def __call__(self, x, orientation=False):
"""
Input is a simplex of the domain. Output is the image simplex.
If optional argument ``orientation`` is True, return a pair
``(image simplex, oriented)`` where ``oriented`` is 1 or `-1`
depending on whether the map preserves or reverses the
orientation of the image simplex.
EXAMPLES::
sage: S = simplicial_complexes.Sphere(2)
sage: T = simplicial_complexes.Sphere(3)
sage: S
Simplicial complex with vertex set (0, 1, 2, 3) and facets {(0, 2, 3), (0, 1, 2), (1, 2, 3), (0, 1, 3)}
sage: T
Simplicial complex with vertex set (0, 1, 2, 3, 4) and 5 facets
sage: f = {0:0,1:1,2:2,3:3}
sage: H = Hom(S,T)
sage: x = H(f)
sage: from sage.homology.simplicial_complex import Simplex
sage: x(Simplex([0,2,3]))
(0, 2, 3)
An orientation-reversing example::
sage: X = SimplicialComplex(1, [[0,1]])
sage: g = Hom(X,X)({0:1, 1:0})
sage: g(Simplex([0,1]))
(0, 1)
sage: g(Simplex([0,1]), orientation=True)
((0, 1), -1)
"""
dim = self._domain.dimension()
if not isinstance(x, simplicial_complex.Simplex) or x.dimension(
) > dim or not x in self._domain.faces()[x.dimension()]:
raise ValueError, "x must be a simplex of the source of f"
tup = x.tuple()
fx = []
for j in tup:
fx.append(self._vertex_dictionary[j])
if orientation:
if len(set(fx)) == len(tup):
oriented = Permutation(convert_perm(fx)).signature()
else:
oriented = 1
return (simplicial_complex.Simplex(set(fx)), oriented)
else:
return simplicial_complex.Simplex(set(fx))
def __call__(self, x, orientation=False):
"""
Input is a simplex of the domain. Output is the image simplex.
If the optional argument ``orientation`` is ``True``, then this
returns a pair ``(image simplex, oriented)`` where ``oriented``
is 1 or `-1` depending on whether the map preserves or reverses
the orientation of the image simplex.
EXAMPLES::
sage: S = simplicial_complexes.Sphere(2)
sage: T = simplicial_complexes.Sphere(3)
sage: S
Minimal triangulation of the 2-sphere
sage: T
Minimal triangulation of the 3-sphere
sage: f = {0:0,1:1,2:2,3:3}
sage: H = Hom(S,T)
sage: x = H(f)
sage: from sage.topology.simplicial_complex import Simplex
sage: x(Simplex([0,2,3]))
(0, 2, 3)
An orientation-reversing example::
sage: X = SimplicialComplex([[0,1]], is_mutable=False)
sage: g = Hom(X,X)({0:1, 1:0})
sage: g(Simplex([0,1]))
(0, 1)
sage: g(Simplex([0,1]), orientation=True)
((0, 1), -1)
"""
dim = self.domain().dimension()
if not isinstance(x, Simplex) or x.dimension(
) > dim or x not in self.domain().faces()[x.dimension()]:
raise ValueError("x must be a simplex of the source of f")
tup = x.tuple()
fx = []
for j in tup:
fx.append(self._vertex_dictionary[j])
if orientation:
if len(set(fx)) == len(tup):
oriented = Permutation(convert_perm(fx)).signature()
else:
oriented = 1
return (Simplex(set(fx)), oriented)
else:
return Simplex(set(fx))
def __call__(self,x,orientation=False):
"""
Input is a simplex of the domain. Output is the image simplex.
If the optional argument ``orientation`` is ``True``, then this
returns a pair ``(image simplex, oriented)`` where ``oriented``
is 1 or `-1` depending on whether the map preserves or reverses
the orientation of the image simplex.
EXAMPLES::
sage: S = simplicial_complexes.Sphere(2)
sage: T = simplicial_complexes.Sphere(3)
sage: S
Simplicial complex with vertex set (0, 1, 2, 3) and facets {(0, 2, 3), (0, 1, 2), (1, 2, 3), (0, 1, 3)}
sage: T
Simplicial complex with vertex set (0, 1, 2, 3, 4) and 5 facets
sage: f = {0:0,1:1,2:2,3:3}
sage: H = Hom(S,T)
sage: x = H(f)
sage: from sage.homology.simplicial_complex import Simplex
sage: x(Simplex([0,2,3]))
(0, 2, 3)
An orientation-reversing example::
sage: X = SimplicialComplex([[0,1]], is_mutable=False)
sage: g = Hom(X,X)({0:1, 1:0})
sage: g(Simplex([0,1]))
(0, 1)
sage: g(Simplex([0,1]), orientation=True)
((0, 1), -1)
"""
dim = self._domain.dimension()
if not isinstance(x,simplicial_complex.Simplex) or x.dimension() > dim or not x in self._domain.faces()[x.dimension()]:
raise ValueError, "x must be a simplex of the source of f"
tup=x.tuple()
fx=[]
for j in tup:
fx.append(self._vertex_dictionary[j])
if orientation:
if len(set(fx)) == len(tup):
oriented = Permutation(convert_perm(fx)).signature()
else:
oriented = 1
return (simplicial_complex.Simplex(set(fx)), oriented)
else:
return simplicial_complex.Simplex(set(fx))
