mjo: replace xrange() with range() for python-3.x compatibility.

diff --git a/mjo/cone/doubly_nonnegative.py b/mjo/cone/doubly_nonnegative.py
index a30a827d158f3b99d7d9df5d295096e7cc349e0f..43a2f61c5e3fa858098175e8c9e37c08acc11e45 100644 (file)
--- a/mjo/cone/doubly_nonnegative.py
+++ b/mjo/cone/doubly_nonnegative.py
@@ -371,8 +371,8 @@ def is_extreme_doubly_nonnegative(A):
     # whenever we come across an index pair `$(i,j)$` with
     # `$A_{ij} = 0$`.
     spanning_set = []
-    for j in xrange(A.ncols()):
-        for i in xrange(j):
+    for j in range(A.ncols()):
+        for i in range(j):
             if A[i,j] == 0:
                 M = A.matrix_space()
                 S = X.transpose() * (stdE(M,i,j) + stdE(M,j,i)) * X

diff --git a/mjo/cone/faces.py b/mjo/cone/faces.py
index 74b58c7f4ebbb0b1fba9f429a1bb449125b70872..acd9802c0ee953d28723da484c148ccd7b4a0b6d 100644 (file)
--- a/mjo/cone/faces.py
+++ b/mjo/cone/faces.py
@@ -53,7 +53,7 @@ def face_generated_by(K,S):
 
         sage: set_random_seed()
         sage: K = random_cone(max_ambient_dim=8, max_rays=10)
-        sage: S = ( K.random_element() for idx in xrange(5) )
+        sage: S = ( K.random_element() for idx in range(5) )
         sage: F = face_generated_by(K, S)
         sage: F.is_face_of(K)
         True
@@ -62,7 +62,7 @@ def face_generated_by(K,S):
 
         sage: set_random_seed()
         sage: K = random_cone(max_ambient_dim=8, max_rays=10)
-        sage: S = ( K.random_element() for idx in xrange(5) )
+        sage: S = ( K.random_element() for idx in range(5) )
         sage: F = face_generated_by(K, S)
         sage: all(F.contains(x) for x in S)
         True

diff --git a/mjo/cone/permutation_invariant.py b/mjo/cone/permutation_invariant.py
index 1c72565fb6532e7692904dc70db7907dab4c3ff1..faa39f76fbe9072c54f1ff29cebb563d1e8524cb 100644 (file)
--- a/mjo/cone/permutation_invariant.py
+++ b/mjo/cone/permutation_invariant.py
@@ -59,8 +59,8 @@ def is_permutation_invariant(K):
     The rearrangement cone is permutation-invariant::
 
         sage: all( is_permutation_invariant(rearrangement_cone(p,n))
-        ....:               for n in xrange(3, 6)
-        ....:               for p in xrange(1, n) )
+        ....:               for n in range(3, 6)
+        ....:               for p in range(1, n) )
         True
 
     As is the nonnegative orthant::

diff --git a/mjo/cone/rearrangement.py b/mjo/cone/rearrangement.py
index fa232bc476f8b4f779a745e47b65aa2ccd2c4763..c65316ebc7dd3737433e7d9e12dfe0891e55ccd7 100644 (file)
--- a/mjo/cone/rearrangement.py
+++ b/mjo/cone/rearrangement.py
@@ -83,8 +83,8 @@ def rearrangement_cone(p,n,lattice=None):
     [Jeong]_ Proposition 5.2.1::
 
         sage: all( rearrangement_cone(p,n).is_proper()
-        ....:              for n in xrange(10)
-        ....:              for p in xrange(1, n) )
+        ....:              for n in range(10)
+        ....:              for p in range(1, n) )
         True
 
     The Lyapunov rank of the rearrangement cone of order ``p`` in ``n``
@@ -92,12 +92,12 @@ def rearrangement_cone(p,n,lattice=None):
     by [Jeong]_ Corollary 5.2.4::
 
         sage: all( rearrangement_cone(p,n).lyapunov_rank() == n
-        ....:              for n in xrange(2, 10)
+        ....:              for n in range(2, 10)
         ....:              for p in [1, n-1] )
         True
         sage: all( rearrangement_cone(p,n).lyapunov_rank() == 1
-        ....:              for n in xrange(3, 10)
-        ....:              for p in xrange(2, n-1) )
+        ....:              for n in range(3, 10)
+        ....:              for p in range(2, n-1) )
         True
 
