| 4.13.2 Commands and Functions for Groebner-Type Computations |
| AffHilbert | the affine Hilbert function |
| AffHilbertFn | the affine Hilbert function |
| AffHilbertSeries | the affine Hilbert-Poincare series |
| AffPoincare | the affine Hilbert-Poincare series |
| BettiDiagram | the diagram of the graded Betti numbers |
| BettiMatrix | the matrix of the graded Betti numbers |
| Colon | ideal or module quotient |
| Dim | the dimension of a ring or quotient object |
| Elim | eliminate variables |
| EquiIsoDec | equidimensional isoradical decomposition |
| FGLM5 | perform a FGLM Groebner Basis conversion |
| GB.Complete | Complete an interactive Groebner-type calculation |
| GB.GetBettiMatrix | returns the Betti matrix computed so far |
| GB.GetNthSyz | returns the part of the Nth syzygy module computed so far |
| GB.GetNthSyzShifts | shifts of the Nth syzygy module computed so far |
| GB.GetRes | returns the resolution computed so far |
| GB.GetResLen | returns the length of the resolution computed so far |
| GB.ResReport | status of an interactive resolution calculation |
| GB.Start_GBasis | start interactive Groebner basis computation |
| GB.Start_MinGens | start interactive minimal generator calculation |
| GB.Start_MinSyzMinGens | start interactive calc., min. syzs. of min. gens. |
| GB.Start_Res | start interactive resolution computation |
| GB.Start_Syz | start interactive syzygy computation |
| GB.Start_SyzMinGens | start interactive calc. of syzygies of min. gens. |
| GB.Stats | status of an interactive Groebner-type calculation |
| GB.Step | take one step in an interactive Groebner-type calculation |
| GB.Steps | take steps in an interactive Groebner-type calculation |
| GBasis | calculate a Groebner basis |
| GBasis5, and more | calculations using the CoCoAServer |
| GBasisTimeout | compute a Groebner basis with a timeout |
| GBM | intersection of ideals for zero-dimensional schemes |
| GCD | greatest common divisor |
| HColon | ideal or module quotient |
| HGBM | intersection of ideals for zero-dimensional schemes |
| Hilbert | the Hilbert-Poincare' function |
| HilbertFn | the Hilbert function |
| HilbertPoly | the Hilbert polynomial |
| HilbertSeries | the Hilbert-Poincare series |
| HilbertSeriesMultiDeg | the Hilbert-Poincare series wrt a multigrading |
| HilbertSeriesShifts | the Hilbert-Poincare series |
| HIntersection | intersection of ideals |
| HIntersectionList | intersection of ideals |
| Homogenized | homogenize with respect to an indeterminate |
| HSaturation | saturation of ideals |
| HVector | the h-vector of a module or quotient object |
| IdealAndSeparatorsOfPoints | ideal and separators for affine points |
| IdealAndSeparatorsOfProjectivePoints | ideal and separators for points |
| IdealOfPoints | ideal of a set of affine points |
| IdealOfProjectivePoints | ideal of a set of projective points |
| Intersection | intersect lists, ideals, or modules |
| IntersectionList | intersect lists, ideals, or modules |
| LCM | least common multiple |
| MinGens | list minimal generators |
| MinSyzMinGens | minimal generators of syzygies of minimal generators |
| Multiplicity | the multiplicity (degree) of a ring or quotient object |
| NF | normal form |
| NFsAreZero | test if normal forms are zero |
| Poincare | the Hilbert-Poincare series |
| PoincareMultiDeg | the Hilbert-Poincare series wrt a multigrading |
| PoincareShifts | the Hilbert-Poincare series |
| Radical | radical of an ideal |
| RadicalOfUnmixed | radical of an unmixed ideal |
| ReducedGBasis | compute reduced Groebner basis |
| Res | free resolution |
| Saturation | saturation of ideals |
| Syz | syzygy modules |
| SyzMinGens | syzygy module for a set of minimal generators |
| SyzOfGens | syzygy module for a given set of generators |