Package edu.jas.gb

Interface WordReduction<C extends RingElem<C>>

    • Method Detail

      • SPolynomials

        java.util.List<GenWordPolynomial<C>> SPolynomials​(GenWordPolynomial<C> Ap,
                                                          GenWordPolynomial<C> Bp)
        S-Polynomials of non-commutative polynomials.
        Parameters:
        Ap - word polynomial.
        Bp - word polynomial.
        Returns:
        list of all spol(Ap,Bp) the S-polynomials of Ap and Bp.
      • SPolynomial

        GenWordPolynomial<C> SPolynomial​(C a,
                                         Word l1,
                                         GenWordPolynomial<C> A,
                                         Word r1,
                                         C b,
                                         Word l2,
                                         GenWordPolynomial<C> B,
                                         Word r2)
        S-Polynomials of non-commutative polynomials.
        Parameters:
        a - leading base coefficient of B.
        l1 - word.
        A - word polynomial.
        r1 - word.
        b - leading base coefficient of A.
        l2 - word.
        B - word polynomial.
        r2 - word.
        Returns:
        list of all spol(Ap,Bp) the S-polynomials of Ap and Bp.
      • isTopReducible

        boolean isTopReducible​(java.util.List<GenWordPolynomial<C>> P,
                               GenWordPolynomial<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<GenWordPolynomial<C>> P,
                            GenWordPolynomial<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<GenWordPolynomial<C>> P,
                             GenWordPolynomial<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<GenWordPolynomial<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<GenWordPolynomial<C>> normalform​(java.util.List<GenWordPolynomial<C>> Pp,
                                                        java.util.List<GenWordPolynomial<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.
      • normalform

        GenWordPolynomial<C> normalform​(java.util.List<GenWordPolynomial<C>> lrow,
                                        java.util.List<GenWordPolynomial<C>> rrow,
                                        java.util.List<GenWordPolynomial<C>> Pp,
                                        GenWordPolynomial<C> Ap)
        Normalform with left and right recording.
        Parameters:
        lrow - left recording matrix, is modified.
        rrow - right recording matrix, is modified.
        Pp - a polynomial list for reduction.
        Ap - a polynomial.
        Returns:
        nf(Pp,Ap), the normal form of Ap wrt. Pp.
      • leftNormalform

        GenWordPolynomial<C> leftNormalform​(java.util.List<GenWordPolynomial<C>> Pp,
                                            GenWordPolynomial<C> Ap)
        Normalform with left recording.
        Parameters:
        Pp - a polynomial list for reduction.
        Ap - a polynomial.
        Returns:
        nf(Pp,Ap), the left normal form of Ap wrt. Pp.
      • leftNormalform

        GenWordPolynomial<C> leftNormalform​(java.util.List<GenWordPolynomial<C>> lrow,
                                            java.util.List<GenWordPolynomial<C>> Pp,
                                            GenWordPolynomial<C> Ap)
        Normalform with left recording.
        Parameters:
        lrow - left recording matrix, is modified.
        Pp - a polynomial list for reduction.
        Ap - a polynomial.
        Returns:
        nf(Pp,Ap), the left normal form of Ap wrt. Pp.
      • irreducibleSet

        java.util.List<GenWordPolynomial<C>> irreducibleSet​(java.util.List<GenWordPolynomial<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<GenWordPolynomial<C>> lrow,
                              java.util.List<GenWordPolynomial<C>> rrow,
                              java.util.List<GenWordPolynomial<C>> Pp,
                              GenWordPolynomial<C> Ap,
                              GenWordPolynomial<C> Np)
        Is reduction of normal form.
        Parameters:
        lrow - left recording matrix.
        rrow - right recording matrix.
        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.
      • rightNormalform

        GenWordPolynomial<C> rightNormalform​(java.util.List<GenWordPolynomial<C>> Pp,
                                             GenWordPolynomial<C> Ap)
        Right normalform with recording.
        Parameters:
        Pp - a polynomial list for reduction.
        Ap - a polynomial.
        Returns:
        nf(Pp,Ap), the right normal form of Ap wrt. Pp.
      • rightNormalform

        GenWordPolynomial<C> rightNormalform​(java.util.List<GenWordPolynomial<C>> rrow,
                                             java.util.List<GenWordPolynomial<C>> Pp,
                                             GenWordPolynomial<C> Ap)
        Right normalform with recording.
        Parameters:
        rrow - right recording matrix, is modified.
        Pp - a polynomial list for reduction.
        Ap - a polynomial.
        Returns:
        nf(Pp,Ap), the right normal form of Ap wrt. Pp.