Am Dienstag, 16. Juni 2020 13:40:45 UTC+2 schrieb kcrisman:
>
>
> so, "Permutation" objects aren't really meant to be a group: 
>>
>
> I think this is the salient point.   Is there any documentation that 
> already has matrix(Permutation(...)) ? 
>
 
The documentation of Permutation.to_matrix 
<https://doc.sagemath.org/html/en/reference/combinat/sage/combinat/permutation.html#sage.combinat.permutation.Permutation.to_matrix>
 
states this:

    Notice that matrix multiplication corresponds to permutation 
multiplication only when the permutation option mult=’r2l’

I am not sure why exactly it was implemented like this, but I imagine this 
makes it generally more predictable, as the conversion to matrices does not 
depend on a global option of Permutations.
 

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