From: Michael Orlitzky <michael@orlitzky.com>
Date: Sat, 6 Jul 2019 22:14:07 +0000 (-0400)
Subject: eja: add an inverse() example.
X-Git-Url: https://gitweb.michael.orlitzky.com/?a=commitdiff_plain;h=d77a9699cd8a0050d004e1c183c42c430a6d7bb2;p=sage.d.git

eja: add an inverse() example.
---

diff --git a/mjo/eja/euclidean_jordan_algebra.py b/mjo/eja/euclidean_jordan_algebra.py
index 636149a..a110246 100644
--- a/mjo/eja/euclidean_jordan_algebra.py
+++ b/mjo/eja/euclidean_jordan_algebra.py
@@ -160,6 +160,26 @@ class FiniteDimensionalEuclideanJordanAlgebra(FiniteDimensionalAlgebra):
             We can't use the superclass method because it relies on the
             algebra being associative.
 
+            EXAMPLES:
+
+            The inverse in the spin factor algebra is given in Alizadeh's
+            Example 11.11::
+
+                sage: set_random_seed()
+                sage: n = ZZ.random_element(1,10).abs()
+                sage: J = JordanSpinSimpleEJA(n)
+                sage: x = J.random_element()
+                sage: while x.is_zero():
+                ....:     x = J.random_element()
+                sage: x_vec = x.vector()
+                sage: x0 = x_vec[0]
+                sage: x_bar = x_vec[1:]
+                sage: coeff = 1/(x0^2 - x_bar.inner_product(x_bar))
+                sage: inv_vec = x_vec.parent()([x0] + (-x_bar).list())
+                sage: x_inverse = coeff*inv_vec
+                sage: x.inverse() == J(x_inverse)
+                True
+
             TESTS:
 
             The identity element is its own inverse::