Merge branch 'public/misc/names_argument_indexed_generators-17039' of…

… git://trac.sagemath.org/sage into public/misc/names_argument_indexed_generators-17039

src/sage/combinat/free_module.py

@@ -15,7 +15,7 @@
 
 from sage.structure.unique_representation import UniqueRepresentation
 from sage.structure.parent import Parent
-from sage.structure.indexed_generators import IndexedGenerators
+from sage.structure.indexed_generators import IndexedGenerators, parse_indices_names
 from sage.modules.module import Module
 from sage.rings.all import Integer
 from sage.structure.element import parent
@@ -236,10 +236,22 @@ class CombinatorialFreeModule(UniqueRepresentation, Module, IndexedGenerators):
         sage: g = 2*G.monomial(3) +     G.monomial(4)
         sage: tensor([f, g])
         2*x[1] # y[3] + x[1] # y[4] + 4*x[2] # y[3] + 2*x[2] # y[4]
+
+    We check that we can use the shorthand ``C.<a,b,...> = ...``::
+
+        sage: C.<x,y,z> = CombinatorialFreeModule(QQ)
+        sage: C
+        Free module generated by {'x', 'y', 'z'} over Rational Field
+        sage: a = x - y + 4*z; a
+        x - y + 4*z
+        sage: a.parent() is C
+        True
+
     """
 
     @staticmethod
-    def __classcall_private__(cls, base_ring, basis_keys, category = None, prefix="B", **keywords):
+    def __classcall_private__(cls, base_ring, basis_keys=None, category=None,
+                              prefix=None, names=None, **keywords):
         """
         TESTS::
 
@@ -283,7 +295,14 @@ def __classcall_private__(cls, base_ring, basis_keys, category = None, prefix="B
         latex_bracket = keywords.get('latex_bracket', None)
         if isinstance(latex_bracket, list):
             keywords['latex_bracket'] = tuple(latex_bracket)
-        return super(CombinatorialFreeModule, cls).__classcall__(cls, base_ring, basis_keys, category = category, prefix=prefix, **keywords)
+
+        names, basis_keys, prefix = parse_indices_names(names, basis_keys, prefix, keywords)
+        if prefix is None:
+            prefix = "B"
+
+        return super(CombinatorialFreeModule, cls).__classcall__(cls,
+            base_ring, basis_keys, category=category, prefix=prefix, names=names,
+            **keywords)
 
     # We make this explicitly a Python class so that the methods,
     #   specifically _mul_, from category framework still works. -- TCS
@@ -325,7 +344,8 @@ def element_class(self):
                                            module=self.__class__.__module__,
                                            inherit=True)
 
-    def __init__(self, R, basis_keys, element_class = None, category = None, prefix="B", **kwds):
+    def __init__(self, R, basis_keys=None, element_class=None, category=None,
+                 prefix=None, names=None, **kwds):
         r"""
         TESTS::
 
@@ -396,6 +416,12 @@ def __init__(self, R, basis_keys, element_class = None, category = None, prefix=
         # (e.g. root systems passes lists)
         basis_keys = Sets()(basis_keys, enumerated_set=True)
 
+        # This is needed for the Cartesian product
+        # TODO: Remove this duplication from __classcall_private__
+        names, basis_keys, prefix = parse_indices_names(names, basis_keys, prefix, kwds)
+        if prefix is None:
+            prefix = "B"
+
         # ignore the optional 'key' since it only affects CachedRepresentation
         kwds.pop('key', None)
         # This needs to be first as per #10127
@@ -418,9 +444,9 @@ def __init__(self, R, basis_keys, element_class = None, category = None, prefix=
         if basis_keys in Sets().Finite():
             category = category.FiniteDimensional()
 
-        Parent.__init__(self, base = R, category = category,
+        Parent.__init__(self, base=R, category=category, names=names,
                         # Could we get rid of this?
-                        element_constructor = self._element_constructor_)
+                        element_constructor=self._element_constructor_)
 
         self._order = None
 
@@ -673,6 +699,30 @@ def _an_element_impl(self):
         """
         return self.element_class(self, {})
 
