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Is there a way to relabel the domain of a permutation group?

asked 2017-02-12 19:12:31 -0600

jaebond gravatar image

Suppose I have a permutation group on the domain {1,2,3,4,5}, but instead I wanted this permutation group to be on the domain {a,b,c,d,e}. Is there a way to achieve this? Hopefully something like the relabel method for graphs...

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answered 2018-01-06 09:19:36 -0600

tmonteil gravatar image

updated 2018-01-06 09:20:52 -0600

I could not find such a method, b ut you can use the generators of your permutations group as follows:

sage: G = PermutationGroup([[(1,2,3),(4,5)],[(3,4)]])
sage: G
Permutation Group with generators [(3,4), (1,2,3)(4,5)]

sage: d = {1:'a',2:'b',3:'c',4:'d',5:'e'}

sage: H = PermutationGroup([[d[i] for i in g.tuple()] for g in G.gens()], domain=d.values())
sage: H
Permutation Group with generators [('c','d'), ('a','b','c')('d','e')]
sage: H.domain()
{'a', 'b', 'c', 'd', 'e'}
sage: H.random_element()
('a','d','b','c')
sage: H.random_element()
('a','c')('b','d','e')
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Asked: 2017-02-12 19:12:31 -0600

Seen: 120 times

Last updated: Jan 06