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 ?
Using GAP interface and the idea from here:
G=SymmetricGroup(3); a=G((1,2)); c=G((2,3))
b, d = c, a # just as an example
C = (G(x) for x in gap.AsList( gap.RightCoset(gap.Centralizer(G,c), gap.RepresentativeAction(G,c,a)) ))
try:
x = next(x for x in C if x*b==d*x)
print('x=',x)
except StopIteration:
print('No x exists!')
Asked: 2023-02-13 16:20:54 +0200
Seen: 64 times
Last updated: Feb 13 '23
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