| 2.14.1 Commands and Functions for MODULE |
| BettiDiagram | the diagram of the graded Betti numbers |
| BettiMatrix | the matrix of the graded Betti numbers |
| BettiNumbers | (Multi-)graded Betti numbers |
| CanonicalBasis | canonical basis of a free module |
| colon | ideal or module quotient |
| elim | eliminate variables |
| GBasis | calculate a Groebner basis |
| GBasis TimeOut | compute a Groebner basis with a timeout |
| GenRepr | representation in terms of generators |
| gens | list of generators of an ideal |
| GensAsCols, GensAsRows | matrix of generators of a module |
| HilbertSeries | the Hilbert-Poincare series |
| HilbertSeriesShifts | the Hilbert-Poincare series |
| homog | homogenize wrt an indeterminate |
| HVector | the h-vector of a module or quotient object |
| IntersectionList | intersect lists, ideals, or modules |
| 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 |
| IsZero | test whether an object is zero |
| LT | the leading term of an object |
| MinGens | list of minimal generators |
| MinSubsetOfGens | list of minimal generators |
| ModuleElem | create a module element |
| ModuleOf | the module environment of the object |
| multiplicity | the multiplicity (degree) of a ring |
| NF | normal form |
| NumCompts | the number of components |
| 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 |
| ReducedGBasis | reduced Groebner basis |
| res | free resolution |
| RingOf | the ring of the object |
| RingsOf | list of the rings of an object |
| rk | rank of a matrix or module |
| submodule | submodule generated by list |
| SubmoduleCols, SubmoduleRows | convert a matrix into a module |
| SubmoduleOfMinGens | submodule generated by minimal generators |
| syz | syzygy modules |
| SyzOfGens | syzygy module for a given set of generators |