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

[sage.d.git] / mjo / eja / eja_element.py

diff --git a/mjo/eja/eja_element.py b/mjo/eja/eja_element.py
index a681ae29652f913246033affb3db74d85b52c9c0..03376bda408b8fde98597ca8e8669e7e72a3e81a 100644 (file)
--- 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
@@ -939,7 +954,7 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
 
         Property 2 (multiply on the right for :trac:`28272`):
 
-            sage: alpha = QQ.random_element()
+            sage: alpha = J.base_ring().random_element()
             sage: (alpha*x).quadratic_representation() == Qx*(alpha^2)
             True
 
@@ -1044,7 +1059,7 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
             sage: set_random_seed()
             sage: A = random_eja().zero().subalgebra_generated_by()
             sage: A
-            Euclidean Jordan algebra of dimension 0 over Rational Field
+            Euclidean Jordan algebra of dimension 0 over...
             sage: A.one()
             0
 
@@ -1176,7 +1191,7 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
             sage: x = J.random_element()
             sage: y = J.random_element()
             sage: z = J.random_element()
-            sage: a = QQ.random_element();
+            sage: a = J.base_ring().random_element();
             sage: actual = (a*(x+z)).trace_inner_product(y)
             sage: expected = ( a*x.trace_inner_product(y) +
             ....:              a*z.trace_inner_product(y) )