/// <summary>
/// Осуществляет решение линейного сравнения.
/// </summary>
/// <param name="a"></param>
/// <param name="b"></param>
/// <param name="m"></param>
/// <param name="Result"></param>
/// <param name="GCD"></param>
/// <returns></returns>
public static bool Solve(BigInteger a, BigInteger b, BigInteger m, out LinearComparison Result,
BigInteger[] GCD = null)
{
//ax=b(mod m)
Result = null;
if (GCD == null)
{
GCD = AdvancedEuclidsalgorithm.GCD(a, m);
}
if (GCD == null)
{
return(false);
}
if (b % GCD[0] != 0)
{
return(false);
}
//a*x0=d(mod m)
BigInteger x_ = GCD[1] * (b / GCD[0]);
while (x_ >= m / GCD[0])
{
x_ -= m / GCD[0];
}
while (x_ < 0)
{
x_ += m / GCD[0];
}
Result = new LinearComparison(x_, m / GCD[0]);
return(true);
}
/// <summary>
/// Метод, осуществляющий попытку решить Диофантово уравнение первой степени.
/// </summary>
/// <param name="Source"></param>
/// <param name="Resultx"></param>
/// <param name="Resulty"></param>
/// <param name="GCD"></param>
/// <returns></returns>
public static bool TrySolve(BigInteger[] Source, out BigInteger[] Resultx, out BigInteger[] Resulty,
BigInteger[] GCD = null)
{
BigInteger First = Source[0];
BigInteger Second = Source[1];
BigInteger Res = Source[2];
Resultx = new BigInteger[2];
Resulty = new BigInteger[2];
if (GCD == null)
{
GCD = AdvancedEuclidsalgorithm.GCD(First, Second);
}
if (GCD == null)
{
return(false);
}
if (Res % GCD[0] != 0)
{
return(false);
}
Resultx = new[] { GCD[1] * (Res / GCD[0]), Second / GCD[0] };
Resulty = new[] { GCD[2] * (Res / GCD[0]), -(First / GCD[0]) };
//Надо сделать решение наименьшим по модулю, но
//Это возможно только когда оба свободных члена уменьшаются
//по модулю при свободном t
while (BigInteger.Abs(Resultx[0] + Resultx[1]) < BigInteger.Abs(Resultx[0]) &&
BigInteger.Abs(Resulty[0] + Resulty[1]) < BigInteger.Abs(Resulty[0]))
{
Resultx[0] += Resultx[1];
Resulty[0] += Resulty[1];
}
while (BigInteger.Abs(Resultx[0] - Resultx[1]) < BigInteger.Abs(Resultx[0]) &&
BigInteger.Abs(Resulty[0] - Resulty[1]) < BigInteger.Abs(Resulty[0]))
{
Resultx[0] -= Resultx[1];
Resulty[0] -= Resulty[1];
}
return(true);
}
