def __init__(self, P, part):
"""
Initialize ``self``.
EXAMPLES::
sage: G = Permutations(5)
sage: g = G([2, 1, 4, 5, 3])
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, Permutation) and part.parent() is P:
elt = part
part = elt.cycle_type()
else:
elt = P.element_in_conjugacy_classes(part)
SymmetricGroupConjugacyClassMixin.__init__(self, range(1, P.n+1), part)
ConjugacyClass.__init__(self, P, elt)
def conjugacy_class(self, g):
r"""
Return the conjugacy class of the element ``g``.
This is a fall-back method for groups not defined over GAP.
EXAMPLES::
sage: A = AbelianGroup([2,2])
sage: c = A.conjugacy_class(A.an_element())
sage: type(c)
<class 'sage.groups.conjugacy_classes.ConjugacyClass_with_category'>
"""
from sage.groups.conjugacy_classes import ConjugacyClass
return ConjugacyClass(self, g)
def conjugacy_class(self):
r"""
Return the conjugacy class 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(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 ConjugacyClass
return ConjugacyClass(self.parent(), self)