better code for first_descent in coxeter groups

[fchapoton]

I propose to treat the unit of the group in a special way. The test is cheap.

CC: @tscrim @stumpc5 @darijgr

Component: combinatorics

Keywords: coxeter

Author: Frédéric Chapoton

Branch/Commit: public/20125 @ 0c6eaaf

Issue created by migration from https://trac.sagemath.org/ticket/20125

[fchapoton]

Changed keywords from none to coxeter

[fchapoton]

Branch: public/20125

[fchapoton]

Commit: 98a56f4

[fchapoton]

New commits:

98a56f4

shortcuts for descents of the unit element in Coxeter groups

[sagetrac-git]

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

0c6eaaf

trac #20125 another try using is_one

[sagetrac-git]

Changed commit from 98a56f4 to 0c6eaaf

[fchapoton]

comment:3

This is not very convincing, it seems to be slower than before..

[tscrim]

comment:4

I think that because the identity element is rare, this won't really help speed up many computations because of the overhead of the extra data needed and function calls.

[fchapoton]

comment:5

ok, then let us close this as invalid.

Maybe the overloading of is_one is still a good idea that could be done in #19870 ?

[tscrim]

comment:6

Yes, that is a good idea.