Trac #18246: remove naive __hash__ from SageObject

Hashing is a critical function in Python. In several places, objects do
use the generic `__hash__` from `SageObject` or a badly implemented one
that makes everything slow. For example:
 - #18215 for quadratic number field elements (in relation with
polyhedra #18241)
 - #18239 for permutation group elements

See also #19016 for a ticket with the same purpose (with `Element`
instead of `SageObject`).

URL: http://trac.sagemath.org/18246
Reported by: vdelecroix
Ticket author(s): Vincent Delecroix
Reviewer(s): Volker Braun, Nils Bruin

src/sage/algebras/commutative_dga.py

@@ -2517,6 +2517,16 @@ def __init__(self, x):
         """
         self._x = x
 
+    def __hash__(self):
+        r"""
+        TESTS::
+
+            sage: from sage.algebras.commutative_dga import CohomologyClass
+            sage: hash(CohomologyClass(sin)) == hash(sin)
+            True
+        """
+        return hash(self._x)
+
     def _repr_(self):
         """
         EXAMPLES::

src/sage/categories/functor.pyx

@@ -181,6 +181,17 @@ cdef class Functor(SageObject):
         self.__domain = domain
         self.__codomain = codomain
 
+    def __hash__(self):
+        r"""
+        TESTS::
+
+            sage: from sage.categories.functor import Functor
+            sage: F = Functor(Rings(), Fields())
+            sage: hash(F)  # random
+            42
+        """
+        return hash(self.__domain) ^ hash(self.__codomain)
+
     def __reduce__(self):
         """
         Generic pickling of functors.

src/sage/combinat/alternating_sign_matrix.py

@@ -890,7 +890,7 @@ def left_key_as_permutation(self):
         """
         return self.left_key().to_permutation()
 
-class AlternatingSignMatrices(Parent, UniqueRepresentation):
+class AlternatingSignMatrices(UniqueRepresentation, Parent):
     r"""
     Class of all `n \times n` alternating sign matrices.
 

src/sage/combinat/cluster_algebra_quiver/quiver.py

@@ -24,7 +24,6 @@
 #*****************************************************************************
 from sage.structure.sage_object import SageObject
 from copy import copy
-from sage.structure.unique_representation import UniqueRepresentation
 from sage.misc.all import cached_method
 from sage.rings.all import ZZ, CC, infinity
 from sage.graphs.all import Graph, DiGraph

src/sage/combinat/cluster_algebra_quiver/quiver_mutation_type.py

@@ -1088,8 +1088,7 @@ def properties(self):
             print '\t- elliptic:         ', self.is_elliptic()
 
 
-class QuiverMutationType_Irreducible(QuiverMutationType_abstract,
-                                     UniqueRepresentation, SageObject):
+class QuiverMutationType_Irreducible(QuiverMutationType_abstract):
     """
     The mutation type for a cluster algebra or a quiver. Should not be
     called directly, but through QuiverMutationType.
@@ -1933,8 +1932,7 @@ def dual(self):
             return self
 
 
-class QuiverMutationType_Reducible(QuiverMutationType_abstract,
-                                   UniqueRepresentation, SageObject):
+class QuiverMutationType_Reducible(QuiverMutationType_abstract):
     """
     The mutation type for a cluster algebra or a quiver. Should not be
     called directly, but through QuiverMutationType.  Inherits from

src/sage/combinat/composition.py

@@ -1308,7 +1308,7 @@ def wll_gt(self, co2):
 
 ##############################################################
 
-class Compositions(Parent, UniqueRepresentation):
+class Compositions(UniqueRepresentation, Parent):
     r"""
     Set of integer compositions.
 

src/sage/combinat/crystals/affinization.py

@@ -24,7 +24,7 @@
 from sage.categories.infinite_enumerated_sets import InfiniteEnumeratedSets
 from sage.rings.infinity import Infinity
 
-class AffinizationOfCrystal(Parent, UniqueRepresentation):
+class AffinizationOfCrystal(UniqueRepresentation, Parent):
     r"""
     An affiniziation of a crystal.
 

src/sage/combinat/crystals/elementary_crystals.py

@@ -181,7 +181,7 @@ def f(self,i):
         """
         return None
 
-class TCrystal(Parent, UniqueRepresentation):
+class TCrystal(UniqueRepresentation, Parent):
     r"""
     The crystal `T_{\lambda}`.
 
