public BigIntPolynomial Multiply(BigIntPolynomial b)
{
BigIntPolynomial c = F1.Multiply(b);
c = F2.Multiply(c);
c.Add(F3.Multiply(b));
return(c);
}
/**
* Calculates a <code>rho</code> modulo <code>m1*m2</code> from
* two resultants whose <code>rho</code>s are modulo <code>m1</code> and <code>m2</code>.<br/>
* </code>res</code> is set to <code>null</code>.
*
* @param modRes1
* @param modRes2
* @return <code>rho</code> modulo <code>modRes1.modulus * modRes2.modulus</code>, and <code>null</code> for </code>res</code>.
*/
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 = (BigIntPolynomial)modRes1.Rho.Clone();
rho1.Multiply(er.x.Multiply(mod2));
BigIntPolynomial rho2 = (BigIntPolynomial)modRes2.Rho.Clone();
rho2.Multiply(er.y.Multiply(mod1));
rho1.Add(rho2);
rho1.Mod(prod);
return(new ModularResultant(rho1, null, prod));
}
/**
* Karazuba multiplication
*/
private BigIntPolynomial MultiplyRecursive(BigIntPolynomial poly2)
{
BigInteger[] a = coeffs;
BigInteger[] b = poly2.coeffs;
int n = poly2.coeffs.Length;
if (n <= 1)
{
BigInteger[] c = new BigInteger[coeffs.Length];
Array.Copy(coeffs, c, coeffs.Length);
for (int i = 0; i < coeffs.Length; i++)
{
c[i] = c[i].Multiply(poly2.coeffs[0]);
}
return(new BigIntPolynomial(c));
}
else
{
int n1 = n / 2;
// TODO: Double Check Conversion (Don't worry too much, it'll explode if wrong)... It Exploded
BigInteger[] a1temp = new BigInteger[n1];
BigInteger[] a2temp = new BigInteger[n - n1];
BigInteger[] b1temp = new BigInteger[n1];
BigInteger[] b2temp = new BigInteger[n - n1];
Array.Copy(a, a1temp, n1);
Array.Copy(a, n1, a2temp, 0, n - n1);
Array.Copy(b, b1temp, n1);
Array.Copy(b, n1, b2temp, 0, n - n1);
BigIntPolynomial a1 = new BigIntPolynomial(a1temp);
BigIntPolynomial a2 = new BigIntPolynomial(a2temp);
BigIntPolynomial b1 = new BigIntPolynomial(b1temp);
BigIntPolynomial b2 = new BigIntPolynomial(b2temp);
BigIntPolynomial A = (BigIntPolynomial)a1.Clone();
A.Add(a2);
BigIntPolynomial B = (BigIntPolynomial)b1.Clone();
B.Add(b2);
BigIntPolynomial c1 = a1.MultiplyRecursive(b1);
BigIntPolynomial c2 = a2.MultiplyRecursive(b2);
BigIntPolynomial c3 = A.MultiplyRecursive(B);
c3.Sub(c1);
c3.Sub(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);
}
}
