eja: test that left-mult matrices are symmetric.

[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 08bce5f7c7b24a96d9fa982bb1ec0c77dc01807a..0b6b15da68fd4404f69ce094f4f96d07ad2c6adc 100644 (file)
--- 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()