def main():
(n, nfsPoly, m, B, M, K) = files.loadParamsFile()
afBase = files.loadFileArray("afbase.txt")
rfBase = files.loadFileArray("rfbase.txt")
smoothsFile = open("smooths.txt", "w")
smoothsCount = 0
q = B
K += K / 10
specialqFile = open("specialq.txt", "w")
while (smoothsCount < K):
while (True):
q = primemath.nextPrime(q)
roots = poly.getRootsModPFast(poly.Poly(nfsPoly), q)
if (len(roots) > 0):
break
roots.sort()
for s in roots:
specialqFile.write(str([s, q]) + "\n")
print "special_q: %s" % [q, s]
I = 1024
J = 512
smooths = sieve_special_q(q, s, I, J, rfBase, afBase,
(n, nfsPoly, m, B, M, K))
smoothsCount += len(smooths)
print "total smooths: %s/%s" % (smoothsCount, K)
smoothsFile = open("smooths.txt", "a")
for smooth in smooths:
smoothsFile.write(str(smooth) + "\n")
smoothsFile.close()
def main():
(n,nfsPoly,m,B,M,K) = files.loadParamsFile()
afBase = files.loadFileArray("afbase.txt")
rfBase = files.loadFileArray("rfbase.txt")
smoothsFile = open("smooths.txt", "w")
smoothsCount = 0
q = B
K+=K/10
specialqFile = open("specialq.txt", "w")
while(smoothsCount < K):
while(True):
q = primemath.nextPrime(q)
roots = poly.getRootsModPFast(poly.Poly(nfsPoly),q)
if(len(roots) > 0):
break
roots.sort()
for s in roots:
specialqFile.write(str([s,q])+"\n")
print "special_q: %s" % [q,s]
I = 1024
J = 512
smooths = sieve_special_q(q,s,I,J,rfBase,afBase,(n,nfsPoly,m,B,M,K))
smoothsCount += len(smooths)
print "total smooths: %s/%s" % (smoothsCount,K)
smoothsFile = open("smooths.txt", "a")
for smooth in smooths:
smoothsFile.write(str(smooth)+"\n")
smoothsFile.close()
def generateQCBase(n, p, nfsPoly):
qcbase = []
while (len(qcbase) < 3 * math.log(n, 10)):
p = primemath.nextPrime(p)
roots = poly.getRootsModPFast(nfsPoly, p)
for root in roots:
if (nfsPoly.derivative().evaluate(root) % p != 0):
qcbase.append([root, p])
return qcbase
def generateQCBase(n,p,nfsPoly): qcbase = [] while(len(qcbase) < 3*math.log(n,10)): p = primemath.nextPrime(p) roots = poly.getRootsModPFast(nfsPoly,p) for root in roots: if(nfsPoly.derivative().evaluate(root) % p != 0): qcbase.append([root,p]) return qcbase
def main():
nfspoly = poly.Poly([8, 29, 15, 1])
NF = poly.NumberField(nfspoly)
while (True):
q = primemath.generateLargePrime(10)
s = poly.getRootsModPFast(nfspoly, q)
if (len(s) > 0):
break
s = s[0]
print "special_q: f(%s) = 0 mod %s" % (s, q)
while (True):
p = primemath.generateLargePrime(7)
r = poly.getRootsModPFast(nfspoly, p)
if (len(r) > 0):
break
r = r[0]
print "p: f(%s) = 0 mod %s" % (r, p)
basis = find_sublattice_basis(q, s, p, r)
print "basis: %s" % basis
basis_r = reduce_basis(basis[0], basis[1])
a0 = basis_r[0][0]
b0 = basis_r[0][1]
a1 = basis_r[1][0]
b1 = basis_r[1][1]
print "reduced basis: %s" % [[a0, b0], [a1, b1]]
print "generating lattice points..."
