There is function is_isomorphic in Sage, but there is not is_conjugate.
For curiosity I looked source, and it seems to be an oneliner to write
one:
def are_conjugates(self, g1, g2):
"""
Returns ``True`` if ``g1`` and ``g2`` are conjugates under the
action of ``self``.
EXAMPLES::
sage: G = SymmetricGroup(4)
sage: G1 = PermutationGroup(['(1,2)(3,4)', '(1,3)(2,4)'])
sage: G2 = PermutationGroup(['(1,2)', '(3,4)'])
sage: G3 = PermutationGroup(['(1,3)', '(2,4)'])
sage: G1.is_isomorphic(G2)
True
sage: G.are_conjugates(G1, G2)
False
sage: G.are_conjugates(G2, G3)
True
"""
# Add check for types here
return gap.IsConjugate(self, g1, g2).bool()
However, I have never before modified the source code of Sage itself. At least
two question came in mind:
- What is naming policy? Should this be is_conjugate? What is best order for
arguments?
- Should there be a function that only looks to cycle structure? I mean
something like
sage: G1 = PermutationGroup(['(1,2)'])
sage: G2 = PermutationGroup(['(2,3)'])
sage: G1.is_conjugate(G2)
True
? I.e. in this example assuming group S_3 as acting group.
and a third one is, of course:
- Is this stupid idea at beginning, and if not, is this oneliner going to blow
up when trying with real examples?
--
Jori Mäntysalo
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