Coxeter groups as permutation groups

[nthiery]

This patch adds a function:

    CoxeterGroup(cartan_type, implementation = "matrix" / "permutation")

to construct Coxeter groups. Whenever possible, the Coxeter group is constructed as a permutation group, using data from GAP3/Chevie; otherwise a Weyl group is returned, as a matrix group. An upcoming implementation is by reduced words, using the Coxeter 3 package.

CC: @sagetrac-sage-combinat

Component: combinatorics

Keywords: Coxeter groups, permutation groups, chevie

Author: Nicolas M. Thiéry

Reviewer: Anne Schilling, Mike Hansen

Merged: sage-5.7.beta3

Issue created by migration from https://trac.sagemath.org/ticket/8359

[anneschilling]

Reviewer: Anne Schilling, Mike Hansen

[anneschilling]

comment:3

This patch was developed and tested on the sage-combinat queue by myself and Mike Hansen. It is ready to go!

[anneschilling]

comment:7

We made changes to make the doctests pass. Not sure what the problem with the plugins are.

[jdemeyer]

comment:8

You should never use except: without an exception type, otherwise you would catch some unwanted exceptions. Catch specific exceptions instead (or except Exception: if you want to catch all actual exceptions).

[jdemeyer]

comment:9

There is a problem with the documentation:

/release/merger/sage-5.7.beta2/local/lib/python2.7/site-packages/sage/combinat/root_system/coxeter_group.py:docstring of sage.combinat.root_system.coxeter_group.CoxeterGroupAsPermutationGroup.Element.has_descent:3: WARNING: more than one target found for cross-reference u'descents': sage.combinat.root_system.root_lattice_realizations.RootLatticeRealizations.ElementMethods.descents, sage.categories.coxeter_groups.CoxeterGroups.ElementMethods.descents, sage.combinat.tableau.Tableau.descents, sage.combinat.sf.ns_macdonald.AugmentedLatticeDiagramFilling.descents, sage.combinat.permutation.Permutation_class.descents, sage.combinat.composition.Composition_class.descents

[anneschilling]

comment:10

Both issues fixed!

[nthiery]

comment:12

Hi Jeroen,

Should we ignore jehova's patchbot failure (the log and shortlog seem empty)?

Is the plugin.startup failure a suggestion for lazy importing CoxeterGroup?

Thanks!

           Nicolas

[anneschilling]

comment:13

In consultation with Nicolas, I fixed some failing doctests in /combinat/root_systems/coxeter_group.py for type H3.

Anne

[anneschilling]

Attachment: trac_8359-coxeter-groups-permutation-nt.patch.gz

[anneschilling]

comment:14

Removed trailing white spaces.

Anne

[jdemeyer]

Merged: sage-5.7.beta3