def test_normPolyB2(self): NF = poly.NumberField(poly.Poly([8,29,15,1])) a = -8 b = 3 NF = poly.NumberField(poly.Poly([8,29,15,1])) polyNormB = NF.getPolyNormB(b) self.assertEqual(polyNormB.evaluate(a),-5696)
def test_numberfield_square2(self): # Brigg's example nfspoly = poly.Poly([8,29,15,1]) NF = poly.NumberField(nfspoly) nfspolyd = NF(nfspoly.derivative()) sqrt = NF(poly.Poly([3889976768, 3686043120, 599923511])) correctSquare = NF(poly.Poly([22939402657683071224L, 54100105785512562427L, 22455983949710645412L])) square = sqrt * sqrt self.assertEqual(square,correctSquare)
def test_numberfield_square1(self): # Spaans's example nfspoly = poly.Poly([161, 134, 2, 1]) NF = poly.NumberField(nfspoly) nfspolyd = NF(nfspoly.derivative()) sqrt = NF(poly.Poly([-41757429265579073242,-34105727598423382475,1681812579256330563])) correctSquare = NF(poly.Poly([21124198049840950371210079793023892077432,18523314201045731615331644622444823801483,884477920457388669411401815623954662863])) square = sqrt * sqrt self.assertEqual(square,correctSquare)
def test_numberfield_mult2(self): # Spaan's example nfspoly = poly.Poly([161, 134, 2, 1]) NF = poly.NumberField(nfspoly) nfspolyd = NF(nfspoly.derivative()) tomult = [[-92,-1],[-57,-1],[-23,-1],[-8,-1],[-7,-1],[2,-1],[10,-1],[17,-1],[29,-1],[35,-1],[84,-1],[115,-1],[139,-1],[-5,-2],[19,-2],[69,-2],[93,-2],[119,-2],[-542,-3],[-28,-3],[-23,-3],[-8,-3]] tomult = [NF(poly.Poly(x)) for x in tomult] correctProduct = NF(poly.Poly([21124198049840950371210079793023892077432,18523314201045731615331644622444823801483,884477920457388669411401815623954662863])) prod = multAllElements(NF(poly.Poly([1])),tomult) prod = prod * nfspolyd * nfspolyd self.assertEqual(prod,correctProduct)
def test_numberfield_mult1(self): # Briggs' example nfspoly = poly.Poly([8,29,15,1]) NF = poly.NumberField(nfspoly) nfspolyd = NF(nfspoly.derivative()) correctProduct = NF(poly.Poly([22939402657683071224L, 54100105785512562427L, 22455983949710645412L])) tomult = [[-1,1],[3,1],[13,1],[104,1],[3,2],[25,2],[-8,3],[48,5],[54,5],[-43,6],[-8,7],[11,7],[856,11]] tomult = [NF(poly.Poly(x)) for x in tomult] prod = multAllElements(NF(poly.Poly([1])),tomult) prod = prod * nfspolyd * nfspolyd self.assertEqual(prod,correctProduct)
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():
(n, nfsPoly, m, B, M, K) = files.loadParamsFile()
NF = poly.NumberField(poly.Poly(nfsPoly))
rfBase = files.loadFileArray("rfbase.txt")
afBase = files.loadFileArray("afbase.txt")
smooths = files.loadFileArray("smooths.txt")
specialq = files.loadFileArray("specialq.txt")
nOfSmooths = len(smooths)
#smooths = sorted(smooths,key=hash)
#smooths = sorted({hash(val): val for val in smooths}, key=hash)
smooths = sorted({hash(val): val for val in smooths}.values(), key=hash)
#for smooth in smooths:
#print smooth
print "%s duplicates removed." % (nOfSmooths - len(smooths))
nOfSmooths = len(smooths)
if (len(smooths) < K + len(specialq)):
print "undersieved by %s." % ((K + len(specialq)) - len(smooths))
raise AssertionError
while (len(smooths) > K + len(specialq)):
smooths.pop()
print "%s extra relations removed." % (nOfSmooths - len(smooths))
smoothsFile = open("smooths-fil.txt", "w")
for smooth in smooths:
smoothsFile.write(str(smooth) + "\n")
rfBaseFile = open("rfbase-fil.txt", "w")
for p in rfBase:
rfBaseFile.write(str(p) + "\n")
afBaseFile = open("afbase-fil.txt", "w")
for p in afBase:
afBaseFile.write(str(p) + "\n")
for p in specialq:
afBaseFile.write(str(p) + "\n")
'''
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])
for r in range(sideLen):
if (zeroRow(matrix[r])):
dep[r] = n & 1
n >>= 1
for r in range(sideLen):
for c in range(r + 1, sideLen):
if (matrix[r][c] == 1):
dep[r] = (dep[c] + dep[r]) % 2
return dep
if __name__ == '__main__':
(n, nfsPoly, m, B, M, K) = files.loadParamsFile()
NF = poly.NumberField(poly.Poly(nfsPoly))
rfBase = files.loadFileArray("rfbase-fil.txt")
rfBase = zip(*rfBase)[1] #grab only the primes
afBase = files.loadFileArray("afbase-fil.txt")
qcBase = matrixmath.generateQCBase(n, afBase[-1][1], poly.Poly(nfsPoly))
smooths = files.loadFileArray("smooths-fil.txt")
print "Building matrix..."
matrix = []
for smoothPair in smooths:
smoothPoly = poly.Poly(smoothPair)
matrixRow = matrixmath.getMatrixRowRat(smoothPoly, m, rfBase)
matrixRow.extend(matrixmath.getMatrixRowAlg(smoothPoly, NF, afBase))
matrixRow.extend(matrixmath.getMatrixRowQC(smoothPoly, qcBase))
matrixRow.extend([0] * (K - len(rfBase) - len(afBase) - len(qcBase) -
while (True):
b += 1
a = -b * s % q
if (a == 0 or b == 0):
continue
if (float(basis1[0]) / a - float(basis1[1]) / b < 0.01):
continue
basis2 = [a, b]
break
return [basis1, basis2]
def sieve_special_q(q, s, I, J, rfBase, afBase, (n, nfsPoly, m, B, M, K)):
nfsPoly = poly.Poly(nfsPoly)
NF = poly.NumberField(nfsPoly)
basis_q = find_lattice_basis(q, s)
basis_q = reduce_basis(basis_q[0], basis_q[1])
(qa0, qb0, qa1, qb1) = frankefy(basis_q)
logB = math.log(B)
lambd_a = 1.5
lambd_r = 1.5
sieve = [[0.0] * (J) for i in range(I)]
print "sieving rational side..."
for prime in rfBase:
r = prime[0]
p = prime[1]
#print [r,p]
basis_r = find_sublattice_basis(basis_q, p, r)
def test_norm(self): NF = poly.NumberField(poly.Poly([8,29,15,1])) smoothElement = NF(poly.Poly([-8,3])) self.assertEqual(smoothElement.norm(),-5696)
def test_normPolyB1(self): NF = poly.NumberField(poly.Poly([8,29,15,1])) b = -5 testPolyNormB = NF.getPolyNormB(b) correctPolyNormB = poly.Poly([1000, 725, 75, 1]) self.assertEqual(testPolyNormB, correctPolyNormB)
