add one test in TestSuite of Coxeter groups

[fchapoton]

coming from affine permutations

CC: @tscrim

Component: combinatorics

Author: Frédéric Chapoton

Branch/Commit: 4008629

Reviewer: Travis Scrimshaw

Issue created by migration from https://trac.sagemath.org/ticket/33564

[fchapoton]

Commit: 150517f

[fchapoton]

Branch: u/chapoton/33564

[fchapoton]

New commits:

150517f

move doctest in category of Coxeter groups

[fchapoton]

comment:2

Hmm, fails for Weyl groups, it seems. Why ?

• maybe one should test that simple reflections are involutions ?

• and also commutation between reflection not linked in the Coxeter diagram ?

[sagetrac-git]

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

8f11b4b

more full check for Coxeter relations

[sagetrac-git]

Changed commit from 150517f to 8f11b4b

[fchapoton]

comment:4

so we have a problem with Weyl groups created from matrices:

sage: cm = CartanMatrix([[2,-5,0],[-2,2,-1],[0,-1,2]])
sage: W = WeylGroup(cm)
sage: TestSuite(W).run()
Failure in _test_coxeter_relations:
Traceback (most recent call last):
  File "/home/chapoton/sage/local/var/lib/sage/venv-python3.8/lib/python3.8/site-packages/sage/misc/sage_unittest.py", line 297, in run
    test_method(tester=tester)
  File "/home/chapoton/sage/local/var/lib/sage/venv-python3.8/lib/python3.8/site-packages/sage/categories/coxeter_groups.py", line 1301, in _test_coxeter_relations
    cox_mat = self.coxeter_matrix()
  File "/home/chapoton/sage/local/var/lib/sage/venv-python3.8/lib/python3.8/site-packages/sage/categories/weyl_groups.py", line 96, in coxeter_matrix
    return self.cartan_type().coxeter_matrix()
  File "sage/misc/cachefunc.pyx", line 2310, in sage.misc.cachefunc.CachedMethodCallerNoArgs.__call__ (build/cythonized/sage/misc/cachefunc.c:13026)
    self.cache = f(self._instance)
  File "/home/chapoton/sage/local/var/lib/sage/venv-python3.8/lib/python3.8/site-packages/sage/combinat/root_system/cartan_type.py", line 1177, in coxeter_matrix
    return CoxeterMatrix(self)
  File "sage/misc/classcall_metaclass.pyx", line 320, in sage.misc.classcall_metaclass.ClasscallMetaclass.__call__ (build/cythonized/sage/misc/classcall_metaclass.c:1848)
    return cls.classcall(cls, *args, **kwds)
  File "/home/chapoton/sage/local/var/lib/sage/venv-python3.8/lib/python3.8/site-packages/sage/combinat/root_system/coxeter_matrix.py", line 194, in __classcall_private__
    return cls._from_coxetertype(coxeter_type)
  File "/home/chapoton/sage/local/var/lib/sage/venv-python3.8/lib/python3.8/site-packages/sage/combinat/root_system/coxeter_matrix.py", line 390, in _from_coxetertype
    for (i, j, l) in coxeter_type.coxeter_graph().edge_iterator():
  File "/home/chapoton/sage/local/var/lib/sage/venv-python3.8/lib/python3.8/site-packages/sage/combinat/root_system/coxeter_type.py", line 502, in coxeter_graph
    return self._cartan_type.coxeter_diagram()
TypeError: 'NotImplementedType' object is not callable
------------------------------------------------------------
The following tests failed: _test_coxeter_relations

[fchapoton]

comment:6

not clear to me if "Weyl groups" associated with arbitrary Cartan matrices are always Coxeter groups..

[tscrim]

comment:7

Every Weyl group is a Coxeter group, but there are a number of restrictions. In particular, it must be crystallographic and when c_ij c_ji > 3, then the corresponding Weyl group has an infinite edge in the Coxeter diagram. Here, the issue seems to be just a lack of complete functionality: arbitrary Cartan matrices do not know how to construct the corresponding Coxeter matrix. The code is essentially already there, but just not at the place.

I will try to fix this today.

[tscrim]

comment:8

Here is a fix. I also fixed a bug with a mismatch between the Cartan matrix and Cartan type of a reducible type. This now passes the tests in categories, groups, and combinat for me.

---

New commits:

952afeb	Merge branch 'u/chapoton/33564' of https://github.com/sagemath/sagetrac-mirror into public/combinat/coxeter_group_test-33564
fbc1e58	Fixing issues with definition of Coxeter matrices.
0bac55b	Use the index set to get the entires in the Coxeter matrix.
b9bee75	Fixing an immutability issue with relabelled Cartan types.

[tscrim]

Reviewer: Travis Scrimshaw

[tscrim]

Changed commit from 8f11b4b to b9bee75

[tscrim]

Changed branch from u/chapoton/33564 to public/combinat/coxeter_group_test-33564

[sagetrac-git]

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

4008629

fix pyflakes warning

[sagetrac-git]

Changed commit from b9bee75 to 4008629

[fchapoton]

comment:10

Thanks. I fixed a pyflakes warning. Now, this should be good to go.

If you agree, you can set to positive.

[tscrim]

comment:11

Thank you.

[vbraun]

Changed branch from public/combinat/coxeter_group_test-33564 to 4008629