/// <summary>
/// Calculates a <c>rho</c> modulo <c>m1*m2</c> from two resultants whose
/// <c>rho</c>s are modulo <c>m1</c> and <c>m2</c>.
/// <para><c>res</c> is set to <c>null</c>.</para>
/// </summary>
///
/// <param name="ModRes1">M1 resultant</param>
/// <param name="ModRes2">M2 resultant</param>
///
/// <returns><c>Rho</c> modulo <c>modRes1.modulus * modRes2.modulus</c>, and <c>null</c> for <c>res</c></returns>
public static ModularResultant CombineRho(ModularResultant ModRes1, ModularResultant ModRes2)
{
BigInteger mod1 = ModRes1._modulus;
BigInteger mod2 = ModRes2._modulus;
BigInteger prod = mod1.Multiply(mod2);
BigIntEuclidean er = BigIntEuclidean.Calculate(mod2, mod1);
BigIntPolynomial rho1 = ModRes1.Rho.Clone();
rho1.Multiply(er.X.Multiply(mod2));
BigIntPolynomial rho2 = ModRes2.Rho.Clone();
rho2.Multiply(er.Y.Multiply(mod1));
rho1.Add(rho2);
rho1.Mod(prod);
return new ModularResultant(rho1, null, prod);
}
/// <summary>
/// Calculates a <c>rho</c> modulo <c>m1*m2</c> from two resultants whose
/// <c>rho</c>s are modulo <c>m1</c> and <c>m2</c>.
/// <para><c>res</c> is set to <c>null</c>.</para>
/// </summary>
///
/// <param name="ModRes1">M1 resultant</param>
/// <param name="ModRes2">M2 resultant</param>
///
/// <returns><c>Rho</c> modulo <c>modRes1.modulus * modRes2.modulus</c>, and <c>null</c> for <c>res</c></returns>
public static ModularResultant CombineRho(ModularResultant ModRes1, ModularResultant ModRes2)
{
BigInteger mod1 = ModRes1._modulus;
BigInteger mod2 = ModRes2._modulus;
BigInteger prod = mod1.Multiply(mod2);
BigIntEuclidean er = BigIntEuclidean.Calculate(mod2, mod1);
BigIntPolynomial rho1 = ModRes1.Rho.Clone();
rho1.Multiply(er.X.Multiply(mod2));
BigIntPolynomial rho2 = ModRes2.Rho.Clone();
rho2.Multiply(er.Y.Multiply(mod1));
rho1.Add(rho2);
rho1.Mod(prod);
return(new ModularResultant(rho1, null, prod));
}