Class ComprehensiveGroebnerBaseSeq<C extends GcdRingElem<C>>

  • Type Parameters:
    C - coefficient type

    public class ComprehensiveGroebnerBaseSeq<C extends GcdRingElem<C>>
    extends java.lang.Object
    Comprehensive Groebner Base sequential algorithm. Implements faithful comprehensive Groebner bases via Groebner systems and CGB test.
    • Field Detail

      • logger

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

        private static final boolean debug
    • Constructor Detail

      • ComprehensiveGroebnerBaseSeq

        public ComprehensiveGroebnerBaseSeq​(RingFactory<C> rf)
        Constructor.
        Parameters:
        rf - base coefficient ring factory.
      • ComprehensiveGroebnerBaseSeq

        public ComprehensiveGroebnerBaseSeq​(CReductionSeq<C> red,
                                            RingFactory<C> rf)
        Constructor.
        Parameters:
        red - C-pseudo-Reduction engine
        rf - base coefficient ring factory.
    • Method Detail

      • isGB

        public boolean isGB​(java.util.List<GenPolynomial<GenPolynomial<C>>> F)
        Comprehensive-Groebner base test.
        Parameters:
        F - polynomial list.
        Returns:
        true, if F is a Comprehensive-Groebner base, else false.
      • isGB

        public boolean isGB​(int modv,
                            java.util.List<GenPolynomial<GenPolynomial<C>>> F)
        Comprehensive-Groebner base test.
        Parameters:
        modv - module variable number.
        F - polynomial list.
        Returns:
        true, if F is a Comprehensive-Groebner base, else false.
      • isGBcol

        public boolean isGBcol​(java.util.List<GenPolynomial<GenPolynomial<C>>> F)
        Comprehensive-Groebner base test using colored systems.
        Parameters:
        F - polynomial list.
        Returns:
        true, if F is a Comprehensive-Groebner base, else false.
      • isGBcol

        public boolean isGBcol​(int modv,
                               java.util.List<GenPolynomial<GenPolynomial<C>>> F)
        Comprehensive-Groebner base test using colored systems.
        Parameters:
        modv - module variable number.
        F - polynomial list.
        Returns:
        true, if F is a Comprehensive-Groebner base, else false.
      • isGBsys

        public boolean isGBsys​(java.util.List<ColoredSystem<C>> CS)
        Comprehensive-Groebner system test.
        Parameters:
        CS - list of colored systems.
        Returns:
        true, if CS is a Comprehensive-Groebner system, else false.
      • isGBsys

        public boolean isGBsys​(int modv,
                               java.util.List<ColoredSystem<C>> CS)
        Comprehensive-Groebner system test.
        Parameters:
        modv - module variable number, unused.
        CS - list of colored systems.
        Returns:
        true, if CS is a Comprehensive-Groebner system, else false.
      • isGBsubst

        public boolean isGBsubst​(java.util.List<GenPolynomial<GenPolynomial<C>>> F)
        Comprehensive-Groebner base test using substitution.
        Parameters:
        F - polynomial list.
        Returns:
        true, if F is a Comprehensive-Groebner base, else false.
      • isGBsubst

        public boolean isGBsubst​(int modv,
                                 java.util.List<GenPolynomial<GenPolynomial<C>>> F)
        Comprehensive-Groebner base test using substitution.
        Parameters:
        modv - module variable number, unused.
        F - polynomial list.
        Returns:
        true, if F is a Comprehensive-Groebner base, else false.
      • isGBsys

        public boolean isGBsys​(GroebnerSystem<C> F)
        Comprehensive-Groebner system test.
        Parameters:
        F - Groebner system.
        Returns:
        true, if F is a Comprehensive-Groebner system, else false.
      • isCGB

        public boolean isCGB​(GroebnerSystem<C> F)
        Comprehensive-Groebner base test.
        Parameters:
        F - Groebner system.
        Returns:
        true, if F is a Comprehensive-Groebner base, else false.
      • isGB

        public boolean isGB​(GroebnerSystem<C> F)
        Comprehensive-Groebner system and base test.
        Parameters:
        F - Groebner system.
        Returns:
        true, if F is a Comprehensive-Groebner system and base, else false.
      • GBsys

        public GroebnerSystem<C> GBsys​(java.util.List<GenPolynomial<GenPolynomial<C>>> F)
        Comprehensive Groebner base system using pairlist class.
        Parameters:
        F - polynomial list.
        Returns:
        GBsys(F) a Comprehensive Groebner system of F.
      • determineAddPairs

        public java.util.List<ColoredSystem<C>> determineAddPairs​(ColoredSystem<C> cs,
                                                                  ColorPolynomial<C> A)
        Determine polynomial relative to a condition of a colored system and add pairs.
        Parameters:
        cs - a colored system.
        A - color polynomial.
        Returns:
        list of colored systems, the conditions extending the condition of cs.
      • minimalGB

        public ColoredSystem<C> minimalGB​(ColoredSystem<C> cs)
        Minimal ordered Groebner basis.
        Parameters:
        cs - colored system.
        Returns:
        a reduced Groebner base of Gp.