eja: fix the natural representation in trivial subalgebras.

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

diff --git a/mjo/eja/eja_element.py b/mjo/eja/eja_element.py
index c47156d31e2c6989e1fe863091794520f395523c..aef1c5d2813660ced5d9fe66314b4f5fd7577a11 100644 (file)
--- a/mjo/eja/eja_element.py
+++ b/mjo/eja/eja_element.py
@@ -165,6 +165,21 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
             sage: x.apply_univariate_polynomial(p)
             0
 
+        The characteristic polynomials of the zero and unit elements
+        should be what we think they are in a subalgebra, too::
+
+            sage: J = RealCartesianProductEJA(3)
+            sage: p1 = J.one().characteristic_polynomial()
+            sage: q1 = J.zero().characteristic_polynomial()
+            sage: e0,e1,e2 = J.gens()
+            sage: A = (e0 + 2*e1 + 3*e2).subalgebra_generated_by() # dim 3
+            sage: p2 = A.one().characteristic_polynomial()
+            sage: q2 = A.zero().characteristic_polynomial()
+            sage: p1 == p2
+            True
+            sage: q1 == q2
+            True
+
         """
         p = self.parent().characteristic_polynomial()
         return p(*self.to_vector())
@@ -368,6 +383,16 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
             sage: x.is_invertible() == (x.det() != 0)
             True
 
+        Ensure that the determinant is multiplicative on an associative
+        subalgebra as in Faraut and Koranyi's Proposition II.2.2::
+
+            sage: set_random_seed()
+            sage: J = random_eja().random_element().subalgebra_generated_by()
+            sage: x = J.random_element()
+            sage: y = J.random_element()
+            sage: (x*y).det() == x.det()*y.det()
+            True
+
         """
         P = self.parent()
         r = P.rank()
@@ -800,7 +825,7 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
 
         """
         B = self.parent().natural_basis()
-        W = B[0].matrix_space()
+        W = self.parent().natural_basis_space()
         return W.linear_combination(zip(B,self.to_vector()))