X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo%2Feja%2Feuclidean_jordan_algebra.py;h=8487e0ecea385d00f45c176bdc43b45d31d617ff;hb=0898205b7a8dc3a44e9fddd371814be6c94107bb;hp=ce6f6e55e18b28aabea82c9118758c1dab061c28;hpb=3cee3d24af1c7606b4c2f30c16a7f6f3e51fd1bd;p=sage.d.git

diff --git a/mjo/eja/euclidean_jordan_algebra.py b/mjo/eja/euclidean_jordan_algebra.py
index ce6f6e5..8487e0e 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):
@@ -85,6 +94,16 @@ class FiniteDimensionalEuclideanJordanAlgebra(FiniteDimensionalAlgebra):
                 sage: (e0 - e1).degree()
                 2
 
+            In the spin factor algebra (of rank two), all elements that
+            aren't multiples of the identity are regular::
+
+                sage: set_random_seed()
+                sage: n = ZZ.random_element(1,10).abs()
+                sage: J = eja_ln(n)
+                sage: x = J.random_element()
+                sage: x == x.coefficient(0)*J.one() or x.degree() == 2
+                True
+
             """
             return self.span_of_powers().dimension()