| 2.12.1 Commands and Functions for IDEAL |
| AreGensMonomial | checks if given gens are monomial |
| AreGensSqFreeMonomial | checks if given gens are squarefree monomial |
| BBasis5 | Border Basis of zero dimensional ideal |
| BettiDiagram | the diagram of the graded Betti numbers |
| BettiMatrix | the matrix of the graded Betti numbers |
| BettiNumbers | (Multi-)graded Betti numbers |
| CallOnGroebnerFanIdeals | apply a function to Groebner fan ideals |
| colon | ideal or module quotient |
| ComputeElimFirst | ComputeElimFirst |
| DenSigma | den of ideal, wrt to ordering sigma |
| depth | Depth of a module |
| elim | eliminate variables |
| EquiIsoDec | equidimensional isoradical decomposition |
| FrbAlexanderDual | Alexander Dual of monomial ideals |
| FrbAssociatedPrimes | Associated primes of monomial ideals |
| FrbIrreducibleDecomposition | Irreducible decomposition of monomial ideals |
| FrbMaximalStandardMonomials | Maximal standard monomials of monomial ideals |
| FrbPrimaryDecomposition | Primary decomposition of monomial ideals |
| FrobeniusMat | matrix of the Frobenius Map |
| GBasis | calculate a Groebner basis |
| GBasis TimeOut | compute a Groebner basis with a timeout |
| GBasisByHomog | calculate a Groebner basis by homogenization |
| GenRepr | representation in terms of generators |
| gens | list of generators of an ideal |
| gin | generic initial ideal |
| GroebnerFanIdeals | all reduced Groebner bases of an ideal |
| GroebnerFanReducedGBases | Groebner fan reduced GBases |
| HasGBasis | checks if the argument has a pre-computed GBasis |
| HColon | ideal or module quotient |
| HilbertFn | the Hilbert function |
| HilbertSeries | the Hilbert-Poincare series |
| homog | homogenize wrt an indeterminate |
| HSaturation | saturation of ideals |
| IdealOfGBasis | ideal generated by GBasis |
| IdealOfMinGens | ideal generated by minimal generators |
| InitialIdeal | Initial ideal |
| intersection | intersect lists, ideals, or modules |
| IntersectionList | intersect lists, ideals, or modules |
| InverseSystem | Inverse system of an ideal of derivations |
| IsContained | checks if A is Contained in B |
| IsElem | checks if A is an element of B |
| IsHomog | test whether given polynomials are homogeneous |
| IsIn | check if one object is contained in another |
| IsInRadical | check if a polynomial (or ideal) is in a radical |
| IsLexSegment | checks if an ideal is lex-segment |
| IsMaximal | maximality test |
| IsOne | test whether an object is one |
| IsPrimary | primary test |
| IsRadical | check if an IDEAL is radical |
| IsSigmaGoodPrime | check if INT is good prime for IDEAL |
| IsStable | checks if an ideal is stable |
| IsStronglyStable | checks if an ideal is strongly stable |
| IsZero | test whether an object is zero |
| IsZeroDim | test whether an ideal is zero-dimensional |
| JanetBasis | the Janet basis of an ideal |
| 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 |
| MayerVietorisTreeN1 | N-1st Betti multidegrees of monomial ideals using Mayer-Vietoris trees |
| MinGens | list of minimal generators |
| MinPolyQuot | minimal polynomial in quotient ring |
| MinPowerInIdeal | the mininum power of a polynomial is an ideal |
| MinSubsetOfGens | list of minimal generators |
| MonsInIdeal | ideal generated by the monomials in an ideal |
| MultiplicationMat | multiplication matrix of a ringelem |
| NewQuotientRing | create a new quotient ring |
| NF | normal form |
| NumGens | number of generators |
| operators, shortcuts | Special characters equivalent to commands |
| PrimaryDecomposition | primary decomposition of an ideal |
| PrimaryDecompositionGTZ0 | primary decomposition of a 0-dimensional ideal |
| PrimaryHilbertSeries | primary |
| PrintBettiDiagram | print the diagram of the graded Betti numbers |
| PrintBettiMatrix | print the matrix of the graded Betti numbers |
| PrintBettiNumbers | print the (multi-)graded Betti numbers |
| PrintSectionalMatrix | print sectional matrix |
| product | the product of the elements of a list |
| QuotientBasis | vector space basis for zero-dimensional quotient rings |
| QuotientBasisSorted | 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 | reduced Groebner basis |
| reg | Castelnuovo-Mumford regularity of a module |
| res | free resolution |
| rgin | generic initial ideal wrt StdDegRevLex |
| RingOf | the ring of the object |
| RingsOf | list of the rings of an object |
| saturate | saturation of ideals |
| SectionalMatrix | sectional matrix |
| StdBasis | Standard basis |
| sum | the sum of the elements of a list |
| syz | syzygy modules |
| SyzOfGens | syzygy module for a given set of generators |
| TgCone | tangent cone |
| ThmProve [PROTOTYPE] | [PROTOTYPE] ThmProve |
| toric | saturate toric ideals |
| UniversalGBasis | universal Groebner basis of the input ideal |
| ZPQ | change field for polynomials and ideals |