CoCoA » CoCoALib

CoCoALib currently offers deg (or equiv. StdDeg) and wdeg. These functions throw an exception if the ring has grading dim zero (i.e. ungraded).
Bruns would like to have a new function which determines the "leading form with respect to the standard grading" regardless of any grading which the ring has.

He also pointed out that to be consistent we should actually call the current LF function wLF (akin to wdeg).

I noticed that in one of his messages he actually wanted a decomposition of a polynomial into homogeneous pieces; should we consider adding such a function?

Why not have a function for decomposing a polynomial into its homogeneous components? There is one in NmzIntegrate.

Here is the function.
I'm still uncertain whether this should be part of cocoalib or not.
Anyway it may be copied and used :-)

  RingElem LF_StdDeg(ConstRefRingElem f)
  {
    if (!IsPolyRing(owner(f)))
      CoCoA_ERROR(ERR::NotElemPolyRing, "LF_StdDeg(f)");
    const SparsePolyRing P = owner(f);
    if (IsZero(f)) CoCoA_ERROR(ERR::ZeroRingElem, "LF_StdDeg(f)");
    RingElem F(P);
    long MaxDeg = 0;
    for (SparsePolyIter it=BeginIter(f) ; !IsEnded(it) ; ++it )
    {
      long d = deg(PP(it));
      if (d > MaxDeg)
      {
        MaxDeg = d;
        F = monomial(P, coeff(it), PP(it));
      }
      else if (d == MaxDeg)
        F += monomial(P, coeff(it), PP(it));
    }
    return F;
  }