public Matrix Build(List <Pair> pairs, RationalFactorbase rfb, AlgebraicFactorbase afb, QuadraticCharacters qfb, BigInteger integerRoot, Polynomial polynomial)
{
var matrix = new int[rfb.Elements.Count + afb.Elements.Count + qfb.Elements.Count + 1, pairs.Count];
for (int index = 0; index < pairs.Count; index++)
{
var pair = pairs[index];
var rational = pair.Item1 + pair.Item2 * integerRoot;
if (rational < 0)
{
matrix[0, index] = 1;
rational = -rational;
}
for (int i = 0; i < rfb.Elements.Count; i++)
{
while (rational % rfb.Elements[i].Item2 == 0)
{
matrix[i + 1, index]++;
rational /= rfb.Elements[i].Item2;
}
matrix[i + 1, index] %= 2;
if (rational == 1)
{
break;
}
}
var normCalculator = new FirstDegreeElementsNormCalculator(polynomial, pair.Item2);
var algebraic = normCalculator.CalculateNorm(pair.Item1);
for (int i = 0; i < afb.Elements.Count; i++)
{
var primeIdeal = afb.Elements[i];
while (algebraic % primeIdeal.Item2 == 0 && (pair.Item1 + pair.Item2 * primeIdeal.Item1) % primeIdeal.Item2 == 0)
{
matrix[i + rfb.Elements.Count, index]++;
algebraic /= afb.Elements[i].Item2;
}
matrix[i + rfb.Elements.Count, index] %= 2;
if (algebraic == 1 || algebraic == -1)
{
break;
}
}
var jacobiSymbol = new JacobiSymbol();
for (int i = 0; i < qfb.Elements.Count; i++)
{
if (jacobiSymbol.Calculate(pair.Item1 + pair.Item2 * qfb.Elements[i].Item1, qfb.Elements[i].Item2) == -1)
{
matrix[rfb.Elements.Count + afb.Elements.Count + 1 + i, index] = 1;
}
}
}
return(new Matrix(matrix));
}
public bool IsSmoothOverAlgebraicFactorbase(BigInteger a, BigInteger b, Polynomial polynomial, AlgebraicFactorbase factorbase)
{
var normCalculator = new FirstDegreeElementsNormCalculator(polynomial, b);
var element = normCalculator.CalculateNorm(a);
if (element == 0)
{
return(false);
}
for (int i = 0; i < factorbase.Elements.Count; i++)
{
if (element == 1 || element == -1)
{
return(true);
}
var currentPair = factorbase.Elements[i];
while (element % currentPair.Item2 == 0)
{
element /= currentPair.Item2;
}
}
return(element == 1 || element == -1);
}
public BigInteger FindFactor()
{
var timer = new Stopwatch();
timer.Start();
_polyInfo = _generator.GeneratePolynomial();
Console.WriteLine(_number.Value());
Console.WriteLine("f(x)=" + _polyInfo.Polynomial);
Console.WriteLine("Root=" + _polyInfo.Root);
var rootFinder = new GcdRootFinder();
var algFbBuilder = new AlgebraicFactorbaseBuilder(_polyInfo.Polynomial, rootFinder, _algebraicPrimeBound);
var rationalFbBuilder = new RationalFactorbaseBuilder(_polyInfo.Root, _rationalPrimeBound);
var quadraticCharFbBuilder = new QuadraticCharactersBuilder(_polyInfo.Polynomial, rootFinder, _algebraicPrimeBound, _quadraticCharFbSize);
var rationalFb = rationalFbBuilder.Build();
var quadraticCharFb = quadraticCharFbBuilder.Build();
var algFb = algFbBuilder.Build();
var sieve = new LogSieve();
Console.WriteLine("\nRational factorbase size: " + rationalFb.Elements.Count);
Console.WriteLine("Algebraic factorbase size: " + algFb.Elements.Count);
Console.WriteLine("Quadratic characters factorbase size: " + quadraticCharFb.Elements.Count);
Console.WriteLine("Init time: " + timer.Elapsed);
timer.Reset();
timer.Start();
var pairs =
sieve.Sieve(
(algFb.Elements.Count + rationalFb.Elements.Count + quadraticCharFb.Elements.Count + _kerDim + 1),
new SieveOptions(_sieveSize, -_sieveSize, algFb, rationalFb, _polyInfo.Polynomial, _polyInfo.Root));
Console.WriteLine();
