X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;ds=sidebyside;f=mjo%2Feja%2Feja_element.py;h=c5cbef9ebca32c2789ece22b0f9c4c46e6fb34a2;hb=f807c8c9046723a059eb4eea03dff89293510160;hp=926f2bf57a612c71eab53b693daa1e3f559ad6bc;hpb=823fb2a587e26436f46854fe44be0e8df46a6715;p=sage.d.git

diff --git a/mjo/eja/eja_element.py b/mjo/eja/eja_element.py
index 926f2bf..c5cbef9 100644
--- a/mjo/eja/eja_element.py
+++ b/mjo/eja/eja_element.py
@@ -346,6 +346,7 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
         SETUP::
 
             sage: from mjo.eja.eja_algebra import (JordanSpinEJA,
+            ....:                                  TrivialEJA,
             ....:                                  random_eja)
 
         EXAMPLES::
@@ -364,6 +365,17 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
             sage: x.det()
             -1
 
+        The determinant of the sole element in the rank-zero trivial
+        algebra is ``1``, by three paths of reasoning. First, its
+        characteristic polynomial is a constant ``1``, so the constant
+        term in that polynomial is ``1``. Second, the characteristic
+        polynomial evaluated at zero is again ``1``. And finally, the
+        (empty) product of its eigenvalues is likewise just unity::
+
+            sage: J = TrivialEJA()
+            sage: J.zero().det()
+            1
+
         TESTS:
 
         An element is invertible if and only if its determinant is
@@ -382,10 +394,16 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
             sage: x,y = J.random_elements(2)
             sage: (x*y).det() == x.det()*y.det()
             True
-
         """
         P = self.parent()
         r = P.rank()
+
+        if r == 0:
+            # Special case, since we don't get the a0=1
+            # coefficient when the rank of the algebra
+            # is zero.
+            return P.base_ring().one()
+
         p = P._charpoly_coefficients()[0]
         # The _charpoly_coeff function already adds the factor of -1
         # to ensure that _charpoly_coefficients()[0] is really what
@@ -857,13 +875,18 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
         TESTS:
 
         The minimal polynomial of the identity and zero elements are
-        always the same::
+        always the same, except in trivial algebras where the minimal
+        polynomial of the unit/zero element is ``1``::
 
             sage: set_random_seed()
-            sage: J = random_eja(nontrivial=True)
-            sage: J.one().minimal_polynomial()
+            sage: J = random_eja()
+            sage: mu = J.one().minimal_polynomial()
+            sage: t = mu.parent().gen()
+            sage: mu + int(J.is_trivial())*(t-2)
             t - 1
-            sage: J.zero().minimal_polynomial()
+            sage: mu = J.zero().minimal_polynomial()
+            sage: t = mu.parent().gen()
+            sage: mu + int(J.is_trivial())*(t-1)
             t
 
         The degree of an element is (by one definition) the degree
@@ -1300,12 +1323,13 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
         TESTS:
 
         Ensure that we can find an idempotent in a non-trivial algebra
-        where there are non-nilpotent elements::
+        where there are non-nilpotent elements, or that we get the dumb
+        solution in the trivial algebra::
 
             sage: set_random_seed()
-            sage: J = random_eja(nontrivial=True)
+            sage: J = random_eja()
             sage: x = J.random_element()
-            sage: while x.is_nilpotent():
+            sage: while x.is_nilpotent() and not J.is_trivial():
             ....:     x = J.random_element()
             sage: c = x.subalgebra_idempotent()
             sage: c^2 == c