X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo%2Feja%2Feuclidean_jordan_algebra.py;h=2404af03d7f249fec64caab63e9954aca91af7ab;hb=59177e7be6376f64fe24061d576a9fde77588d57;hp=1281a029a8f5c4557d9d35ee50342caecdc51054;hpb=a09a7e14df9b7dcae39fe558d42a6d74fb1c52b0;p=sage.d.git

diff --git a/mjo/eja/euclidean_jordan_algebra.py b/mjo/eja/euclidean_jordan_algebra.py
index 1281a02..2404af0 100644
--- a/mjo/eja/euclidean_jordan_algebra.py
+++ b/mjo/eja/euclidean_jordan_algebra.py
@@ -127,7 +127,44 @@ class FiniteDimensionalEuclideanJordanAlgebra(FiniteDimensionalAlgebra):
 
 
         def characteristic_polynomial(self):
-            return self.matrix().characteristic_polynomial()
+            """
+            Return my characteristic polynomial (if I'm a regular
+            element).
+
+            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')
+
+
+        def det(self):
+            """
+            Return my determinant, the product of my eigenvalues.
+
+            EXAMPLES::
+
+                sage: J = eja_ln(2)
+                sage: e0,e1 = J.gens()
+                sage: x = e0 + e1
+                sage: x.det()
+                0
+                sage: J = eja_ln(3)
+                sage: e0,e1,e2 = J.gens()
+                sage: x = e0 + e1 + e2
+                sage: x.det()
+                -1
+
+            """
+            cs = self.characteristic_polynomial().coefficients(sparse=False)
+            r = len(cs) - 1
+            if r >= 0:
+                return cs[0] * (-1)**r
+            else:
+                raise ValueError('charpoly had no coefficients')
 
 
         def is_nilpotent(self):
@@ -451,6 +488,25 @@ class FiniteDimensionalEuclideanJordanAlgebra(FiniteDimensionalAlgebra):
             return self.parent().linear_combination(zip(c_coordinates, basis))
 
 
+        def trace(self):
+            """
+            Return my trace, the sum of my eigenvalues.
+
+            EXAMPLES::
+
+                sage: J = eja_ln(3)
+                sage: e0,e1,e2 = J.gens()
+                sage: x = e0 + e1 + e2
+                sage: x.trace()
+                2
+
+            """
+            cs = self.characteristic_polynomial().coefficients(sparse=False)
+            if len(cs) >= 2:
+                return -1*cs[-2]
+            else:
+                raise ValueError('charpoly had fewer than 2 coefficients')
+
 
 def eja_rn(dimension, field=QQ):
     """