Merge branch 'public/11111-more_support_for_finite_dimensional_module…

…s_and_algebras_with_basis' of trac.sagemath.org:sage into t/11111/more_support_for_finite_dimensional_modules_and_algebras_with_basis

src/sage/categories/finite_dimensional_modules_with_basis.py

@@ -193,13 +193,13 @@ def annihilator_basis(self, S, action=operator.mul, side='right'):
             By specifying the standard Lie bracket as action, one can
             compute the commutator of a subspace of `F`::
 
-                sage: F.annihilator_basis([a+b], action = F.bracket)
+                sage: F.annihilator_basis([a+b], action=F.bracket)
                 [x + y, a, b]
 
             In particular one can compute a basis of the center of the
             algebra. In our example, it is reduced to the identity::
 
-                sage: F.annihilator_basis(F.algebra_generators(), action = F.bracket)
+                sage: F.annihilator_basis(F.algebra_generators(), action=F.bracket)
                 [x + y]
 
             But see also

src/sage/categories/modules_with_basis.py

@@ -601,7 +601,7 @@ def submodule(self, gens,
 
             - ``gens`` -- a list or family of elements of ``self``
 
-            - ``check`` -- (default: True) whether to verify that the
+            - ``check`` -- (default: ``True``) whether to verify that the
                elements of ``gens`` are in ``self``.
 
             - ``already_echelonized`` -- (default: ``False``) whether
@@ -677,6 +677,20 @@ def submodule(self, gens,
                 ...
                 ValueError: x[0] is not in the image
 
+            It is not necessary that the generators of the submodule form
+            a basis (an explicit basis will be computed)::
+
+                sage: X = CombinatorialFreeModule(QQ, range(3), prefix="x")
+                sage: x = X.basis()
+                sage: gens = [x[0] - x[1], 2*x[1] - 2*x[2], x[0] - x[2]]; gens
+                [x[0] - x[1], 2*x[1] - 2*x[2], x[0] - x[2]]
+                sage: Y = X.submodule(gens, already_echelonized=False)
+                sage: Y.print_options(prefix='y')
+                sage: Y
+                Free module generated by {0, 1} over Rational Field
+                sage: [b.lift() for b in Y.basis()]
+                [x[0] - x[2], x[1] - x[2]]
+
             We now implement by hand the center of the algebra of the
             symmetric group `S_3`::
 

src/sage/combinat/free_module.py

@@ -1590,11 +1590,11 @@ def set_order(self, order):
         the one used in the generation of the elements of self's
         associated enumerated set.
 
-        .. warning:: many cached methods depend on this order, in
-           particular for constructing subspaces and
-           quotients. Changing the order after computing such does
-           currently not invalidate those cache, and is likely to
-           bring in inconsistencies.
+        .. warning:: Many cached methods depend on this order, in
+           particular for constructing subspaces and quotients.
+           Changing the order after some computations have been
+           cached does not invalidate the cache, and is likely to
+           introduce inconsistencies.
 
         EXAMPLES::
 
@@ -1626,7 +1626,7 @@ def get_order(self):
 
     def get_order_cmp(self):
         """
-        Returns a comparison function on the basis indices which is
+        Returns a comparison function on the basis indices that is
         compatible with the current term order.
 
         EXAMPLES::
@@ -2068,15 +2068,15 @@ def echelon_form(self, elements, base_ring=None):
         INPUT:
 
         - ``elements`` - a list of elements of ``self``.
-        
+
         - ``base_ring`` - ring (default: ``None``): compute the echelon
           form over the given ring; if ``base_ring`` is ``None``, then uses
           the base ring of ``self``.
 
         OUTPUT:
-        
+
         - list of elements of ``self``
-        
+
         EXAMPLES::
 
             sage: F = CombinatorialFreeModule(ZZ, [1,2,3,4])

src/sage/combinat/symmetric_group_algebra.py

@@ -191,7 +191,7 @@ def SymmetricGroupAlgebra(R, W):
         True
         sage: TestSuite(SGA).run()
 
