From 4156fccce1265f500fe432b0f5567e43fbbc23d6 Mon Sep 17 00:00:00 2001 From: Michael Orlitzky Date: Mon, 15 Jul 2019 20:18:41 -0400 Subject: [PATCH] eja: add a test for power-operator-commutativity. --- mjo/eja/euclidean_jordan_algebra.py | 12 ++++++++++++ 1 file changed, 12 insertions(+) diff --git a/mjo/eja/euclidean_jordan_algebra.py b/mjo/eja/euclidean_jordan_algebra.py index 3a98324..1426d5e 100644 --- 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: -- 2.44.2