Package edu.jas.gb

Interface Reduction<C extends RingElem<C>>

    • Method Detail

      • SPolynomial

        GenPolynomial<CSPolynomial​(java.util.List<GenPolynomial<C>> S,
                                     int i,
                                     GenPolynomial<C> Ap,
                                     int j,
                                     GenPolynomial<C> Bp)
        S-Polynomial with recording.
        Parameters:
        S - recording matrix, is modified.
        i - index of Ap in basis list.
        Ap - a polynomial.
        j - index of Bp in basis list.
        Bp - a polynomial.
        Returns:
        Spol(Ap, Bp), the S-Polynomial for Ap and Bp.
      • moduleCriterion

        boolean moduleCriterion​(int modv,
                                GenPolynomial<C> A,
                                GenPolynomial<C> B)
        Module criterium.
        Parameters:
        modv - number of module variables.
        A - polynomial.
        B - polynomial.
        Returns:
        true if the module S-polynomial(i,j) is required.
      • moduleCriterion

        boolean moduleCriterion​(int modv,
                                ExpVector ei,
                                ExpVector ej)
        Module criterium.
        Parameters:
        modv - number of module variables.
        ei - ExpVector.
        ej - ExpVector.
        Returns:
        true if the module S-polynomial(i,j) is required.
      • criterion4

        boolean criterion4​(GenPolynomial<C> A,
                           GenPolynomial<C> B,
                           ExpVector e)
        GB criterium 4. Use only for commutative polynomial rings.
        Parameters:
        A - polynomial.
        B - polynomial.
        e - = lcm(ht(A),ht(B))
        Returns:
        true if the S-polynomial(i,j) is required, else false.
      • criterion4

        boolean criterion4​(GenPolynomial<C> A,
                           GenPolynomial<C> B)
        GB criterium 4. Use only for commutative polynomial rings.
        Parameters:
        A - polynomial.
        B - polynomial.
        Returns:
        true if the S-polynomial(i,j) is required, else false.
      • criterion4

        boolean criterion4​(ExpVector ei,
                           ExpVector ej,
                           ExpVector e)
        GB criterium 4.
        Parameters:
        ei - exponent vector.
        ej - exponent vector.
        e - = lcm(ei,ej)
        Returns:
        true if the S-polynomial(i,j) is required, else false.
      • isTopReducible

        boolean isTopReducible​(java.util.List<GenPolynomial<C>> P,
                               GenPolynomial<C> A)
        Is top reducible. Condition is lt(B) | lt(A) for some B in F.
        Parameters:
        A - polynomial.
        P - polynomial list.
        Returns:
        true if A is top reducible with respect to P.
      • isReducible

        boolean isReducible​(java.util.List<GenPolynomial<C>> P,
                            GenPolynomial<C> A)
        Is reducible.
        Parameters:
        A - polynomial.
        P - polynomial list.
        Returns:
        true if A is reducible with respect to P.
      • isNormalform

        boolean isNormalform​(java.util.List<GenPolynomial<C>> P,
                             GenPolynomial<C> A)
        Is in Normalform.
        Parameters:
        A - polynomial.
        P - polynomial list.
        Returns:
        true if A is in normalform with respect to P.
      • isNormalform

        boolean isNormalform​(java.util.List<GenPolynomial<C>> Pp)
        Is in Normalform.
        Parameters:
        Pp - polynomial list.
        Returns:
        true if each A in Pp is in normalform with respect to Pp\{A}.
      • normalform

        java.util.List<GenPolynomial<C>> normalform​(java.util.List<GenPolynomial<C>> Pp,
                                                    java.util.List<GenPolynomial<C>> Ap)
        Normalform Set.
        Parameters:
        Ap - polynomial list.
        Pp - polynomial list.
        Returns:
        list of nf(a) with respect to Pp for all a in Ap.
      • irreducibleSet

        java.util.List<GenPolynomial<C>> irreducibleSet​(java.util.List<GenPolynomial<C>> Pp)
        Irreducible set.
        Parameters:
        Pp - polynomial list.
        Returns:
        a list P of polynomials which are in normalform wrt. P and with ideal(Pp) = ideal(P).
      • isReductionNF

        boolean isReductionNF​(java.util.List<GenPolynomial<C>> row,
                              java.util.List<GenPolynomial<C>> Pp,
                              GenPolynomial<C> Ap,
                              GenPolynomial<C> Np)
        Is reduction of normal form.
        Parameters:
        row - recording matrix, is modified.
        Pp - a polynomial list for reduction.
        Ap - a polynomial.
        Np - nf(Pp,Ap), a normal form of Ap wrt. Pp.
        Returns:
        true, if Np + sum( row[i]*Pp[i] ) == Ap, else false.