We also recently had a ticket about correcting the permutation action on a
matrix, so we also need that to also be consistent.
Best,
Travis
On Tuesday, June 16, 2020 at 4:02:11 AM UTC+10, Nils Bruin wrote:
>
> On Monday, June 15, 2020 at 10:43:51 AM UTC-7, Nils Bruin wrote:
>>
>> There's obviously the choice for letting permutations/matrices on the
>> left/right, but I think there's a definite preferred choice for how to
>> convert to a permutation matrix: the one that makes it a homomorphism. And
>> for that, "Permutation" fails presently:
>>
>> sage: matrix(Permutation('(1,2,3)')*Permutation('(1,3)')) ==
>> matrix(Permutation('(1,2,3)'))*matrix(Permutation('(1,3)'))
>> False
>>
>> To make things worse, there is actually an option to fix this:
>
> sage: sage.combinat.permutation.Permutations.options(mult="r2l")
> sage: matrix(Permutation('(1,2,3)')*Permutation('(1,3)')) ==
> matrix(Permutation('(1,2,3)'))*matrix(Permutatio
> ....: n('(1,3)'))
>
> Quoting from the documentation:
>
> It is best for code not to rely on this setting being set to a
> particular
> standard, but rather use the methods "left_action_product()" and
> "right_action_product()" for multiplying permutations (these
> methods don't depend on the setting). See
> https://trac.sagemath.org/14885 for more details.
>
> so, "Permutation" objects aren't really meant to be a group: they are just
> objects on which two different groups can be overlaid (the opposites). So
> that means "matrix" can't possibly get it right in all cases. There should
> be a left_action_permutation_matrix and right_action_permutation_matrix on
> Permutation objects.
>
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