4.11.2 Commands and Functions for Ideals |
AffHilbert | the affine Hilbert function |
AffHilbertFn | the affine Hilbert function |
AffHilbertSeries | the affine Hilbert-Poincare series |
AffPoincare | the affine Hilbert-Poincare series |
BBasis5 | Border Basis of zero dimensional ideal |
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 |
FGLM5 | perform a FGLM Groebner Basis conversion |
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 |
GBasisTimeout | compute a Groebner basis with a timeout |
GBM | intersection of ideals for zero-dimensional schemes |
GenRepr | representation in terms of generators |
gens | list of generators of an ideal |
Gin, Gin5 | generic initial ideal |
HColon | ideal or module quotient |
HGBM | intersection of ideals for zero-dimensional schemes |
HIntersection | intersection of ideals |
HIntersectionList | intersection of ideals |
homog | 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 |
intersect | intersect lists, ideals, or modules |
IntersectionList | intersect lists, ideals, or modules |
InverseSystem | Inverse system of an ideal of derivations |
IsIn | check if one object is contained in another |
IsInRadical | check if a polynomial (or ideal) is in a radical |
IsZero | test whether an object is zero |
len | the length of an object |
LexSegmentIdeal | lex-segment ideal containing L, or with the same Hilbert fn as I |
LT | the leading term of an object |
Max | a maximum element of a sequence or list |
Min | a minimum element of a sequence or list |
MinGens | list of minimal generators |
Minimalize | remove redundant generators |
Minimalized | remove redundant generators |
MinPowerInIdeal | the mininum power of a polynomial is an ideal |
MonsInIdeal | ideal generated by the monomials in an ideal |
NF | normal form |
NFsAreZero | test if normal forms are zero |
Poincare | the Hilbert-Poincare series |
PoincareMultiDeg | the Hilbert-Poincare series wrt a multigrading |
PoincareShifts | the Hilbert-Poincare series |
PrimaryDecomposition | primary decomposition of an ideal |
product | the product of the elements of a list |
QuotientBasis | 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 | compute reduced Groebner basis |
Reg, Reg5 | Castelnuovo-Mumford regularity of a module |
res | free resolution |
saturate | saturation of ideals |
Size | the amount of memory used by an object |
StableIdeal | stable ideal containing L |
StronglyStableIdeal | strongly stable ideal containing L |
sum | the sum of the elements of a list |
Syz | syzygy modules |
SyzOfGens | syzygy module for a given set of generators |
toric | saturate toric ideals |
ZPQ | change field for polynomials and ideals |