def conjugacy_classes(self):
r"""
Return a list with all the conjugacy classes of ``self``.
EXAMPLES::
sage: G = SL(2, GF(2))
sage: G.conjugacy_classes()
(Conjugacy class of [1 0]
[0 1] in Special Linear Group of degree 2 over Finite Field of size 2,
Conjugacy class of [0 1]
[1 0] in Special Linear Group of degree 2 over Finite Field of size 2,
Conjugacy class of [0 1]
[1 1] in Special Linear Group of degree 2 over Finite Field of size 2)
::
sage: GL(2,ZZ).conjugacy_classes()
Traceback (most recent call last):
...
NotImplementedError: only implemented for finite groups
"""
if not self.is_finite():
raise NotImplementedError("only implemented for finite groups")
from sage.groups.conjugacy_classes import ConjugacyClassGAP
return tuple(
ConjugacyClassGAP(self, self(g))
for g in self.conjugacy_classes_representatives())
def __init__(self, group, part):
"""
Initialize ``self``.
EXAMPLES::
sage: G = SymmetricGroup(5)
sage: g = G([(1,2), (3,4,5)])
sage: C = G.conjugacy_class(g)
sage: TestSuite(C).run()
sage: C = G.conjugacy_class(Partition([3,2]))
sage: TestSuite(C).run()
"""
if isinstance(part, PermutationGroupElement) and part.parent() is group:
elt = part
part = sorted([len(x) for x in part.cycle_tuples(True)], reverse=True)
else:
elt = default_representative(part, group)
SymmetricGroupConjugacyClassMixin.__init__(self, group.domain(), part)
ConjugacyClassGAP.__init__(self, group, elt)
def conjugacy_class(self):
r"""
Return the conjugacy class of ``self``.
EXAMPLES::
sage: G = SL(2, GF(2))
sage: g = G.gens()[0]
sage: g.conjugacy_class()
Conjugacy class of [1 1]
[0 1] in Special Linear Group of degree 2 over Finite Field of size 2
"""
from sage.groups.conjugacy_classes import ConjugacyClassGAP
return ConjugacyClassGAP(self.parent(), self)
def __init__(self, group, part):
"""
Initialize ``self``.
EXAMPLES::
sage: G = SymmetricGroup(5)
sage: g = G([(1,2), (3,4,5)])
sage: C = G.conjugacy_class(g)
sage: TestSuite(C).run()
sage: C = G.conjugacy_class(Partition([3,2]))
sage: TestSuite(C).run()
"""
P = Partitions_n( len(group.domain()) )
if isinstance(part, PermutationGroupElement) and part.parent() is group:
elt = part
part = P( sorted(map(len, part.cycle_tuples(True)), reverse=True) )
else:
part = P(part)
elt = default_representative(part, group)
self._part = part
self._set = None
ConjugacyClassGAP.__init__(self, group, elt)
def conjugacy_classes(self):
r"""
Return a list with all the conjugacy classes of ``self``.
EXAMPLES::
sage: G = SL(2, GF(2))
sage: G.conjugacy_classes()
(Conjugacy class of [1 0]
[0 1] in Special Linear Group of degree 2 over Finite Field of size 2,
Conjugacy class of [0 1]
[1 0] in Special Linear Group of degree 2 over Finite Field of size 2,
Conjugacy class of [0 1]
[1 1] in Special Linear Group of degree 2 over Finite Field of size 2)
"""
from sage.groups.conjugacy_classes import ConjugacyClassGAP
return tuple(
ConjugacyClassGAP(self, self(g))
for g in self.conjugacy_class_representatives())
def conjugacy_class(self, g):
r"""
Return the conjugacy class of ``g``.
OUTPUT:
The conjugacy class of ``g`` in the group ``self``. If ``self`` is the
group denoted by `G`, this method computes the set
`\{x^{-1}gx\ \vert\ x\in G\}`.
EXAMPLES::
sage: G = SL(2, QQ)
sage: g = G([[1,1],[0,1]])
sage: G.conjugacy_class(g)
Conjugacy class of [1 1]
[0 1] in Special Linear Group of degree 2 over Rational Field
"""
from sage.groups.conjugacy_classes import ConjugacyClassGAP
return ConjugacyClassGAP(self, self(g))
def conjugacy_classes(self):
r"""
Return a list with all the conjugacy classes of ``self``.
EXAMPLES::
sage: G = SL(2, GF(2))
sage: G.conjugacy_classes()
[Conjugacy class of [1 0]
[0 1] in Special Linear Group of degree 2 over Finite Field of size 2, Conjugacy class of [0 1]
[1 0] in Special Linear Group of degree 2 over Finite Field of size 2, Conjugacy class of [0 1]
[1 1] in Special Linear Group of degree 2 over Finite Field of size 2]
"""
CC = self._gap_().ConjugacyClasses()
reps = list(gap.List(CC, 'x -> Representative(x)'))
return [
ConjugacyClassGAP(self,
self(g._matrix_(self.field_of_definition())))
for g in reps
]
def conjugacy_class(self, g):
r"""
Return the conjugacy class of ``g`` inside of ``self``.
INPUT:
- ``g`` -- an element of ``self``
OUTPUT:
The conjugacy class of ``g`` in the group ``self``. If ``self`` is the
group denoted by `G`, this method computes the set
`\{x^{-1}gx\ \vert\ x\in G\}`.
EXAMPLES::
sage: G = SL(3, GF(3))
sage: g = G.gens()[0]
sage: G.conjugacy_class(g)
Conjugacy class of [1 1 0]
[0 1 0]
[0 0 1] in Special Linear Group of degree 3 over Finite Field of size 3
"""
return ConjugacyClassGAP(self, g)