+    def _first_ngens(self, n):
+        """
+        Used by the preparser for ``F.<x> = ...``.
+
+        EXAMPLES::
+
+            sage: C = CombinatorialFreeModule(QQ, ZZ)
+            sage: C._first_ngens(3)
+            (B[0], B[1], B[-1])
+
+            sage: R.<x,y> = FreeAlgebra(QQ, 2)
+            sage: x,y
+            (x, y)
+        """
+        try:
+            # Try gens first for compatibility with classes that
+            #   rely on this (e.g., FreeAlgebra)
+            return tuple(self.gens())[:n]
+        except (AttributeError, ValueError, TypeError):
+            pass
+        B = self.basis()
+        it = iter(self._indices)
+        return tuple(B[next(it)] for i in range(n))
+
     def dimension(self):
         """
         Return the dimension of the free module (which is given

src/sage/monoids/free_monoid.py

@@ -107,10 +107,14 @@ def FreeMonoid(index_set=None, names=None, commutative=False, **kwds):
         Free abelian monoid on 3 generators (x, y, z)
         sage: FreeMonoid(index_set=ZZ, commutative=True)
         Free abelian monoid indexed by Integer Ring
+
+    TESTS::
+
+        sage: FreeMonoid(index_set=ZZ, names='x,y,z')
+        Free monoid indexed by Integer Ring
     """
     if 'abelian' in kwds:
-        commutative = kwds['abelian']
-        del kwds['abelian']
+        commutative = kwds.pop('abelian')
 
     if commutative:
         from sage.monoids.free_abelian_monoid import FreeAbelianMonoid
@@ -127,7 +131,7 @@ def FreeMonoid(index_set=None, names=None, commutative=False, **kwds):
 
     if index_set not in ZZ:
         if names is not None:
-            names = normalize_names(len(names), names)
+            names = normalize_names(-1, names)
         from sage.monoids.indexed_free_monoid import IndexedFreeMonoid
         return IndexedFreeMonoid(index_set, names=names, **kwds)
 

src/sage/monoids/indexed_free_monoid.py

@@ -20,7 +20,7 @@
 from sage.structure.parent import Parent
 from sage.structure.unique_representation import UniqueRepresentation
 from sage.structure.element import MonoidElement
-from sage.structure.indexed_generators import IndexedGenerators
+from sage.structure.indexed_generators import IndexedGenerators, parse_indices_names
 from sage.structure.richcmp import op_EQ, op_NE, richcmp, rich_to_bool
 import sage.data_structures.blas_dict as blas
 
@@ -633,7 +633,7 @@ class IndexedMonoid(Parent, IndexedGenerators, UniqueRepresentation):
     :class:`~sage.structure.indexed_generators.IndexedGenerators`.
     """
     @staticmethod
-    def __classcall__(cls, indices, prefix="F", **kwds):
+    def __classcall__(cls, indices, prefix=None, names=None, **kwds):
         """
         TESTS::
 
@@ -651,16 +651,11 @@ def __classcall__(cls, indices, prefix="F", **kwds):
             sage: Groups.Commutative.free()
             Traceback (most recent call last):
             ...
-            ValueError: no index set specified
+            ValueError: either the indices or names must be given
         """
-        if isinstance(indices, str):
-            indices = FiniteEnumeratedSet(list(indices))
-        elif isinstance(indices, (list, tuple)):
-            indices = FiniteEnumeratedSet(indices)
-        elif indices is None:
-            if kwds.get('names', None) is None:
-                raise ValueError("no index set specified")
-            indices = FiniteEnumeratedSet(kwds['names'])
+        names, indices, prefix = parse_indices_names(names, indices, prefix, kwds)
+        if prefix is None:
+            prefix = "F"
 
         # bracket or latex_bracket might be lists, so convert
         # them to tuples so that they're hashable.
@@ -670,7 +665,9 @@ def __classcall__(cls, indices, prefix="F", **kwds):
         latex_bracket = kwds.get('latex_bracket', None)
         if isinstance(latex_bracket, list):
             kwds['latex_bracket'] = tuple(latex_bracket)
-        return super(IndexedMonoid, cls).__classcall__(cls, indices, prefix, **kwds)
+
+        return super(IndexedMonoid, cls).__classcall__(cls, indices, prefix,
+                                                       names=names, **kwds)
 
     def __init__(self, indices, prefix, category=None, names=None, **kwds):
         """
@@ -708,9 +705,9 @@ def _first_ngens(self, n):
 
         EXAMPLES::
 
-            sage: F.<x,y,z> = FreeMonoid(index_set=ZZ)
-            sage: [x, y, z]
-            [F[0], F[1], F[-1]]
+            sage: F = FreeMonoid(index_set=ZZ)
+            sage: F._first_ngens(3)
+            (F[0], F[1], F[-1])
         """
         it = iter(self._indices)
         return tuple(self.gen(next(it)) for i in range(n))