X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo%2Feja%2Feuclidean_jordan_algebra.py;h=0b6b15da68fd4404f69ce094f4f96d07ad2c6adc;hb=4b1bdeb8c097e6c162cb0a32c07ba2740d89b1e5;hp=52e1383383cac83a8fa91e3f63c39c8795d8b533;hpb=bb8418eb800cae28a844f40b5f04480d64b2250b;p=sage.d.git

diff --git a/mjo/eja/euclidean_jordan_algebra.py b/mjo/eja/euclidean_jordan_algebra.py
index 52e1383..0b6b15d 100644
--- a/mjo/eja/euclidean_jordan_algebra.py
+++ b/mjo/eja/euclidean_jordan_algebra.py
@@ -39,6 +39,15 @@ class FiniteDimensionalEuclideanJordanAlgebra(FiniteDimensionalAlgebra):
     class Element(FiniteDimensionalAlgebraElement):
         """
         An element of a Euclidean Jordan algebra.
+
+        Since EJAs are commutative, the "right multiplication" matrix is
+        also the left multiplication matrix and must be symmetric::
+
+            sage: set_random_seed()
+            sage: J = eja_ln(5)
+            sage: J.random_element().matrix().is_symmetric()
+            True
+
         """
 
         def __pow__(self, n):
@@ -57,6 +66,18 @@ class FiniteDimensionalEuclideanJordanAlgebra(FiniteDimensionalAlgebra):
                 return A.element_class(A, self.vector()*(self.matrix()**(n-1)))
 
 
+        def span_of_powers(self):
+            """
+            Return the vector space spanned by successive powers of
+            this element.
+            """
+            # 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()
+            return V.span( (self**d).vector() for d in xrange(V.dimension()) )
+
+
         def degree(self):
             """
             Compute the degree of this element the straightforward way
@@ -74,13 +95,8 @@ class FiniteDimensionalEuclideanJordanAlgebra(FiniteDimensionalAlgebra):
                 2
 
             """
-            d = 0
-            V = self.vector().parent()
-            vectors = [(self**d).vector()]
-            while V.span(vectors).dimension() > d:
-                d += 1
-                vectors.append((self**d).vector())
-            return d
+            return self.span_of_powers().dimension()
+
 
         def minimal_polynomial(self):
             return self.matrix().minimal_polynomial()
@@ -122,9 +138,6 @@ def eja_rn(dimension, field=QQ):
     Qs = [ matrix(field, dimension, dimension, lambda k,j: 1*(k == j == i))
            for i in xrange(dimension) ]
 
-    # Assuming associativity is wrong here, but it works to
-    # temporarily trick the Jordan algebra constructor into using the
-    # multiplication table.
     return FiniteDimensionalEuclideanJordanAlgebra(field,Qs)