public static IPolynomial Divide(IPolynomial left, IPolynomial right, out IPolynomial remainder)
{
if (left == null)
{
throw new ArgumentNullException(nameof(left));
}
if (right == null)
{
throw new ArgumentNullException(nameof(right));
}
if (right.Degree > left.Degree || right.CompareTo(left) == 1)
{
remainder = Polynomial.Zero; return(left);
}
int rightDegree = right.Degree;
int quotientDegree = (left.Degree - rightDegree) + 1;
BigInteger leadingCoefficent = new BigInteger(right[rightDegree].ToByteArray());
Polynomial rem = (Polynomial)left.Clone();
Polynomial quotient = (Polynomial)Polynomial.Zero;
// The leading coefficient is the only number we ever divide by
// (so if right is monic, polynomial division does not involve division at all!)
for (int i = quotientDegree - 1; i >= 0; i--)
{
quotient[i] = BigInteger.Divide(rem[rightDegree + i], leadingCoefficent);
rem[rightDegree + i] = BigInteger.Zero;
for (int j = rightDegree + i - 1; j >= i; j--)
{
rem[j] = BigInteger.Subtract(rem[j], BigInteger.Multiply(quotient[i], right[j - i]));
}
}
// Remove zeros
rem.RemoveZeros();
quotient.RemoveZeros();
remainder = rem;
return(quotient);
}
