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();
}
public static void CLOSecn2Pt8Exerc5()
{
Monomial.orderingScheme = "lex";
PolynomialBasis pb = new PolynomialBasis
(
"4x^3+4xy^2-8x-3",
"4y^3+4yx^2-8y-3"
);
PolynomialBasis gb = pb.SimplifiedBuchberger();
gb.PrettyPrint();
}
public static void CLOSecn2Pt8Exerc3()
{
Monomial.orderingScheme = "lex";
PolynomialBasis pb = new PolynomialBasis
(
"x^2 + y^2 + z^2 - 1", // Ensure that y appears before z in the equations.
"x^2 + y^2 + z^2 - 2x",
"2x - 3y - z"
);
PolynomialBasis gb = pb.SimplifiedBuchberger();
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 TestString2GroebnerBasis()
{
Monomial.orderingScheme = "grlex";
PolynomialBasis pb = new PolynomialBasis
(
"x^2 + y^2 + z^2 - 8",
"x^2 + z^2 - y",
"x - z + y - 2"
);
pb.SimplifiedBuchberger();
pb.PrettyPrint();
}
public static void CLOSecn2Pt8Exerc7()
{
Monomial.orderingScheme = "lex";
PolynomialBasis pb = new PolynomialBasis
(
"ut - x",
"1-u-y",
"u+t-ut-z"
);
PolynomialBasis gb = pb.SimplifiedBuchberger();
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 CLOSecn2Pt8Exerc2()
{
Monomial.orderingScheme = "lex";
PolynomialBasis pb = new PolynomialBasis
(
"xy + 2z^2", // Ensure that y appears before z in the equations.
"y - z",
"xz - y",
"x^3z - 2y^2"
);
PolynomialBasis gb = pb.SimplifiedBuchberger();
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();
}
public static void CLOSecn2Pt8Exerc8()
{
Monomial.orderingScheme = "lex";
PolynomialBasis pb = new PolynomialBasis
(
"a^2 + b^2 -1",
"c^2 + d^2 -1",
"ac + 2c - x",
"ad + 2d - y",
"b - z"
);
PolynomialBasis gb = pb.SimplifiedBuchberger();
gb.PrettyPrint();
}