for i in range(-20, 20):
for j in range(-20, 20):
a = a0 * i + a1 * j
b = b0 * i + b1 * j
if (a == 0 or b == 0):
continue
NFelement = NF(poly.Poly([a, b]))
if (NFelement.norm() % q == 0 and NFelement.norm() % p == 0):
print "%s is q-divisible and p-divisible" % [a, b]
else:
raise AssertionError("%s is not q-divisible or p-divisible" %
[a, b])
def main():
nfspoly = poly.Poly([8,29,15,1])
NF = poly.NumberField(nfspoly)
while(True):
q = primemath.generateLargePrime(10)
s = poly.getRootsModPFast(nfspoly,q)
if(len(s) > 0):
break
s = s[0]
print "special_q: f(%s) = 0 mod %s" %(s,q)
while(True):
p = primemath.generateLargePrime(7)
r = poly.getRootsModPFast(nfspoly,p)
if(len(r) > 0):
break
r = r[0]
print "p: f(%s) = 0 mod %s" %(r,p)
basis = find_sublattice_basis(q,s,p,r)
print "basis: %s" % basis
basis_r = reduce_basis(basis[0],basis[1])
a0 = basis_r[0][0]
b0 = basis_r[0][1]
a1 = basis_r[1][0]
b1 = basis_r[1][1]
print "reduced basis: %s" % [[a0,b0],[a1,b1]]
print "generating lattice points..."
for i in range(-20,20):
for j in range(-20,20):
a = a0*i+a1*j
b = b0*i+b1*j
if(a == 0 or b == 0):
continue
NFelement = NF(poly.Poly([a,b]))
if(NFelement.norm()%q == 0 and NFelement.norm()%p == 0):
print "%s is q-divisible and p-divisible" % [a,b]
else:
raise AssertionError("%s is not q-divisible or p-divisible" % [a,b])
def test_polyRootModPFast(self): # Briggs polynomial = poly.Poly([8,29,15,1]) testRoots = poly.getRootsModPFast(polynomial,67) correctRoots = [2,44,6] correctRoots.sort() testRoots.sort() self.assertEqual(len(correctRoots),len(testRoots)) for i in range(len(correctRoots)): self.assertEqual(correctRoots[i], testRoots[i])
def test_polyRootModPFastDeg5_2(self): p = 157 polynomial = poly.Poly([11,1])*poly.Poly([-23,1])*poly.Poly([-1,1])*poly.Poly([-1,1])*poly.Poly([-1,1]) correctRoots = poly.getRootsModPSlow(polynomial,p) testRoots = poly.getRootsModPFast(polynomial,p) correctRoots.sort() testRoots.sort() self.assertEqual(len(correctRoots),len(testRoots)) for i in range(len(correctRoots)): self.assertEqual(correctRoots[i], testRoots[i])
def test_polyRootModPFastRandomDeg5(self): # no roots p = 503 polynomial = poly.Poly([2034,234,24,123,101,1]) correctRoots = poly.getRootsModPSlow(polynomial,p) testRoots = poly.getRootsModPFast(polynomial,p) correctRoots.sort() testRoots.sort() self.assertEqual(len(correctRoots),len(testRoots)) for i in range(len(correctRoots)): self.assertEqual(correctRoots[i], testRoots[i])
def test_polyRootModPFastRandomZeroRoot(self): p = 503 polynomial = poly.Poly([0,1])*poly.Poly([-11,1])*poly.Poly([-51,1])*poly.Poly([-231,1]) correctRoots = poly.getRootsModPSlow(polynomial,p) testRoots = poly.getRootsModPFast(polynomial,p) correctRoots.sort() testRoots.sort() self.assertEqual(len(correctRoots),len(testRoots)) for i in range(len(correctRoots)): self.assertEqual(correctRoots[i], testRoots[i])
def main():
nfspoly = poly.Poly([8,29,15,1])
NF = poly.NumberField(nfspoly)
while(True):
q = primemath.generateLargePrime(20)
r = poly.getRootsModPFast(nfspoly,q)
if(len(r) > 0):
break
r = r[0]
print "special_q: f(%s) = 0 mod %s" %(r,q)
basis = []
b = 1
for i in range(2):
a = -b*r + i*q
basis.append([a,b])
print "basis: %s" % basis
basis_r = reduce_basis(basis[0],basis[1])
a0 = basis_r[0][0]
b0 = basis_r[0][1]
a1 = basis_r[1][0]
b1 = basis_r[1][1]
print "reduced basis: %s" % [[a0,b0],[a1,b1]]
print "generating lattice points..."
