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4.11.2 Commands and Functions for Ideals
The following are commands and functions for ideals:
: ideal or module quotient
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
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, Intersection5, Elim5 calculations using the CoCoAServer
GBM intersection of ideals for zero-dimensional schemes
GenRepr representation in terms of generators
Gens list of generators of an ideal
Gin 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
IsStable, IsStronglyStable, IsLexSegment checks if an ideal is stable (resp. strongly stable or a lex-segment)
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
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, Sum the product or sum of the elements of a list
QuotientBasis vector space basis for zero-dimensional quotient rings
QZP, ZPQ change field for polynomials and ideals
Radical radical of an ideal
RadicalOfUnmixed radical of an unmixed ideal
ReducedGBasis compute a reduced Groebner basis
Res free resolution
Saturation saturation of ideals
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
Toric saturate toric ideals
Toric.CheckInput check input to Toric


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