/// <summary>
/// Multiplies the polynomial by an <c>IntegerPolynomial</c>,
/// taking the indices mod <c>N</c>.
/// </summary>
///
/// <param name="Factor">A polynomial factor</param>
///
/// <returns>The product of the two polynomials</returns>
public BigIntPolynomial Multiply(BigIntPolynomial Factor)
{
BigIntPolynomial c = _f1.Multiply(Factor);
c = _f2.Multiply(c);
c.Add(_f3.Multiply(Factor));
return(c);
}
private BigIntPolynomial MultRecursive(BigIntPolynomial Factor)
{
// Karatsuba multiplication
BigInteger[] a = Coeffs;
BigInteger[] b = Factor.Coeffs;
int n = Factor.Coeffs.Length;
if (n <= 1)
{
BigInteger[] c = (BigInteger[])Coeffs.Clone();
for (int i = 0; i < Coeffs.Length; i++)
{
c[i] = c[i].Multiply(Factor.Coeffs[0]);
}
return(new BigIntPolynomial(c));
}
else
{
int n1 = n / 2;
BigIntPolynomial a1 = new BigIntPolynomial(a.CopyOf(n1));
BigIntPolynomial a2 = new BigIntPolynomial(a.CopyOfRange(n1, n));
BigIntPolynomial b1 = new BigIntPolynomial(b.CopyOf(n1));
BigIntPolynomial b2 = new BigIntPolynomial(b.CopyOfRange(n1, n));
BigIntPolynomial A = (BigIntPolynomial)a1.Clone();
A.Add(a2);
BigIntPolynomial B = (BigIntPolynomial)b1.Clone();
B.Add(b2);
BigIntPolynomial c1 = a1.MultRecursive(b1);
BigIntPolynomial c2 = a2.MultRecursive(b2);
BigIntPolynomial c3 = A.MultRecursive(B);
c3.Subtract(c1);
c3.Subtract(c2);
BigIntPolynomial c = new BigIntPolynomial(2 * n - 1);
for (int i = 0; i < c1.Coeffs.Length; i++)
{
c.Coeffs[i] = c1.Coeffs[i];
}
for (int i = 0; i < c3.Coeffs.Length; i++)
{
c.Coeffs[n1 + i] = c.Coeffs[n1 + i].Add(c3.Coeffs[i]);
}
for (int i = 0; i < c2.Coeffs.Length; i++)
{
c.Coeffs[2 * n1 + i] = c.Coeffs[2 * n1 + i].Add(c2.Coeffs[i]);
}
return(c);
}
}
/// <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));
}