Package edu.jas.gb

Interface SolvableGroebnerBase<C extends RingElem<C>>

Type Parameters:
C - coefficient type
All Superinterfaces:
Serializable
All Known Implementing Classes:
SGBProxy, SolvableGroebnerBaseAbstract, SolvableGroebnerBaseParallel, SolvableGroebnerBasePseudoRecSeq, SolvableGroebnerBasePseudoSeq, SolvableGroebnerBaseSeq, SolvableGroebnerBaseSeqPairParallel

public interface SolvableGroebnerBase<C extends RingElem<C>> extends Serializable
Solvable Groebner Bases interface. Defines methods for left, right and twosided Groebner bases and left, right and twosided GB tests.
  • Method Details

    • isLeftGB

      boolean isLeftGB(List<GenSolvablePolynomial<C>> F)
      Left Groebner base test.
      Parameters:
      F - solvable polynomial list.
      Returns:
      true, if F is a left Groebner base, else false.
    • isLeftGB

      boolean isLeftGB(int modv, List<GenSolvablePolynomial<C>> F)
      Left Groebner base test.
      Parameters:
      modv - number of module variables.
      F - solvable polynomial list.
      Returns:
      true, if F is a left Groebner base, else false.
    • isTwosidedGB

      boolean isTwosidedGB(List<GenSolvablePolynomial<C>> Fp)
      Twosided Groebner base test.
      Parameters:
      Fp - solvable polynomial list.
      Returns:
      true, if Fp is a two-sided Groebner base, else false.
    • isTwosidedGB

      boolean isTwosidedGB(int modv, List<GenSolvablePolynomial<C>> Fp)
      Twosided Groebner base test.
      Parameters:
      modv - number of module variables.
      Fp - solvable polynomial list.
      Returns:
      true, if Fp is a two-sided Groebner base, else false.
    • isRightGB

      boolean isRightGB(List<GenSolvablePolynomial<C>> F)
      Right Groebner base test.
      Parameters:
      F - solvable polynomial list.
      Returns:
      true, if F is a right Groebner base, else false.
    • isRightGB

      boolean isRightGB(int modv, List<GenSolvablePolynomial<C>> F)
      Right Groebner base test.
      Parameters:
      modv - number of module variables.
      F - solvable polynomial list.
      Returns:
      true, if F is a right Groebner base, else false.
    • leftGB

      Left Groebner base using pairlist class.
      Parameters:
      F - solvable polynomial list.
      Returns:
      leftGB(F) a left Groebner base of F.
    • leftGB

      Left Groebner base using pairlist class.
      Parameters:
      modv - number of module variables.
      F - solvable polynomial list.
      Returns:
      leftGB(F) a left Groebner base of F.
    • extLeftGB

      Solvable Extended Groebner base using critical pair class.
      Parameters:
      F - solvable polynomial list.
      Returns:
      a container for an extended left Groebner base of F.
    • extLeftGB

      SolvableExtendedGB<C> extLeftGB(int modv, List<GenSolvablePolynomial<C>> F)
      Solvable Extended Groebner base using critical pair class.
      Parameters:
      modv - module variable number.
      F - solvable polynomial list.
      Returns:
      a container for an extended left Groebner base of F.
    • leftMinimalGB

      Left minimal ordered groebner basis.
      Parameters:
      Gp - a left Groebner base.
      Returns:
      leftGBmi(F) a minimal left Groebner base of Gp.
    • twosidedGB

      Twosided Groebner base using pairlist class.
      Parameters:
      Fp - solvable polynomial list.
      Returns:
      tsGB(Fp) a twosided Groebner base of Fp.
    • twosidedGB

      List<GenSolvablePolynomial<C>> twosidedGB(int modv, List<GenSolvablePolynomial<C>> Fp)
      Twosided Groebner base using pairlist class.
      Parameters:
      modv - number of module variables.
      Fp - solvable polynomial list.
      Returns:
      tsGB(Fp) a twosided Groebner base of Fp.
    • rightGB

      Right Groebner base using opposite ring left GB.
      Parameters:
      F - solvable polynomial list.
      Returns:
      rightGB(F) a right Groebner base of F.
    • rightGB

      Right Groebner base using opposite ring left GB.
      Parameters:
      modv - number of module variables.
      F - solvable polynomial list.
      Returns:
      rightGB(F) a right Groebner base of F.
    • isLeftReductionMatrix

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

      Test if left reduction matrix.
      Parameters:
      F - a solvable polynomial list.
      G - a left Groebner base.
      Mf - a possible left reduction matrix.
      Mg - a possible left reduction matrix.
      Returns:
      true, if Mg and Mf are left reduction matrices, else false.
    • isLeftGB

      boolean isLeftGB(ModuleList<C> M)
      Module left Groebner base test.
      Parameters:
      M - a module basis.
      Returns:
      true, if M is a left Groebner base, else false.
    • leftGB

      ModuleList<C> leftGB(ModuleList<C> M)
      Left Groebner base using pairlist class.
      Parameters:
      M - a module basis.
      Returns:
      leftGB(M) a left Groebner base for M.
    • isTwosidedGB

      boolean isTwosidedGB(ModuleList<C> M)
      Module twosided Groebner base test.
      Parameters:
      M - a module basis.
      Returns:
      true, if M is a twosided Groebner base, else false.
    • twosidedGB

      ModuleList<C> twosidedGB(ModuleList<C> M)
      Twosided Groebner base using pairlist class.
      Parameters:
      M - a module basis.
      Returns:
      tsGB(M) a twosided Groebner base for M.
    • isRightGB

      boolean isRightGB(ModuleList<C> M)
      Module right Groebner base test.
      Parameters:
      M - a module basis.
      Returns:
      true, if M is a right Groebner base, else false.
    • rightGB

      ModuleList<C> rightGB(ModuleList<C> M)
      Right Groebner base using pairlist class.
      Parameters:
      M - a module basis.
      Returns:
      rightGB(M) a right Groebner base for M.