prime, and False otherwise. The result is proven correct - *this is NOT a pseudo-primality test!*. INPUT: - ``flag`` - int - ``0`` (default) - use a combination of algorithms. - ``1`` - certify primality using the Pocklington-Lehmer Test. - ``2`` - certify primality using the APRCL test.
|
Returns ``True`` if `n` is prime, and ``False`` otherwise. AUTHORS: - Kevin Stueve [email protected] (2010-01-17): delegated calculation to ``n.is_prime()`` INPUT: - ``n`` - the object for which to determine primality
|
def is_prime(n, flag=0): r""" Returns True if `x` is prime, and False otherwise. The result is proven correct - *this is NOT a pseudo-primality test!*. INPUT: - ``flag`` - int - ``0`` (default) - use a combination of algorithms. - ``1`` - certify primality using the Pocklington-Lehmer Test. - ``2`` - certify primality using the APRCL test. OUTPUT: - ``bool`` - True or False .. note:: We do not consider negatives of prime numbers as prime. EXAMPLES:: sage: is_prime(389) True sage: is_prime(2000) False sage: is_prime(2) True sage: is_prime(-1) False sage: factor(-6) -1 * 2 * 3 sage: is_prime(1) False sage: is_prime(-2) False IMPLEMENTATION: Calls the PARI isprime function. """ n = ZZ(n) return pari(n).isprime()
|
bd4a8cfafce1ad06ab866905b52f8bdaee588220 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/bd4a8cfafce1ad06ab866905b52f8bdaee588220/arith.py
|
- ``bool`` - True or False .. note:: We do not consider negatives of prime numbers as prime.
|
- ``bool`` - ``True`` or ``False``
|
def is_prime(n, flag=0): r""" Returns True if `x` is prime, and False otherwise. The result is proven correct - *this is NOT a pseudo-primality test!*. INPUT: - ``flag`` - int - ``0`` (default) - use a combination of algorithms. - ``1`` - certify primality using the Pocklington-Lehmer Test. - ``2`` - certify primality using the APRCL test. OUTPUT: - ``bool`` - True or False .. note:: We do not consider negatives of prime numbers as prime. EXAMPLES:: sage: is_prime(389) True sage: is_prime(2000) False sage: is_prime(2) True sage: is_prime(-1) False sage: factor(-6) -1 * 2 * 3 sage: is_prime(1) False sage: is_prime(-2) False IMPLEMENTATION: Calls the PARI isprime function. """ n = ZZ(n) return pari(n).isprime()
|
bd4a8cfafce1ad06ab866905b52f8bdaee588220 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/bd4a8cfafce1ad06ab866905b52f8bdaee588220/arith.py
|
IMPLEMENTATION: Calls the PARI isprime function. """ n = ZZ(n) return pari(n).isprime()
|
ALGORITHM:: Calculation is delegated to the ``n.is_prime()`` method, or in special cases (e.g., Python ``int``s) to ``Integer(n).is_prime()``. If an ``n.is_prime()`` method is not available, it otherwise raises a ``TypeError``. """ if type(n) == int or type(n)==long: from sage.rings.integer import Integer return Integer(n).is_prime() else: try: return n.is_prime() except AttributeError: raise TypeError, "is_prime() is not written for this type"
|
def is_prime(n, flag=0): r""" Returns True if `x` is prime, and False otherwise. The result is proven correct - *this is NOT a pseudo-primality test!*. INPUT: - ``flag`` - int - ``0`` (default) - use a combination of algorithms. - ``1`` - certify primality using the Pocklington-Lehmer Test. - ``2`` - certify primality using the APRCL test. OUTPUT: - ``bool`` - True or False .. note:: We do not consider negatives of prime numbers as prime. EXAMPLES:: sage: is_prime(389) True sage: is_prime(2000) False sage: is_prime(2) True sage: is_prime(-1) False sage: factor(-6) -1 * 2 * 3 sage: is_prime(1) False sage: is_prime(-2) False IMPLEMENTATION: Calls the PARI isprime function. """ n = ZZ(n) return pari(n).isprime()
|
bd4a8cfafce1ad06ab866905b52f8bdaee588220 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/bd4a8cfafce1ad06ab866905b52f8bdaee588220/arith.py
|
command = 'magma'
|
command = 'sage-native-execute magma'
|
def __init__(self, maxread=10000, script_subdirectory=None, logfile=None, server=None, server_tmpdir=None, user_config=False): """ INPUT:
|
39520572ba573c42e357468c1a8474ad6e44f0a0 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/39520572ba573c42e357468c1a8474ad6e44f0a0/magma.py
|
console('magma')
|
console('sage-native-execute magma')
|
def magma_console(): """ Run a command line Magma session. EXAMPLES:: sage: magma_console() # not tested Magma V2.14-9 Sat Oct 11 2008 06:36:41 on one [Seed = 1157408761] Type ? for help. Type <Ctrl>-D to quit. > Total time: 2.820 seconds, Total memory usage: 3.95MB """ console('magma')
|
39520572ba573c42e357468c1a8474ad6e44f0a0 /local1/tlutelli/issta_data/temp/all_python//python/2010_temp/2010/9417/39520572ba573c42e357468c1a8474ad6e44f0a0/magma.py
|
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