eja: do an extra ambient_vector_space() in one method in case its a module.

[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 fb92a310c2edaa27cd9b9cab35dd86d908790469..4a2979248fc5e7b90938a0c18b8a7545bb780e97 100644 (file)
--- a/mjo/eja/euclidean_jordan_algebra.py
+++ b/mjo/eja/euclidean_jordan_algebra.py
@@ -626,6 +626,13 @@ class FiniteDimensionalEuclideanJordanAlgebra(FiniteDimensionalAlgebra):
 
         def minimal_polynomial(self):
             """
+            ALGORITHM:
+
+            We restrict ourselves to the associative subalgebra
+            generated by this element, and then return the minimal
+            polynomial of this element's operator matrix (in that
+            subalgebra). This works by Baes Proposition 2.3.16.
+
             EXAMPLES::
 
                 sage: set_random_seed()
@@ -660,25 +667,13 @@ class FiniteDimensionalEuclideanJordanAlgebra(FiniteDimensionalAlgebra):
                 True
 
             """
-            # The element we're going to call "minimal_polynomial()" on.
-            # Either myself, interpreted as an element of a finite-
-            # dimensional algebra, or an element of an associative
-            # subalgebra.
-            elt = None
-
-            if self.parent().is_associative():
-                elt = FiniteDimensionalAlgebraElement(self.parent(), self)
-            else:
-                V = self.span_of_powers()
-                assoc_subalg = self.subalgebra_generated_by()
-                # Mis-design warning: the basis used for span_of_powers()
-                # and subalgebra_generated_by() must be the same, and in
-                # the same order!
-                elt = assoc_subalg(V.coordinates(self.vector()))
-
-            # Recursive call, but should work since elt lives in an
-            # associative algebra.
-            return elt.minimal_polynomial()
+            V = self.span_of_powers()
+            assoc_subalg = self.subalgebra_generated_by()
+            # Mis-design warning: the basis used for span_of_powers()
+            # and subalgebra_generated_by() must be the same, and in
+            # the same order!
+            elt = assoc_subalg(V.coordinates(self.vector()))
+            return elt.operator_matrix().minimal_polynomial()
 
 
         def natural_representation(self):
@@ -881,7 +876,10 @@ class FiniteDimensionalEuclideanJordanAlgebra(FiniteDimensionalAlgebra):
             # The dimension of the subalgebra can't be greater than
             # the big algebra, so just put everything into a list
             # and let span() get rid of the excess.
-            V = self.vector().parent()
+            #
+            # We do the extra ambient_vector_space() in case we're messing
+            # with polynomials and the direct parent is a module.
+            V = self.vector().parent().ambient_vector_space()
             return V.span( (self**d).vector() for d in xrange(V.dimension()) )