for i in range(-2,2):
for j in range(-2,2):
a = a0*i+a1*j
b = b0*i+b1*j
if(a == 0 or b == 0):
continue
NFelement = NF(poly.Poly([a,b]))
if(NFelement.norm()%q == 0):
print "%s is q-divisible" % [a,b]
else:
raise AssertionError("%s is not q-divisible" % [a,b])
def main():
nfspoly = poly.Poly([8, 29, 15, 1])
NF = poly.NumberField(nfspoly)
while (True):
q = primemath.generateLargePrime(20)
r = poly.getRootsModPFast(nfspoly, q)
if (len(r) > 0):
break
r = r[0]
print "special_q: f(%s) = 0 mod %s" % (r, q)
basis = []
b = 1
for i in range(2):
a = -b * r + i * q
basis.append([a, b])
print "basis: %s" % basis
basis_r = reduce_basis(basis[0], basis[1])
a0 = basis_r[0][0]
b0 = basis_r[0][1]
a1 = basis_r[1][0]
b1 = basis_r[1][1]
print "reduced basis: %s" % [[a0, b0], [a1, b1]]
print "generating lattice points..."
for i in range(-2, 2):
for j in range(-2, 2):
a = a0 * i + a1 * j
b = b0 * i + b1 * j
if (a == 0 or b == 0):
continue
NFelement = NF(poly.Poly([a, b]))
if (NFelement.norm() % q == 0):
print "%s is q-divisible" % [a, b]
else:
raise AssertionError("%s is not q-divisible" % [a, b])
(m,nfsPoly) = nfspolygen.generateNFSPoly(n,d)
print "Using poly %s, m = %s" % (nfsPoly,m)
B = M = etcmath.calculateB(n)
print "Using bound %s" % B
prefactorBase = primemath.generatePrimes(B)
K = (int)(3*math.log(n,10)) # for quadratic characters
afBaseFile = open("afbase.txt", "w")
rfBaseFile = open("rfbase.txt", "w")
print "Generating af and rf bases..."
for p in prefactorBase:
if(p > B): break
rfBaseFile.write(str([m%p,p])+"\n")
K += 1
roots = poly.getRootsModPFast(nfsPoly,p)
for root in roots:
afBaseFile.write(str([root,p])+"\n")
K += 1
afBaseFile.close()
rfBaseFile.close()
K += 10
paramsFile = open("params.txt", "w")
paramsFile.write("n = " +str(n)+"\n")
paramsFile.write("B = " +str(B)+"\n")
paramsFile.write("M = " +str(M)+"\n")
paramsFile.write("nfsPoly = " +str(nfsPoly)+"\n")
paramsFile.write("m = " +str(m)+"\n")
(m,nfsPoly) = nfspolygen.generateNFSPoly(n,d)
print "Using poly %s, m = %s" % (nfsPoly,m)
B = M = etcmath.calculateB(n)
print "Using bound %s" % B
prefactorBase = primemath.generatePrimes(B)
K = (int)(3*math.log(n,10)) # for quadratic characters
afBaseFile = open("afbase.txt", "w")
rfBaseFile = open("rfbase.txt", "w")
print "Generating af and rf bases..."
for p in prefactorBase:
if(p > B): break
rfBaseFile.write(str([m%p,p])+"\n")
K += 1
roots = poly.getRootsModPFast(nfsPoly,p)
for root in roots:
afBaseFile.write(str([root,p])+"\n")
K += 1
afBaseFile.close()
rfBaseFile.close()
K += 10
paramsFile = open("params.txt", "w")
paramsFile.write("n = " +str(n)+"\n")
paramsFile.write("B = " +str(B)+"\n")
paramsFile.write("M = " +str(M)+"\n")
paramsFile.write("nfsPoly = " +str(nfsPoly)+"\n")
paramsFile.write("m = " +str(m)+"\n")