eja: add a new TrivialEJA class and some tests for it.

[sage.d.git] / mjo / eja / eja_element.py

diff --git a/mjo/eja/eja_element.py b/mjo/eja/eja_element.py
index bd45b179541487bd82e3b06768a902a77cd0899d..166c9d217cf71d43fe4bfc0911e6fe6c3e1ec9d2 100644 (file)
--- 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()