/// <summary>
/// Finds the Greatest Common Divisor between this and another polynomial
/// </summary>
/// <param name="otherPolynomial">The other polynomial with which the GCD is to be calculated</param>
/// <returns>The Greatest Common Divisor</returns>
public OneVariablePolynomial GCD(OneVariablePolynomial otherPolynomial)
{
OneVariablePolynomial h = this;
OneVariablePolynomial s = otherPolynomial;
OneVariablePolynomial rem = new OneVariablePolynomial();
while (!s.IsZero())
{
rem = h.Divide(s)["remainder"];
h = s;
s = rem;
}
return(rem);
}
/// <summary>
/// Divides the polynomial with the divisor.
/// </summary>
/// <param name="divisor">The divisor. Denoted by g in the CLO book.</param>
/// <returns>The quotient and remainder in the form of a tuple.</returns>
public Dictionary <string, OneVariablePolynomial> Divide(OneVariablePolynomial divisor)
{
OneVariablePolynomial quotient = new OneVariablePolynomial();
OneVariablePolynomial remainder = this;
while (!remainder.IsZero() && divisor.LeadingTerm().degree <= remainder.LeadingTerm().degree)
{
OneVariableMonomial update = remainder.LeadingTerm().Divide(divisor.LeadingTerm());
quotient = quotient.Add(new OneVariablePolynomial(update));
remainder = remainder.Add(divisor.Multiply(update), false); // A false addition is basically a subtraction.
}
return(new Dictionary <string, OneVariablePolynomial>()
{
{ "quotient", quotient },
{ "remainder", remainder }
});
}