Console.WriteLine(pairs.Count + " relations collected.");
Console.WriteLine("Sieve time: " + timer.Elapsed);
timer.Reset();
timer.Start();
var matrixBuilder = new MatrixBuilder();
var matrix = matrixBuilder.Build(pairs, rationalFb, algFb, quadraticCharFb, _polyInfo.Root, _polyInfo.Polynomial);
var matrixSolver = new GaussianEliminationOverGf2();
//Console.WriteLine("{0}x{1} matrix builded. ",matrix.ColumnsCount,matrix.RowsCount);
var solutions = matrixSolver.Solve(matrix);
// var solutions =matrix.Solve();
Console.WriteLine();
Console.WriteLine("Linear algebra time: " + timer.Elapsed);
Console.WriteLine("{0} solution computed. ", solutions.Count);
timer.Reset();
timer.Start();
var polyMath = new PolynomialMath(-1);
var df = new PolynomialDerivative().Derivative(_polyInfo.Polynomial);
var sqrDf = polyMath.Mul(df, df);
var solutionsCheked = -1;
foreach (var solution in solutions)
{
timer.Reset();
timer.Start();
var sqr = new Polynomial(new BigInteger[] { 1 });
BigInteger sqrtNorm = 1;
BigInteger x = 1;
for (int i = 0; i < solution.Length; i++)
{
if (solution[i] == 1)
{
var tmp = new Polynomial(new BigInteger[] { pairs[i].Item1, pairs[i].Item2 });
x *= pairs[i].Item1 + _polyInfo.Root * pairs[i].Item2;
sqr = polyMath.Rem(polyMath.Mul(tmp, sqr), _polyInfo.Polynomial);
var normCalculator = new FirstDegreeElementsNormCalculator(_polyInfo.Polynomial, pairs[i].Item2);
sqrtNorm *= normCalculator.CalculateNorm(pairs[i].Item1);
}
}
x *= sqrDf.Value(_polyInfo.Root);
if (x < 0)
{
throw new Exception();
}
sqr = polyMath.Rem(polyMath.Mul(sqrDf, sqr), _polyInfo.Polynomial);
var integerSqrt = new IntegerSquareRoot();
var sqrtX = integerSqrt.Sqrt(x);
if (sqrtX * sqrtX != x)
{
if (sqrtX * sqrtX != x)
{
if (sqrtX * sqrtX != x)
{
throw new Exception();
}
}
}
var algSqrt = new AlgebraicSqrt();
sqrtNorm = BigInteger.Abs(sqrtNorm);
var tmpNorm = sqrtNorm;
sqrtNorm = integerSqrt.Sqrt(BigInteger.Abs(sqrtNorm));
timer.Stop();
Console.WriteLine(timer.Elapsed + " Умножение");
if (sqrtNorm * sqrtNorm != tmpNorm)
{
if (sqrtNorm * sqrtNorm != tmpNorm)
{
if (sqrtNorm * sqrtNorm != tmpNorm)
{
throw new Exception();
}
}
}
timer.Reset();
timer.Start();
var sqrt = algSqrt.Sqrt(sqr, _polyInfo.Polynomial, df, sqrtNorm);
timer.Stop();
Console.WriteLine(timer.Elapsed + " Квадратный корень");
if (algSqrt.DontExist)
{
Console.Write("\r{0}/{1} solutions cheked. (BAD SQRT) ", ++solutionsCheked, solutions.Count);
continue;
}
var sqrtY = sqrt.Value(_polyInfo.Root);
var check = polyMath.Rem(polyMath.Mul(sqrt, sqrt), _polyInfo.Polynomial);
if (check != sqr)
{
var primes = new EratosthenesSieve().GetPrimes(5, 10000);
int i;
for (i = 0; i < primes.Length; i++)
{
if (!algSqrt.IsSqr(sqr, _polyInfo.Polynomial, primes[i]))
{
break;
}
}
if (i == primes.Length)
{
throw new Exception();
}
Console.Write("\r{0}/{1} solutions cheked. (BAD SQRT) ", ++solutionsCheked, solutions.Count);
continue;
}
if ((sqrtY * sqrtY - sqrtX * sqrtX) % _number.Value() != 0)
{
throw new Exception();
}
var factor = BigInteger.GreatestCommonDivisor(sqrtX - sqrtY, _number.Value());
if (factor > 1 && factor < _number.Value())
{
Console.Write("\r{0}/{1} solutions cheked ", ++solutionsCheked, solutions.Count);
return(factor);
}
Console.Write("\r{0}/{1} solutions cheked. (BAD SOLUTION)", ++solutionsCheked, solutions.Count);
}
Console.Write("\r{0}/{1} solutions cheked. ", solutionsCheked, solutions.Count);
return(1);
}
