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());
}
}
public static void TestGroebnerBasisCLOSecn2Pt7Example1()
{
Monomial.orderingScheme = "grlex";
Polynomial f = new Polynomial(new Monomial(new int[] { 3, 0 })); // x^3
f.AddMonomial(new Monomial(new int[] { 1, 1 }), -2.0); // -2xy
Polynomial g = new Polynomial(new Monomial(new int[] { 2, 1 })); // x^2y
g.AddMonomial(new Monomial(new int[] { 0, 2 }), -2.0); // -2y^2
g.AddMonomial(new Monomial(new int[] { 1, 0 })); // x
PolynomialBasis gb = PolynomialBasis.GetGroebnerBasis(f, g);
PrintPolynomialBasis(gb);
}
public static void TestGroebnerBasisLinearSystem()
{
Monomial.orderingScheme = "lex";
Polynomial f = new Polynomial(new Monomial(new int[] { 1, 0 }));
f.AddMonomial(new Monomial(new int[] { 0, 1 }), 2);
f.AddMonomial(new Monomial(new int[] { 0, 0 }), -3);
Polynomial g = new Polynomial(new Monomial(new int[] { 1, 0 }));
g.AddMonomial(new Monomial(new int[] { 0, 1 }), -2);
g.AddMonomial(new Monomial(new int[] { 0, 0 }), -7);
PolynomialBasis gb = PolynomialBasis.GetGroebnerBasis(f, g);
PrintPolynomialBasis(gb);
}
public static void TestSPolynomial()
{
Polynomial f = new Polynomial(new Monomial(new int[] { 3, 2 }), 1);
f.AddMonomial(new Monomial(new int[] { 2, 3 }), -1);
f.AddMonomial(new Monomial(new int[] { 1, 0 }), 1);
Polynomial g = new Polynomial(new Monomial(new int[] { 4, 1 }), 3);
g.AddMonomial(new Monomial(new int[] { 0, 2 }), 1);
Polynomial s = f.GetSPolynomial(g);
foreach (Monomial m in s.monomialData.Keys)
{
System.Console.WriteLine(string.Join(",", m.powers));
}
}
/// <summary>
/// Test method for Groebner basis.
/// </summary>
public static void TestGroebnerBasis()
{
Monomial.orderingScheme = "lex";
//1st order
var del_x = 1.0;
var del_y = 2.0;
//2nd order
var del_x_x = 3.5;
var del_x_y = 1.5;
var del_y_y = 2.7;
//3rd order
var del_y_y_y = 1.1;
var del_x_y_y = 1.9;
var del_x_x_y = 2.3;
var del_x_x_x = 1.4;
Polynomial f = new Polynomial(new Monomial(new int[] { 2, 0 }), del_x_x_x);
f.AddMonomial(new Monomial(new int[] { 1, 1 }), 2 * del_x_x_y);
f.AddMonomial(new Monomial(new int[] { 0, 2 }), del_x_y_y);
f.AddMonomial(new Monomial(new int[] { 1, 0 }), del_x_y);
f.AddMonomial(new Monomial(new int[] { 0, 1 }), del_y_y);
f.AddMonomial(new Monomial(new int[] { 0, 0 }), -del_x);
Polynomial g = new Polynomial(new Monomial(new int[] { 2, 0 }), del_x_x_y);
g.AddMonomial(new Monomial(new int[] { 1, 1 }), 2 * del_x_y_y);
g.AddMonomial(new Monomial(new int[] { 0, 2 }), del_y_y_y);
g.AddMonomial(new Monomial(new int[] { 1, 0 }), del_x_x);
g.AddMonomial(new Monomial(new int[] { 0, 1 }), del_x_y);
g.AddMonomial(new Monomial(new int[] { 0, 0 }), -del_y);
PolynomialBasis gb = PolynomialBasis.GetGroebnerBasis(f, g);
PrintPolynomialBasis(gb);
}
public static void TestGroebnerBasisCLOSec2Pt7Exerc3()
{
Monomial.orderingScheme = "lex";
Polynomial f = new Polynomial(new Monomial(new int[] { 2, 1 }));
f.AddMonomial(new Monomial(new int[] { 0, 0 }), -1);
Polynomial g = new Polynomial(new Monomial(new int[] { 1, 2 }));
g.AddMonomial(new Monomial(new int[] { 1, 0 }), -1);
PolynomialBasis gb = PolynomialBasis.GetGroebnerBasis(f, g);
PrintPolynomialBasis(gb);
}