Implementation of the Demazure product in Coxeter groups

[stumpc5]

The provided patch implements the Demazure product of a word in the generators of a Coxeter group.

The definition can be found e.g. in "Knutson, Miller - Subword complexes for Coxeter groups".

            sage: W = CoxeterGroup(['A',2],index_set=[1,2])

            sage: w = W.demazure_product([2,2,1])
            sage: w.reduced_word()
            word: 21

            sage: w = W.demazure_product([2,1,2,1,2])
            sage: w.reduced_word()
            word: 121

            sage: W = CoxeterGroup(['B',2],index_set=[1,2])

            sage: w = W.demazure_product([2,1,2,1,2])
            sage: w.reduced_word()
            word: 2121

As I also needed it, the patch provides in addition a method returning the cartan type of a Coxeter group.

Duplicate of #12774.

Component: combinatorics

Keywords: Demazure product, subword complex

Reviewer: Christian Stump

Issue created by migration from https://trac.sagemath.org/ticket/11122

[stumpc5]

comment:2

Attachment: trac_11122-demazure_product-cs.patch.gz

[stumpc5]

Dependencies: 11187

[fchapoton]

Changed dependencies from 11187 to #11187

[fchapoton]

Changed dependencies from #11187 to #11187, #8359

[sagetrac-mshimo]

comment:6

This has been folded into 12774.

[sagetrac-mshimo]

Reviewer: mshimo

[tscrim]

Changed dependencies from #11187, #8359 to none

[tscrim]

comment:9

Removed dependencies so this looks like a duplicate ticket.

[jdemeyer]

Changed reviewer from mshimo to Christian Stump

[jdemeyer]

Changed author from Christian Stump to none