@@ -416,7 +416,7 @@ def weight(self):
             """
             return self.parent()._weight
 
-class RCrystal(Parent, UniqueRepresentation):
+class RCrystal(UniqueRepresentation, Parent):
     r"""
     The crystal `R_{\lambda}`.
 
@@ -672,7 +672,7 @@ def weight(self):
             """
             return self.parent()._weight
 
-class ElementaryCrystal(Parent, UniqueRepresentation):
+class ElementaryCrystal(UniqueRepresentation, Parent):
     r"""
     The elementary crystal `B_i`.
 
@@ -986,7 +986,7 @@ def weight(self):
             Q = self.parent().weight_lattice_realization()
             return self._m * Q.simple_root(self.parent()._i)
 
-class ComponentCrystal(Parent,UniqueRepresentation):
+class ComponentCrystal(UniqueRepresentation, Parent):
     r"""
     The component crystal.
 

src/sage/combinat/crystals/generalized_young_walls.py

@@ -641,7 +641,7 @@ def in_highest_weight_crystal(self,La):
         return True
 
 
-class InfinityCrystalOfGeneralizedYoungWalls(Parent,UniqueRepresentation):
+class InfinityCrystalOfGeneralizedYoungWalls(UniqueRepresentation, Parent):
     r"""
     The crystal `\mathcal{Y}(\infty)` of generalized Young walls of
     type `A_n^{(1)}` as defined in [KS10]_.

src/sage/combinat/crystals/induced_structure.py

@@ -27,7 +27,7 @@
 from sage.structure.parent import Parent
 from sage.structure.element_wrapper import ElementWrapper
 
-class InducedCrystal(Parent, UniqueRepresentation):
+class InducedCrystal(UniqueRepresentation, Parent):
     r"""
     A crystal induced from an injection.
 
@@ -396,7 +396,7 @@ def weight(self):
             """
             return self.parent()._phi(self.value).weight()
 
-class InducedFromCrystal(Parent, UniqueRepresentation):
+class InducedFromCrystal(UniqueRepresentation, Parent):
     r"""
     A crystal induced from an injection.
 

src/sage/combinat/crystals/monomial_crystals.py

@@ -759,7 +759,7 @@ def f(self,i):
         d[(i,kf)] = d.get((i,kf),0) - 1
         return self.__class__(self.parent(), d)
 
-class InfinityCrystalOfNakajimaMonomials(Parent,UniqueRepresentation):
+class InfinityCrystalOfNakajimaMonomials(UniqueRepresentation, Parent):
     r"""
     Let `Y_{i,k}`, for `i \in I` and `k \in \ZZ`, be a commuting set of
     variables, and let `\boldsymbol{1}` be a new variable which commutes with

src/sage/combinat/crystals/subcrystal.py

@@ -33,7 +33,7 @@
 from sage.rings.integer import Integer
 from sage.rings.infinity import infinity
 
-class Subcrystal(Parent, UniqueRepresentation):
+class Subcrystal(UniqueRepresentation, Parent):
     """
     A subcrystal `X` of an ambient crystal `Y` is a crystal formed by taking a
     subset of `Y` and whose crystal structure is induced by `Y`.

src/sage/combinat/derangements.py

@@ -70,7 +70,7 @@ def to_permutation(self):
             raise ValueError("Can only convert to a permutation for derangements of [1, 2, ..., n]")
         return Permutation(list(self))
 
-class Derangements(Parent, UniqueRepresentation):
+class Derangements(UniqueRepresentation, Parent):
     r"""
     The class of all derangements of a set or multiset.
 

src/sage/combinat/descent_algebra.py

@@ -30,7 +30,7 @@
 from sage.combinat.symmetric_group_algebra import SymmetricGroupAlgebra
 from sage.combinat.ncsf_qsym.ncsf import NonCommutativeSymmetricFunctions
 
-class DescentAlgebra(Parent, UniqueRepresentation):
+class DescentAlgebra(UniqueRepresentation, Parent):
     r"""
     Solomon's descent algebra.
 

src/sage/combinat/dyck_word.py

@@ -3102,7 +3102,7 @@ def to_alternating_sign_matrix(self):
         return A.from_monotone_triangle(monotone_triangle)
 
