Create CombinatorialFreeModule if basis keys given

src/sage/modules/free_module.py

@@ -389,9 +389,46 @@ def create_object(self, version, key):
         except NotImplementedError:
             return FreeModule_ambient(base_ring, rank, sparse=sparse)
 
+FreeModuleFactory_with_standard_basis = FreeModuleFactory("FreeModule")
 
-FreeModule = FreeModuleFactory("FreeModule")
+def FreeModule(base_ring, rank_or_basis_keys=None, sparse=False, inner_product_matrix=None, *,
+               with_basis='standard', rank=None, basis_keys=None, **args):
+    """
+
+    EXAMPLES::
 
+        sage: FreeModule(QQ, ['a', 'b', 'c'])
+        Free module generated by {'a', 'b', 'c'} over Rational Field
+        sage: _.category()
+        Category of finite dimensional vector spaces with basis over Rational Field
+
+        sage: FreeModule(QQ, 3, with_basis=None)
+        3-dimensional vector space over the Rational Field
+        sage: _.category()
+        Category of finite dimensional vector spaces over Rational Field
+
+    """
+    if rank_or_basis_keys is not None:
+        if rank_or_basis_keys in sage.rings.integer_ring.IntegerRing():
+            rank = rank_or_basis_keys
+        else:
+            basis_keys = rank_or_basis_keys
+    if not with_basis:
+        if inner_product_matrix is not None:
+            raise NotImplementedError
+        from sage.tensor.modules.finite_rank_free_module import FiniteRankFreeModule
+        return FiniteRankFreeModule(base_ring, rank, **args)
+    elif with_basis == 'standard':
+        if rank is not None:
+            return FreeModuleFactory_with_standard_basis(base_ring, rank, sparse,
+                                                        inner_product_matrix, **args)
+        else:
+            if inner_product_matrix is not None:
+                raise NotImplementedError
+            from sage.combinat.free_module import CombinatorialFreeModule
+            return CombinatorialFreeModule(base_ring, basis_keys, **args)
+    else:
+        raise NotImplementedError
 
 def VectorSpace(K, dimension, sparse=False, inner_product_matrix=None):
     """