FiniteRankFreeModuleMorphism.display: Show matrix decorated with basis element names

src/sage/manifolds/differentiable/diff_map.py

@@ -133,9 +133,9 @@ class is
         sage: Phi.display()
         Phi: S^2 → R^3
         on U: (x, y) ↦ (X, Y, Z) = (2*x/(x^2 + y^2 + 1), 2*y/(x^2 + y^2 + 1),
-         (x^2 + y^2 - 1)/(x^2 + y^2 + 1))
+                                    (x^2 + y^2 - 1)/(x^2 + y^2 + 1))
         on V: (u, v) ↦ (X, Y, Z) = (2*u/(u^2 + v^2 + 1), 2*v/(u^2 + v^2 + 1),
-         -(u^2 + v^2 - 1)/(u^2 + v^2 + 1))
+                                    -(u^2 + v^2 - 1)/(u^2 + v^2 + 1))
 
     It is possible to create the map via the method
     :meth:`~sage.manifolds.differentiable.manifold.DifferentiableManifold.diff_map`
@@ -163,7 +163,7 @@ class is
         sage: Phi1.display()
         Phi: S^2 → R^3
         on U: (x, y) ↦ (X, Y, Z) = (2*x/(x^2 + y^2 + 1), 2*y/(x^2 + y^2 + 1),
-         (x^2 + y^2 - 1)/(x^2 + y^2 + 1))
+                                    (x^2 + y^2 - 1)/(x^2 + y^2 + 1))
 
     The definition can be completed by means of the method
     :meth:`~sage.manifolds.continuous_map.ContinuousMap.add_expr`::
@@ -173,9 +173,9 @@ class is
         sage: Phi1.display()
         Phi: S^2 → R^3
         on U: (x, y) ↦ (X, Y, Z) = (2*x/(x^2 + y^2 + 1), 2*y/(x^2 + y^2 + 1),
-         (x^2 + y^2 - 1)/(x^2 + y^2 + 1))
+                                    (x^2 + y^2 - 1)/(x^2 + y^2 + 1))
         on V: (u, v) ↦ (X, Y, Z) = (2*u/(u^2 + v^2 + 1), 2*v/(u^2 + v^2 + 1),
-         -(u^2 + v^2 - 1)/(u^2 + v^2 + 1))
+                                    -(u^2 + v^2 - 1)/(u^2 + v^2 + 1))
 
     At this stage, ``Phi1`` and ``Phi`` are fully equivalent::
 
@@ -227,6 +227,14 @@ class is
         Basis (∂/∂X,∂/∂Y,∂/∂Z) on the Tangent space at Point Phi(N) on the
          3-dimensional differentiable manifold R^3
 
+    A convenient way to display the matrix of the differential::
+
+        sage: Phi.differential(np).display()
+             ∂/∂u ∂/∂v
+        ∂/∂X⎛   2    0⎞
+        ∂/∂Y⎜   0    2⎟
+        ∂/∂Z⎝   0    0⎠
+
     Differentiable maps can be composed by means of the operator ``*``: let
     us introduce the map `\RR^3\rightarrow \RR^2` corresponding to
     the projection from the point `(X,Y,Z)=(0,0,1)` onto the equatorial plane

src/sage/tensor/modules/free_module_morphism.py

@@ -1022,6 +1022,58 @@ def is_identity(self):
     # End of Morphism methods
     #
 
+    def _modules_and_bases(self, basis1=None, basis2=None):
+        r"""
+        Return domain, codomain, domain basis, and codomain basis.
+
+        This method implements default argument handling for methods
+        :meth:`matrix` and :meth:`display`.
+
+        INPUT:
+
+        - ``basis1`` -- (default: ``None``) basis of the domain of ``self``; if
+          none is provided, the domain's default basis is assumed
+        - ``basis2`` -- (default: ``None``) basis of the codomain of ``self``;
+          if none is provided, ``basis2`` is set to ``basis1`` if ``self`` is
+          an endomorphism, otherwise, ``basis2`` is set to the codomain's
+          default basis.
+
+        EXAMPLES::
+
+            sage: M = FiniteRankFreeModule(ZZ, 3, name='M')
+            sage: N = FiniteRankFreeModule(ZZ, 2, name='N')
+            sage: e = M.basis('e'); f = N.basis('f')
+            sage: phi = M.hom(N, [[-1,2,0], [5,1,2]])
+            sage: phi._modules_and_bases()
+            (Rank-3 free module M over the Integer Ring,
+             Rank-2 free module N over the Integer Ring,
+             Basis (e_0,e_1,e_2) on the Rank-3 free module M over the Integer Ring,
+             Basis (f_0,f_1) on the Rank-2 free module N over the Integer Ring)
+            sage: a = M.automorphism(matrix=[[-1,0,0],[0,1,2],[0,1,3]], basis=e)
+            sage: ep = e.new_basis(a, 'ep', latex_symbol="e'")
+            sage: phi._modules_and_bases(ep)
+            (Rank-3 free module M over the Integer Ring,
+             Rank-2 free module N over the Integer Ring,
+             Basis (ep_0,ep_1,ep_2) on the Rank-3 free module M over the Integer Ring,
+             Basis (f_0,f_1) on the Rank-2 free module N over the Integer Ring)
+        """
+        fmodule1 = self.domain()
+        fmodule2 = self.codomain()
+        if basis1 is None:
+            basis1 = fmodule1.default_basis()
+        elif basis1 not in fmodule1.bases():
+            raise TypeError(str(basis1) + " is not a basis on the " +
+                            str(fmodule1) + ".")
+        if basis2 is None:
+            if self.is_endomorphism():
+                basis2 = basis1
+            else:
+                basis2 = fmodule2.default_basis()
+        elif basis2 not in fmodule2.bases():
+            raise TypeError(str(basis2) + " is not a basis on the " +
+                            str(fmodule2) + ".")
+        return fmodule1, fmodule2, basis1, basis2
+
     def matrix(self, basis1=None, basis2=None):
         r"""
         Return the matrix of ``self`` w.r.t to a pair of bases.
@@ -1109,21 +1161,7 @@ def matrix(self, basis1=None, basis2=None):
 
