X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo%2Feja%2Feja_algebra.py;h=d31b5b71a0df190dee14d86f1544cff547f025ef;hb=6ea32f02e6631f22a2140fa8428bd0a8d932d7c0;hp=0f2b655f21795cb1feb0e8b41cfc878261a67962;hpb=c4203897950b84665ea41ed103f87f68aee0852e;p=sage.d.git

diff --git a/mjo/eja/eja_algebra.py b/mjo/eja/eja_algebra.py
index 0f2b655..d31b5b7 100644
--- a/mjo/eja/eja_algebra.py
+++ b/mjo/eja/eja_algebra.py
@@ -94,8 +94,10 @@ class FiniteDimensionalEuclideanJordanAlgebra(CombinatorialFreeModule):
         # long run to have the multiplication table be in terms of
         # algebra elements. We do this after calling the superclass
         # constructor so that from_vector() knows what to do.
-        self._multiplication_table = [ map(lambda x: self.from_vector(x), ls)
-                                       for ls in mult_table ]
+        self._multiplication_table = [
+            list(map(lambda x: self.from_vector(x), ls))
+            for ls in mult_table
+        ]
 
 
     def _element_constructor_(self, elt):
@@ -407,7 +409,7 @@ class FiniteDimensionalEuclideanJordanAlgebra(CombinatorialFreeModule):
         S = PolynomialRing(S, R.variable_names())
         t = S(t)
 
-        return sum( a[k]*(t**k) for k in xrange(len(a)) )
+        return sum( a[k]*(t**k) for k in range(len(a)) )
 
 
     def inner_product(self, x, y):
@@ -493,7 +495,7 @@ class FiniteDimensionalEuclideanJordanAlgebra(CombinatorialFreeModule):
 
         """
         M = list(self._multiplication_table) # copy
-        for i in xrange(len(M)):
+        for i in range(len(M)):
             # M had better be "square"
             M[i] = [self.monomial(i)] + M[i]
         M = [["*"] + list(self.gens())] + M
@@ -765,7 +767,7 @@ class FiniteDimensionalEuclideanJordanAlgebra(CombinatorialFreeModule):
             True
 
         """
-        return  tuple( self.random_element() for idx in xrange(count) )
+        return  tuple( self.random_element() for idx in range(count) )
 
 
     def rank(self):
@@ -944,8 +946,8 @@ class RealCartesianProductEJA(FiniteDimensionalEuclideanJordanAlgebra,
     """
     def __init__(self, n, field=QQ, **kwargs):
         V = VectorSpace(field, n)
-        mult_table = [ [ V.gen(i)*(i == j) for j in xrange(n) ]
-                       for i in xrange(n) ]
+        mult_table = [ [ V.gen(i)*(i == j) for j in range(n) ]
+                       for i in range(n) ]
 
         fdeja = super(RealCartesianProductEJA, self)
         return fdeja.__init__(field, mult_table, rank=n, **kwargs)
@@ -1099,9 +1101,9 @@ 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 xrange(n)] for i in xrange(n)]
-        for i in xrange(n):
-            for j in xrange(n):
+        mult_table = [[W.zero() for j in range(n)] for i in range(n)]
+        for i in range(n):
+            for j in range(n):
                 mat_entry = (basis[i]*basis[j] + basis[j]*basis[i])/2
                 mult_table[i][j] = W.coordinate_vector(_mat2vec(mat_entry))
 
@@ -1272,8 +1274,8 @@ class RealSymmetricEJA(RealMatrixEuclideanJordanAlgebra, KnownRankEJA):
         # The basis of symmetric matrices, as matrices, in their R^(n-by-n)
         # coordinates.
         S = []
-        for i in xrange(n):
-            for j in xrange(i+1):
+        for i in range(n):
+            for j in range(i+1):
                 Eij = matrix(field, n, lambda k,l: k==i and l==j)
                 if i == j:
                     Sij = Eij
@@ -1403,8 +1405,8 @@ class ComplexMatrixEuclideanJordanAlgebra(MatrixEuclideanJordanAlgebra):
         # Go top-left to bottom-right (reading order), converting every
         # 2-by-2 block we see to a single complex element.
         elements = []
-        for k in xrange(n/2):
-            for j in xrange(n/2):
+        for k in range(n/2):
+            for j in range(n/2):
                 submat = M[2*k:2*k+2,2*j:2*j+2]
                 if submat[0,0] != submat[1,1]:
                     raise ValueError('bad on-diagonal submatrix')
@@ -1555,8 +1557,8 @@ class ComplexHermitianEJA(ComplexMatrixEuclideanJordanAlgebra, KnownRankEJA):
         #   * The diagonal will (as a result) be real.
         #
         S = []
-        for i in xrange(n):
-            for j in xrange(i+1):
+        for i in range(n):
+            for j in range(i+1):
                 Eij = matrix(F, n, lambda k,l: k==i and l==j)
                 if i == j:
                     Sij = cls.real_embed(Eij)
@@ -1693,8 +1695,8 @@ class QuaternionMatrixEuclideanJordanAlgebra(MatrixEuclideanJordanAlgebra):
         # 4-by-4 block we see to a 2-by-2 complex block, to a 1-by-1
         # quaternion block.
         elements = []
-        for l in xrange(n/4):
-            for m in xrange(n/4):
+        for l in range(n/4):
+            for m in range(n/4):
                 submat = ComplexMatrixEuclideanJordanAlgebra.real_unembed(
                     M[4*l:4*l+4,4*m:4*m+4] )
                 if submat[0,0] != submat[1,1].conjugate():
@@ -1846,8 +1848,8 @@ class QuaternionHermitianEJA(QuaternionMatrixEuclideanJordanAlgebra,
         #   * The diagonal will (as a result) be real.
         #
         S = []
-        for i in xrange(n):
-            for j in xrange(i+1):
+        for i in range(n):
+            for j in range(i+1):
                 Eij = matrix(Q, n, lambda k,l: k==i and l==j)
                 if i == j:
                     Sij = cls.real_embed(Eij)
@@ -1914,9 +1916,9 @@ class JordanSpinEJA(FiniteDimensionalEuclideanJordanAlgebra, KnownRankEJA):
     """
     def __init__(self, n, field=QQ, **kwargs):
         V = VectorSpace(field, 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):
+        mult_table = [[V.zero() for j in range(n)] for i in range(n)]
+        for i in range(n):
+            for j in range(n):
                 x = V.gen(i)
                 y = V.gen(j)
                 x0 = x[0]