Package edu.jas.gb

Interface SigReduction<C extends RingElem<C>>

  • Type Parameters:
    C - coefficient type
    All Superinterfaces:
    java.io.Serializable
    All Known Implementing Classes:
    SigReductionSeq

    public interface SigReduction<C extends RingElem<C>>
    extends java.io.Serializable
    Polynomial SigReduction interface. Defines S-Polynomial, normalform with respect to signatures.
    • Method Detail

      • SPolynomial

        GenPolynomial<C> SPolynomial​(SigPoly<C> Ap,
                                     SigPoly<C> Bp)
        S-Polynomial.
        Parameters:
        Ap - polynomial.
        Bp - polynomial.
        Returns:
        spol(Ap,Bp) the S-polynomial of Ap and Bp.
      • isSigReducible

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

        boolean isSigNormalform​(java.util.List<SigPoly<C>> F,
                                java.util.List<SigPoly<C>> G,
                                SigPoly<C> A)
        Is in Normalform.
        Parameters:
        A - polynomial.
        F - polynomial list.
        G - polynomial list.
        Returns:
        true if A is in normalform with respect to F and G.
      • sigNormalform

        SigPoly<C> sigNormalform​(java.util.List<GenPolynomial<C>> F,
                                 java.util.List<SigPoly<C>> G,
                                 SigPoly<C> A)
        Normalform.
        Parameters:
        A - polynomial.
        F - polynomial list.
        G - polynomial list.
        Returns:
        nf(A) with respect to F and G.