CoCoA » CoCoALib

The following should compute a LT ideal of a small ideal (using lex).
It takes longer than I would expect over QQ -- it is quite fast over ZZ/(p), and produces ideal(x,y,z^10).
Over QQ it is really too slow (>20mins on my current computer)... JAA thinks there may really be a bug.

  ring QQ = RingQQ();
  PolyRing P = NewPolyRing(QQ, symbols("x","y","z"), lex);
  RingElem x = indet(P,0);
  RingElem y = indet(P,1);
  RingElem z = indet(P,2);
  RingElem g1 = x*x*x +x*x*z +x*z;
  RingElem g2 = x*x*x +x*y*y +1;
  RingElem g3 = x*x +x*y*z +y*y*y;

  ideal I(g1,g2,g3);

  cout << "LT(I)=" << LT(I) << endl;

Estimated time is only for locating the problem; it will have to be updated when the root cause is discovered.