From: Michael Orlitzky <michael@orlitzky.com>
Date: Sun, 21 Jul 2019 16:00:08 +0000 (-0400)
Subject: eja: simplify (and cite) the minimal_polynomial() implementation.
X-Git-Url: https://gitweb.michael.orlitzky.com/?a=commitdiff_plain;h=9c34119f1c650df0a4c2c20ea4723152de80edae;p=sage.d.git

eja: simplify (and cite) the minimal_polynomial() implementation.
---

diff --git a/mjo/eja/euclidean_jordan_algebra.py b/mjo/eja/euclidean_jordan_algebra.py
index fb92a31..0ea9a4d 100644
--- a/mjo/eja/euclidean_jordan_algebra.py
+++ b/mjo/eja/euclidean_jordan_algebra.py
@@ -626,6 +626,13 @@ class FiniteDimensionalEuclideanJordanAlgebra(FiniteDimensionalAlgebra):
 
         def minimal_polynomial(self):
             """
+            ALGORITHM:
+
+            We restrict ourselves to the associative subalgebra
+            generated by this element, and then return the minimal
+            polynomial of this element's operator matrix (in that
+            subalgebra). This works by Baes Proposition 2.3.16.
+
             EXAMPLES::
 
                 sage: set_random_seed()
@@ -660,25 +667,13 @@ class FiniteDimensionalEuclideanJordanAlgebra(FiniteDimensionalAlgebra):
                 True
 
             """
-            # The element we're going to call "minimal_polynomial()" on.
-            # Either myself, interpreted as an element of a finite-
-            # dimensional algebra, or an element of an associative
-            # subalgebra.
-            elt = None
-
-            if self.parent().is_associative():
-                elt = FiniteDimensionalAlgebraElement(self.parent(), self)
-            else:
-                V = self.span_of_powers()
-                assoc_subalg = self.subalgebra_generated_by()
-                # Mis-design warning: the basis used for span_of_powers()
-                # and subalgebra_generated_by() must be the same, and in
-                # the same order!
-                elt = assoc_subalg(V.coordinates(self.vector()))
-
-            # Recursive call, but should work since elt lives in an
-            # associative algebra.
-            return elt.minimal_polynomial()
+            V = self.span_of_powers()
+            assoc_subalg = self.subalgebra_generated_by()
+            # Mis-design warning: the basis used for span_of_powers()
+            # 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()
 
 
         def natural_representation(self):