AllReducedGroebnerBases [OBSOLESCENT]
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all reduced Groebner bases of an ideal
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AreGensMonomial
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checks if given gens are monomial
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AreGensSqFreeMonomial
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checks if given gens are squarefree monomial
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BBasis5
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Border Basis of zero dimensional ideal
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BettiDiagram
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the diagram of the graded Betti numbers
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BettiMatrix
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the matrix of the graded Betti numbers
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CallOnGroebnerFanIdeals
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apply a function to Groebner fan ideals
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colon
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ideal or module quotient
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ComputeElimFirst
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ComputeElimFirst
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depth
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Depth of a module
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elim
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eliminate variables
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EquiIsoDec
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equidimensional isoradical decomposition
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FrbAlexanderDual
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Alexander Dual of monomial ideals
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FrbAssociatedPrimes
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Associated primes of monomial ideals
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FrbIrreducibleDecomposition
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Irreducible decomposition of monomial ideals
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FrbMaximalStandardMonomials
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Maximal standard monomials of monomial ideals
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FrbPrimaryDecomposition
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Primary decomposition of monomial ideals
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FrobeniusMat
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compute a matrix of the Frobenius Map
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GBasis
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calculate a Groebner basis
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GBasisTimeout
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compute a Groebner basis with a timeout
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GenRepr
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representation in terms of generators
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gens
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list of generators of an ideal
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gin
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generic initial ideal
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GroebnerFanIdeals
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all reduced Groebner bases of an ideal
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HasGBasis
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checks if the argument has a pre-computed GBasis
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HColon
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ideal or module quotient
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HilbertFn
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the Hilbert function
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HilbertSeries
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the Hilbert-Poincare series
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homog
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homogenize with respect to an indeterminate
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HSaturation
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saturation of ideals
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InitialIdeal
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Initial ideal
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intersection
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intersect lists, ideals, or modules
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IntersectList
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intersect lists, ideals, or modules
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InverseSystem
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Inverse system of an ideal of derivations
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IsContained
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checks if A is Contained in B
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IsElem
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checks if A is an element of B
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IsHomog
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test whether given polynomials are homogeneous
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IsIn
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check if one object is contained in another
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IsInRadical
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check if a polynomial (or ideal) is in a radical
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IsLexSegment
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checks if an ideal is lex-segment
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IsMaximal
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maximality test
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IsOne
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test whether an object is one
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IsPrimary
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primary test
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IsRadical
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check if an IDEAL is radical
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IsStable
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checks if an ideal is stable
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IsStronglyStable
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checks if an ideal is strongly stable
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IsZero
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test whether an object is zero
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IsZeroDim
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test whether an ideal is zero-dimensional
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JanetBasis
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the Janet basis of an ideal
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LexSegmentIdeal
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lex-segment ideal containing L, or with the same HilbertFn as I
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LF
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the leading form of a polynomial or an ideal
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LT
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the leading term of an object
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MayerVietorisTreeN1
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N-1st Betti multidegrees of monomial ideals using Mayer-Vietoris trees
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MinGens
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list of minimal generators
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minimalize
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ideal, submodule with minimal generators
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minimalized
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ideal, submodule with minimal generators
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MinPolyModular
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minimal polynomial with modular method
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MinPolyQuotDef, MinPolyQuotElim, MinPolyQuotMat
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compute a minimal polynomial
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MinPowerInIdeal
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the mininum power of a polynomial is an ideal
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MinSubsetOfGens
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list of minimal generators
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MonsInIdeal
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ideal generated by the monomials in an ideal
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MultiplicationMat
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the multiplication matrix of a ringelem
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NewQuotientRing
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create a new quotient ring
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NF
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normal form
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NumGens
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number of generators
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operators, shortcuts
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Special characters equivalent to commands
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poincare [OBSOLESCENT]
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[OBSOLESCENT] the Hilbert-Poincare series
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PrimaryDecomposition
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primary decomposition of an ideal
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PrimaryDecomposition0
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primary decomposition of a 0-dimensional ideal
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PrimaryDecompositionGTZ0
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primary decomposition of a 0-dimensional ideal
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PrimaryHilbertSeries
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primary
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PrintBettiDiagram
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the diagram of the graded Betti numbers
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PrintBettiMatrix
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print the matrix of the graded Betti numbers
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product
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the product of the elements of a list
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QuotientBasis
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vector space basis for zero-dimensional quotient rings
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QZP
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change field for polynomials and ideals
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radical
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radical of an ideal
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RadicalOfUnmixed
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radical of an unmixed ideal
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ReducedGBasis
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compute reduced Groebner basis
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reg
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Castelnuovo-Mumford regularity of a module
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res
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free resolution
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RingOf
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the ring of the object
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RingsOf
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list of the rings of an object
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saturate
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saturation of ideals
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StdBasis
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Standard basis
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sum
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the sum of the elements of a list
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syz
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syzygy modules
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SyzOfGens
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syzygy module for a given set of generators
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TgCone
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tangent cone
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toric
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saturate toric ideals
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UniversalGBasis
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universal Groebner basis of the input ideal
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ZPQ
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change field for polynomials and ideals
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