X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo%2Feja%2Feja_element.py;h=166c9d217cf71d43fe4bfc0911e6fe6c3e1ec9d2;hb=72a75a3d30bb108a4d2be13c096a16578f0bb0e6;hp=2eb267727235946ed94681d973c915407c5d3dc1;hpb=ce96a6f610c1c2a6837bacd893fed164d2085a03;p=sage.d.git

diff --git a/mjo/eja/eja_element.py b/mjo/eja/eja_element.py
index 2eb2677..166c9d2 100644
--- a/mjo/eja/eja_element.py
+++ b/mjo/eja/eja_element.py
@@ -731,15 +731,29 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
 
             sage: from mjo.eja.eja_algebra import (JordanSpinEJA,
             ....:                                  RealSymmetricEJA,
+            ....:                                  TrivialEJA,
             ....:                                  random_eja)
 
+        EXAMPLES:
+
+        Keeping in mind that the polynomial ``1`` evaluates the identity
+        element (also the zero element) of the trivial algebra, it is clear
+        that the polynomial ``1`` is the minimal polynomial of the only
+        element in a trivial algebra::
+
+            sage: J = TrivialEJA()
+            sage: J.one().minimal_polynomial()
+            1
+            sage: J.zero().minimal_polynomial()
+            1
+
         TESTS:
 
         The minimal polynomial of the identity and zero elements are
         always the same::
 
             sage: set_random_seed()
-            sage: J = random_eja()
+            sage: J = random_eja(nontrivial=True)
             sage: J.one().minimal_polynomial()
             t - 1
             sage: J.zero().minimal_polynomial()
@@ -1217,14 +1231,23 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
         """
         Return my trace, the sum of my eigenvalues.
 
+        In a trivial algebra, however you want to look at it, the trace is
+        an empty sum for which we declare the result to be zero.
+
         SETUP::
 
             sage: from mjo.eja.eja_algebra import (JordanSpinEJA,
             ....:                                  RealCartesianProductEJA,
+            ....:                                  TrivialEJA,
             ....:                                  random_eja)
 
         EXAMPLES::
 
+            sage: J = TrivialEJA()
+            sage: J.zero().trace()
+            0
+
+        ::
             sage: J = JordanSpinEJA(3)
             sage: x = sum(J.gens())
             sage: x.trace()
@@ -1248,6 +1271,12 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
         """
         P = self.parent()
         r = P.rank()
+
+        if r == 0:
+            # Special case for the trivial algebra where
+            # the trace is an empty sum.
+            return P.base_ring().zero()
+
         p = P._charpoly_coeff(r-1)
         # The _charpoly_coeff function already adds the factor of
         # -1 to ensure that _charpoly_coeff(r-1) is really what