src/sage/tensor/modules/finite_rank_free_module.py: WIP isomorphism_w…

…ith_fixed_basis with codomain=symmetric matrices
sagemath · Aug 27, 2022 · 06e0cd8 · 06e0cd8
1 parent eb517b2
commit 06e0cd8
Showing 1 changed file with 36 additions and 0 deletions.
diff --git a/src/sage/tensor/modules/finite_rank_free_module.py b/src/sage/tensor/modules/finite_rank_free_module.py
@@ -846,6 +846,42 @@ def isomorphism_with_fixed_basis(self, basis=None, codomain=None):
             [2 4 5]
             [3 5 6]
 
+        Same but explicitly in the subspace of symmetric bilinear forms::
+
+            sage: Sym2Vdual = V.dual_symmetric_power(2); Sym2Vdual
+            Free module of type-(0,2) tensors with Fully symmetric 2-indices components w.r.t. (1, 2, 3) on the 3-dimensional vector space over the Rational Field
+            sage: Sym2Vdual.is_submodule(T02)
+            True
+            sage: Sym2Vdual.rank()
+            6
+            sage: e_Sym2Vdual = Sym2Vdual.basis("e"); e_Sym2Vdual
+            Standard basis on the Free module of type-(0,2) tensors
+             with Fully symmetric 2-indices components w.r.t. (1, 2, 3)
+             on the 3-dimensional vector space over the Rational Field
+             induced by Basis (e_1,e_2,e_3) on the 3-dimensional vector space over the Rational Field
+            sage: [phi_e_T02(b) for b in e_T02]
+            [
+            [0 0 0]  [0 0 0]  [0 0 0]  [0 0 0]  [0 0 0]  [0 0 0]  [0 0 0]  [0 0 0]
+            [0 0 0]  [0 0 0]  [0 0 0]  [0 0 0]  [0 0 0]  [0 0 0]  [0 0 0]  [0 0 0]
+            [0 0 0], [0 0 0], [0 0 0], [0 0 0], [0 0 0], [0 0 0], [0 0 0], [0 0 0],
+            <BLANKLINE>
+            [0 0 0]
+            [0 0 0]
+            [0 0 0]
+            ]
+            sage: W_basis = [phi_e_T02(b) for b in e_Sym2Vdual]; W_basis
+            [
+            [0 0 0]  [0 0 0]  [0 0 0]  [0 0 0]  [0 0 0]  [0 0 0]
+            [0 0 0]  [0 0 0]  [0 0 0]  [0 0 0]  [0 0 0]  [0 0 0]
+            [0 0 0], [0 0 0], [0 0 0], [0 0 0], [0 0 0], [0 0 0]
+            ]
+            sage: W = MatrixSpace(QQ, 3).submodule(W_basis); W
+            Free module generated by {} over Rational Field
+            sage: phi_e_Sym2Vdual = Sym2Vdual.isomorphism_with_fixed_basis(e_Sym2Vdual, codomain=W); phi_e_Sym2Vdual
+            Traceback (most recent call last):
+            ...
+            ValueError: domain and codomain must have the same rank
+
         Sending tensors to elements of the tensor square of :class:`CombinatorialFreeModule`::
 
             sage: T20 = V.tensor_module(2, 0); T20