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

GBasis5, and more

calculations using the CoCoAServer

GBasisTimeout

compute a Groebner basis with a timeout

GBM

intersection of ideals for zerodimensional 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 zerodimensional 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

IsZero

test whether an object is zero

Len

the length of an object

LexSegmentIdeal

lexsegment ideal containing L, or with the
same Hilbert fn as I

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

the product of the elements of a list

QuotientBasis

vector space basis for zerodimensional 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

Res

free resolution

Saturation

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

SyzMinGens

syzygy module for a set of minimal generators

SyzOfGens

syzygy module for a given set of generators

Toric

saturate toric ideals

ZPQ

change field for polynomials and ideals
