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Specifying cardinality for action of permutation group

asked 2011-06-21 19:09:49 -0500

Cody gravatar image

updated 2011-06-22 08:29:54 -0500

In Magma, it is possible to create a permutation group with something like G := PermutationGroup<n|relations>, where $n$ is to be the cardinality of the set the group acts on. One needs this cardinality to use a GModule method. I would like to create such a group in Sage and then port it to Magma to create a GModule, but I always end up with a Magma element having too small a cardinality. Is it possible to specify such a cardinality in Sage? Can it be created as a subgroup of $S_n$? I did not have luck with that.

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answered 2011-06-22 07:19:51 -0500

Mike Hansen gravatar image

updated 2011-06-22 07:54:22 -0500

niles gravatar image

In ticket 10335, there is a patch which will allow one to specify the domain of the permutation group (and hence its cardinality). For example, you'll be able to do something like

sage: P = PermutationGroup([[(1,2)], [(1,3),(2,4)]], domain=[1,2,3,4,5])
sage: P.degree()
5

where as now in Sage you would get 4 for the degree. This will also be passed on to Magma. I'm hoping that this will be in the next release of Sage.

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Thanks! Can you point me a reference on how to apply the patches?

Cody gravatar imageCody ( 2011-06-22 09:06:48 -0500 )edit

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Asked: 2011-06-21 19:09:49 -0500

Seen: 125 times

Last updated: Jun 22 '11