Package edu.jas.gb

Interface GroebnerBase<C extends RingElem<C>>

    • Method Detail

      • isGB

        boolean isGB​(java.util.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,
                     java.util.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

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

        java.util.List<GenPolynomial<C>> GB​(int modv,
                                            java.util.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.
      • extGB

        ExtendedGB<CextGB​(java.util.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<CextGB​(int modv,
                            java.util.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

        java.util.List<GenPolynomial<C>> minimalGB​(java.util.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​(java.util.List<GenPolynomial<C>> F,
                                  java.util.List<GenPolynomial<C>> G,
                                  java.util.List<java.util.List<GenPolynomial<C>>> Mf,
                                  java.util.List<java.util.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.