X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo%2Feja%2Feuclidean_jordan_algebra.py;h=cc44f61aa5ed24934e753599557ab2210b393cf9;hb=aa66e172b613a14b00df501c210fb334e1effcc5;hp=7967fccea47a472282a1e3bd547b2ebcf6b2c34e;hpb=82cfafa14e389cf966702df4319e57184c61152d;p=sage.d.git

diff --git a/mjo/eja/euclidean_jordan_algebra.py b/mjo/eja/euclidean_jordan_algebra.py
index 7967fcc..cc44f61 100644
--- a/mjo/eja/euclidean_jordan_algebra.py
+++ b/mjo/eja/euclidean_jordan_algebra.py
@@ -28,8 +28,11 @@ class FiniteDimensionalEuclideanJordanAlgebraOperator(Map):
 
         # We need to supply something here to avoid getting the
         # default Homset of the parent FiniteDimensionalAlgebra class,
-        # which messes up e.g. equality testing.
-        parent = Hom(domain_eja, codomain_eja, VectorSpaces(F))
+        # which messes up e.g. equality testing. We use FreeModules(F)
+        # instead of VectorSpaces(F) because our characteristic polynomial
+        # algorithm will need to F to be a polynomial ring at some point.
+        # When F is a field, FreeModules(F) returns VectorSpaces(F) anyway.
+        parent = Hom(domain_eja, codomain_eja, FreeModules(F))
 
         # The Map initializer will set our parent to a homset, which
         # is explicitly NOT what we want, because these ain't algebra
@@ -1349,7 +1352,7 @@ class FiniteDimensionalEuclideanJordanAlgebra(FiniteDimensionalAlgebra):
 
             # We get back a symbolic polynomial in 'x' but want a real
             # polynomial in 't'.
-            p_of_x = elt.operator_matrix().minimal_polynomial()
+            p_of_x = elt.operator().matrix().minimal_polynomial()
             return p_of_x.change_variable_name('t')
 
 
@@ -1419,34 +1422,11 @@ class FiniteDimensionalEuclideanJordanAlgebra(FiniteDimensionalAlgebra):
 
             """
             P = self.parent()
+            fda_elt = FiniteDimensionalAlgebraElement(P, self)
             return FiniteDimensionalEuclideanJordanAlgebraOperator(
-                     P,P,
-                     self.operator_matrix() )
-
-
-
-        def operator_matrix(self):
-            """
-            Return the matrix that represents left- (or right-)
-            multiplication by this element in the parent algebra.
-
-            We implement this ourselves to work around the fact that
-            our parent class represents everything with row vectors.
-
-            EXAMPLES:
-
-            Ensure that our operator's ``matrix`` method agrees with
-            this implementation::
-
-                sage: set_random_seed()
-                sage: J = random_eja()
-                sage: x = J.random_element()
-                sage: x.operator().matrix() == x.operator_matrix()
-                True
-
-            """
-            fda_elt = FiniteDimensionalAlgebraElement(self.parent(), self)
-            return fda_elt.matrix().transpose()
+                     P,
+                     P,
+                     fda_elt.matrix().transpose() )
 
 
         def quadratic_representation(self, other=None):
@@ -1591,13 +1571,13 @@ class FiniteDimensionalEuclideanJordanAlgebra(FiniteDimensionalAlgebra):
                 sage: x.subalgebra_generated_by().is_associative()
                 True
 
-            Squaring in the subalgebra should be the same thing as
-            squaring in the superalgebra::
+            Squaring in the subalgebra should work the same as in
+            the superalgebra::
 
                 sage: set_random_seed()
                 sage: x = random_eja().random_element()
                 sage: u = x.subalgebra_generated_by().random_element()
-                sage: u.operator_matrix()*u.vector() == (u**2).vector()
+                sage: u.operator()(u) == u^2
                 True
 
             """
@@ -1668,7 +1648,7 @@ class FiniteDimensionalEuclideanJordanAlgebra(FiniteDimensionalAlgebra):
             s = 0
             minimal_dim = V.dimension()
             for i in xrange(1, V.dimension()):
-                this_dim = (u**i).operator_matrix().image().dimension()
+                this_dim = (u**i).operator().matrix().image().dimension()
                 if this_dim < minimal_dim:
                     minimal_dim = this_dim
                     s = i
@@ -1685,7 +1665,7 @@ class FiniteDimensionalEuclideanJordanAlgebra(FiniteDimensionalAlgebra):
             # Beware, solve_right() means that we're using COLUMN vectors.
             # Our FiniteDimensionalAlgebraElement superclass uses rows.
             u_next = u**(s+1)
-            A = u_next.operator_matrix()
+            A = u_next.operator().matrix()
             c_coordinates = A.solve_right(u_next.vector())
 
             # Now c_coordinates is the idempotent we want, but it's in