| 2.12.2 Commands and Functions returning IDEAL |
| colon | ideal or module quotient |
| DefiningIdeal | defining ideal of a quotient ring |
| elim | eliminate variables |
| EquiIsoDec | equidimensional isoradical decomposition |
| GBM | intersection of ideals for zero-dimensional schemes |
| gin | generic initial ideal |
| HColon | ideal or module quotient |
| HGBM | intersection of ideals for zero-dimensional schemes |
| homog | homogenize with respect to an indeterminate |
| HSaturation | saturation of ideals |
| ideal | ideal generated by list |
| IdealOfPoints | ideal of a set of affine points |
| IdealOfProjectivePoints | ideal of a set of projective points |
| implicit | implicitization |
| InitialIdeal | Initial ideal |
| intersection | intersect lists, ideals, or modules |
| IntersectList | intersect lists, ideals, or modules |
| ker | Kernel of a homomorphism |
| LexSegmentIdeal | lex-segment ideal containing L, or with the same HilbertFn as I |
| LF | the leading form of a polynomial or an ideal |
| LT | the leading term of an object |
| minimalized | ideal, submodule with minimal generators |
| MonsInIdeal | ideal generated by the monomials in an ideal |
| PerpIdealOfForm | Ideal of derivations annihilating a form |
| PrimaryDecomposition | primary decomposition of an ideal |
| PrimaryDecomposition0 | primary decomposition of a 0-dimensional ideal |
| PrimaryDecompositionGTZ0 | primary decomposition of a 0-dimensional ideal |
| QZP | change field for polynomials and ideals |
| radical | radical of an ideal |
| RadicalOfUnmixed | radical of an unmixed ideal |
| saturate | saturation of ideals |
| StableIdeal | stable ideal containing L |
| StagedTrees | staged trees from Statistics |
| StronglyStableIdeal | strongly stable ideal containing L |
| TgCone | tangent cone |
| toric | saturate toric ideals |
| ZPQ | change field for polynomials and ideals |