Class ComprehensiveGroebnerBaseSeq<C extends GcdRingElem<C>>

java.lang.Object
edu.jas.application.ComprehensiveGroebnerBaseSeq<C>
Type Parameters:
C - coefficient type
public class ComprehensiveGroebnerBaseSeq<C extends GcdRingElem<C>> extends Object
Comprehensive Groebner Base sequential algorithm. Implements faithful comprehensive Groebner bases via Groebner systems and CGB test.

  • Field Details

    • logger

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

    • debug

      private static final boolean debug

    • engine

      protected final SquarefreeAbstract<C extends GcdRingElem<C>> engine
      Squarefree for coefficient content and primitive parts.

    • cred

      protected final CReductionSeq<C extends GcdRingElem<C>> cred
      Comprehensive reduction engine.

    • cofac

      protected final RingFactory<C extends GcdRingElem<C>> cofac
      Polynomial coefficient ring factory.

  • Constructor Details

    • 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 Details

    • isGB

      public boolean isGB(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, 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(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, 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(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, 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(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, 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(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 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.

    • GB

      public List<GenPolynomial<GenPolynomial<C>>> GB(List<GenPolynomial<GenPolynomial<C>>> F)
      Comprehensive Groebner base via Groebner system.
      Parameters:
      F - polynomial list.
      Returns:
      GB(F) a Comprehensive Groebner base of F.

    • minimalGB

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