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(); }