X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;ds=sidebyside;f=mjo%2Feja%2Feuclidean_jordan_algebra.py;h=5f01556b0f0cecf52437f0a115ab343cbeeb2b18;hb=ca41a63e824257c972f275e4b47e474adf13bc2e;hp=fa11aed040a152de2cfe8f9c398b77af39c33276;hpb=ddeec50e00df46e4d794a0583369cf506af0a83f;p=sage.d.git

diff --git a/mjo/eja/euclidean_jordan_algebra.py b/mjo/eja/euclidean_jordan_algebra.py
index fa11aed..5f01556 100644
--- a/mjo/eja/euclidean_jordan_algebra.py
+++ b/mjo/eja/euclidean_jordan_algebra.py
@@ -16,8 +16,10 @@ from sage.algebras.finite_dimensional_algebras.finite_dimensional_algebra_morphi
 
 class FiniteDimensionalEuclideanJordanAlgebraMorphism(FiniteDimensionalAlgebraMorphism):
     """
-    A very thin wrapper around FiniteDimensionalAlgebraMorphism that
-    does only three things:
+    A linear map between two finite-dimensional EJAs.
+
+    This is a very thin wrapper around FiniteDimensionalAlgebraMorphism
+    that does only a few things:
 
       1. Avoids the ``unitary`` and ``check`` arguments to the constructor
          that will always be ``False``. This is necessary because these
@@ -28,14 +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, 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/invert them.
+    our EJA, and you can't add/multiply/etc. them.
     """
 
     def __add__(self, other):
@@ -85,6 +86,112 @@ class FiniteDimensionalEuclideanJordanAlgebraMorphism(FiniteDimensionalAlgebraMo
                                                   check=False)
 
 
+    def __invert__(self):
+        """
+        EXAMPLES::
+
+            sage: J = RealSymmetricEJA(2)
+            sage: x = J.linear_combination(zip(range(len(J.gens())), J.gens()))
+            sage: x.is_invertible()
+            True
+            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
+            [-3/2    2 -1/2]
+            [   1    0    0]
+            [-1/2    0  1/2]
+            sage: x.operator_matrix().inverse()
+            [-3/2    2 -1/2]
+            [   1    0    0]
+            [-1/2    0  1/2]
+
+        TESTS::
+
+            sage: set_random_seed()
+            sage: J = random_eja()
+            sage: x = J.random_element()
+            sage: not x.is_invertible() or (
+            ....:   (~x.operator()).matrix() == x.operator_matrix().inverse() )
+            True
+
+        """
+        A = self.matrix()
+        if not A.is_invertible():
+            raise ValueError("morphism is not invertible")
+
+        P = self.parent()
+        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,
@@ -119,6 +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