/**
* Resultant of this polynomial with <code>x^n-1</code> using a probabilistic algorithm.
* <p>
* Unlike EESS, this implementation does not compute all resultants modulo primes
* such that their product exceeds the maximum possible resultant, but rather stops
* when <code>NUM_EQUAL_RESULTANTS</code> consecutive modular resultants are equal.<br>
* This means the return value may be incorrect. Experiments show this happens in
* about 1 out of 100 cases when <code>N=439</code> and <code>NUM_EQUAL_RESULTANTS=2</code>,
* so the likelyhood of leaving the loop too early is <code>(1/100)^(NUM_EQUAL_RESULTANTS-1)</code>.
* <p>
* Because of the above, callers must verify the output and try a different polynomial if necessary.
*
* @return <code>(rho, res)</code> satisfying <code>res = rho*this + t*(x^n-1)</code> for some integer <code>t</code>.
*/
public Resultant Resultant()
{
int N = coeffs.Length;
// Compute resultants modulo prime numbers. Continue until NUM_EQUAL_RESULTANTS consecutive modular resultants are equal.
LinkedList <ModularResultant> modResultants = new LinkedList <ModularResultant>();
BigInteger pProd = Constants.BIGINT_ONE;
BigInteger res = Constants.BIGINT_ONE;
int numEqual = 1; // number of consecutive modular resultants equal to each other
PrimeGenerator primes = new PrimeGenerator();
BigInteger pProd2;
BigInteger pProd2n;
while (true)
{
BigInteger prime = primes.nextPrime();
ModularResultant crr = Resultant(prime.IntValue);
modResultants.AddLast(crr); //Was just add in Java
BigInteger temp = pProd.Multiply(prime);
BigIntEuclidean er = BigIntEuclidean.Calculate(prime, pProd);
BigInteger resPrev = res;
res = res.Multiply(er.x.Multiply(prime));
BigInteger res2 = crr.Res.Multiply(er.y.Multiply(pProd));
res = res.Add(res2).Mod(temp);
pProd = temp;
pProd2 = pProd.Divide(BigInteger.ValueOf(2));
pProd2n = pProd2.Negate();
if (res.CompareTo(pProd2) > 0)
{
res = res.Subtract(pProd);
}
else if (res.CompareTo(pProd2n) < 0)
{
res = res.Add(pProd);
}
if (res.Equals(resPrev))
{
numEqual++;
if (numEqual >= NUM_EQUAL_RESULTANTS)
{
break;
}
}
else
{
numEqual = 1;
}
}
// Combine modular rho's to obtain the final rho.
// For efficiency, first combine all pairs of small resultants to bigger resultants,
// then combine pairs of those, etc. until only one is left.
while (modResultants.Count > 1)
{
ModularResultant modRes1 = modResultants.First.Value;
modResultants.RemoveFirst();
ModularResultant modRes2 = modResultants.First.Value;
modResultants.RemoveFirst();
ModularResultant modRes3 = ModularResultant.CombineRho(modRes1, modRes2);
modResultants.AddLast(modRes3);
}
BigIntPolynomial rhoP = modResultants.First.Value.Rho;
pProd2 = pProd.Divide(BigInteger.ValueOf(2));
pProd2n = pProd2.Negate();
if (res.CompareTo(pProd2) > 0)
{
res = res.Subtract(pProd);
}
if (res.CompareTo(pProd2n) < 0)
{
res = res.Add(pProd);
}
for (int i = 0; i < N; i++)
{
BigInteger c = rhoP.coeffs[i];
if (c.CompareTo(pProd2) > 0)
{
rhoP.coeffs[i] = c.Subtract(pProd);
}
if (c.CompareTo(pProd2n) < 0)
{
rhoP.coeffs[i] = c.Add(pProd);
}
}
return(new Resultant(rhoP, res));
}
public ModularResultant call()
{
return(ModularResultant.CombineRho(modRes1, modRes2));
}