-        sage: SG=SymmetricGroupAlgebra(ZZ,3)
+        sage: SG = SymmetricGroupAlgebra(ZZ, 3)
         sage: SG.group().conjugacy_classes_representatives()
         [[1, 2, 3], [2, 1, 3], [2, 3, 1]]
 

src/sage/modules/with_basis/subquotient.py

@@ -2,7 +2,7 @@
 Quotients of Modules With Basis
 """
 #*****************************************************************************
-#  Copyright (C) 2010 Florent Hivert <Florent.Hivert@univ-mlv.fr>
+#  Copyright (C) 2010-2015 Florent Hivert <Florent.Hivert@univ-mlv.fr>
 #
 #  Distributed under the terms of the GNU General Public License (GPL)
 #                  http://www.gnu.org/licenses/
@@ -26,7 +26,7 @@ class QuotientModuleWithBasis(CombinatorialFreeModule):
     should implement a method ``reduce``. Futheremore its ``lift``
     method should have a method ``.cokernel_basis_indices`` that
     computes the indexing set of a subset of the basis of ``self``
-    that spans some suplementary of ``submodule`` in the ambient
+    that spans some supplementary of ``submodule`` in the ambient
     space. Mathematically speaking, ``submodule`` should be a free
     submodule whose basis can be put in unitriangular echelon form.
 
@@ -57,7 +57,7 @@ class QuotientModuleWithBasis(CombinatorialFreeModule):
     @staticmethod
     def __classcall_private__(cls, submodule, category=None):
         r"""
-        Normalize the input
+        Normalize the input.
 
         TESTS::
 
@@ -76,18 +76,21 @@ def __classcall_private__(cls, submodule, category=None):
 
     def __init__(self, submodule, category):
         r"""
+        Initialization quotients of a module with basis by a submodule.
+
         TESTS::
 
             sage: from sage.modules.with_basis.subquotient import QuotientModuleWithBasis
-            sage: X = CombinatorialFreeModule(QQ, range(3)); x = X.basis()
+            sage: X = CombinatorialFreeModule(QQ, range(3), prefix="x"); x = X.basis()
             sage: I = X.submodule( (x[0]-x[1], x[1]-x[2]) )
             sage: Y = QuotientModuleWithBasis(I)
+            sage: Y.print_options(prefix='y')
             sage: Y
             Free module generated by {2} over Rational Field
             sage: Y.category()
             Join of Category of finite dimensional modules with basis over Rational Field and Category of vector spaces with basis over Rational Field and Category of quotients of sets
             sage: Y.basis().list()
-            [B[2]]
+            [y[2]]
             sage: TestSuite(Y).run()
         """
         self._submodule = submodule
@@ -104,15 +107,15 @@ def ambient(self):
 
         EXAMPLES::
 
-            sage: X = CombinatorialFreeModule(QQ, range(3), prefix = "x"); x = X.basis()
+            sage: X = CombinatorialFreeModule(QQ, range(3), prefix="x"); x = X.basis()
             sage: Y = X.quotient_module((x[0]-x[1], x[1]-x[2]))
             sage: Y.ambient() is X
             True
         """
         return self._ambient
 
     def lift(self, x):
-        """
+        r"""
         Lift ``x`` to the ambient space of ``self``.
 
         INPUT:
@@ -121,8 +124,8 @@ def lift(self, x):
 
         EXAMPLES::
 
-            sage: X = CombinatorialFreeModule(QQ, range(3), prefix = "x"); x = X.basis()
-            sage: Y = X.quotient_module((x[0]-x[1], x[1]-x[2]));           y = Y.basis()
+            sage: X = CombinatorialFreeModule(QQ, range(3), prefix="x"); x = X.basis()
+            sage: Y = X.quotient_module((x[0]-x[1], x[1]-x[2]));         y = Y.basis()
             sage: Y.lift(y[2])
             x[2]
         """
@@ -139,8 +142,8 @@ def retract(self, x):
 
         EXAMPLES::
 
-            sage: X = CombinatorialFreeModule(QQ, range(3), prefix = "x"); x = X.basis()
-            sage: Y = X.quotient_module((x[0]-x[1], x[1]-x[2]));           y = Y.basis()
+            sage: X = CombinatorialFreeModule(QQ, range(3), prefix="x"); x = X.basis()
+            sage: Y = X.quotient_module((x[0]-x[1], x[1]-x[2]));         y = Y.basis()
             sage: Y.print_options(prefix='y')
             sage: Y.retract(x[0])
             y[2]
@@ -159,7 +162,7 @@ class SubmoduleWithBasis(CombinatorialFreeModule):
 
     INPUT:
 
-    - ``basis`` -- a family of vectors in echelon form in some
+    - ``basis`` -- a family of elements in echelon form in some
       :class:`module with basis <ModulesWithBasis>` `V`, or data that
       can be converted into such a family
 