         """
         from sage.matrix.constructor import matrix
-        fmodule1 = self.domain()
-        fmodule2 = self.codomain()
-        if basis1 is None:
-            basis1 = fmodule1.default_basis()
-        elif basis1 not in fmodule1.bases():
-            raise TypeError(str(basis1) + " is not a basis on the " +
-                            str(fmodule1) + ".")
-        if basis2 is None:
-            if self.is_endomorphism():
-                basis2 = basis1
-            else:
-                basis2 = fmodule2.default_basis()
-        elif basis2 not in fmodule2.bases():
-            raise TypeError(str(basis2) + " is not a basis on the " +
-                            str(fmodule2) + ".")
+        fmodule1, fmodule2, basis1, basis2 = self._modules_and_bases(basis1, basis2)
         if (basis1, basis2) not in self._matrices:
             if self._is_identity:
                 # The identity endomorphism
@@ -1248,3 +1286,73 @@ def _common_bases(self, other):
                 except ValueError:
                     continue
         return resu
+
+    def display(self, basis1=None, basis2=None):
+        r"""
+        Display ``self`` as a matrix w.r.t to a pair of bases.
+
+        If the matrix is not known already, it is computed from the matrix in
+        another pair of bases by means of the change-of-basis formula.
+
+        INPUT:
+
+        - ``basis1`` -- (default: ``None``) basis of the domain of ``self``; if
+          none is provided, the domain's default basis is assumed
+        - ``basis2`` -- (default: ``None``) basis of the codomain of ``self``;
+          if none is provided, ``basis2`` is set to ``basis1`` if ``self`` is
+          an endomorphism, otherwise, ``basis2`` is set to the codomain's
+          default basis.
+
+        EXAMPLES::
+
+            sage: M = FiniteRankFreeModule(ZZ, 3, name='M')
+            sage: N = FiniteRankFreeModule(ZZ, 2, name='N')
+            sage: e = M.basis('e'); f = N.basis('f')
+            sage: phi = M.hom(N, [[-1,2,0], [5,1,2]])
+            sage: phi.display()     # default bases
+                e_0 e_1 e_2
+            f_0⎛ -1   2   0⎞
+            f_1⎝  5   1   2⎠
+            sage: phi.display(e, f)  # given bases
+                e_0 e_1 e_2
+            f_0⎛ -1   2   0⎞
+            f_1⎝  5   1   2⎠
+
+        Matrix of an endomorphism::
+
+            sage: a = M.automorphism(matrix=[[-1,0,0],[0,1,2],[0,1,3]], basis=e)
+            sage: ep = e.new_basis(a, 'ep', latex_symbol="e'")
+            sage: phi = M.endomorphism([[1,2,3], [4,5,6], [7,8,9]], basis=ep)
+            sage: phi.display(ep)
+                 ep_0 ep_1 ep_2
+            ep_0⎛   1    2    3⎞
+            ep_1⎜   4    5    6⎟
+            ep_2⎝   7    8    9⎠
+            sage: phi.display(ep, ep)  # same as above
+                 ep_0 ep_1 ep_2
+            ep_0⎛   1    2    3⎞
+            ep_1⎜   4    5    6⎟
+            ep_2⎝   7    8    9⎠
+            sage: phi.display()  # matrix w.r.t to the module's default basis
+                e_0 e_1 e_2
+            e_0⎛  1  -3   1⎞
+            e_1⎜-18  39 -18⎟
+            e_2⎝-25  54 -25⎠
+        """
+        from sage.misc.latex import latex
+        from .format_utilities import is_atomic, FormattedExpansion
+        fmodule1, fmodule2, basis1, basis2 = self._modules_and_bases(basis1, basis2)
+        matrix = self.matrix(basis1, basis2)
+        if all(element._name for element in basis1):
+            basis1_names = [element._name for element in basis1]
+        else:
+            basis1_names = None
+        if all(element._name for element in basis2):
+            basis2_names = [element._name for element in basis2]
+        else:
+            basis2_names = None
+        resu_txt = matrix.str(unicode=True,
+                              top_border=basis1_names,
+                              left_border=basis2_names)
+        resu_latex = latex(matrix)
+        return FormattedExpansion(resu_txt, resu_latex)