eja: switch to the "real" element characteristic_polynomial() implementation.

diff --git a/mjo/eja/euclidean_jordan_algebra.py b/mjo/eja/euclidean_jordan_algebra.py
index b5cef0a8ba16f8a2afb0a66a0f38a6ac6daaa6ae..421c70bfa42d1e0ae8f837086437c491a9ab98f9 100644 (file)
--- a/mjo/eja/euclidean_jordan_algebra.py
+++ b/mjo/eja/euclidean_jordan_algebra.py
@@ -410,17 +410,37 @@ class FiniteDimensionalEuclideanJordanAlgebra(FiniteDimensionalAlgebra):
 
         def characteristic_polynomial(self):
             """
-            Return my characteristic polynomial (if I'm a regular
-            element).
+            Return the characteristic polynomial of this element.
+
+            EXAMPLES:
+
+            The rank of `R^3` is three, and the minimal polynomial of
+            the identity element is `(t-1)` from which it follows that
+            the characteristic polynomial should be `(t-1)^3`::
+
+                sage: J = RealCartesianProductEJA(3)
+                sage: J.one().characteristic_polynomial()
+                t^3 - 3*t^2 + 3*t - 1
+
+            Likewise, the characteristic of the zero element in the
+            rank-three algebra `R^{n}` should be `t^{3}`::
+
+                sage: J = RealCartesianProductEJA(3)
+                sage: J.zero().characteristic_polynomial()
+                t^3
+
+            The characteristic polynomial of an element should evaluate
+            to zero on that element::
+
+                sage: set_random_seed()
+                sage: x = RealCartesianProductEJA(3).random_element()
+                sage: p = x.characteristic_polynomial()
+                sage: x.apply_univariate_polynomial(p)
+                0
 
-            Eventually this should be implemented in terms of the parent
-            algebra's characteristic polynomial that works for ALL
-            elements.
             """
-            if self.is_regular():
-                return self.minimal_polynomial()
-            else:
-                raise NotImplementedError('irregular element')
+            p = self.parent().characteristic_polynomial()
+            return p(*self.vector())
 
 
         def inner_product(self, other):