eja: use 't' for the minimal polynomial variable name.

diff --git a/mjo/eja/euclidean_jordan_algebra.py b/mjo/eja/euclidean_jordan_algebra.py
index 29248fcfaabfad33567070eaa65efffef7df87ff..8f508bc305304d249440294267cc56f6099c631b 100644 (file)
--- a/mjo/eja/euclidean_jordan_algebra.py
+++ b/mjo/eja/euclidean_jordan_algebra.py
@@ -675,6 +675,9 @@ class FiniteDimensionalEuclideanJordanAlgebra(FiniteDimensionalAlgebra):
 
         def minimal_polynomial(self):
             """
+            Return the minimal polynomial of this element,
+            as a function of the variable `t`.
+
             ALGORITHM:
 
             We restrict ourselves to the associative subalgebra
@@ -682,14 +685,20 @@ class FiniteDimensionalEuclideanJordanAlgebra(FiniteDimensionalAlgebra):
             polynomial of this element's operator matrix (in that
             subalgebra). This works by Baes Proposition 2.3.16.
 
-            EXAMPLES::
+            TESTS:
+
+            The minimal polynomial of the identity and zero elements are
+            always the same::
 
                 sage: set_random_seed()
-                sage: x = random_eja().random_element()
-                sage: x.degree() == x.minimal_polynomial().degree()
-                True
+                sage: J = random_eja()
+                sage: J.one().minimal_polynomial()
+                t - 1
+                sage: J.zero().minimal_polynomial()
+                t
 
-            ::
+            The degree of an element is (by one definition) the degree
+            of its minimal polynomial::
 
                 sage: set_random_seed()
                 sage: x = random_eja().random_element()
@@ -710,8 +719,8 @@ class FiniteDimensionalEuclideanJordanAlgebra(FiniteDimensionalAlgebra):
                 sage: y0 = y.vector()[0]
                 sage: y_bar = y.vector()[1:]
                 sage: actual = y.minimal_polynomial()
-                sage: x = SR.symbol('x', domain='real')
-                sage: expected = x^2 - 2*y0*x + (y0^2 - norm(y_bar)^2)
+                sage: t = PolynomialRing(J.base_ring(),'t').gen(0)
+                sage: expected = t^2 - 2*y0*t + (y0^2 - norm(y_bar)^2)
                 sage: bool(actual == expected)
                 True
 
@@ -722,7 +731,11 @@ class FiniteDimensionalEuclideanJordanAlgebra(FiniteDimensionalAlgebra):
             # and subalgebra_generated_by() must be the same, and in
             # the same order!
             elt = assoc_subalg(V.coordinates(self.vector()))
-            return elt.operator_matrix().minimal_polynomial()
+
+            # We get back a symbolic polynomial in 'x' but want a real
+            # polynomial in 't'.
+            p_of_x = elt.operator_matrix().minimal_polynomial()
+            return p_of_x.change_variable_name('t')
 
 
         def natural_representation(self):