X-Git-Url: http://gitweb.michael.orlitzky.com/?p=sage.d.git;a=blobdiff_plain;f=mjo%2Feja%2Feja_utils.py;h=a8abeff6be073b2b0aea3dd4f5af933c251666a5;hp=0b2d2a315989949c2431641c8f82dea9b576f9b8;hb=HEAD;hpb=5154ccb39a8fd2d69330ae440bd6d92a12f67e7c

diff --git a/mjo/eja/eja_utils.py b/mjo/eja/eja_utils.py
index 0b2d2a3..a8abeff 100644
--- a/mjo/eja/eja_utils.py
+++ b/mjo/eja/eja_utils.py
@@ -1,6 +1,4 @@
-from sage.functions.other import sqrt
-from sage.matrix.constructor import matrix
-from sage.modules.free_module_element import vector
+from sage.structure.element import is_Matrix
 
 def _scale(x, alpha):
     r"""
@@ -54,7 +52,9 @@ def _all2list(x):
     SETUP::
 
         sage: from mjo.eja.eja_utils import _all2list
-        sage: from mjo.octonions import Octonions, OctonionMatrixAlgebra
+        sage: from mjo.hurwitz import (QuaternionMatrixAlgebra,
+        ....:                          Octonions,
+        ....:                          OctonionMatrixAlgebra)
 
     EXAMPLES::
 
@@ -86,6 +86,13 @@ def _all2list(x):
         sage: _all2list(OctonionMatrixAlgebra(1).one())
         [1, 0, 0, 0, 0, 0, 0, 0]
 
+    ::
+
+        sage: _all2list(QuaternionAlgebra(QQ, -1, -1).one())
+        [1, 0, 0, 0]
+        sage: _all2list(QuaternionMatrixAlgebra(1).one())
+        [1, 0, 0, 0]
+
     ::
 
         sage: V1 = VectorSpace(QQ,2)
@@ -102,9 +109,16 @@ def _all2list(x):
         # first needing to convert them to a list of octonions and
         # then recursing down into the list. It also avoids the wonky
         # list(x) when x is an element of a CFM. I don't know what it
-        # returns but it aint the coordinates. This will fall through
-        # to the iterable case the next time around.
-        return _all2list(x.to_vector())
+        # returns but it aint the coordinates. We don't recurse
+        # because vectors can only contain ring elements as entries.
+        return x.to_vector().list()
+
+    if is_Matrix(x):
+        # This sucks, but for performance reasons we don't want to
+        # call _all2list recursively on the contents of a matrix
+        # when we don't have to (they only contain ring elements
+        # as entries)
+        return x.list()
 
     try:
         xl = list(x)
@@ -115,16 +129,9 @@ def _all2list(x):
         # Avoid the retardation of list(QQ(1)) == [1].
         return [x]
 
-    return sum(list( map(_all2list, xl) ), [])
+    return sum( map(_all2list, xl) , [])
 
 
-
-def _mat2vec(m):
-        return vector(m.base_ring(), m.list())
-
-def _vec2mat(v):
-        return matrix(v.base_ring(), sqrt(v.degree()), v.list())
-
 def gram_schmidt(v, inner_product=None):
     """
     Perform Gram-Schmidt on the list ``v`` which are assumed to be
@@ -237,55 +244,39 @@ def gram_schmidt(v, inner_product=None):
         sage: v = [v1,v2,v3]
         sage: len(gram_schmidt(v)) == 2
         True
-    """
-    if inner_product is None:
-        inner_product = lambda x,y: x.inner_product(y)
-    def norm(x):
-        ip = inner_product(x,x)
-        # Don't expand the given field; the inner-product's codomain
-        # is already correct. For example QQ(2).sqrt() returns sqrt(2)
-        # in SR, and that will give you weird errors about symbolics
-        # when what's really going wrong is that you're trying to
-        # orthonormalize in QQ.
-        return ip.parent()(ip.sqrt())
-
-    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()
+    V = v[0].parent()
 
-    # Our "zero" needs to belong to the right space for sum() to work.
-    zero = v[0].parent().zero()
+    if inner_product is None:
+        inner_product = lambda x,y: x.inner_product(y)
 
     sc = lambda x,a: a*x
-    if hasattr(v[0], 'cartesian_factors'):
+    if hasattr(V, 'cartesian_factors'):
         # Only use the slow implementation if necessary.
         sc = _scale
 
     def proj(x,y):
+        # project y onto the span of {x}
         return sc(x, (inner_product(x,y)/inner_product(x,x)))
 
-    # First orthogonalize...
-    for i in range(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() ),
-                     zero )
+    def normalize(x):
+        # Don't extend the given field with the necessary
+        # square roots. This will probably throw weird
+        # errors about the symbolic ring if you e.g. try
+        # to use it on a set of rational vectors that isn't
+        # already orthonormalized.
+        return sc(x, ~inner_product(x,x).sqrt())
 
-    # 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() ]
+    v_out = [] # make a copy, don't clobber the input
 
-    # 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 range(len(v)):
-        v[i] = sc(v[i], ~norm(v[i]))
+    for (i, v_i) in enumerate(v):
+        ortho_v_i = v_i - V.sum( proj(v_out[j],v_i) for j in range(i) )
+        if not ortho_v_i.is_zero():
+            v_out.append(normalize(ortho_v_i))
 
-    return v
+    return v_out