 
-class DyckWords(Parent, UniqueRepresentation):
+class DyckWords(UniqueRepresentation, Parent):
     r"""
     Dyck words.
 

src/sage/combinat/gelfand_tsetlin_patterns.py

@@ -507,7 +507,7 @@ def Tokuyama_coefficient(self, name='t'):
         return (t+1)**(self.number_of_special_entries()) * t**(self.number_of_boxes())
 
 
-class GelfandTsetlinPatterns(Parent, UniqueRepresentation):
+class GelfandTsetlinPatterns(UniqueRepresentation, Parent):
     """
     Gelfand-Tsetlin patterns.
 

src/sage/combinat/partition.py

@@ -6830,7 +6830,7 @@ def _repr_(self):
 # Partitions Greatest EQ #
 ##########################
 
-class PartitionsGreatestEQ(IntegerListsLex, UniqueRepresentation):
+class PartitionsGreatestEQ(UniqueRepresentation, IntegerListsLex):
     """
     The class of all (unordered) "restricted" partitions of the integer `n`
     having its greatest part equal to the integer `k`.

src/sage/combinat/permutation.py

@@ -4834,7 +4834,7 @@ def shifted_shuffle(self, other):
 ################################################################
 
 # Base class for permutations
-class Permutations(Parent, UniqueRepresentation):
+class Permutations(UniqueRepresentation, Parent):
     r"""
     Permutations.
 

src/sage/combinat/ribbon_tableau.py

@@ -147,7 +147,7 @@ def to_word(self):
 # Ribbon Tableaux   #
 #####################
 
-class RibbonTableaux(Parent, UniqueRepresentation):
+class RibbonTableaux(UniqueRepresentation, Parent):
     r"""
     Ribbon tableaux.
 
@@ -952,7 +952,7 @@ def _inversion_pairs_from_position(self, k, ij):
         return res
 
 
-class MultiSkewTableaux(Parent, UniqueRepresentation):
+class MultiSkewTableaux(UniqueRepresentation, Parent):
     r"""
     Multiskew tableaux.
     """

src/sage/combinat/rigged_configurations/kleber_tree.py

@@ -469,7 +469,7 @@ def _latex_(self):
 # Kleber tree classes #
 #######################
 
-class KleberTree(Parent, UniqueRepresentation):
+class KleberTree(UniqueRepresentation, Parent):
     r"""
     The tree that is generated by Kleber's algorithm.
 

src/sage/combinat/rigged_configurations/rc_crystal.py

@@ -39,7 +39,7 @@
 from sage.combinat.rigged_configurations.rigged_partition import RiggedPartition
 
 # Note on implementation, this class is used for simply-laced types only
-class CrystalOfRiggedConfigurations(Parent, UniqueRepresentation):
+class CrystalOfRiggedConfigurations(UniqueRepresentation, Parent):
     r"""
     A highest weight crystal of rigged configurations.
 

src/sage/combinat/rigged_configurations/rc_infinity.py

@@ -34,7 +34,7 @@
 from sage.combinat.rigged_configurations.rigged_partition import RiggedPartition
 
 # Note on implementation, this class is used for simply-laced types only
-class InfinityCrystalOfRiggedConfigurations(Parent, UniqueRepresentation):
+class InfinityCrystalOfRiggedConfigurations(UniqueRepresentation, Parent):
     r"""
     Rigged configuration model for `\mathcal{B}(\infty)`.
 

src/sage/combinat/rigged_configurations/rigged_configurations.py

@@ -129,7 +129,7 @@ def KirillovReshetikhinCrystal(cartan_type, r, s):
     return RiggedConfigurations(cartan_type, [[r,s]])
 
 # Note on implementation, this class is used for simply-laced types only
-class RiggedConfigurations(Parent, UniqueRepresentation):
+class RiggedConfigurations(UniqueRepresentation, Parent):
     r"""
     Rigged configurations as `U_q^{\prime}(\mathfrak{g})`-crystals.
 
