public Monomial Multiply(Monomial monomial)
{
return(new Monomial(this.coefficient * monomial.coefficient, this.exponent + monomial.exponent));
}
// This method assures that the list of terms is
// always simplified (cannot exist multiple terms
// with same degree) and sorted from largest to
// smaller degree.
public void Append(Monomial monomial)
{
// The monomial to add must be different than zero.
if (monomial.Coefficient != 0)
{
// If the actual polynomial is zero, internal list
// only contains one monomial and this monomial will
// be replaced with the one received.
if (this.terms.Count == 1 && this.terms[0].Coefficient == 0)
{
this.terms[0] = monomial;
}
else
{
bool appended = false;
int i = 0;
while (!appended && i < this.terms.Count)
{
// If the exponent of the monomial to append is greater
// than the exponent of the monomial [i] analyzed, it
// means that monomial to append does not exists in the
// polynomial, so it is inserted in the currente position
// to maintain the order of the list.
if (monomial.Exponent > this.terms[i].Exponent)
{
this.terms.Insert(i, monomial);
appended = true;
}
// If the exponent of the monomial to append is equal to
// the exponent of the monomial [i] analyzed, perform
// addition between monomials and replaces the current
// monomial; in the case the sum of the monomials is zero,
// removes the current monomial from the list.
else if (monomial.Exponent == this.terms[i].Exponent)
{
if (this.terms[i].Coefficient + monomial.Coefficient != 0)
{
this.terms[i] = this.terms[i].Add(monomial);
}
else
{
this.terms.RemoveAt(i);
}
appended = true;
}
// Go to the next monomial in the internal list.
else
{
i++;
}
}
// If monomial has not been appended at this point, append it
// at the end of the list.
if (!appended)
{
this.terms.Add(monomial);
}
// If the list becomes empty, it means that the polynomial is
// zero, so append a monomial equal to zero.
if (this.terms.Count == 0)
{
this.terms.Add(new Monomial());
}
// If the list has only one monomial and its coefficient is
// zero, it means the that polynomial is zero, so replace
// with a monomial equal to zero (this is only for consistency
// of monomial representation).
else if (this.terms.Count == 1 && this.terms[0].Coefficient == 0)
{
this.terms[0] = new Monomial();
}
}
}
}
public static void TestMultiVariatePolynomialDivision()
{
Monomial m1 = new Monomial(new int[] { 3, 0, 0 }); Monomial m2 = new Monomial(new int[] { 2, 1, 0 }); Monomial m3 = new Monomial(new int[] { 2, 0, 1 }); Monomial m4 = new Monomial(new int[] { 1, 0, 0 });
Polynomial dividend = new Polynomial(m1);
dividend.AddMonomial(m2, -1);
dividend.AddMonomial(m3, -1);
dividend.AddMonomial(m4);
dividend = new Polynomial(new Monomial(new int[] { 1, 0, 0 }));
dividend.AddMonomial(new Monomial(new int[] { 0, 0, 1 }), -1);
Polynomial divisor1 = new Polynomial(new Monomial(new int[] { 2, 1, 0 })); // (y^2 - 1)
divisor1.AddMonomial(new Monomial(new int[] { 0, 0, 1 }), -1);
Polynomial divisor2 = new Polynomial(new Monomial(new int[] { 1, 1, 0 })); // (xy - 1)
divisor2.AddMonomial(new Monomial(new int[] { 0, 0, 0 }), -1);
List <Polynomial> quotients = dividend.DivideBy(divisor1, divisor2);
foreach (Monomial m in quotients.LastOrDefault().monomialData.Keys)
{
System.Console.WriteLine(string.Join(",", m.powers) + " coefficient: " + quotients.LastOrDefault().monomialData[m].ToString());
}
}