From: Michael Orlitzky <michael@orlitzky.com>
Date: Wed, 21 Aug 2019 15:00:58 +0000 (-0400)
Subject: eja: add a test for basis-invariance of minimal polynomial.
X-Git-Url: https://gitweb.michael.orlitzky.com/?a=commitdiff_plain;h=517fbc3c451b7b3914d455653bccf2ec647dbc30;p=sage.d.git

eja: add a test for basis-invariance of minimal polynomial.
---

diff --git a/mjo/eja/eja_element.py b/mjo/eja/eja_element.py
index 90c236a..03376bd 100644
--- a/mjo/eja/eja_element.py
+++ b/mjo/eja/eja_element.py
@@ -709,6 +709,7 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
         SETUP::
 
             sage: from mjo.eja.eja_algebra import (JordanSpinEJA,
+            ....:                                  RealSymmetricEJA,
             ....:                                  random_eja)
 
         TESTS:
@@ -758,6 +759,20 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
             sage: x.apply_univariate_polynomial(p)
             0
 
+        The minimal polynomial is invariant under a change of basis,
+        and in particular, a re-scaling of the basis::
+
+            sage: set_random_seed()
+            sage: n = ZZ.random_element(1,5).abs()
+            sage: J1 = RealSymmetricEJA(n)
+            sage: J2 = RealSymmetricEJA(n,QQ,False)
+            sage: X = random_matrix(QQ,n)
+            sage: X = X*X.transpose()
+            sage: x1 = J1(X)
+            sage: x2 = J2(X)
+            sage: x1.minimal_polynomial() == x2.minimal_polynomial()
+            True
+
         """
         if self.is_zero():
             # We would generate a zero-dimensional subalgebra