AllReducedGroebnerBases [OBSOLESCENT]

all reduced Groebner bases of an ideal

AreGensMonomial

checks if given gens are monomial

AreGensSqFreeMonomial

checks if given gens are squarefree monomial

BBasis5

Border Basis of zero dimensional ideal

BettiDiagram

the diagram of the graded Betti numbers

BettiMatrix

the matrix of the graded Betti numbers

BettiNumbers

(Multi)graded Betti numbers

CallOnGroebnerFanIdeals

apply a function to Groebner fan ideals

colon

ideal or module quotient

ComputeElimFirst

ComputeElimFirst

DenSigma

den of ideal, wrt to ordering sigma

depth

Depth of a module

elim

eliminate variables

EquiIsoDec

equidimensional isoradical decomposition

FrbAlexanderDual

Alexander Dual of monomial ideals

FrbAssociatedPrimes

Associated primes of monomial ideals

FrbIrreducibleDecomposition

Irreducible decomposition of monomial ideals

FrbMaximalStandardMonomials

Maximal standard monomials of monomial ideals

FrbPrimaryDecomposition

Primary decomposition of monomial ideals

FrobeniusMat

matrix of the Frobenius Map

GBasis

calculate a Groebner basis

GBasisByHomog

calculate a Groebner basis by homogenization

GBasisTimeout

compute a Groebner basis with a timeout

GenRepr

representation in terms of generators

gens

list of generators of an ideal

gin

generic initial ideal

GroebnerFanIdeals

all reduced Groebner bases of an ideal

GroebnerFanReducedGBases

Groebner fan reduced GBases

HasGBasis

checks if the argument has a precomputed GBasis

HColon

ideal or module quotient

HilbertFn

the Hilbert function

HilbertSeries

the HilbertPoincare series

homog

homogenize wrt an indeterminate

HSaturation

saturation of ideals

IdealOfGBasis

ideal generated by GBasis

IdealOfMinGens

ideal generated by minimal generators

InitialIdeal

Initial ideal

intersection

intersect lists, ideals, or modules

IntersectionList

intersect lists, ideals, or modules

InverseSystem

Inverse system of an ideal of derivations

IsContained

checks if A is Contained in B

IsElem

checks if A is an element of B

IsHomog

test whether given polynomials are homogeneous

IsIn

check if one object is contained in another

IsInRadical

check if a polynomial (or ideal) is in a radical

IsLexSegment

checks if an ideal is lexsegment

IsMaximal

maximality test

IsOne

test whether an object is one

IsPrimary

primary test

IsRadical

check if an IDEAL is radical

IsSigmaGoodPrime

check if INT is good primt for IDEAL

IsStable

checks if an ideal is stable

IsStronglyStable

checks if an ideal is strongly stable

IsZero

test whether an object is zero

IsZeroDim

test whether an ideal is zerodimensional

JanetBasis

the Janet basis of an ideal

LexSegmentIdeal

lexsegment ideal containing L, or with the same HilbertFn as I

LF

the leading form of a polynomial or an ideal

LT

the leading term of an object

MayerVietorisTreeN1

N1st Betti multidegrees of monomial ideals using MayerVietoris trees

MinGens

list of minimal generators

minimalize [OBSOLESCENT]

[OBSOLESCENT]

MinPolyQuot

minimal polynomial in quotient ring

MinPowerInIdeal

the mininum power of a polynomial is an ideal

MinSubsetOfGens

list of minimal generators

MonsInIdeal

ideal generated by the monomials in an ideal

MultiplicationMat

multiplication matrix of a ringelem

NewQuotientRing

create a new quotient ring

NF

normal form

NumGens

number of generators

operators, shortcuts

Special characters equivalent to commands

poincare [OBSOLESCENT]

[OBSOLESCENT] the HilbertPoincare series

PrimaryDecomposition

primary decomposition of an ideal

PrimaryDecompositionGTZ0

primary decomposition of a 0dimensional ideal

PrimaryHilbertSeries

primary

PrintBettiDiagram

the diagram of the graded Betti numbers

PrintBettiMatrix

print the matrix of the graded Betti numbers

PrintBettiNumbers

print the (multi)graded Betti numbers

PrintSectionalMatrix

print sectional matrix

product

the product of the elements of a list

QuotientBasis

vector space basis for zerodimensional quotient rings

QuotientBasisSorted

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

reduced Groebner basis

reg

CastelnuovoMumford regularity of a module

res

free resolution

rgin

generic initial ideal wrt StdDegRevLex

RingOf

the ring of the object

RingsOf

list of the rings of an object

saturate

saturation of ideals

SectionalMatrix

sectional matrix

StdBasis

Standard basis

sum

the sum of the elements of a list

syz

syzygy modules

SyzOfGens

syzygy module for a given set of generators

TgCone

tangent cone

toric

saturate toric ideals

UniversalGBasis

universal Groebner basis of the input ideal

ZPQ

change field for polynomials and ideals
