eja: improve tests for morphism addition.

[sage.d.git] / mjo / eja / euclidean_jordan_algebra.py

diff --git a/mjo/eja/euclidean_jordan_algebra.py b/mjo/eja/euclidean_jordan_algebra.py
index fcaf10032ebf10885e047a55114fe0506235531b..fa11aed040a152de2cfe8f9c398b77af39c33276 100644 (file)
--- a/mjo/eja/euclidean_jordan_algebra.py
+++ b/mjo/eja/euclidean_jordan_algebra.py
@@ -17,7 +17,7 @@ from sage.algebras.finite_dimensional_algebras.finite_dimensional_algebra_morphi
 class FiniteDimensionalEuclideanJordanAlgebraMorphism(FiniteDimensionalAlgebraMorphism):
     """
     A very thin wrapper around FiniteDimensionalAlgebraMorphism that
-    does only two things:
+    does only three things:
 
       1. Avoids the ``unitary`` and ``check`` arguments to the constructor
          that will always be ``False``. This is necessary because these
@@ -28,11 +28,55 @@ class FiniteDimensionalEuclideanJordanAlgebraMorphism(FiniteDimensionalAlgebraMo
       2. Inputs and outputs the underlying matrix with respect to COLUMN
          vectors, unlike the parent class.
 
+      3. Allows us to add morphisms in the obvious way.
+
+      4. Allows us to invert morphisms.
+
     If this seems a bit heavyweight, it is. I would have been happy to
     use a the ring morphism that underlies the finite-dimensional
     algebra morphism, but they don't seem to be callable on elements of
-    our EJA.
+    our EJA, and you can't add/invert them.
     """
+
+    def __add__(self, other):
+        """
+        Add two EJA morphisms in the obvious way.
+
+        EXAMPLES::
+
+            sage: J = RealSymmetricEJA(3)
+            sage: x = J.zero()
+            sage: y = J.one()
+            sage: x.operator() + y.operator()
+            Morphism from Euclidean Jordan algebra of degree 6 over Rational
+            Field to Euclidean Jordan algebra of degree 6 over Rational Field
+            given by matrix
+            [1 0 0 0 0 0]
+            [0 1 0 0 0 0]
+            [0 0 1 0 0 0]
+            [0 0 0 1 0 0]
+            [0 0 0 0 1 0]
+            [0 0 0 0 0 1]
+
+        TESTS::
+
+            sage: set_random_seed()
+            sage: J = random_eja()
+            sage: x = J.random_element()
+            sage: y = J.random_element()
+            sage: (x.operator() + y.operator()) in J.Hom(J)
+            True
+
+        """
+        P = self.parent()
+        if not other in P:
+            raise ValueError("summands must live in the same space")
+
+        return FiniteDimensionalEuclideanJordanAlgebraMorphism(
+                  P,
+                  self.matrix() + other.matrix() )
+
+
     def __init__(self, parent, f):
         FiniteDimensionalAlgebraMorphism.__init__(self,
                                                   parent,
@@ -1074,6 +1118,30 @@ class FiniteDimensionalEuclideanJordanAlgebra(FiniteDimensionalAlgebra):
             return W.linear_combination(zip(self.vector(), B))
 
 
+        def operator(self):
+            """
+            Return the left-multiplication-by-this-element
+            operator on the ambient algebra.
+
+            TESTS::
+
+                sage: set_random_seed()
+                sage: J = random_eja()
+                sage: x = J.random_element()
+                sage: y = J.random_element()
+                sage: x.operator()(y) == x*y
+                True
+                sage: y.operator()(x) == x*y
+                True
+
+            """
+            P = self.parent()
+            return FiniteDimensionalEuclideanJordanAlgebraMorphism(
+                     Hom(P,P),
+                     self.operator_matrix() )
+
+
+
         def operator_matrix(self):
             """
             Return the matrix that represents left- (or right-)