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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