eja: add composition (multiplication) for morphisms.

The whatever-superclass composition of morphisms returned a formal
composition, which can't be treated like a morphism itself. Since all
of our morphisms are represented by matrices, we can simply perform
the composition ourself via matrix multiplication to return something
useful.

diff --git a/mjo/eja/euclidean_jordan_algebra.py b/mjo/eja/euclidean_jordan_algebra.py
index 78fa6b7c0f96725af4da2e96f09ee2d7eb5449cf..d459ebe97540abe88f1aef603e29ec994bd1cb74 100644 (file)
--- a/mjo/eja/euclidean_jordan_algebra.py
+++ b/mjo/eja/euclidean_jordan_algebra.py
@@ -30,14 +30,13 @@ 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.
+      3. Allows us to add, multiply (compose), and invert morphisms in
+         the obvious way.
 
     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, and you can't add/invert them.
+    our EJA, and you can't add/multiply/invert them.
     """
 
     def __add__(self, other):
@@ -125,6 +124,44 @@ class FiniteDimensionalEuclideanJordanAlgebraMorphism(FiniteDimensionalAlgebraMo
         return FiniteDimensionalEuclideanJordanAlgebraMorphism(self.parent(),
                                                                 A.inverse())
 
+    def __mul__(self, other):
+        """
+        Compose two EJA morphisms using multiplicative notation.
+
+        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
+            [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]
+
+        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
+
+        """
+        if not other.codomain() is self.domain():
+            raise ValueError("(co)domains must agree for composition")
+
+        return FiniteDimensionalEuclideanJordanAlgebraMorphism(
+                  self.parent(),
+                  self.matrix()*other.matrix() )
+
+
     def _repr_(self):
         """
         We override only the representation that is shown to the user,