Implement reflections for affine Weyl groups

[tscrim]

The code just needs to be slightly modified in order to support affine Weyl groups since we have a method to generate all positive real roots.

Depends on #20027

CC: @sagetrac-sage-combinat @nthiery @fchapoton @stumpc5 @jplab

Component: combinatorics

Keywords: reflections, Weyl groups

Author: Travis Scrimshaw

Branch/Commit: 72541a3

Reviewer: Frédéric Chapoton

Issue created by migration from https://trac.sagemath.org/ticket/20170

[tscrim]

New commits:

90b278a	Reversing the family for reflections.
8c9b809	Making CoxeterGroup.reflections return a Family and some touchups.
2595826	Removing caching of CoxeterGroup.positive_roots().
7ed4c2a	Merge 7.1.beta6.
3c32075	Fixing doctest failures in the thematic tutorials.
35eb71c	Fixing some documentation and adding note to WeylGroup.reflections.
762aaf1	Adding support for reflections for affine Weyl groups.

[tscrim]

Commit: 762aaf1

[tscrim]

Branch: public/combinat/reflections_infinite_weyl_groups-20170

[fchapoton]

Reviewer: Frédéric Chapoton

[fchapoton]

comment:2

ok, good to go

[tscrim]

comment:4

Thanks.

[vbraun]

comment:5

Probably interaction with some other ticket in beta1:

sage -t --long src/sage/categories/coxeter_groups.py
**********************************************************************
File "src/sage/categories/coxeter_groups.py", line 1315, in sage.categories.coxeter_groups.CoxeterGroups.ElementMethods.absolute_covers
Failed example:
    w0.absolute_covers()
Expected:
    [
    [0 0 0 1]  [0 0 1 0]  [0 1 0 0]  [0 1 0 0]  [0 1 0 0]
    [1 0 0 0]  [1 0 0 0]  [0 0 1 0]  [0 0 0 1]  [1 0 0 0]
    [0 0 1 0]  [0 1 0 0]  [1 0 0 0]  [0 0 1 0]  [0 0 0 1]
    [0 1 0 0], [0 0 0 1], [0 0 0 1], [1 0 0 0], [0 0 1 0]
    ]
Got:
    [
    [0 0 1 0]  [0 1 0 0]  [0 0 0 1]  [0 1 0 0]  [0 1 0 0]
    [1 0 0 0]  [1 0 0 0]  [1 0 0 0]  [0 0 1 0]  [0 0 0 1]
    [0 1 0 0]  [0 0 0 1]  [0 0 1 0]  [1 0 0 0]  [0 0 1 0]
    [0 0 0 1], [0 0 1 0], [0 1 0 0], [0 0 0 1], [1 0 0 0]
    ]
**********************************************************************
1 item had failures:
   1 of   6 in sage.categories.coxeter_groups.CoxeterGroups.ElementMethods.absolute_covers
    [469 tests, 1 failure, 16.41 s]

[sagetrac-git]

Changed commit from 762aaf1 to 72541a3

[sagetrac-git]

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

cc3bf03	Merge branch 'public/combinat/reflections_infinite_weyl_groups-20170' of trac.sagemath.org:sage into public/combinat/reflections_infinite_weyl_groups-20170
72541a3	Fixing trivial doctest ordering.

[vbraun]

Changed branch from public/combinat/reflections_infinite_weyl_groups-20170 to 72541a3