ASKSAGE: Sage Q&A Forum - RSS feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Mon, 13 Feb 2023 16:20:54 +0100simultaneous conjugacy in Snhttps://ask.sagemath.org/question/66368/simultaneous-conjugacy-in-sn/ Is there a built-in function in sage to determine whether two pairs (a,b) and (c,d) of elements of S_n (symmetric group of n letters) are simultaneously conjugate, i.e. checking whether there exists x such that
xa=cx and xb=dx ?matrixmanMon, 13 Feb 2023 16:20:54 +0100https://ask.sagemath.org/question/66368/Determining if two subgroups of a symmetric group are conjugatehttps://ask.sagemath.org/question/44357/determining-if-two-subgroups-of-a-symmetric-group-are-conjugate/If I have two particular subgroups of a symmetric group, is there any built-in way in Sage to determine if the groups are conjugate to one another? I tried creating a `ConjugacyClass` for each and then comparing them, but this gives an error:
S = SymmetricGroup(3)
gen1 = Permutation('(1,2,3)')
gen2 = Permutation('(1,3,2)')
gen3 = Permutation('(1,2)')
gen4 = Permutation('(1,3)')
G1 = PermutationGroup([gen1, gen3])
G2 = PermutationGroup([gen2, gen4])
ConjugacyClass(S, G1) == ConjugacyClass(S, G2)
When executing the very last line I get the error
TypeError: For implementing multiplication, provide the method '_mul_' for (1,2) resp. Permutation Group with generators [(1,2), (1,2,3)]
cjohnsonTue, 20 Nov 2018 20:06:56 +0100https://ask.sagemath.org/question/44357/