X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo%2Feja%2Feja_subalgebra.py;h=9326793f9dfd1a1619241c3dcd2e5bb8dcda1351;hb=251d80b3473331d895be87f736b688f57963a9bb;hp=2318d12bfd0ebbfc765ca74766af9ab0e73ce02c;hpb=723fd0f50c7997768c3d098c707df30197b88afd;p=sage.d.git

diff --git a/mjo/eja/eja_subalgebra.py b/mjo/eja/eja_subalgebra.py
index 2318d12..9326793 100644
--- a/mjo/eja/eja_subalgebra.py
+++ b/mjo/eja/eja_subalgebra.py
@@ -2,7 +2,7 @@ from sage.matrix.constructor import matrix
 
 from mjo.eja.eja_algebra import FiniteDimensionalEuclideanJordanAlgebra
 from mjo.eja.eja_element import FiniteDimensionalEuclideanJordanAlgebraElement
-
+from mjo.eja.eja_utils import gram_schmidt
 
 class FiniteDimensionalEuclideanJordanElementSubalgebraElement(FiniteDimensionalEuclideanJordanAlgebraElement):
     """
@@ -99,7 +99,7 @@ class FiniteDimensionalEuclideanJordanElementSubalgebra(FiniteDimensionalEuclide
         1
 
     """
-    def __init__(self, elt):
+    def __init__(self, elt, orthonormalize_basis):
         self._superalgebra = elt.parent()
         category = self._superalgebra.category().Associative()
         V = self._superalgebra.vector_space()
@@ -135,31 +135,36 @@ class FiniteDimensionalEuclideanJordanElementSubalgebra(FiniteDimensionalEuclide
                                   natural_basis=natural_basis)
 
 
-        # First compute the vector subspace spanned by the powers of
-        # the given element.
-        superalgebra_basis = [self._superalgebra.one()]
-        # 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)
-
-        # Now figure out the entries of the right-multiplication
-        # matrix for the successive basis elements b0, b1,... of
-        # that subspace.
+        # This list is guaranteed to contain all independent powers,
+        # because it's the maximal set of powers that could possibly
+        # be independent (by a dimension argument).
+        powers = [ elt**k for k in range(V.dimension()) ]
+
+        if orthonormalize_basis == False:
+            # In this case, we just need to figure out which elements
+            # of the "powers" list are redundant... First compute the
+            # vector subspace spanned by the powers of the given
+            # element.
+            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
+            # 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)
+        else:
+            # If we're going to orthonormalize the basis anyway, we
+            # might as well just do Gram-Schmidt on the whole list of
+            # powers. The redundant ones will get zero'd out.
+            superalgebra_basis = gram_schmidt(powers)
+            basis_vectors = [ b.to_vector() for b in superalgebra_basis ]
+
+        W = V.span_of_basis( V.from_vector(v) for v in basis_vectors )
         n = len(superalgebra_basis)
         mult_table = [[W.zero() for i in range(n)] for j in range(n)]
         for i in range(n):
@@ -236,7 +241,7 @@ class FiniteDimensionalEuclideanJordanElementSubalgebra(FiniteDimensionalEuclide
 
             sage: J = RealSymmetricEJA(3)
             sage: x = sum( i*J.gens()[i] for i in range(6) )
-            sage: K = FiniteDimensionalEuclideanJordanElementSubalgebra(x)
+            sage: K = FiniteDimensionalEuclideanJordanElementSubalgebra(x,False)
             sage: [ K(x^k) for k in range(J.rank()) ]
             [f0, f1, f2]
 
@@ -342,20 +347,20 @@ class FiniteDimensionalEuclideanJordanElementSubalgebra(FiniteDimensionalEuclide
         EXAMPLES::
 
             sage: J = RealSymmetricEJA(3)
-            sage: x = sum( i*J.gens()[i] for i in range(6) )
-            sage: K = FiniteDimensionalEuclideanJordanElementSubalgebra(x)
+            sage: x = J.monomial(0) + 2*J.monomial(2) + 5*J.monomial(5)
+            sage: K = FiniteDimensionalEuclideanJordanElementSubalgebra(x,False)
             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