eja: add __invert__ method 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 b239dc7287326f95815708ca3b80fd2c64d99b1a..78fa6b7c0f96725af4da2e96f09ee2d7eb5449cf 100644 (file)
--- 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
@@ -30,31 +32,42 @@ class FiniteDimensionalEuclideanJordanAlgebraMorphism(FiniteDimensionalAlgebraMo
 
       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, and you can't add them.
+    our EJA, and you can't add/invert them.
     """
 
     def __add__(self, other):
         """
         Add two EJA morphisms in the obvious way.
 
-        EXAMPLES:
+        EXAMPLES::
 
             sage: J = RealSymmetricEJA(3)
             sage: x = J.zero()
-            sage: y = 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]
+            [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()
@@ -74,6 +87,44 @@ 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 _repr_(self):
         """
         We override only the representation that is shown to the user,