Interface GroebnerBase<C extends RingElem<C>>

Type Parameters:
C - coefficient type
All Superinterfaces:
Serializable
All Known Implementing Classes:
DGroebnerBaseSeq, EGroebnerBaseSeq, GBOptimized, GBProxy, GroebnerBaseAbstract, GroebnerBaseArriSigSeqIter, GroebnerBaseDistributedEC, GroebnerBaseDistributedHybridEC, GroebnerBaseF5zSigSeqIter, GroebnerBaseFGLM, GroebnerBaseGGVSigSeqIter, GroebnerBaseParallel, GroebnerBaseParIter, GroebnerBasePartial, GroebnerBasePseudoParallel, GroebnerBasePseudoRecParallel, GroebnerBasePseudoRecSeq, GroebnerBasePseudoSeq, GroebnerBaseQuotient, GroebnerBaseRational, GroebnerBaseSeq, GroebnerBaseSeqIter, GroebnerBaseSeqPairDistributed, GroebnerBaseSeqPairParallel, GroebnerBaseSeqPairSeq, GroebnerBaseSigSeqIter, GroebnerBaseWalk, RGroebnerBasePseudoSeq, RGroebnerBaseSeq
public interface GroebnerBase<C extends RingElem<C>> extends Serializable
Groebner Bases interface. Defines methods for Groebner bases and GB test.
See Also:

  • Method Details

    • isGB

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

    • isGB

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

    • GB

      List<GenPolynomial<C>> GB(List<GenPolynomial<C>> F)
      Groebner base using pairlist class.
      Parameters:
      F - polynomial list.
      Returns:
      GB(F) a Groebner base of F.

    • GB

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

    • isGB

      boolean isGB(ModuleList<C> M)
      isGB.
      Parameters:
      M - a module basis.
      Returns:
      true, if M is a Groebner base, else false.

    • GB

      ModuleList<C> GB(ModuleList<C> M)
      GB.
      Parameters:
      M - a module basis.
      Returns:
      GB(M), a Groebner base of M.

    • extGB

      ExtendedGB<C> extGB(List<GenPolynomial<C>> F)
      Extended Groebner base using critical pair class.
      Parameters:
      F - polynomial list.
      Returns:
      a container for a Groebner base G of F together with back-and-forth transformations.

    • extGB

      ExtendedGB<C> extGB(int modv, List<GenPolynomial<C>> F)
      Extended Groebner base using critical pair class.
      Parameters:
      modv - module variable number.
      F - polynomial list.
      Returns:
      a container for a Groebner base G of F together with back-and-forth transformations.

    • minimalGB

      List<GenPolynomial<C>> minimalGB(List<GenPolynomial<C>> Gp)
      Minimal ordered groebner basis.
      Parameters:
      Gp - a Groebner base.
      Returns:
      a reduced Groebner base of Gp.

    • isReductionMatrix

      boolean isReductionMatrix(ExtendedGB<C> exgb)
      Test if reduction matrix.
      Parameters:
      exgb - an ExtendedGB container.
      Returns:
      true, if exgb contains a reduction matrix, else false.

    • isReductionMatrix

      boolean isReductionMatrix(List<GenPolynomial<C>> F, List<GenPolynomial<C>> G, List<List<GenPolynomial<C>>> Mf, List<List<GenPolynomial<C>>> Mg)
      Test if reduction matrix.
      Parameters:
      F - a polynomial list.
      G - a Groebner base.
      Mf - a possible reduction matrix.
      Mg - a possible reduction matrix.
      Returns:
      true, if Mg and Mf are reduction matrices, else false.