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diff --git a/src/secp256k1/sage/group_prover.sage b/src/secp256k1/sage/group_prover.sage
--- a/src/secp256k1/sage/group_prover.sage
+++ b/src/secp256k1/sage/group_prover.sage
@@ -65,7 +65,7 @@
return self.top in I and self.bot not in I
def reduce(self,assumeZero):
- zero = self.R.ideal(map(numerator, assumeZero))
+ zero = self.R.ideal(list(map(numerator, assumeZero)))
return fastfrac(self.R, zero.reduce(self.top)) / fastfrac(self.R, zero.reduce(self.bot))
def __add__(self,other):
@@ -100,7 +100,7 @@
"""Multiply something else with a fraction."""
return self.__mul__(other)
- def __div__(self,other):
+ def __truediv__(self,other):
"""Divide two fractions."""
if parent(other) == ZZ:
return fastfrac(self.R,self.top,self.bot * other)
@@ -108,6 +108,11 @@
return fastfrac(self.R,self.top * other.bot,self.bot * other.top)
return NotImplemented
+ # Compatibility wrapper for Sage versions based on Python 2
+ def __div__(self,other):
+ """Divide two fractions."""
+ return self.__truediv__(other)
+
def __pow__(self,other):
"""Compute a power of a fraction."""
if parent(other) == ZZ:
@@ -175,7 +180,7 @@
def conflicts(R, con):
"""Check whether any of the passed non-zero assumptions is implied by the zero assumptions"""
- zero = R.ideal(map(numerator, con.zero))
+ zero = R.ideal(list(map(numerator, con.zero)))
if 1 in zero:
return True
# First a cheap check whether any of the individual nonzero terms conflict on
@@ -195,7 +200,7 @@
def get_nonzero_set(R, assume):
"""Calculate a simple set of nonzero expressions"""
- zero = R.ideal(map(numerator, assume.zero))
+ zero = R.ideal(list(map(numerator, assume.zero)))
nonzero = set()
for nz in map(numerator, assume.nonzero):
for (f,n) in nz.factor():
@@ -208,7 +213,7 @@
def prove_nonzero(R, exprs, assume):
"""Check whether an expression is provably nonzero, given assumptions"""
- zero = R.ideal(map(numerator, assume.zero))
+ zero = R.ideal(list(map(numerator, assume.zero)))
nonzero = get_nonzero_set(R, assume)
expl = set()
ok = True
@@ -250,7 +255,7 @@
r, e = prove_nonzero(R, dict(map(lambda x: (fastfrac(R, x.bot, 1), exprs[x]), exprs)), assume)
if not r:
return (False, map(lambda x: "Possibly zero denominator: %s" % x, e))
- zero = R.ideal(map(numerator, assume.zero))
+ zero = R.ideal(list(map(numerator, assume.zero)))
nonzero = prod(x for x in assume.nonzero)
expl = []
for expr in exprs:
@@ -265,8 +270,8 @@
"""Describe what assumptions are added, given existing assumptions"""
zerox = assume.zero.copy()
zerox.update(assumeExtra.zero)
- zero = R.ideal(map(numerator, assume.zero))
- zeroextra = R.ideal(map(numerator, zerox))
+ zero = R.ideal(list(map(numerator, assume.zero)))
+ zeroextra = R.ideal(list(map(numerator, zerox)))
nonzero = get_nonzero_set(R, assume)
ret = set()
# Iterate over the extra zero expressions
diff --git a/src/secp256k1/sage/weierstrass_prover.sage b/src/secp256k1/sage/weierstrass_prover.sage
--- a/src/secp256k1/sage/weierstrass_prover.sage
+++ b/src/secp256k1/sage/weierstrass_prover.sage
@@ -175,24 +175,24 @@
def check_exhaustive_jacobian_weierstrass(name, A, B, branches, formula, p):
"""Verify an implementation of addition of Jacobian points on a Weierstrass curve, by executing and validating the result for every possible addition in a prime field"""
F = Integers(p)
- print "Formula %s on Z%i:" % (name, p)
+ print("Formula %s on Z%i:" % (name, p))
points = []
- for x in xrange(0, p):
- for y in xrange(0, p):
+ for x in range(0, p):
+ for y in range(0, p):
point = affinepoint(F(x), F(y))
r, e = concrete_verify(on_weierstrass_curve(A, B, point))
if r:
points.append(point)
- for za in xrange(1, p):
- for zb in xrange(1, p):
+ for za in range(1, p):
+ for zb in range(1, p):
for pa in points:
for pb in points:
- for ia in xrange(2):
- for ib in xrange(2):
+ for ia in range(2):
+ for ib in range(2):
pA = jacobianpoint(pa.x * F(za)^2, pa.y * F(za)^3, F(za), ia)
pB = jacobianpoint(pb.x * F(zb)^2, pb.y * F(zb)^3, F(zb), ib)
- for branch in xrange(0, branches):
+ for branch in range(0, branches):
assumeAssert, assumeBranch, pC = formula(branch, pA, pB)
pC.X = F(pC.X)
pC.Y = F(pC.Y)
@@ -206,13 +206,13 @@
r, e = concrete_verify(assumeLaw)
if r:
if match:
- print " multiple branches for (%s,%s,%s,%s) + (%s,%s,%s,%s)" % (pA.X, pA.Y, pA.Z, pA.Infinity, pB.X, pB.Y, pB.Z, pB.Infinity)
+ print(" multiple branches for (%s,%s,%s,%s) + (%s,%s,%s,%s)" % (pA.X, pA.Y, pA.Z, pA.Infinity, pB.X, pB.Y, pB.Z, pB.Infinity))
else:
match = True
r, e = concrete_verify(require)
if not r:
- print " failure in branch %i for (%s,%s,%s,%s) + (%s,%s,%s,%s) = (%s,%s,%s,%s): %s" % (branch, pA.X, pA.Y, pA.Z, pA.Infinity, pB.X, pB.Y, pB.Z, pB.Infinity, pC.X, pC.Y, pC.Z, pC.Infinity, e)
- print
+ print(" failure in branch %i for (%s,%s,%s,%s) + (%s,%s,%s,%s) = (%s,%s,%s,%s): %s" % (branch, pA.X, pA.Y, pA.Z, pA.Infinity, pB.X, pB.Y, pB.Z, pB.Infinity, pC.X, pC.Y, pC.Z, pC.Infinity, e))
+ print()
def check_symbolic_function(R, assumeAssert, assumeBranch, f, A, B, pa, pb, pA, pB, pC):
@@ -242,9 +242,9 @@
for key in laws_jacobian_weierstrass:
res[key] = []
- print ("Formula " + name + ":")
+ print("Formula " + name + ":")
count = 0
- for branch in xrange(branches):
+ for branch in range(branches):
assumeFormula, assumeBranch, pC = formula(branch, pA, pB)
pC.X = lift(pC.X)
pC.Y = lift(pC.Y)
@@ -255,10 +255,10 @@
res[key].append((check_symbolic_function(R, assumeFormula, assumeBranch, laws_jacobian_weierstrass[key], A, B, pa, pb, pA, pB, pC), branch))
for key in res:
- print " %s:" % key
+ print(" %s:" % key)
val = res[key]
for x in val:
if x[0] is not None:
- print " branch %i: %s" % (x[1], x[0])
+ print(" branch %i: %s" % (x[1], x[0]))
- print
+ print()

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