eja: add a test for power-operator-commutativity.

diff --git a/mjo/eja/euclidean_jordan_algebra.py b/mjo/eja/euclidean_jordan_algebra.py
index 3a98324cbb7c9a7f18a86677a53785a81988d28b..1426d5e16be4b6acc7c68a4494e2c6f1c4d61819 100644 (file)
--- a/mjo/eja/euclidean_jordan_algebra.py
+++ b/mjo/eja/euclidean_jordan_algebra.py
@@ -124,6 +124,18 @@ class FiniteDimensionalEuclideanJordanAlgebra(FiniteDimensionalAlgebra):
                 sage: (x*x)*(x*x*x) == x^5
                 True
 
+            We also know that powers operator-commute (Koecher, Chapter
+            III, Corollary 1)::
+
+                sage: set_random_seed()
+                sage: x = random_eja().random_element()
+                sage: m = ZZ.random_element(0,10)
+                sage: n = ZZ.random_element(0,10)
+                sage: Lxm = (x^m).matrix()
+                sage: Lxn = (x^n).matrix()
+                sage: Lxm*Lxn == Lxn*Lxm
+                True
+
             """
             A = self.parent()
             if n == 0: