X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo%2Feja%2Feja_utils.py;h=b6b0a0327c19842ce654023b00bf6e0b9af539a1;hb=1e9700cdd04434465ffcad148d078f7fa361e426;hp=cf75e325697dcefb3bf682b855f8d83e3e4f89e2;hpb=c16c11d5b4cd015b6d7516a175a92f46e03bd2d7;p=sage.d.git

diff --git a/mjo/eja/eja_utils.py b/mjo/eja/eja_utils.py
index cf75e32..b6b0a03 100644
--- a/mjo/eja/eja_utils.py
+++ b/mjo/eja/eja_utils.py
@@ -1,76 +1,4 @@
 from sage.modules.free_module_element import vector
-from sage.rings.number_field.number_field import NumberField
-from sage.rings.polynomial.polynomial_ring_constructor import PolynomialRing
-from sage.rings.real_lazy import RLF
 
 def _mat2vec(m):
         return vector(m.base_ring(), m.list())
-
-def gram_schmidt(v):
-    """
-    Perform Gram-Schmidt on the list ``v`` which are assumed to be
-    vectors over the same base ring. Returns a list of orthonormalized
-    vectors over the smallest extention ring containing the necessary
-    roots.
-
-    SETUP::
-
-        sage: from mjo.eja.eja_utils import gram_schmidt
-
-    EXAMPLES::
-
-        sage: v1 = vector(QQ,(1,2,3))
-        sage: v2 = vector(QQ,(1,-1,6))
-        sage: v3 = vector(QQ,(2,1,-1))
-        sage: v = [v1,v2,v3]
-        sage: u = gram_schmidt(v)
-        sage: all( u_i.inner_product(u_i).sqrt() == 1 for u_i in u )
-        True
-        sage: bool(u[0].inner_product(u[1]) == 0)
-        True
-        sage: bool(u[0].inner_product(u[2]) == 0)
-        True
-        sage: bool(u[1].inner_product(u[2]) == 0)
-        True
-
-    TESTS:
-
-    Ensure that zero vectors don't get in the way::
-
-        sage: v1 = vector(QQ,(1,2,3))
-        sage: v2 = vector(QQ,(1,-1,6))
-        sage: v3 = vector(QQ,(0,0,0))
-        sage: v = [v1,v2,v3]
-        sage: len(gram_schmidt(v)) == 2
-        True
-
-    """
-    def proj(x,y):
-        return (y.inner_product(x)/x.inner_product(x))*x
-
-    v = list(v) # make a copy, don't clobber the input
-
-    # Drop all zero vectors before we start.
-    v = [ v_i for v_i in v if not v_i.is_zero() ]
-
-    if len(v) == 0:
-        # cool
-        return v
-
-    R = v[0].base_ring()
-
-    # First orthogonalize...
-    for i in xrange(1,len(v)):
-        # Earlier vectors can be made into zero so we have to ignore them.
-        v[i] -= sum( proj(v[j],v[i]) for j in range(i) if not v[j].is_zero() )
-
-    # And now drop all zero vectors again if they were "orthogonalized out."
-    v = [ v_i for v_i in v if not v_i.is_zero() ]
-
-    # Just normalize. If the algebra is missing the roots, we can't add
-    # them here because then our subalgebra would have a bigger field
-    # than the superalgebra.
-    for i in xrange(len(v)):
-        v[i] = v[i] / v[i].norm()
-
-    return v