PolyUfdUtil
edu.jas.ufd

Class PolyUfdUtil



  • public class PolyUfdUtilextends Object
    Polynomial ufd utilities, like conversion between different representations and Hensel lifting.
    • Constructor Detail

      • PolyUfdUtil

        public PolyUfdUtil()
    • Method Detail

      • integralFromQuotientCoefficients

        public static <C extends GcdRingElem<C>> GenPolynomial<GenPolynomial<C>> integralFromQuotientCoefficients(GenPolynomialRing<GenPolynomial<C>> fac,                                                                                          GenPolynomial<Quotient<C>> A)
        Integral polynomial from rational function coefficients. Represent as polynomial with integral polynomial coefficients by multiplication with the lcm of the numerators of the rational function coefficients.
        Parameters:
        fac - result polynomial factory.
        A - polynomial with rational function coefficients to be converted.
        Returns:
        polynomial with integral polynomial coefficients.
      • integralFromQuotientCoefficients

        public static <C extends GcdRingElem<C>> List<GenPolynomial<GenPolynomial<C>>> integralFromQuotientCoefficients(GenPolynomialRing<GenPolynomial<C>> fac,                                                                                                Collection<GenPolynomial<Quotient<C>>> L)
        Integral polynomial from rational function coefficients. Represent as polynomial with integral polynomial coefficients by multiplication with the lcm of the numerators of the rational function coefficients.
        Parameters:
        fac - result polynomial factory.
        L - list of polynomial with rational function coefficients to be converted.
        Returns:
        list of polynomials with integral polynomial coefficients.
      • quotientFromIntegralCoefficients

        public static <C extends GcdRingElem<C>> GenPolynomial<Quotient<C>> quotientFromIntegralCoefficients(GenPolynomialRing<Quotient<C>> fac,                                                                                     GenPolynomial<GenPolynomial<C>> A)
        Rational function from integral polynomial coefficients. Represent as polynomial with type Quotient coefficients.
        Parameters:
        fac - result polynomial factory.
        A - polynomial with integral polynomial coefficients to be converted.
        Returns:
        polynomial with type Quotient coefficients.
      • quotientFromIntegralCoefficients

        public static <C extends GcdRingElem<C>> List<GenPolynomial<Quotient<C>>> quotientFromIntegralCoefficients(GenPolynomialRing<Quotient<C>> fac,                                                                                           Collection<GenPolynomial<GenPolynomial<C>>> L)
        Rational function from integral polynomial coefficients. Represent as polynomial with type Quotient coefficients.
        Parameters:
        fac - result polynomial factory.
        L - list of polynomials with integral polynomial coefficients to be converted.
        Returns:
        list of polynomials with type Quotient coefficients.
      • fromIntegerCoefficients

        public static <C extends RingElem<C>> GenPolynomial<GenPolynomial<C>> fromIntegerCoefficients(GenPolynomialRing<GenPolynomial<C>> fac,                                                                              GenPolynomial<GenPolynomial<BigInteger>> A)
        From BigInteger coefficients. Represent as polynomial with type GenPolynomial<C> coefficients, e.g. ModInteger or BigRational.
        Parameters:
        fac - result polynomial factory.
        A - polynomial with GenPolynomial<BigInteger> coefficients to be converted.
        Returns:
        polynomial with type GenPolynomial<C> coefficients.
      • fromIntegerCoefficients

        public static <C extends RingElem<C>> List<GenPolynomial<GenPolynomial<C>>> fromIntegerCoefficients(GenPolynomialRing<GenPolynomial<C>> fac,                                                                                    List<GenPolynomial<GenPolynomial<BigInteger>>> L)
        From BigInteger coefficients. Represent as polynomial with type GenPolynomial<C> coefficients, e.g. ModInteger or BigRational.
        Parameters:
        fac - result polynomial factory.
        L - polynomial list with GenPolynomial<BigInteger> coefficients to be converted.
        Returns:
        polynomial list with polynomials with type GenPolynomial<C> coefficients.
      • introduceLowerVariable

        public static <C extends GcdRingElem<C>> GenPolynomial<GenPolynomial<C>> introduceLowerVariable(GenPolynomialRing<GenPolynomial<C>> rfac,                                                                                GenPolynomial<C> A)
        Introduce lower variable. Represent as polynomial with type GenPolynomial<C> coefficients.
        Parameters:
        rfac - result polynomial factory.
        A - polynomial to be extended.
        Returns:
        polynomial with type GenPolynomial<C> coefficients.
      • substituteFromAlgebraicCoefficients

