public static void CLOSecn2Pt7Exerc2a()
{
Monomial.orderingScheme = "lex";
Polynomial p1 = new Polynomial(new double[] { 1, -1 }, new Monomial(2, 1), new Monomial(0, 0));
Polynomial p2 = new Polynomial(new double[] { 1, -1 }, new Monomial(1, 2), new Monomial(1, 0));
PolynomialBasis gb = PolynomialBasis.GetGroebnerBasis(p1, p2);
PrintPolynomialBasis(gb);
}
public static void CLOSec2Pt7Exerc9()
{
Monomial.orderingScheme = "lex";
Polynomial p1 = new Polynomial(new double[] { 3, -6, -2 }, new Monomial(1, 0, 0, 0), new Monomial(0, 1, 0, 0), new Monomial(0, 0, 1, 0));
Polynomial p2 = new Polynomial(new double[] { 2, -4, 4 }, new Monomial(1, 0, 0, 0), new Monomial(0, 1, 0, 0), new Monomial(0, 0, 0, 1));
Polynomial p3 = new Polynomial(new double[] { 1, -2, -1, -1 }, new Monomial(1, 0, 0, 0), new Monomial(0, 1, 0, 0), new Monomial(0, 0, 1, 0), new Monomial(0, 0, 0, 1));
PolynomialBasis gb = PolynomialBasis.GetGroebnerBasis(p1, p2, p3);
PrintPolynomialBasis(gb);
}
public static void CLOSectn2Pt8Exerc11()
{
Monomial.orderingScheme = "lex";
Polynomial p1 = new Polynomial(new double[] { 1, 1, 1, -3 }, new Monomial(1, 0, 0), new Monomial(0, 1, 0), new Monomial(0, 0, 1), new Monomial(0, 0, 0));
Polynomial p2 = new Polynomial(new double[] { 1, 1, 1, -5 }, new Monomial(2, 0, 0), new Monomial(0, 2, 0), new Monomial(0, 0, 2), new Monomial(0, 0, 0));
Polynomial p3 = new Polynomial(new double[] { 1, 1, 1, -7 }, new Monomial(3, 0, 0), new Monomial(0, 3, 0), new Monomial(0, 0, 3), new Monomial(0, 0, 0));
Polynomial p4 = new Polynomial(new double[] { 1, 1, 1, -9 }, new Monomial(4, 0, 0), new Monomial(0, 4, 0), new Monomial(0, 0, 4), new Monomial(0, 0, 0));
PolynomialBasis gb = PolynomialBasis.GetGroebnerBasis(p1, p2, p3, p4);
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);
}
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);
}
/// <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);
}