eja: add a WIP gram-schmidt for EJA elements.

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

diff --git a/mjo/eja/eja_subalgebra.py b/mjo/eja/eja_subalgebra.py
index 8f6e56b55f309d10967ee5aae2bb8b2fe7261566..fee718b14ff32d96a00e7b8c9f1e8ed09066d733 100644 (file)
--- 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()
@@ -135,26 +135,36 @@ class FiniteDimensionalEuclideanJordanElementSubalgebra(FiniteDimensionalEuclide
                                   natural_basis=natural_basis)
 
 
-        # First compute the vector subspace spanned by the powers of
-        # the given element.
+        # 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()) ]
-        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()
+        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 ]
 
-        # Pick those out of the list of all powers.
-        superalgebra_basis = tuple(map(powers.__getitem__, ind_rows))
+            # Figure out which powers form a linearly-independent set.
+            ind_rows = matrix(field, power_vectors).pivot_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)
-        W = V.span_of_basis( V.from_vector(v) for v in basis_vectors )
+            # Pick those out of the list of all powers.
+            superalgebra_basis = tuple(map(powers.__getitem__, ind_rows))
 
-        # Now figure out the entries of the right-multiplication
-        # matrix for the successive basis elements b0, b1,... of
-        # that subspace.
+            # 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):