FiniteRankFreeModule_abstract.isomorphism_with_fixed_basis: Add examp…

…le with codomain= tensor square of a CombinatorialFreeModule

src/sage/tensor/modules/finite_rank_free_module.py

@@ -842,6 +842,23 @@ def isomorphism_with_fixed_basis(self, basis=None, codomain=None):
             [2 4 5]
             [3 5 6]
 
+        Sending tensors to elements of the tensor square of :class:`CombinatorialFreeModule`::
+
+            sage: T20 = V.tensor_module(2, 0); T20
+            Free module of type-(2,0) tensors on the 3-dimensional vector space over the Rational Field
+            sage: e_T20 = T02.basis("e"); e_T20
+            <sage.tensor.modules.tensor_free_submodule_basis.TensorFreeSubmoduleBasis_comp_with_category object at 0x7fc9b93d1d60>
+            sage: W = CombinatorialFreeModule(QQ, [1, 2, 3]).tensor_square(); W
+            Free module generated by {1, 2, 3} over Rational Field # Free module generated by {1, 2, 3} over Rational Field
+            sage: phi_e_T20 = T20.isomorphism_with_fixed_basis(e_T20, codomain=W); phi_e_T20
+            Generic morphism:
+            From: Free module of type-(2,0) tensors on the 3-dimensional vector space over the Rational Field
+            To:   Free module generated by {1, 2, 3} over Rational Field # Free module generated by {1, 2, 3} over Rational Field
+            sage: t = T20.an_element(); t.display()
+            1/2 e_1⊗e_1
+            sage: phi_e_T20(t)
+            1/2*B[1] # B[1]
+
         TESTS::
 
             sage: V = FiniteRankFreeModule(QQ, 3); V