def automorphism_group(self):
"""
Returns the group of permutations whose action on this structure
leave it fixed.
EXAMPLES::
sage: p = PermutationGroupElement((2,3,4))
sage: P = species.PermutationSpecies()
sage: a = P.structures(["a", "b", "c", "d"]).random_element(); a
['a', 'c', 'b', 'd']
sage: a.automorphism_group()
Permutation Group with generators [(2,3), (1,4)]
::
sage: [a.transport(perm) for perm in a.automorphism_group()]
[['a', 'c', 'b', 'd'],
['a', 'c', 'b', 'd'],
['a', 'c', 'b', 'd'],
['a', 'c', 'b', 'd']]
"""
from sage.groups.all import SymmetricGroup, PermutationGroup
S = SymmetricGroup(len(self._labels))
p = self.permutation_group_element()
return PermutationGroup(S.centralizer(p).gens())
def automorphism_group(self):
"""
Returns the group of permutations whose action on this structure
leave it fixed.
EXAMPLES::
sage: p = PermutationGroupElement((2,3,4))
sage: P = species.PermutationSpecies()
sage: a = P.structures(["a", "b", "c", "d"]).random_element(); a
['a', 'c', 'b', 'd']
sage: a.automorphism_group()
Permutation Group with generators [(2,3), (1,4)]
::
sage: [a.transport(perm) for perm in a.automorphism_group()]
[['a', 'c', 'b', 'd'],
['a', 'c', 'b', 'd'],
['a', 'c', 'b', 'd'],
['a', 'c', 'b', 'd']]
"""
from sage.groups.all import SymmetricGroup, PermutationGroup
S = SymmetricGroup(len(self._labels))
p = self.permutation_group_element()
return PermutationGroup(S.centralizer(p).gens())
def automorphism_group(self):
"""
Returns the group of permutations whose action on this structure
leave it fixed.
EXAMPLES::
sage: P = species.CycleSpecies()
sage: a = P.structures([1, 2, 3, 4]).random_element(); a
(1, 2, 3, 4)
sage: a.automorphism_group()
Permutation Group with generators [(1,2,3,4)]
::
sage: [a.transport(perm) for perm in a.automorphism_group()]
[(1, 2, 3, 4), (1, 2, 3, 4), (1, 2, 3, 4), (1, 2, 3, 4)]
"""
from sage.groups.all import SymmetricGroup, PermutationGroup
S = SymmetricGroup(len(self._labels))
p = self.permutation_group_element()
return PermutationGroup(S.centralizer(p).gens())
def automorphism_group(self):
"""
Returns the group of permutations whose action on this structure
leave it fixed.
EXAMPLES::
sage: P = species.CycleSpecies()
sage: a = P.structures([1, 2, 3, 4]).random_element(); a
(1, 2, 3, 4)
sage: a.automorphism_group()
Permutation Group with generators [(1,2,3,4)]
::
sage: [a.transport(perm) for perm in a.automorphism_group()]
[(1, 2, 3, 4), (1, 2, 3, 4), (1, 2, 3, 4), (1, 2, 3, 4)]
"""
from sage.groups.all import SymmetricGroup, PermutationGroup
S = SymmetricGroup(len(self._labels))
p = self.permutation_group_element()
return PermutationGroup(S.centralizer(p).gens())
