Package edu.jas.gb

Interface SolvableGroebnerBase<C extends RingElem<C>>

    • Method Detail

      • isLeftGB

        boolean isLeftGB​(java.util.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,
                         java.util.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​(java.util.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,
                             java.util.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​(java.util.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,
                          java.util.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

        java.util.List<GenSolvablePolynomial<C>> leftGB​(java.util.List<GenSolvablePolynomial<C>> F)
        Left Groebner base using pairlist class.
        Parameters:
        F - solvable polynomial list.
        Returns:
        leftGB(F) a left Groebner base of F.
      • leftGB

        java.util.List<GenSolvablePolynomial<C>> leftGB​(int modv,
                                                        java.util.List<GenSolvablePolynomial<C>> F)
        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

        SolvableExtendedGB<C> extLeftGB​(java.util.List<GenSolvablePolynomial<C>> F)
        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,
                                        java.util.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

        java.util.List<GenSolvablePolynomial<C>> leftMinimalGB​(java.util.List<GenSolvablePolynomial<C>> Gp)
        Left minimal ordered groebner basis.
        Parameters:
        Gp - a left Groebner base.
        Returns:
        leftGBmi(F) a minimal left Groebner base of Gp.
      • twosidedGB

        java.util.List<GenSolvablePolynomial<C>> twosidedGB​(java.util.List<GenSolvablePolynomial<C>> Fp)
        Twosided Groebner base using pairlist class.
        Parameters:
        Fp - solvable polynomial list.
        Returns:
        tsGB(Fp) a twosided Groebner base of Fp.
      • twosidedGB

        java.util.List<GenSolvablePolynomial<C>> twosidedGB​(int modv,
                                                            java.util.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

        java.util.List<GenSolvablePolynomial<C>> rightGB​(java.util.List<GenSolvablePolynomial<C>> F)
        Right Groebner base using opposite ring left GB.
        Parameters:
        F - solvable polynomial list.
        Returns:
        rightGB(F) a right Groebner base of F.
      • rightGB

        java.util.List<GenSolvablePolynomial<C>> rightGB​(int modv,
                                                         java.util.List<GenSolvablePolynomial<C>> F)
        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

        boolean isLeftReductionMatrix​(java.util.List<GenSolvablePolynomial<C>> F,
                                      java.util.List<GenSolvablePolynomial<C>> G,
                                      java.util.List<java.util.List<GenSolvablePolynomial<C>>> Mf,
                                      java.util.List<java.util.List<GenSolvablePolynomial<C>>> Mg)
        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.