        public static <C extends GcdRingElem<C>> GenPolynomial<GenPolynomial<C>> substituteFromAlgebraicCoefficients(GenPolynomialRing<GenPolynomial<C>> rfac,                                                                                             GenPolynomial<AlgebraicNumber<C>> A,                                                                                             long k)
        From AlgebraicNumber coefficients. Represent as polynomial with type GenPolynomial<C> coefficients, e.g. ModInteger or BigRational.
        Parameters:
        rfac - result polynomial factory.
        A - polynomial with AlgebraicNumber coefficients to be converted.
        k - for (y-k x) substitution.
        Returns:
        polynomial with type GenPolynomial<C> coefficients.
      • substituteConvertToAlgebraicCoefficients

        public static <C extends GcdRingElem<C>> GenPolynomial<AlgebraicNumber<C>> substituteConvertToAlgebraicCoefficients(GenPolynomialRing<AlgebraicNumber<C>> pfac,                                                                                                    GenPolynomial<C> A,                                                                                                    long k)
        Convert to AlgebraicNumber coefficients. Represent as polynomial with AlgebraicNumber coefficients, C is e.g. ModInteger or BigRational.
        Parameters:
        pfac - result polynomial factory.
        A - polynomial with GenPolynomial<BigInteger> coefficients to be converted.
        k - for (y-k x) substitution.
        Returns:
        polynomial with AlgebraicNumber<C> coefficients.
      • norm

        public static <C extends GcdRingElem<C>> GenPolynomial<C> norm(GenPolynomial<AlgebraicNumber<C>> A,                                               long k)
        Norm of a polynomial with AlgebraicNumber coefficients.
        Parameters:
        A - polynomial from GenPolynomial<AlgebraicNumber<C>>.
        k - for (y - k x) substitution.
        Returns:
        norm(A) = res_x(A(x,y),m(x)) in GenPolynomialRing<C>.
      • norm

        public static <C extends GcdRingElem<C>> GenPolynomial<C> norm(GenPolynomial<AlgebraicNumber<C>> A)
        Norm of a polynomial with AlgebraicNumber coefficients.
        Parameters:
        A - polynomial from GenPolynomial<AlgebraicNumber<C>>.
        Returns:
        norm(A) = resultant_x( A(x,y), m(x) ) in K[y].
      • ensureFieldProperty

        public static <C extends GcdRingElem<C>> void ensureFieldProperty(AlgebraicNumberRing<C> afac)
        Ensure that the field property is determined. Checks if modul is irreducible and modifies the algebraic number ring.
        Parameters:
        afac - algebraic number ring.
      • substituteKronecker

        public static <C extends GcdRingElem<C>> GenPolynomial<C> substituteKronecker(GenPolynomial<C> A)
        Kronecker substitution. Substitute x_i by x**d**(i-1) to construct a univariate polynomial.
        Parameters:
        A - polynomial to be converted.
        Returns:
        a univariate polynomial.
      • substituteKronecker

        public static <C extends GcdRingElem<C>> GenPolynomial<C> substituteKronecker(GenPolynomial<C> A,                                                              long d)
        Kronecker substitution. Substitute x_i by x**d**(i-1) to construct a univariate polynomial.
        Parameters:
        A - polynomial to be converted.
        Returns:
        a univariate polynomial.
      • substituteKronecker

        public static <C extends GcdRingElem<C>> List<GenPolynomial<C>> substituteKronecker(List<GenPolynomial<C>> A,                                                                    int d)
        Kronecker substitution. Substitute x_i by x**d**(i-1) to construct a univariate polynomials.
        Parameters:
        A - list of polynomials to be converted.
        Returns:
        a list of univariate polynomials.
      • backSubstituteKronecker

        public static <C extends GcdRingElem<C>> GenPolynomial<C> backSubstituteKronecker(GenPolynomialRing<C> fac,                                                                  GenPolynomial<C> A,                                                                  long d)
        Kronecker back substitution. Substitute x**d**(i-1) to x_i to construct a multivariate polynomial.
        Parameters:
        A - polynomial to be converted.
        fac - result polynomial factory.
        Returns:
        a multivariate polynomial.
      • backSubstituteKronecker

        public static <C extends GcdRingElem<C>> List<GenPolynomial<C>> backSubstituteKronecker(GenPolynomialRing<C> fac,                                                                        List<GenPolynomial<C>> A,                                                                        long d)
        Kronecker back substitution. Substitute x**d**(i-1) to x_i to construct a multivariate polynomials.
        Parameters:
        A - list of polynomials to be converted.
        fac - result polynomial factory.
        Returns:
        a list of multivariate polynomials.

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