faster iteration for complex non-real reflection group and new hash

src/sage/combinat/root_system/reflection_group_complex.py

@@ -205,6 +205,7 @@
 from sage.sets.family import Family
 from sage.structure.unique_representation import UniqueRepresentation
 from sage.groups.perm_gps.permgroup import PermutationGroup_generic
+from sage.combinat.permutation import Permutation
 from sage.rings.integer_ring import ZZ
 from sage.rings.rational_field import QQ
 from sage.matrix.all import Matrix, identity_matrix
@@ -298,6 +299,8 @@ def __init__(self, W_types, index_set=None, hyperplane_index_set=None, reflectio
                                           canonicalize=False,
                                           category=category)
 
+        self._length_of_permutation_representation = len(Permutation(self.gens()[0]))
+
         l_set = list(range(1, len(self.gens()) + 1))
         if self._index_set is None:
             self._index_set = tuple(l_set)
@@ -366,17 +369,20 @@ def _repr_(self):
         type_str = type_str[:-3]
         return 'Reducible complex reflection group of rank %s and type %s' % (self._rank, type_str)
 
-    def __iter__(self):
+    def iteration_tracking_words(self):
         r"""
-        Return an iterator going through all elements in ``self``.
+        Return an iterator going through all elements in ``self`` which tracks the reduced expressions.
+
+        This is much slower than using the iteration as a permutation group with strong
+        generating set.
 
         EXAMPLES::
 
             sage: W = ReflectionGroup((1,1,3))                          # optional - gap3
-            sage: for w in W: w                                         # optional - gap3
+            sage: for w in W.iteration_tracking_words(): w              # optional - gap3
             ()
-            (1,3)(2,5)(4,6)
             (1,4)(2,3)(5,6)
+            (1,3)(2,5)(4,6)
             (1,6,2)(3,5,4)
             (1,2,6)(3,4,5)
             (1,5)(2,4)(3,6)

src/sage/combinat/root_system/reflection_group_element.pxd

@@ -1,6 +1,7 @@
 from sage.groups.perm_gps.permgroup_element cimport PermutationGroupElement
 
 cdef class ComplexReflectionGroupElement(PermutationGroupElement):
+    cpdef test_hash(self)
     cpdef action(self, vec, on_space=*)
     cpdef action_on_root_indices(self, i)
 

src/sage/combinat/root_system/reflection_group_element.pyx

@@ -74,6 +74,12 @@ cdef class ComplexReflectionGroupElement(PermutationGroupElement):
         """
         return hash(self._parent) | hash(tuple(self._reduced_word))
 
+    cpdef test_hash(self):
+        cdef int i
+        cdef int l = self.parent()._length_of_permutation_representation
+        cdef tuple perm = tuple([self.perm[i] for i in range(l)])
+        return hash(self._parent) | hash(perm)
+
     def reduced_word(self):
         r"""
         Return a word in the simple reflections to obtain ``self``.