X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo%2Feja%2Feja_algebra.py;h=79ccc7904830dc739e4af0a532c1bace2a801936;hb=9528af011cbb4d5e6a38ef972e0d14e7928d5eef;hp=8ab1381665711ee3c09f1a0e3387c9e4dd85bcf3;hpb=ed093213197d2ffa48849b0089ebe391b7574b93;p=sage.d.git

diff --git a/mjo/eja/eja_algebra.py b/mjo/eja/eja_algebra.py
index 8ab1381..79ccc79 100644
--- a/mjo/eja/eja_algebra.py
+++ b/mjo/eja/eja_algebra.py
@@ -5,7 +5,7 @@ are used in optimization, and have some additional nice methods beyond
 what can be supported in a general Jordan Algebra.
 """
 
-from itertools import repeat
+from itertools import izip, repeat
 
 from sage.algebras.quatalg.quaternion_algebra import QuaternionAlgebra
 from sage.categories.magmatic_algebras import MagmaticAlgebras
@@ -409,7 +409,7 @@ class FiniteDimensionalEuclideanJordanAlgebra(CombinatorialFreeModule):
             # assign a[r] goes out-of-bounds.
             a.append(1) # corresponds to x^r
 
-        return sum( a[k]*(t**k) for k in range(len(a)) )
+        return sum( a[k]*(t**k) for k in xrange(len(a)) )
 
 
     def inner_product(self, x, y):
@@ -491,7 +491,7 @@ class FiniteDimensionalEuclideanJordanAlgebra(CombinatorialFreeModule):
 
         """
         M = list(self._multiplication_table) # copy
-        for i in range(len(M)):
+        for i in xrange(len(M)):
             # M had better be "square"
             M[i] = [self.monomial(i)] + M[i]
         M = [["*"] + list(self.gens())] + M
@@ -799,8 +799,8 @@ class RealCartesianProductEJA(FiniteDimensionalEuclideanJordanAlgebra):
     """
     def __init__(self, n, field=QQ, **kwargs):
         V = VectorSpace(field, n)
-        mult_table = [ [ V.gen(i)*(i == j) for j in range(n) ]
-                       for i in range(n) ]
+        mult_table = [ [ V.gen(i)*(i == j) for j in xrange(n) ]
+                       for i in xrange(n) ]
 
         fdeja = super(RealCartesianProductEJA, self)
         return fdeja.__init__(field, mult_table, rank=n, **kwargs)
@@ -938,7 +938,7 @@ class MatrixEuclideanJordanAlgebra(FiniteDimensionalEuclideanJordanAlgebra):
             (_,x,_,_) = J._charpoly_matrix_system()
             p = J._charpoly_coeff(i)
             # p might be missing some vars, have to substitute "optionally"
-            pairs = zip(x.base_ring().gens(), self._basis_normalizers)
+            pairs = izip(x.base_ring().gens(), self._basis_normalizers)
             substitutions = { v: v*c for (v,c) in pairs }
             return p.subs(substitutions)
 
@@ -964,9 +964,9 @@ class MatrixEuclideanJordanAlgebra(FiniteDimensionalEuclideanJordanAlgebra):
         V = VectorSpace(field, dimension**2)
         W = V.span_of_basis( _mat2vec(s) for s in basis )
         n = len(basis)
-        mult_table = [[W.zero() for j in range(n)] for i in range(n)]
-        for i in range(n):
-            for j in range(n):
+        mult_table = [[W.zero() for j in xrange(n)] for i in xrange(n)]
+        for i in xrange(n):
+            for j in xrange(n):
                 mat_entry = (basis[i]*basis[j] + basis[j]*basis[i])/2
                 mult_table[i][j] = W.coordinate_vector(_mat2vec(mat_entry))
 
@@ -1737,9 +1737,9 @@ class JordanSpinEJA(FiniteDimensionalEuclideanJordanAlgebra):
     """
     def __init__(self, n, field=QQ, **kwargs):
         V = VectorSpace(field, n)
-        mult_table = [[V.zero() for j in range(n)] for i in range(n)]
-        for i in range(n):
-            for j in range(n):
+        mult_table = [[V.zero() for j in xrange(n)] for i in xrange(n)]
+        for i in xrange(n):
+            for j in xrange(n):
                 x = V.gen(i)
                 y = V.gen(j)
                 x0 = x[0]