ASKSAGE: Sage Q&A Forum - Individual question feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Mon, 08 Feb 2016 13:41:08 -0600Need to shift a permutation (1,2,3)(4,5)->(6,7,8)(9,10)https://ask.sagemath.org/question/32499/need-to-shift-a-permutation-12345-678910/So I've been trying to shift a permutation group upwards to be able to make a cartesian product of two arbitrary permutation groups into a permutation group. My idea was to simply shift one permutation group up enough so that it commutes with the other. However I am stuck trying to figure out how to shift it up, i.e. add 5 to each number in the permutation. Anyone have any ideas?
ThanksMon, 08 Feb 2016 10:25:37 -0600https://ask.sagemath.org/question/32499/need-to-shift-a-permutation-12345-678910/Answer by vdelecroix for <p>So I've been trying to shift a permutation group upwards to be able to make a cartesian product of two arbitrary permutation groups into a permutation group. My idea was to simply shift one permutation group up enough so that it commutes with the other. However I am stuck trying to figure out how to shift it up, i.e. add 5 to each number in the permutation. Anyone have any ideas?</p>
<p>Thanks</p>
https://ask.sagemath.org/question/32499/need-to-shift-a-permutation-12345-678910/?answer=32500#post-id-32500You can simply use conjugation
sage: S5 = SymmetricGroup(5)
sage: S10 = SymmetricGroup(10)
sage: t = S10("(1,6)(2,7)(3,8)(4,9)(5,10)")
sage: s = S5("(1,2,3)(4,5)")
sage: t*s*~t
(6,7,8)(9,10)
Or be more direct with
sage: f = lambda s: S10(range(1,6) + [s(i)+5 for i in range(1,6)])
sage: f(s)
(6,7,8)(9,10)
Mon, 08 Feb 2016 13:41:08 -0600https://ask.sagemath.org/question/32499/need-to-shift-a-permutation-12345-678910/?answer=32500#post-id-32500