     TESTS:
@@ -123,8 +123,8 @@ def rearrangement_cone(p,n,lattice=None):
         ....:      rearrangement_cone(p,n).random_element(),
         ....:      p
         ....:    )
-        ....:    for n in xrange(2, 10)
-        ....:    for p in xrange(1, n-1)
+        ....:    for n in range(2, 10)
+        ....:    for p in range(1, n-1)
         ....: )
         True
 

diff --git a/mjo/cone/schur.py b/mjo/cone/schur.py
index d9371fb98750b63e84149003761890ca19824dd9..edf282da30794fc33b246485e27d3b378817d03f 100644 (file)
--- a/mjo/cone/schur.py
+++ b/mjo/cone/schur.py
@@ -69,7 +69,7 @@ def schur_cone(n, lattice=None):
         sage: n = ZZ.random_element(10)
         sage: K = schur_cone(n).dual()
         sage: x = K.random_element()
-        sage: all( x[i] >= x[i+1] for i in xrange(n-1) )
+        sage: all( x[i] >= x[i+1] for i in range(n-1) )
         True
 
     TESTS:
@@ -84,7 +84,7 @@ def schur_cone(n, lattice=None):
         sage: set_random_seed()
         sage: def majorized_by(x,y):
         ....:     return (all(sum(x[0:i]) <= sum(y[0:i])
-        ....:                 for i in xrange(x.degree()-1))
+        ....:                 for i in range(x.degree()-1))
         ....:             and sum(x) == sum(y))
         sage: n = ZZ.random_element(10)
         sage: V = VectorSpace(QQ, n)

diff --git a/mjo/eja/eja_algebra.py b/mjo/eja/eja_algebra.py
index 0f2b655f21795cb1feb0e8b41cfc878261a67962..dfb15c627fe021a3d3b47348a42ea56dc666e6fc 100644 (file)
--- a/mjo/eja/eja_algebra.py
+++ b/mjo/eja/eja_algebra.py
@@ -407,7 +407,7 @@ 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 +493,7 @@ 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 +765,7 @@ 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 +944,8 @@ 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 +1099,9 @@ 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 +1272,8 @@ 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 +1403,8 @@ 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 +1555,8 @@ 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 +1693,8 @@ 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 +1846,8 @@ 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 +1914,9 @@ 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]

diff --git a/mjo/eja/eja_element.py b/mjo/eja/eja_element.py
index b7061bfdcf27167715eb91cf1518942dbfab9db9..f78af2519c15eb1aeb07eaa4a45b56cbd0a40d4f 100644 (file)
--- a/mjo/eja/eja_element.py
+++ b/mjo/eja/eja_element.py
@@ -1315,7 +1315,7 @@ class FiniteDimensionalEuclideanJordanAlgebraElement(IndexedFreeModuleElement):
         # will be minimal for some natural number s...
         s = 0
         minimal_dim = J.dimension()
-        for i in xrange(1, minimal_dim):
+        for i in range(1, minimal_dim):
             this_dim = (u**i).operator().matrix().image().dimension()
             if this_dim < minimal_dim:
                 minimal_dim = this_dim

diff --git a/mjo/interpolation.py b/mjo/interpolation.py
index d3b406a56d0b9c50fbb1ffd48b4ff454ee5b6a03..25fb11f75f7944e678ba37fb422d9e9b7d70881a 100644 (file)
--- a/mjo/interpolation.py
+++ b/mjo/interpolation.py
@@ -18,7 +18,7 @@ def lagrange_denominator(k, xs):
     The product of all xs[j] with j != k.
 
     """
-    return product( xs[k] - xs[j] for j in xrange(len(xs)) if j != k )
+    return product( xs[k] - xs[j] for j in range(len(xs)) if j != k )
 
 
 def lagrange_coefficient(k, x, xs):
@@ -96,8 +96,8 @@ def lagrange_polynomial(x, xs, ys):
         True
 
     """
-    ls = [ lagrange_coefficient(k, x, xs) for k in xrange(len(xs)) ]
-    return sum( ys[k] * ls[k] for k in xrange(len(xs)) )
+    ls = [ lagrange_coefficient(k, x, xs) for k in range(len(xs)) ]
+    return sum( ys[k] * ls[k] for k in range(len(xs)) )
 
 
 
@@ -160,7 +160,7 @@ def divided_difference_coefficients(xs):
         [1/2/pi^2, -1/pi^2, 1/2/pi^2]
 
     """
-    return [ ~lagrange_denominator(k, xs) for k in xrange(len(xs)) ]
+    return [ ~lagrange_denominator(k, xs) for k in range(len(xs)) ]
 
 
 def divided_difference(xs, ys):
@@ -248,7 +248,7 @@ def newton_polynomial(x, xs, ys):
 
     """
     return sum( divided_difference(xs[:k+1], ys[:k+1])*lagrange_psi(x, xs[:k])
-                for k in xrange(len(xs)) )
+                for k in range(len(xs)) )
 
 
 def hermite_coefficient(k, x, xs):
@@ -337,10 +337,10 @@ def hermite_interpolant(x, xs, ys, y_primes):
 
