/// <summary>
/// Divides the current polynomial by a list of divisor polynomials given by the argument.
/// Based on the algorithm in section 2.3 of CLO book.
/// </summary>
/// <param name="divisorList">Comma saperated list with all the divisors.</param>
/// <returns>The quotient and remainder in the form of a two element dictinoary.</returns>
public List <Polynomial> DivideBy(params Polynomial[] divisorList)
{
Polynomial remainder = new Polynomial();
Polynomial p = this;
List <Polynomial> quotients = new List <Polynomial>();
int s = divisorList.Length;
foreach (Polynomial p1 in divisorList)
{
quotients.Add(new Polynomial());
}
while (!p.IsZero)
{
int i = 1;
bool divisionoccurred = false;
while (i <= s && !divisionoccurred)
{
if (p.GetLeadingTerm().IsDividedBy(divisorList[i - 1].GetLeadingTerm()))
{
Monomial cancellingMonomial = p.GetLeadingTerm().DivideBy(divisorList[i - 1].GetLeadingTerm());
double cancellingCoefficient = p.monomialData[p.GetLeadingTerm()] / divisorList[i - 1].monomialData[divisorList[i - 1].GetLeadingTerm()];
quotients[i - 1].Add(new Polynomial(cancellingMonomial, cancellingCoefficient));
Polynomial cancellingPolynomial = new Polynomial(divisorList[i - 1]);
cancellingPolynomial.MultiplyMonomial(cancellingMonomial, -cancellingCoefficient);
p.Add(cancellingPolynomial);
divisionoccurred = true;
}
else
{
i++;
}
}
if (!divisionoccurred)
{
remainder.Add(p.GetLeadingTermAsPolynomial());
p.Add(p.GetLeadingTermAsPolynomial(false)); // A false addition is basically a subtraction. TODO: This is ugly! the Add method should have the flag to indicate subtraction.
}
}
quotients.Add(remainder);
return(quotients);
}
/// <summary>
/// Gets the S-polynomial as defined in section 2.6 of CLO
/// </summary>
/// <param name="other">The other polynomial with respect to which the S-polynomial is to be calculated.s</param>
/// <returns>The S-polynomial of the combination - this and other.</returns>
public Polynomial GetSPolynomial(Polynomial other)
{
Monomial lcm = this.GetLeadingTerm().LCM(other.GetLeadingTerm());
Polynomial thisTerm = new Polynomial(this);
thisTerm.MultiplyMonomial(lcm.DivideBy(this.GetLeadingTerm()));
thisTerm.MultiplyScalar(1 / this.GetLeadingCoefficient());
Polynomial otherTerm = new Polynomial(other);
otherTerm.MultiplyMonomial(lcm.DivideBy(other.GetLeadingTerm()));
otherTerm.MultiplyScalar(1 / other.GetLeadingCoefficient());
thisTerm.Add(otherTerm, -1);
return(thisTerm);
}