Trac #30237: Make .coxeter_matrix() return a CoxeterMatrix for coxete…

…r3-implemented groups

This patch fixes all of the following, which currently throw errors:

{{{#!python
W = CoxeterGroup(['B', 3], implementation='coxeter3')
W.coxeter_type()
# AttributeError:
'sage.matrix.matrix_integer_dense.Matrix_integer_dense' object has no
attribute 'coxeter_type'
W([1,2,1]).reduced_words()
# IndexError: matrix index out of range
R.<v> = LaurentPolynomialRing(ZZ)
IwahoriHeckeAlgebra(W, v, -1/v)
# AttributeError:
'sage.matrix.matrix_integer_dense.Matrix_integer_dense' object has no
attribute 'coxeter_type'
}}}

The underlying problem in all cases is that `W.coxeter_matrix()` does
not return a `CoxeterMatrix`; I've altered this to return the (correctly
indexed) coxeter matrix and added a test.

This also removes a completely unused function `CoxeterGroup.m(i, j)`
which seemingly existed only to workaround the fact that
`.coxeter_matrix()` was incorrectly indexed (and in fact is ill-founded,
it would cause an error on a group with affine Cartan type). This
removal breaks no tests in `libs/coxeter3`.

URL: https://trac.sagemath.org/30237
Reported by: gh-cemulate
Ticket author(s): Chase Meadors
Reviewer(s): Travis Scrimshaw

src/sage/libs/coxeter3/coxeter_group.py

@@ -18,6 +18,8 @@
 from sage.categories.all import CoxeterGroups
 from sage.structure.parent import Parent
 
+from sage.combinat.root_system.coxeter_matrix import CoxeterMatrix
+
 from sage.rings.integer_ring import ZZ
 from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
 
@@ -214,13 +216,15 @@ def coxeter_matrix(self):
         EXAMPLES::
 
             sage: W = CoxeterGroup(['A', 3], implementation='coxeter3')    # optional - coxeter3
-            sage: W.coxeter_matrix()                                       # optional - coxeter3
+            sage: m = W.coxeter_matrix(); m                                # optional - coxeter3
             [1 3 2]
             [3 1 3]
             [2 3 1]
+            sage: m.index_set() == W.index_set()                           # optional - coxeter3
+            True
 
         """
-        return self._coxgroup.coxeter_matrix()
+        return CoxeterMatrix(self._coxgroup.coxeter_matrix(), self.index_set())
 
     def root_system(self):
         """
@@ -251,19 +255,21 @@ def _an_element_(self):
         return self.element_class(self, [])
 
     def m(self, i, j):
-        """
-        Return the entry in the Coxeter matrix between the generator
-        with label ``i`` and the generator with label ``j``.
+        r"""
+        This is deprecated, use ``self.coxeter_matrix()[i,j]`` instead.
 
-        EXAMPLES::
+        TESTS::
 
-            sage: W = CoxeterGroup(['A', 3], implementation='coxeter3')   # optional - coxeter3
-            sage: W.m(1,1)                                                # optional - coxeter3
+            sage: W = CoxeterGroup(['A', 3], implementation='coxeter3') # optional - coxeter3
+            sage: W.m(1, 1)                                             # optional - coxeter3
+            doctest:warning...:
+            DeprecationWarning: the .m(i, j) method has been deprecated; use .coxeter_matrix()[i,j] instead.
+            See https://trac.sagemath.org/30237 for details.
             1
-            sage: W.m(1,0)                                                # optional - coxeter3
-            2
         """
-        return self.coxeter_matrix()[i-1,j-1]
+        from sage.misc.superseded import deprecation
+        deprecation(30237, "the .m(i, j) method has been deprecated; use .coxeter_matrix()[i,j] instead.")
+        return self.coxeter_matrix()[i,j]
 
     def kazhdan_lusztig_polynomial(self, u, v, constant_term_one=True):
         r"""