X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo%2Feja%2Feja_utils.py;h=8334f516094fcbea657637da037f825c1cf4cbd2;hb=dc92538d3fc92d16c9b6432ad17c37cb0d6b2be9;hp=3942e70811c6d69e59c9581d23f17af05c261dfa;hpb=cf5e64b70869df65c7bb38888de54b1083e60d45;p=sage.d.git

diff --git a/mjo/eja/eja_utils.py b/mjo/eja/eja_utils.py
index 3942e70..8334f51 100644
--- a/mjo/eja/eja_utils.py
+++ b/mjo/eja/eja_utils.py
@@ -1,40 +1,4 @@
-from sage.functions.other import sqrt
-from sage.matrix.constructor import matrix
-from sage.modules.free_module_element import vector
-
-def _charpoly_sage_input(s):
-    r"""
-    Helper function that you can use on the string output from sage
-    to convert a charpoly coefficient into the corresponding input
-    to be cached.
-
-    SETUP::
-
-        sage: from mjo.eja.eja_utils import _charpoly_sage_input
-
-    EXAMPLES::
-
-        sage: J = JordanSpinEJA(4,QQ)
-        sage: J._charpoly_coefficients()[0]
-        X1^2 - X2^2 - X3^2 - X4^2
-        sage: _charpoly_sage_input("X1^2 - X2^2 - X3^2 - X4^2")
-        'X[0]**2 - X[1]**2 - X[2]**2 - X[3]**2'
-
-    """
-    import re
-
-    exponent_out = r"\^"
-    exponent_in = r"**"
-
-    digit_out = r"X([0-9]+)"
-
-    def replace_digit(m):
-        # m is a match object
-        return "X[" + str(int(m.group(1)) - 1) + "]"
-
-    s = re.sub(exponent_out, exponent_in, s)
-    return re.sub(digit_out, replace_digit, s)
-
+from sage.structure.element import is_Matrix
 
 def _scale(x, alpha):
     r"""
@@ -145,9 +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)
@@ -158,16 +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
@@ -281,54 +245,40 @@ def gram_schmidt(v, inner_product=None):
         sage: len(gram_schmidt(v)) == 2
         True
     """
+    if len(v) == 0:
+        # cool
+        return v
+
+    V = v[0].parent()
+
     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()
-
-    # Our "zero" needs to belong to the right space for sum() to work.
-    zero = v[0].parent().zero()
+        return V.base_ring()(inner_product(x,x).sqrt())
 
     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):
+        return sc(x, ~norm(x))
 
-    # 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