X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;ds=sidebyside;f=mjo%2Feja%2Feja_subalgebra.py;h=8f6e56b55f309d10967ee5aae2bb8b2fe7261566;hb=32723f51147eb6260c8b41549208c851e54a4c56;hp=e39792a91732724b5fc7bc8b352e8fd977c80940;hpb=6d30ad670e205bcfd299835ca67d93d7e1bfc2ec;p=sage.d.git

diff --git a/mjo/eja/eja_subalgebra.py b/mjo/eja/eja_subalgebra.py
index e39792a..8f6e56b 100644
--- a/mjo/eja/eja_subalgebra.py
+++ b/mjo/eja/eja_subalgebra.py
@@ -137,25 +137,20 @@ class FiniteDimensionalEuclideanJordanElementSubalgebra(FiniteDimensionalEuclide
 
         # First compute the vector subspace spanned by the powers of
         # the given element.
-        superalgebra_basis = [self._superalgebra.one()]
+        powers = [ elt**k for k in range(V.dimension()) ]
+        power_vectors = [ p.to_vector() for p in powers ]
+
+        # Figure out which powers form a linearly-independent set.
+        ind_rows = matrix(field, power_vectors).pivot_rows()
+
+        # Pick those out of the list of all powers.
+        superalgebra_basis = tuple(map(powers.__getitem__, ind_rows))
+
         # If our superalgebra is a subalgebra of something else, then
-        # superalgebra.one().to_vector() won't have the right
-        # coordinates unless we use V.from_vector() below.
-        basis_vectors = [V.from_vector(self._superalgebra.one().to_vector())]
-        W = V.span_of_basis(basis_vectors)
-        for exponent in range(1, V.dimension()):
-            new_power = elt**exponent
-            basis_vectors.append( V.from_vector(new_power.to_vector()) )
-            try:
-                W = V.span_of_basis(basis_vectors)
-                superalgebra_basis.append( new_power )
-            except ValueError:
-                # Vectors weren't independent; bail and keep the
-                # last subspace that worked.
-                break
-
-        # Make the basis hashable for UniqueRepresentation.
-        superalgebra_basis = tuple(superalgebra_basis)
+        # these vectors won't have the right coordinates for
+        # V.span_of_basis() unless we use V.from_vector() on them.
+        basis_vectors = map(power_vectors.__getitem__, ind_rows)
+        W = V.span_of_basis( V.from_vector(v) for v in basis_vectors )
 
         # Now figure out the entries of the right-multiplication
         # matrix for the successive basis elements b0, b1,... of
@@ -313,6 +308,18 @@ class FiniteDimensionalEuclideanJordanElementSubalgebra(FiniteDimensionalEuclide
             return self.monomial(self.one_basis())
 
 
+    def natural_basis_space(self):
+        """
+        Return the natural basis 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.
+        """
+        return self.superalgebra().natural_basis_space()
+
+
     def superalgebra(self):
         """
         Return the superalgebra that this algebra was generated from.
@@ -330,20 +337,20 @@ class FiniteDimensionalEuclideanJordanElementSubalgebra(FiniteDimensionalEuclide
         EXAMPLES::
 
             sage: J = RealSymmetricEJA(3)
-            sage: x = sum( i*J.gens()[i] for i in range(6) )
+            sage: x = J.monomial(0) + 2*J.monomial(2) + 5*J.monomial(5)
             sage: K = FiniteDimensionalEuclideanJordanElementSubalgebra(x)
             sage: K.vector_space()
-            Vector space of degree 6 and dimension 3 over Rational Field
+            Vector space of degree 6 and dimension 3 over...
             User basis matrix:
             [ 1  0  1  0  0  1]
-            [ 0  1  2  3  4  5]
-            [10 14 21 19 31 50]
+            [ 1  0  2  0  0  5]
+            [ 1  0  4  0  0 25]
             sage: (x^0).to_vector()
             (1, 0, 1, 0, 0, 1)
             sage: (x^1).to_vector()
-            (0, 1, 2, 3, 4, 5)
+            (1, 0, 2, 0, 0, 5)
             sage: (x^2).to_vector()
-            (10, 14, 21, 19, 31, 50)
+            (1, 0, 4, 0, 0, 25)
 
         """
         return self._vector_space