public static void TestOptimizedBuchberger()
{
Monomial.orderingScheme = "grlex";
PolynomialBasis pb = new PolynomialBasis
(
"x^3 - 2xy",
"x^2y - 2y^2 + x"
);
PolynomialBasis gb = pb.OptimizedBuchberger(); // since gb doesn't have pb's indiceToVariable, we will get old fashioned printing.
gb.PrettyPrint();
}
/**************************
* Now for expercies from section 8 of CLO
*************************/
public static void CLOSecn2Pt8Exerc1()
{
Monomial.orderingScheme = "lex";
PolynomialBasis pb = new PolynomialBasis
(
"xy^3 - z^2 + y^5 - z^3",
"-x^3 + y",
"x^2y - z"
);
PolynomialBasis gb = pb.OptimizedBuchberger();
gb.PrettyPrint();
}
public static void CLOSecn2Pt8Exerc6()
{
Monomial.orderingScheme = "lex";
PolynomialBasis pb = new PolynomialBasis
(
"t + u -x",
"t^2 + 2tu - y",
"t^3+3t^2u-z"
);
PolynomialBasis gb = pb.OptimizedBuchberger();
gb.PrettyPrint();
}
public static void CLOSecn2Pt8Exerc10()
{
Monomial.orderingScheme = "lex";
PolynomialBasis pb = new PolynomialBasis
(
"4lx + 2x - 2",
"2ly + 2y - 2",
"2lz + 2z - 2",
"x^4 + y^2 + z^2 -1"
);
PolynomialBasis gb = pb.OptimizedBuchberger();
gb.PrettyPrint();
}
public static void CLOSecn2Pt8Exerc9()
{
Monomial.orderingScheme = "lex";
PolynomialBasis pb = new PolynomialBasis
(
"a^2 + b^2 -1",
"8a^5 -2a^3 -3a - x",
"8b^5 - 18b^3 + 9b -y",
"2ab - z"
);
PolynomialBasis gb = pb.OptimizedBuchberger();
gb.PrettyPrint();
}
public static void CLOSecn2Pt8Exerc4()
{
Monomial.orderingScheme = "lex";
PolynomialBasis pb = new PolynomialBasis
(
"x^2y - z^3",
"2xy - 4z - 1",
"z - y^2",
"x^3 - 4zy"
);
PolynomialBasis gb = pb.OptimizedBuchberger();
gb.PrettyPrint();
}