diff --git a/sage/group_prover.sage b/sage/group_prover.sage index 8521f07999..53ffee24c5 100644 --- a/sage/group_prover.sage +++ b/sage/group_prover.sage @@ -65,7 +65,7 @@ class fastfrac: 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 @@ class fastfrac: """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 @@ class fastfrac: 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 @@ class constraints: 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 conflicts(R, con): 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 get_nonzero_set(R, assume): 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 @@ def prove_zero(R, exprs, assume): 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 @@ def describe_extra(R, assume, assumeExtra): """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/sage/weierstrass_prover.sage b/sage/weierstrass_prover.sage index 03ef2ec901..b770c6dafe 100644 --- a/sage/weierstrass_prover.sage +++ b/sage/weierstrass_prover.sage @@ -175,24 +175,24 @@ laws_jacobian_weierstrass = { 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 @@ def check_exhaustive_jacobian_weierstrass(name, A, B, branches, formula, p): 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 @@ def check_symbolic_jacobian_weierstrass(name, A, B, branches, formula): 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 @@ def check_symbolic_jacobian_weierstrass(name, A, B, branches, formula): 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()