|
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 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
|
|
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 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
|
|
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 Hilbert-Poincare series
|
|
PrimaryDecomposition
|
primary decomposition of an ideal
|
|
PrimaryDecomposition0
|
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
|
|
product
|
the product of the elements of a list
|
|
QuotientBasis
|
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
|
|
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
|