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4.12.4 Commands and Functions for Modules
The following are commands and functions for modules:
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
E_ canonical vector
Elim eliminate variables
Ext presentation Ext modules as quotients of free modules
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
GenRepr representation in terms of generators
Gens list of generators of an ideal
HColon ideal or module quotient
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
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
MinimalPresentation minimal presentation for a quotient
MinSyzMinGens minimal generators of syzygies of minimal generators
Module convert an expression into a module
NF normal form
NFsAreZero test if normal forms are zero
Rank rank of a module
ReducedGBasis compute reduced Groebner basis
Res free resolution
Size the amount of memory used by an object
Syz syzygy modules
SyzMinGens syzygy module for a set of minimal generators
SyzOfGens syzygy module for a given set of generators

For details look up each item by name. Online, try ?ItemName or H.Syntax("ItemName").