eja: fix element matrices.

The superclass matrix() method of elements sometimes computes the
right-matrix acting on row vectors. Nobody wants that shit. This
commit overrides it (to simply return the transpose of the superclass
matrix), and thus fixes the subalgebra_idempotent() method. Some tests
were added for the latter method, too.

diff --git a/mjo/eja/euclidean_jordan_algebra.py b/mjo/eja/euclidean_jordan_algebra.py
index ef5249bc6abe4f9d4dd62bf0f5de07caa85fed26..835f76337f9449612bcd113de950afd011317107 100644 (file)
--- a/mjo/eja/euclidean_jordan_algebra.py
+++ b/mjo/eja/euclidean_jordan_algebra.py
@@ -168,6 +168,19 @@ class FiniteDimensionalEuclideanJordanAlgebra(FiniteDimensionalAlgebra):
             return self.span_of_powers().dimension()
 
 
+        def matrix(self):
+            """
+            Return the matrix that represents left- (or right-)
+            multiplication by this element in the parent algebra.
+
+            We have to override this because the superclass method
+            returns a matrix that acts on row vectors (that is, on
+            the right).
+            """
+            fda_elt = FiniteDimensionalAlgebraElement(self.parent(), self)
+            return fda_elt.matrix().transpose()
+
+
         def subalgebra_generated_by(self):
             """
             Return the associative subalgebra of the parent EJA generated
@@ -351,6 +364,19 @@ class FiniteDimensionalEuclideanJordanAlgebra(FiniteDimensionalAlgebra):
             """
             Find an idempotent in the associative subalgebra I generate
             using Proposition 2.3.5 in Baes.
+
+            TESTS::
+
+                sage: set_random_seed()
+                sage: J = eja_rn(5)
+                sage: c = J.random_element().subalgebra_idempotent()
+                sage: c^2 == c
+                True
+                sage: J = eja_ln(5)
+                sage: c = J.random_element().subalgebra_idempotent()
+                sage: c^2 == c
+                True
+
             """
             if self.is_nilpotent():
                 raise ValueError("this only works with non-nilpotent elements!")