Merge branch 'public/11187' into u/stumpc5/20402

src/sage/combinat/root_system/coxeter_group.py

@@ -76,7 +76,9 @@ def CoxeterGroup(data, implementation="reflection", base_ring=None, index_set=No
         sage: W                                                         # optional - gap3
         Permutation Group with generators [(1,3)(2,5)(4,6), (1,4)(2,3)(5,6)]
         sage: W.category()                       # optional - gap3
-        Join of Category of finite permutation groups and Category of finite coxeter groups
+        Join of Category of finite permutation groups
+             and Category of finite coxeter groups
+             and Category of well generated finite irreducible complex reflection groups
 
         sage: W = CoxeterGroup(["A",2], implementation="matrix")
         sage: W
@@ -204,8 +206,8 @@ def __init__(self, cartan_type):
             sage: W = CoxeterGroupAsPermutationGroup(CartanType(["H",3])) # optional - gap3
             sage: TestSuite(W).run()             # optional - gap3
         """
-        assert cartan_type.is_finite()
-        assert cartan_type.is_irreducible()
+        if not (cartan_type.is_finite() and cartan_type.is_irreducible()):
+            raise ValueError("must be a finite irreducible type")
         self._semi_simple_rank = cartan_type.n
         from sage.interfaces.gap3 import gap3
         gap3._start()
@@ -218,7 +220,8 @@ def __init__(self, cartan_type):
         from sage.categories.finite_permutation_groups import FinitePermutationGroups
         from sage.categories.finite_coxeter_groups import FiniteCoxeterGroups
         PermutationGroup_generic.__init__(self, gens=generators,
-                                          category=(FinitePermutationGroups(), FiniteCoxeterGroups()))
+                                          category=(FinitePermutationGroups(),
+                                                    FiniteCoxeterGroups().Irreducible()))
 
     def _element_class(self):
         """
@@ -227,8 +230,9 @@ def _element_class(self):
 
         TESTS::
 
-            sage: W = CoxeterGroup(["H",3])                                  # optional - gap3
-            sage: W._element_class() is W.element_class                      # optional - gap3
+            sage: from sage.combinat.root_system.coxeter_group import CoxeterGroupAsPermutationGroup
+            sage: W = CoxeterGroupAsPermutationGroup("H3")   # optional - gap3
+            sage: W._element_class() is W.element_class      # optional - gap3
             True
         """
         return self.element_class
@@ -251,12 +255,12 @@ def reflection(self, i):
         """
         Returns the `i`-th reflection of ``self``.
 
-        For `i` in `1,\dots,n`, this gives the `i`-th simple
+        For `i` in `1, \ldots, n`, this gives the `i`-th simple
         reflection of ``self``.
 
         EXAMPLES::
 
-            sage: W = CoxeterGroup(["H",3], implementation = "permutation") # optional - gap3
+            sage: W = CoxeterGroup(["H",3], implementation="permutation") # optional - gap3
             sage: W.simple_reflection(1) # optional - gap3
             (1,16)(2,5)(4,7)(6,9)(8,10)(11,13)(12,14)(17,20)(19,22)(21,24)(23,25)(26,28)(27,29)
             sage: W.simple_reflection(2) # optional - gap3
@@ -274,6 +278,30 @@ def reflection(self, i):
 
     simple_reflection = reflection
 
+    @cached_method
+    def degrees(self):
+        r"""
+        Return the degrees of ``self`` ordered within each irreducible
+        component of ``self``.
+
+        EXAMPLES::
+
+            sage: from sage.combinat.root_system.coxeter_group import CoxeterGroupAsPermutationGroup
+            sage: W = CoxeterGroupAsPermutationGroup("A3")    # optional - gap3
+            sage: W.degrees()                                 # optional - gap3
+            (2, 3, 4)
+            sage: W = CoxeterGroupAsPermutationGroup("H3")    # optional - gap3
+            sage: W.degrees()                                 # optional - gap3
+            (2, 6, 10)
+        """
+        if self.is_irreducible():
+            try:
+                return tuple(sorted(self._gap_group.degrees.sage()))
+            except AttributeError:
+                return tuple(sorted(self._gap_group.ReflectionDegrees().sage()))
+        else:
+            return sum([comp.degrees() for comp in self.irreducible_components()],tuple())
+
     class Element(PermutationGroupElement):
 
         def has_descent(self, i, side = 'right', positive=False):
@@ -338,3 +366,4 @@ def __cmp__(self, other):
                 1
             """
             return super(CoxeterGroupAsPermutationGroup.Element, self).__cmp__(other)
+

src/sage/combinat/root_system/reflection_group_complex.py

@@ -952,7 +952,7 @@ def degrees(self):
         if self.is_irreducible():
             try:
                 return tuple(sorted(self._gap_group.degrees.sage()))
-            except:
+            except AttributeError:
                 return tuple(sorted(self._gap_group.ReflectionDegrees().sage()))
         else:
             return sum([comp.degrees() for comp in self.irreducible_components()],tuple())

src/sage/combinat/root_system/reflection_group_real.py

@@ -100,15 +100,15 @@ def ReflectionGroup(*args,**kwds):
     the complex infinite family `G(r,p,n)` with `p` divides `r`::
 
         sage: W = ReflectionGroup((1,1,4)); W                           # optional - gap3
-        Irreducible complex reflection group of rank 3 and type A3
+        Irreducible real reflection group of rank 3 and type A3
 
         sage: W = ReflectionGroup((2,1,3)); W                           # optional - gap3
-        Irreducible complex reflection group of rank 3 and type B3
+        Irreducible real reflection group of rank 3 and type B3
 
     Chevalley-Shepard-Todd exceptional classification types::
 
         sage: W = ReflectionGroup(23); W                                # optional - gap3
-         Irreducible complex reflection group of rank 3 and type H3
+        Irreducible real reflection group of rank 3 and type H3
 
     Cartan types and matrices::
 
@@ -268,7 +268,7 @@ def _repr_(self):
 
             sage: W = ReflectionGroup(['A',3],['B',2],['I',5],['I',6])  # optional - gap3
             sage: W._repr_()                                            # optional - gap3
-            Reducible real reflection group of rank 9 and type A3 x B2 x I2(5) x G2
+            'Reducible real reflection group of rank 9 and type A3 x B2 x I2(5) x G2'
         """
         type_str = ''
         for W_type in self._type:
@@ -615,6 +615,7 @@ def permutahedron(self, point=None):
 
         TESTS::
 
+            sage: W = ReflectionGroup(['A',3])                          # optional - gap3
             sage: W.permutahedron([3,5,8])                              # optional - gap3
             A 3-dimensional polyhedron in QQ^3 defined as the convex hull
             of 24 vertices