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3.11.2. Commands and Functions for Ideals
The following are commands and functions for ideals:

  * Colon, :, HColon -- ideal or module quotient
  * Elim -- eliminate variables
  * EquiIsoDec -- equidimensional isoradical decomposition
  * 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
  * GBM, HGBM -- intersection of ideals for zero-dimensional schemes
  * GenRepr -- representation in terms of generators
  * Gens -- list of generators of an ideal
  * Gin -- generic initial ideal
  * HIntersection, HIntersectionList -- intersection of ideals
  * Homogenized -- homogenize with respect to an indeterminate
  * Ideal -- convert an expression into an ideal
  * IdealAndSeparatorsOfPoints -- ideal & separators for affine points
  * IdealAndSeparatorsOfProjectivePoints -- ideal & 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, 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, 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, HSaturation -- 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'

Details can be found by looking up each item by name.  Online, try
'?ItemName' or 'H.Syntax("ItemName")'.