From 5a2de76fe9fa3a4b25ad44f8b3a64ce12cea83b9 Mon Sep 17 00:00:00 2001 From: Michael Orlitzky Date: Fri, 19 Jul 2019 16:15:55 -0400 Subject: [PATCH] eja: text the inner product axiom of an EJA. --- mjo/eja/euclidean_jordan_algebra.py | 14 ++++++++++++++ 1 file changed, 14 insertions(+) diff --git a/mjo/eja/euclidean_jordan_algebra.py b/mjo/eja/euclidean_jordan_algebra.py index b258398..3cec4fa 100644 --- a/mjo/eja/euclidean_jordan_algebra.py +++ b/mjo/eja/euclidean_jordan_algebra.py @@ -94,6 +94,20 @@ class FiniteDimensionalEuclideanJordanAlgebra(FiniteDimensionalAlgebra): The inner product associated with this Euclidean Jordan algebra. Will default to the trace inner product if nothing else. + + EXAMPLES: + + The inner product must satisfy its axiom for this algebra to truly + be a Euclidean Jordan Algebra:: + + sage: set_random_seed() + sage: J = random_eja() + sage: x = J.random_element() + sage: y = J.random_element() + sage: z = J.random_element() + sage: (x*y).inner_product(z) == y.inner_product(x*z) + True + """ if (not x in self) or (not y in self): raise TypeError("arguments must live in this algebra") -- 2.44.2