eja: fix the subalgebra generated by zero.

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

diff --git a/mjo/eja/eja_element.py b/mjo/eja/eja_element.py
index e38012eb3bf9cda640c8cc4c4ef8d822e194ce43..97c048dceb3e299e7a36ac1a15767ebb33af8fad 100644 (file)
--- a/mjo/eja/eja_element.py
+++ b/mjo/eja/eja_element.py
@@ -490,7 +490,9 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
             False
 
         """
-        zero = self.parent().zero()
+        # In fact, we only need to know if the constant term is non-zero,
+        # so we can pass in the field's zero element instead.
+        zero = self.base_ring().zero()
         p = self.minimal_polynomial()
         return not (p(zero) == zero)
 
@@ -801,10 +803,12 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
 
         """
         P = self.parent()
+        left_mult_by_self = lambda y: self*y
+        L = P.module_morphism(function=left_mult_by_self, codomain=P)
         return FiniteDimensionalEuclideanJordanAlgebraOperator(
                  P,
                  P,
-                 self.to_matrix() )
+                 L.matrix() )
 
 
     def quadratic_representation(self, other=None):
@@ -960,6 +964,15 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
             sage: A(x^2) == A(x)*A(x)
             True
 
+        The subalgebra generated by the zero element is trivial::
+
+            sage: set_random_seed()
+            sage: A = random_eja().zero().subalgebra_generated_by()
+            sage: A
+            Euclidean Jordan algebra of dimension 0 over Rational Field
+            sage: A.one()
+            0
+
         """
         return FiniteDimensionalEuclideanJordanElementSubalgebra(self)