@@ -249,7 +249,7 @@ class RiggedConfigurations(Parent, UniqueRepresentation):
         6
         sage: len(RC.list()) == RC.cardinality()
         True
-        sage: RC.list()
+        sage: RC.list() # random
         [
         <BLANKLINE>
                                                  0[ ]0
@@ -489,11 +489,11 @@ def __iter__(self):
             <BLANKLINE>
             (/)
             <BLANKLINE>
-            sage: next(g)
+            sage: next(g) # random
             <BLANKLINE>
-            (/)
+            0[ ]0
             <BLANKLINE>
-            -1[ ]-1
+            0[ ]0
             <BLANKLINE>
             (/)
             <BLANKLINE>
@@ -858,12 +858,18 @@ def cardinality(self):
             sage: RC = RiggedConfigurations(['A', 3, 1], [[3, 2], [1, 2]])
             sage: RC.cardinality()
             100
-            sage: RC = RiggedConfigurations(['B', 3, 1], [[2,2],[1,2]])
-            sage: RC.cardinality()
-            5130
+            sage: len(RC.list())
+            100
+
             sage: RC = RiggedConfigurations(['E', 7, 1], [[1,1]])
             sage: RC.cardinality()
             134
+            sage: len(RC.list())
+            134
+
+            sage: RC = RiggedConfigurations(['B', 3, 1], [[2,2],[1,2]])
+            sage: RC.cardinality()
+            5130
         """
         CWLR = self.cartan_type().classical().root_system().ambient_space()
         return sum(CWLR.weyl_dimension(mg.classical_weight()) for mg in self.module_generators)

src/sage/combinat/root_system/hecke_algebra_representation.py

@@ -11,14 +11,15 @@
 import functools
 from sage.misc.abstract_method import abstract_method
 from sage.misc.cachefunc import cached_method
+from sage.misc.fast_methods import WithEqualityById
 from sage.structure.sage_object import SageObject
 from sage.structure.unique_representation import UniqueRepresentation
 from sage.sets.family import Family
 from sage.combinat.subset import Subsets
 from sage.rings.infinity import infinity
 from sage.rings.integer_ring import ZZ
 
-class HeckeAlgebraRepresentation(SageObject):
+class HeckeAlgebraRepresentation(WithEqualityById, SageObject):
     r"""
     A representation of an (affine) Hecke algebra given by the action of the `T` generators
 
@@ -64,6 +65,16 @@ class HeckeAlgebraRepresentation(SageObject):
         sage: H.Y()
         Lazy family (...)_{i in Coroot lattice of the Root system of type ['A', 3, 1]}
 
+    TESTS::
+
+        sage: from sage.combinat.root_system.hecke_algebra_representation import HeckeAlgebraRepresentation
+        sage: W = SymmetricGroup(3)
+        sage: domain = W.algebra(QQ)
+        sage: action = lambda x,i: domain.monomial(x.apply_simple_reflection(i, side="right"))
+        sage: r = HeckeAlgebraRepresentation(domain, action, CartanType(["A",2]), 1, -1)
+        sage: hash(r) # random
+        3
+
     REFERENCES:
 
     .. [HST2008] F. Hivert, A. Schilling, N. Thiery,

src/sage/combinat/root_system/integrable_representations.py

@@ -20,7 +20,7 @@
 from sage.combinat.root_system.weyl_characters import WeylCharacterRing
 
 # TODO: Make this a proper parent and implement actions
-class IntegrableRepresentation(CategoryObject, UniqueRepresentation):
+class IntegrableRepresentation(UniqueRepresentation, CategoryObject):
     r"""
     An irreducible integrable highest weight representation of
     an affine Lie algebra.

src/sage/combinat/root_system/root_system.py

@@ -447,6 +447,11 @@ def __cmp__(self, other):
             True
             sage: r1 == r2
             False
+
+        Check that they inherit a hash method from ``UniqueRepresentation``::
+
+            sage: hash(r1)  # random
+            42
         """
         if self.__class__ != other.__class__:
             return cmp(self.__class__, other.__class__)

src/sage/combinat/root_system/type_folded.py

@@ -19,7 +19,7 @@
 from sage.sets.family import Family
 from sage.combinat.root_system.cartan_type import CartanType
 
-class CartanTypeFolded(SageObject, UniqueRepresentation):
+class CartanTypeFolded(UniqueRepresentation, SageObject):
     r"""
     A Cartan type realized from a (Dynkin) diagram folding.
 
@@ -193,6 +193,8 @@ def __init__(self, cartan_type, folding_of, orbit):
 
             sage: fct = CartanType(['C',4,1]).as_folding()
             sage: TestSuite(fct).run()
+            sage: hash(fct)  # random
+            42
         """
         self._cartan_type = cartan_type
         self._folding = folding_of