| 4.11.2 Commands and Functions for Ideals |
| BBasis5 | Border Basis of zero dimensional ideal |
| BettiDiagram | the diagram of the graded Betti numbers |
| BettiMatrix | the matrix of the graded Betti numbers |
| Colon | ideal or module quotient |
| Depth | Depth of a module |
| Elim | eliminate variables |
| EquiIsoDec | equidimensional isoradical decomposition |
| Ext | presentation Ext modules as quotients of free modules |
| FGLM5 | perform a FGLM Groebner Basis conversion |
| 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 |
| 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 |
| GenRepr | representation in terms of generators |
| Gens | list of generators of an ideal |
| Gin, Gin5 | generic initial ideal |
| HColon | ideal or module quotient |
| HGBM | intersection of ideals for zero-dimensional schemes |
| HIntersection | intersection of ideals |
| HIntersectionList | intersection of ideals |
| Homogenized | homogenize with respect to an indeterminate |
| HSaturation | saturation of ideals |
| Ideal | convert an expression into an ideal |
| 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 |
| Interreduce, Interreduced | interreduce a list of polynomials or vectors |
| Intersection | intersect lists, ideals, or modules |
| IntersectionList | intersect lists, ideals, or modules |
| IsIn | check if one object is contained in another |
| IsZero | test whether an object is zero |
| Len | the length of an object |
| LexSegmentIdeal | lex-segment ideal containing L, or with the same Hilbert fn as I |
| LT | the leading term of an object |
| Max, Min | a maximum or minimum element of a sequence or list |
| MinGens | list minimal generators |
| Minimalize | remove redundant generators |
| Minimalized | remove redundant generators |
| MinSyzMinGens | minimal generators of syzygies of minimal generators |
| MonsInIdeal | ideal generated by the monomials in an ideal |
| NF | normal form |
| NFsAreZero | test if normal forms are zero |
| PrimaryDecomposition | primary decomposition of an ideal |
| Product | the product of the elements of a list |
| QuotientBasis | vector space basis for zero-dimensional quotient rings |
| QZP | change field for polynomials and ideals |
| Radical | radical of an ideal |
| RadicalOfUnmixed | radical of an unmixed ideal |
| ReducedGBasis | compute reduced Groebner basis |
| Res | free resolution |
| Saturation | saturation of ideals |
| Size | the amount of memory used by an object |
| StableIdeal | stable ideal containing L |
| StronglyStableIdeal | strongly stable ideal containing L |
| Sum | the sum of the elements of a list |
| Syz | syzygy modules |
| SyzMinGens | syzygy module for a set of minimal generators |
| SyzOfGens | syzygy module for a given set of generators |
| Toric | saturate toric ideals |
| ZPQ | change field for polynomials and ideals |