eja: add negation/subtraction for morphisms.

[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 78fa6b7c0f96725af4da2e96f09ee2d7eb5449cf..5f01556b0f0cecf52437f0a115ab343cbeeb2b18 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.
 
       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, 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
 
     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/etc. them.

     """
 
     def __add__(self, other):
     """
 
     def __add__(self, other):


@@ -125,6 +124,74 @@ class FiniteDimensionalEuclideanJordanAlgebraMorphism(FiniteDimensionalAlgebraMo
         return FiniteDimensionalEuclideanJordanAlgebraMorphism(self.parent(),
                                                                 A.inverse())
 
         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 __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,
     def _repr_(self):
         """
         We override only the representation that is shown to the user,


@@ -159,6 +226,36 @@ class FiniteDimensionalEuclideanJordanAlgebraMorphism(FiniteDimensionalAlgebraMo
         return "Morphism from {} to {} given by matrix\n{}".format(
             self.domain(), self.codomain(), self.matrix())
 
         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
     def matrix(self):
         """
         Return the matrix of this morphism with respect to a left-action