Package edu.jas.gb

Class DGroebnerBaseSeq<C extends RingElem<C>>

  • Type Parameters:
    C - coefficient type
    All Implemented Interfaces:
    GroebnerBase<C>, java.io.Serializable
    Direct Known Subclasses:
    EGroebnerBaseSeq

    public class DGroebnerBaseSeq<C extends RingElem<C>>
    extends GroebnerBaseAbstract<C>
    D-Groebner Base sequential algorithm. Implements D-Groebner bases and GB test. Note: Minimal reduced GBs are not unique. see BWK, section 10.1.
    See Also:
    Serialized Form
    • Field Detail

      • logger

        private static final org.apache.logging.log4j.Logger logger
      • debug

        private static final boolean debug
    • Constructor Detail

      • DGroebnerBaseSeq

        public DGroebnerBaseSeq()
        Constructor.
      • DGroebnerBaseSeq

        public DGroebnerBaseSeq​(DReduction<C> dred)
        Constructor.
        Parameters:
        dred - D-Reduction engine
    • Method Detail

      • GB

        public java.util.List<GenPolynomial<C>> GB​(int modv,
                                                   java.util.List<GenPolynomial<C>> F)
        D-Groebner base using pairlist class.
        Parameters:
        modv - module variable number.
        F - polynomial list.
        Returns:
        GB(F) a D-Groebner base of F.
      • minimalExtendedGB

        public ExtendedGB<C> minimalExtendedGB​(int flen,
                                               java.util.List<GenPolynomial<C>> Gp,
                                               java.util.List<java.util.List<GenPolynomial<C>>> M)
        Minimal extended groebner basis.
        Overrides:
        minimalExtendedGB in class GroebnerBaseAbstract<C extends RingElem<C>>
        Parameters:
        flen - length of rows.
        Gp - a Groebner base.
        M - a reduction matrix.
        Returns:
        a (partially) reduced Groebner base of Gp in a (fake) container.
      • inverse

        public GenPolynomial<C> inverse​(GenPolynomial<C> h,
                                        java.util.List<GenPolynomial<C>> F)
        Inverse for element modulo ideal.
        Parameters:
        h - polynomial
        F - polynomial list
        Returns:
        inverse of h with respect to ideal(F), if defined