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

[nthiery]

Description changed:

--- 
+++ 
@@ -1 +1,10 @@
-Patch in dev on the sage-combinat server
+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.
+
+Depends on #8380.
+
+The patch on the sage-combinat server is almost ready, up to a glitch to be investigated during the Sage-Combinat/Chevie workshop.

[anneschilling]

Description changed:

--- 
+++ 
@@ -7,4 +7,3 @@
 
 Depends on #8380.
 
-The patch on the sage-combinat server is almost ready, up to a glitch to be investigated during the Sage-Combinat/Chevie workshop.

[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!

[jdemeyer]

Description changed:

--- 
+++ 
@@ -4,6 +4,3 @@
     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.
-
-Depends on #8380.
-