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);
}
public BigInteger FindFactor(BigInteger n)
{
Console.WriteLine(n);
Init(n);
var smoothPairs = new List <SmoothPair>();
var timer = new Stopwatch();
timer.Start();
var polyCount = 0;
while (smoothPairs.Count < _factorBase.Length + _kerSize)
{
var polynomials = GeneratePolynomials(n);
if (polynomials == null)
{
return(1);
}
foreach (var sievePolynomial in polynomials)
{
smoothPairs.AddRange(LogSieve(sievePolynomial, n));
polyCount++;
Console.Write("\r" + smoothPairs.Count + "/" + _factorBase.Length + " [polynomials used:" + polyCount + "] ");
if (smoothPairs.Count >= _factorBase.Length + _kerSize)
{
break;
}
}
}
if (smoothPairs.Count < _factorBase.Length + _kerSize)
{
return(1);
}
timer.Stop();
Console.WriteLine();
Console.WriteLine("sieve time: " + timer.Elapsed);
timer.Restart();
var matrix = BuildMatrix(smoothPairs);
var matrixSolver = new GaussianEliminationOverGf2();
var solutions = matrixSolver.Solve(matrix);
Console.WriteLine("linear algebra time: " + timer.Elapsed);
foreach (var solution in solutions)
{
var x = BigInteger.One;
var y = new Dictionary <long, int>();
y.Add(-1, 0);
for (int i = 0; i < _factorBase.Length; i++)
{
y.Add(_factorBase[i], 0);
}
for (int i = 0; i < solution.Length; i++)
{
if (solution[i] == 1)
{
x = x * smoothPairs[i].X;
y[-1] += smoothPairs[i].Y[-1];
for (int j = 0; j < _factorBase.Length; j++)
{
if (smoothPairs[i].Y.ContainsKey(_factorBase[j]))
{
y[_factorBase[j]] += smoothPairs[i].Y[_factorBase[j]];
}
}
}
}
if (y[-1] % 2 != 0)
{
throw new Exception();
}
for (int j = 0; j < _factorBase.Length; j++)
{
if (y[_factorBase[j]] % 2 != 0)
{
throw new Exception();
}
y[_factorBase[j]] /= 2;
}
BigInteger sqrtY = 1;
foreach (var pair in y)
{
sqrtY *= BigInteger.Pow(pair.Key, pair.Value);
}
var factor = BigInteger.GreatestCommonDivisor(sqrtY - x, n);
if (factor < n && factor > 1)
{
return(factor);
}
}
return(1);
}
