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

CallOnGroebnerFanIdeals

apply a function to Groebner fan ideals

colon

ideal or module quotient

ComputeElimFirst

ComputeElimFirst

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

compute a matrix of the Frobenius Map

GBasis

calculate a Groebner basis

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

HasGBasis

checks if the argument has a precomputed GBasis

HColon

ideal or module quotient

HilbertFn

the Hilbert function

HilbertSeries

the HilbertPoincare series

homog

homogenize with respect to an indeterminate

HSaturation

saturation of ideals

InitialIdeal

Initial ideal

intersection

intersect lists, ideals, or modules

IntersectList

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

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

ideal, submodule with minimal generators

minimalized

ideal, submodule with minimal generators

MinPolyModular

minimal polynomial with modular method

MinPolyQuotDef, MinPolyQuotElim, MinPolyQuotMat

compute a minimal polynomial

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

the 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

PrimaryDecomposition0

primary decomposition of a 0dimensional 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

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

reg

CastelnuovoMumford regularity of a module

res

free resolution

RingOf

the ring of the object

RingsOf

list of the rings of an object

saturate

saturation of ideals

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
