X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo%2Feja%2Feja_subalgebra.py;h=e7e559f80466d8b4da96c9a14ecea74bfd9351d4;hb=9a30998022fdc8eccaf724833a4cd88e545e4f0e;hp=110b049573bbc8d8aeaaab768e9cebceadbf3c7e;hpb=0d9367ac61e9350dbfa3547b93c484243c749d7d;p=sage.d.git

diff --git a/mjo/eja/eja_subalgebra.py b/mjo/eja/eja_subalgebra.py
index 110b049..e7e559f 100644
--- a/mjo/eja/eja_subalgebra.py
+++ b/mjo/eja/eja_subalgebra.py
@@ -11,14 +11,14 @@ class FiniteDimensionalEuclideanJordanSubalgebraElement(FiniteDimensionalEuclide
 
     TESTS::
 
-    The natural representation of an element in the subalgebra is
-    the same as its natural representation in the superalgebra::
+    The matrix representation of an element in the subalgebra is
+    the same as its matrix representation in the superalgebra::
 
         sage: set_random_seed()
         sage: A = random_eja().random_element().subalgebra_generated_by()
         sage: y = A.random_element()
-        sage: actual = y.natural_representation()
-        sage: expected = y.superalgebra_element().natural_representation()
+        sage: actual = y.to_matrix()
+        sage: expected = y.superalgebra_element().to_matrix()
         sage: actual == expected
         True
 
@@ -121,11 +121,11 @@ class FiniteDimensionalEuclideanJordanSubalgebra(FiniteDimensionalEuclideanJorda
         sage: E22 = matrix(AA, [ [0,0],
         ....:                    [0,1] ])
         sage: K1 = FiniteDimensionalEuclideanJordanSubalgebra(J, (J(E11),))
-        sage: K1.one().natural_representation()
+        sage: K1.one().to_matrix()
         [1 0]
         [0 0]
         sage: K2 = FiniteDimensionalEuclideanJordanSubalgebra(J, (J(E22),))
-        sage: K2.one().natural_representation()
+        sage: K2.one().to_matrix()
         [0 0]
         [0 1]
 
@@ -177,6 +177,10 @@ class FiniteDimensionalEuclideanJordanSubalgebra(FiniteDimensionalEuclideanJorda
 
         n = len(basis)
         mult_table = [[W.zero() for i in range(n)] for j in range(n)]
+        ip_table = [ [ self._superalgebra.inner_product(basis[i],basis[j])
+                       for i in range(n) ]
+                     for j in range(n) ]
+
         for i in range(n):
             for j in range(n):
                 product = basis[i]*basis[j]
@@ -187,7 +191,8 @@ class FiniteDimensionalEuclideanJordanSubalgebra(FiniteDimensionalEuclideanJorda
                 product_vector = V.from_vector(product.to_vector())
                 mult_table[i][j] = W.coordinate_vector(product_vector)
 
-        natural_basis = tuple( b.natural_representation() for b in basis )
+        self._inner_product_matrix = matrix(field, ip_table)
+        matrix_basis = tuple( b.to_matrix() for b in basis )
 
 
         self._vector_space = W
@@ -197,7 +202,7 @@ class FiniteDimensionalEuclideanJordanSubalgebra(FiniteDimensionalEuclideanJorda
                        mult_table,
                        prefix=prefix,
                        category=category,
-                       natural_basis=natural_basis,
+                       matrix_basis=matrix_basis,
                        check_field=False,
                        check_axioms=check_axioms)
 
@@ -251,16 +256,16 @@ class FiniteDimensionalEuclideanJordanSubalgebra(FiniteDimensionalEuclideanJorda
 
 
 
-    def natural_basis_space(self):
+    def matrix_space(self):
         """
-        Return the natural basis space of this algebra, which is identical
-        to that of its superalgebra.
+        Return the matrix space of this algebra, which is identical to
+        that of its superalgebra.
 
-        This is correct "by definition," and avoids a mismatch when the
-        subalgebra is trivial (with no natural basis to infer anything
-        from) and the parent is not.
+        This is correct "by definition," and avoids a mismatch when
+        the subalgebra is trivial (with no matrix basis elements to
+        infer anything from) and the parent is not.
         """
-        return self.superalgebra().natural_basis_space()
+        return self.superalgebra().matrix_space()
 
 
     def superalgebra(self):