Coxeter groups: all elements of length N, random elements

[tom denton]

Two commonly desired constructions in a Coxeter group are to: a) Iterate over all elements of a given length - this happens especially in affine or other infinite coxeter groups in order to test hypotheses, construct homogenous elements, etc... b) Choose a random element, possibly with length specified. This often occurs to see if a non-special element has a given property.

Iterating over all elements of a given length in particular has a nice solution (due to N. Thiery) and anecdotally has been implemented (usually in an inelegant fashion) by numerous community members in response to short-term problems.

We provide some code implementing these functions!

[Frédéric Chapoton]

Where is the code ?

[tom denton]

That's strange; I'm not sure why it isn't there.

The code should be the same used in the AffinePermutationGroup for the methods elements_of_length and random_element.

Example:

sage: A=AffinePermutationGroup?(['A',4,1])

sage: len(list(A.elements_of_length(1)))

5

sage: A.random_element(4)

Type A affine permutation with window [0, 4, 3, 2, 6]

[Frédéric Chapoton]

Maybe we should then move the code to Coxeter groups, it it works.

[Frédéric Chapoton]

here is a git branch, moving elements_of_length into the category of coxeter groups

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New commits:

​c2ce1c2

trac #13248 first step : moving elements_of_length to coxeter groups

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​93faac6

Merge branch 'u/chapoton/13248' of trac.sagemath.org:sage into 13248

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​34cb3f9	Merge branch 'u/chapoton/13248' of ssh://trac.sagemath.org:22/sage into 13248
​a94f968	trac #13248 first step towards random

[git]

Branch pushed to git repo; I updated commit sha1. New commits:

​fb613e2

trac #13248 remove code duplication

[Frédéric Chapoton]

ping ?

[Travis Scrimshaw]

Hey Frederic,

I've done some minor tweaks and made it so that random_element chooses the length at random in [0, 1000] (so the word is not too long) if not specified. LGTM otherwise, so if you're happy with my changes, then positive review.

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New commits:

​ec5652c	Merge branch 'u/chapoton/13248' of trac.sagemath.org:sage into u/tscrim/13248
​707c9c3	Some review tweaks.

[Frédéric Chapoton]

Hello, and thanks.

I just corrected a typo in "chosen".

I'm setting this to positive review.

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New commits:

​a96be6f

trac #13248 just corrected a typo in "chosen"