#11122: Implementation of the Demazure product in Coxeter groups
-----------------------------+----------------------------------------------
Reporter: stumpc5 | Owner:
Type: enhancement | Status: needs_work
Priority: major | Milestone: sage-4.7.1
Component: combinatorics | Keywords: Demazure product, subword
complex
Work_issues: | Upstream: N/A
Reviewer: | Author: Christian Stump
Merged: | Dependencies: 11187
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Changes (by stumpc5):
* owner: tbd =>
* dependencies: => 11187
* milestone: => sage-4.7.1
Old description:
> 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])
>
> sage: w = W.demazure_product([2,2,1])
> sage: w.reduced_word()
> [2, 1]
>
> sage: w = W.demazure_product([2,1,2,1,2])
> sage: w.reduced_word()
> [1, 2, 1]
>
> sage: W = CoxeterGroup(['B',2])
>
> sage: w = W.demazure_product([2,1,2,1,2])
> sage: w.reduced_word()
> [2, 1, 2, 1]
> }}}
>
> As I also needed it, the patch provides in addition a method returning
> the cartan type of a Coxeter group.
>
> Depends on Ticket #8359.
New description:
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.
Depends on Ticket #8359.
--
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/11122#comment:2>
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