     """
     s1 = sum( ys[k] * hermite_coefficient(k, x, xs)
-               for k in xrange(len(xs)) )
+               for k in range(len(xs)) )
 
     s2 = sum( y_primes[k] * hermite_deriv_coefficient(k, x, xs)
-               for k in xrange(len(xs)) )
+               for k in range(len(xs)) )
 
     return (s1 + s2)
 

diff --git a/mjo/matrix_vector.py b/mjo/matrix_vector.py
index 2a0e9e8d54a8dd45dd473a04780a63823e5030cd..111712b863d3a0dcf9f730798a5efc9fcd236de6 100644 (file)
--- a/mjo/matrix_vector.py
+++ b/mjo/matrix_vector.py
@@ -33,7 +33,7 @@ def isomorphism(matrix_space):
 
         sage: M = MatrixSpace(QQ,4,4)
         sage: (p, p_inv) = isomorphism(M)
-        sage: m = M(xrange(16))
+        sage: m = M(range(16))
         sage: p_inv(p(m)) == m
         True
 
@@ -148,8 +148,8 @@ def matrix_of_transformation(T, V):
             return L(x)
 
     entries = []
-    for j in xrange(n):
-        for i in xrange(n):
+    for j in range(n):
+        for i in range(n):
             entry = inner_product(apply(T,B[i]), B[j])
             entries.append(entry)
 

diff --git a/mjo/orthogonal_polynomials.py b/mjo/orthogonal_polynomials.py
index 7544f65c048c72662ff72c40bbcb1197a98382a7..15c695611fb3e287c357075f45e55eeddf550f7f 100644 (file)
--- a/mjo/orthogonal_polynomials.py
+++ b/mjo/orthogonal_polynomials.py
@@ -79,7 +79,7 @@ def legendre_p(n, x, a = -1, b = 1):
         ....:     return sum( inner_product(v, b)*b/norm(b)**2
         ....:                 for b in basis)
         sage: f = sin(x)
-        sage: legendre_basis = [ legendre_p(k, x, a, b) for k in xrange(4) ]
+        sage: legendre_basis = [ legendre_p(k, x, a, b) for k in range(4) ]
         sage: proj = project(legendre_basis, f)
         sage: proj.simplify_trig()
         5/2*(7*(pi^2 - 15)*x^3 - 3*(pi^4 - 21*pi^2)*x)/pi^6
@@ -89,7 +89,7 @@ def legendre_p(n, x, a = -1, b = 1):
     We should agree with Maxima for all `n`::
 
         sage: eq = lambda k: bool(legendre_p(k,x) == legendre_P(k,x))
-        sage: all( eq(k) for k in xrange(20) ) # long time
+        sage: all( eq(k) for k in range(20) ) # long time
         True
 
     We can evaluate the result of the zeroth polynomial::
@@ -193,6 +193,6 @@ def legendre_p(n, x, a = -1, b = 1):
 
     # From Abramowitz & Stegun, (22.3.2) with alpha = beta = 0.
     # Also massaged to support finite field elements.
-    P = sum( c(m)*g(m) for m in xrange(n+1) )/(2**n)
+    P = sum( c(m)*g(m) for m in range(n+1) )/(2**n)
 
     return P

diff --git a/mjo/symbol_sequence.py b/mjo/symbol_sequence.py
index 3878b7505ba2c34289c1cc3e3b558d82bed1cfc4..563bab6ad4d190f0cbcaa82e428acc6ea86e2ddf 100644 (file)
--- a/mjo/symbol_sequence.py
+++ b/mjo/symbol_sequence.py
@@ -38,7 +38,7 @@ class SymbolSequence:
     degree::
 
         sage: a = SymbolSequence('a')
-        sage: p = sum( a[i]*x^i for i in xrange(5) )
+        sage: p = sum( a[i]*x^i for i in range(5) )
         sage: p
         a_4*x^4 + a_3*x^3 + a_2*x^2 + a_1*x + a_0
 
@@ -57,7 +57,7 @@ class SymbolSequence:
         a_0_1_2
         sage: latex(a[0,1,2])
         a_{0}_{1}_{2}
-        sage: [ a[i,j] for i in xrange(2) for j in xrange(2) ]
+        sage: [ a[i,j] for i in range(2) for j in range(2) ]
         [a_0_0, a_0_1, a_1_0, a_1_1]
 
     You can pass slices instead of integers to obtain a list of
@@ -284,7 +284,7 @@ class SymbolSequence:
         # If the user asks for a slice, we'll be returning a list
         # of symbols.
         return [ self._subscript_integer_(idx)
-                 for idx in xrange(start, s.stop, step) ]
+                 for idx in range(start, s.stop, step) ]