eja: add negation/subtraction for morphisms.

diff --git a/mjo/eja/euclidean_jordan_algebra.py b/mjo/eja/euclidean_jordan_algebra.py
index d459ebe97540abe88f1aef603e29ec994bd1cb74..5f01556b0f0cecf52437f0a115ab343cbeeb2b18 100644 (file)
--- a/mjo/eja/euclidean_jordan_algebra.py
+++ b/mjo/eja/euclidean_jordan_algebra.py
@@ -30,13 +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, multiply (compose), and invert morphisms in
-         the obvious way.
+      3. Allows us to add, subtract, negate, 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/multiply/invert them.
+    our EJA, and you can't add/multiply/etc. them.
     """
 
     def __add__(self, other):
@@ -162,6 +162,36 @@ class FiniteDimensionalEuclideanJordanAlgebraMorphism(FiniteDimensionalAlgebraMo
                   self.matrix()*other.matrix() )
 
 
+    def __neg__(self):
+        """
+        Negate this morphism.
+
+        EXAMPLES::
+
+            sage: J = RealSymmetricEJA(2)
+            sage: x = J.one()
+            sage: -x.operator()
+            Morphism from Euclidean Jordan algebra of degree 3 over Rational
+            Field to Euclidean Jordan algebra of degree 3 over Rational Field
+            given by matrix
+            [-1  0  0]
+            [ 0 -1  0]
+            [ 0  0 -1]
+
+        TESTS::
+
+            sage: set_random_seed()
+            sage: J = random_eja()
+            sage: x = J.random_element()
+            sage: -x.operator() in J.Hom(J)
+            True
+
+        """
+        return FiniteDimensionalEuclideanJordanAlgebraMorphism(
+                  self.parent(),
+                  -self.matrix() )
+
+
     def _repr_(self):
         """
         We override only the representation that is shown to the user,
@@ -196,6 +226,36 @@ class FiniteDimensionalEuclideanJordanAlgebraMorphism(FiniteDimensionalAlgebraMo
         return "Morphism from {} to {} given by matrix\n{}".format(
             self.domain(), self.codomain(), self.matrix())
 
+
+    def __sub__(self, other):
+        """
+        Subtract one morphism from another using addition and negation.
+
+        EXAMPLES::
+
+            sage: J = RealSymmetricEJA(2)
+            sage: L1 = J.one().operator()
+            sage: L1 - L1
+            Morphism from Euclidean Jordan algebra of degree 3 over Rational
+            Field to Euclidean Jordan algebra of degree 3 over Rational
+            Field given by matrix
+            [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
+
+        """
+        return self + (-other)
+
+
     def matrix(self):
         """
         Return the matrix of this morphism with respect to a left-action