def automorphism_group(self):
"""
EXAMPLES::
sage: p = PermutationGroupElement((2,3))
sage: S = species.SetSpecies()
sage: F = S * S
sage: a = F.structures([1,2,3,4]).random_element(); a
{1}*{2, 3, 4}
sage: a.automorphism_group()
Permutation Group with generators [(2,3), (2,3,4)]
::
sage: [a.transport(g) for g in a.automorphism_group()]
[{1}*{2, 3, 4},
{1}*{2, 3, 4},
{1}*{2, 3, 4},
{1}*{2, 3, 4},
{1}*{2, 3, 4},
{1}*{2, 3, 4}]
::
sage: a = F.structures([1,2,3,4]).random_element(); a
{2, 3}*{1, 4}
sage: [a.transport(g) for g in a.automorphism_group()]
[{2, 3}*{1, 4}, {2, 3}*{1, 4}, {2, 3}*{1, 4}, {2, 3}*{1, 4}]
"""
from sage.groups.all import PermutationGroupElement, PermutationGroup, SymmetricGroup
from sage.misc.misc import uniq
from sage.combinat.species.misc import change_support
left, right = self._list
n = len(self._labels)
#Get the supports for each of the sides
l_support = self._subset._list
r_support = self._subset.complement()._list
#Get the automorphism group for the left object and
#make it have the correct support. Do the same to the
#right side.
l_aut = change_support(left.automorphism_group(), l_support)
r_aut = change_support(right.automorphism_group(), r_support)
identity = PermutationGroupElement([])
gens = l_aut.gens() + r_aut.gens()
gens = [g for g in gens if g != identity]
gens = uniq(gens) if len(gens) > 0 else [[]]
return PermutationGroup(gens)
def automorphism_group(self):
"""
EXAMPLES::
sage: p = PermutationGroupElement((2,3))
sage: S = species.SetSpecies()
sage: F = S * S
sage: a = F.structures([1,2,3,4]).random_element(); a
{1}*{2, 3, 4}
sage: a.automorphism_group()
Permutation Group with generators [(2,3), (2,3,4)]
::
sage: [a.transport(g) for g in a.automorphism_group()]
[{1}*{2, 3, 4},
{1}*{2, 3, 4},
{1}*{2, 3, 4},
{1}*{2, 3, 4},
{1}*{2, 3, 4},
{1}*{2, 3, 4}]
::
sage: a = F.structures([1,2,3,4]).random_element(); a
{2, 3}*{1, 4}
sage: [a.transport(g) for g in a.automorphism_group()]
[{2, 3}*{1, 4}, {2, 3}*{1, 4}, {2, 3}*{1, 4}, {2, 3}*{1, 4}]
"""
from sage.groups.all import PermutationGroupElement, PermutationGroup, SymmetricGroup
from sage.misc.misc import uniq
from sage.combinat.species.misc import change_support
left, right = self._list
n = len(self._labels)
#Get the supports for each of the sides
l_support = self._subset._list
r_support = self._subset.complement()._list
#Get the automorphism group for the left object and
#make it have the correct support. Do the same to the
#right side.
l_aut = change_support(left.automorphism_group(), l_support)
r_aut = change_support(right.automorphism_group(), r_support)
identity = PermutationGroupElement([])
gens = l_aut.gens() + r_aut.gens()
gens = [g for g in gens if g != identity]
gens = uniq(gens) if len(gens) > 0 else [[]]
return PermutationGroup(gens)