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2.12.1 Commands and Functions for IDEAL
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
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
GroebnerFanReducedGBases Groebner fan reduced GBases
HasGBasis checks if the argument has a pre-computed GBasis
HColon ideal or module quotient
HilbertFn the Hilbert function
HilbertSeries the Hilbert-Poincare series
homog homogenize with respect to 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 lex-segment
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 zero-dimensional
JanetBasis the Janet basis of an ideal
LexSegmentIdeal lex-segment 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 N-1st Betti multidegrees of monomial ideals using Mayer-Vietoris trees
MinGens list of minimal generators
minimalize ideal, submodule with minimal generators
minimalized ideal, submodule with minimal generators
MinPolyQuot, 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 Hilbert-Poincare series
PrimaryDecomposition primary decomposition of an ideal
PrimaryDecomposition0 primary decomposition of a 0-dimensional ideal
PrimaryDecompositionCore0 primary decomposition of a 0-dimensional ideal
PrimaryDecompositionGTZ0 primary decomposition of a 0-dimensional 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 zero-dimensional quotient rings
QuotientBasisSorted 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 Castelnuovo-Mumford 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