@@ -196,7 +199,7 @@ def __classcall_private__(cls, basis, ambient=None, category=None, *args, **opts
         basis = Family(basis)
         if ambient is None:
             ambient = basis.an_element().parent()
-        default_category=ModulesWithBasis(ambient.category().base_ring()).Subobjects()
+        default_category = ModulesWithBasis(ambient.category().base_ring()).Subobjects()
         category = default_category.or_subcategory(category, join=True)
         return super(SubmoduleWithBasis, cls).__classcall__(
             cls, basis, ambient, category, *args, **opts)
@@ -208,13 +211,14 @@ def __init__(self, basis, ambient, category):
         TESTS::
 
             sage: from sage.modules.with_basis.subquotient import SubmoduleWithBasis
-            sage: X = CombinatorialFreeModule(QQ, range(3)); x = X.basis()
+            sage: X = CombinatorialFreeModule(QQ, range(3), prefix="x"); x = X.basis()
             sage: ybas = (x[0]-x[1], x[1]-x[2])
             sage: Y = SubmoduleWithBasis(ybas, X)
+            sage: Y.print_options(prefix='y')
             sage: Y.basis().list()
-            [B[0], B[1]]
+            [y[0], y[1]]
             sage: [ y.lift() for y in Y.basis() ]
-            [B[0] - B[1], B[1] - B[2]]
+            [x[0] - x[1], x[1] - x[2]]
             sage: TestSuite(Y).run()
         """
         import operator
@@ -245,20 +249,21 @@ def lift(self):
 
         EXAMPLES::
 
-            sage: X = CombinatorialFreeModule(QQ, range(3));                         x = X.basis()
+            sage: X = CombinatorialFreeModule(QQ, range(3), prefix="x");             x = X.basis()
             sage: Y = X.submodule((x[0]-x[1], x[1]-x[2]), already_echelonized=True); y = Y.basis()
             sage: Y.lift
             Generic morphism:
               From: Free module generated by {0, 1} over Rational Field
               To:   Free module generated by {0, 1, 2} over Rational Field
             sage: [ Y.lift(u) for u in y ]
-            [B[0] - B[1], B[1] - B[2]]
+            [x[0] - x[1], x[1] - x[2]]
             sage: (y[0] + y[1]).lift()
-            B[0] - B[2]
+            x[0] - x[2]
         """
         return self.module_morphism(self.lift_on_basis,
                                     codomain=self.ambient(),
-                                    triangular="lower", cmp=self.ambient().get_order_cmp(),
+                                    triangular="lower",
+                                    cmp=self.ambient().get_order_cmp(),
                                     inverse_on_support="compute")
 
     @lazy_attribute
@@ -271,14 +276,14 @@ def reduce(self):
 
         EXAMPLES::
 
-            sage: X = CombinatorialFreeModule(QQ, range(3));                         x = X.basis()
+            sage: X = CombinatorialFreeModule(QQ, range(3), prefix="x"); x = X.basis()
             sage: Y = X.submodule((x[0]-x[1], x[1]-x[2]), already_echelonized=True)
             sage: Y.reduce
             Generic endomorphism of Free module generated by {0, 1, 2} over Rational Field
             sage: Y.reduce(x[1])
-            B[2]
+            x[2]
             sage: Y.reduce(2*x[0] + x[1])
-            3*B[2]
+            3*x[2]
 
         TESTS::
 
@@ -294,14 +299,15 @@ def retract(self):
 
         EXAMPLES::
 
-            sage: X = CombinatorialFreeModule(QQ, range(3));                         x = X.basis()
+            sage: X = CombinatorialFreeModule(QQ, range(3), prefix="x"); x = X.basis()
             sage: Y = X.submodule((x[0]-x[1], x[1]-x[2]), already_echelonized=True)
+            sage: Y.print_options(prefix='y')
             sage: Y.retract
             Generic morphism:
               From: Free module generated by {0, 1, 2} over Rational Field
               To:   Free module generated by {0, 1} over Rational Field
             sage: Y.retract(x[0] - x[2])
-            B[0] + B[1]
+            y[0] + y[1]
 
         TESTS::
 
@@ -334,7 +340,7 @@ def is_submodule(self, other):
         if other is self.ambient():
             return True
         if not isinstance(self, SubmoduleWithBasis) and self.ambient() is other.ambient():
-            raise ValueError("other (=%s) should be a submodule of the same ambient space"%other)
+            raise ValueError("other (=%s) should be a submodule of the same ambient space" % other)
         if not self in ModulesWithBasis.FiniteDimensional:
             raise NotImplementedError("is_submodule for infinite dimensional modules")
         for b in self.basis():