apply

apply homomorphism

ApproxSolve

Approximate real solutions for polynomial system

ArrBettiNumbers

Betti numbers of an arrangement of hyperplanes

ArrBoolean

boolean arrangement

ArrBraid

braid arrangement

ArrCatalanA

Catalan arrangement of type A

ArrCatalanB

Catalan arrangement of type B

ArrCatalanD

Catalan arrangement of type D

ArrCone

cone of an arrangement of hyperplanes

ArrDeletion

deletes a hyperplane from a list of hyperplanes

ArrExponents

exponents of a free arrangement of hyperplanes

ArrFlats

list of flats of an arrangement of hyperplanes

ArrGraphical

graphical arrangement

ArrLattice

lattice of an arrangement of hyperplanes

ArrRestriction

arrangement of hyperplanes A restricted to a hyperplane

ArrShiA

Shi arrangement of type A

ArrShiB

Shi arrangement of type B

ArrShiCatalanA

ShiCatalan arrangement of type A with multiplicities

ArrShiCatalanB

ShiCatalan arrangement of type B with given multiplicities

ArrShiCatalanD

ShiCatalan arrangement of type D with given multiplicities

ArrShiD

Shi arrangement of type D

ArrSignedGraphical

signed graphical arrangement

ArrToMultiArr

multiarrangement from an arrangement and a list of multiplicities

ArrTypeB

reflection arrangement of type B

ArrTypeD

reflection arrangement of type D

ascii

convert between characters and ascii code

BBasis5

Border Basis of zero dimensional ideal

BettiNumbers

(Multi)graded Betti numbers

BinomialRepr, BinomialReprShift

binomial representation of integers

CartesianProduct, CartesianProductList

Cartesian product of lists

CFApproximants

continued fraction approximants

coefficients

list of coefficients of a polynomial

CoefficientsWRT

list of coeffs and PPs of a poly wrt indet or list of indets

CoeffListWRT

list of coefficients of a polynomial wrt an indet

CoeffListWRTSupport

list of coefficients of a polynomial wrt a powerproduct basis

compts

list of components of a ModuleElem

concat

concatenate lists

ConcatLists

concatenate a list of lists

ContFrac

continued fraction quotients

CoprimeFactorBasis

determine coprime factor base for a set of integers or ring elements

covers

a poset description from the list of the strict relations

CurrentTypes

lists all data types

diff

returns the difference between two lists

distrib

the distribution of objects in a list

eigenfactors

eigenfactors of a matrix

eigenvectors

eigenvalues and eigenvectors of a matrix

EquiIsoDec

equidimensional isoradical decomposition

exponents

the list of exponents of the leading term of a polynomial

ExternalLibs

Linked external libraries

FGLM5

perform a FGLM Groebner Basis conversion

fields

list the fields of a record

flatten

flatten a list

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

GBasis

calculate a Groebner basis

GBasisByHomog

calculate a Groebner basis by homogenization

GBasisTimeout

compute a Groebner basis with a timeout

GenericPoints

random projective points

GenRepr

representation in terms of generators

gens

list of generators of an ideal

GensJacobian

set of generators of the Jacobian ideal of a polynomial

GetCol

convert a column of a matrix into a list

GetCols

convert a matrix into a list of lists

GetRow

convert a row of a matrix into a list

GetRows

convert a matrix into a list of lists

GraverBasis

Graver basis

GroebnerFanIdeals

all reduced Groebner bases of an ideal

GroebnerFanReducedGBases

Groebner fan reduced GBases

HilbertBasisKer

Hilbert basis for a monoid

homog

homogenize wrt an indeterminate

HVector

the hvector of a module or quotient object

in

list element selector in list constructor

indets

list of indeterminates in a PolyRing

IndetSubscripts

the indices in the name of an indeterminate

interreduced

interreduce a list of polynomials

intersection

intersect lists, ideals, or modules

IntersectionList

intersect lists, ideals, or modules

InverseSystem

Inverse system of an ideal of derivations

JanetBasis

the Janet basis of an ideal

LinKerBasis

find the kernel of a matrix

MakeSet

remove duplicates from a list

MaxChains

computes all the maximal chains from the relations of the poset

MinGens

list of minimal generators

minors

list of minor determinants of a matrix

MinSubsetOfGens

list of minimal generators

moebius

Moebius function of a poset

monomials

the list of monomials of a polynomial

MultiArrExponents

exponents of a free multiarrangement of hyperplanes

MultiArrRestrictionZiegler

Ziegler multirestriction of the arrangement of hyperplanes wrt a hyperplane

MultiArrToArr

underling arrangement from a multiarrangement

NewList

create a new list

NmzDiagInvariants

ring of invariants of a diagonalizable group action

NmzEhrhartRing

Ehrhart ring

NmzFiniteDiagInvariants

ring of invariants of a finite group action

NmzIntClosureMonIdeal

integral closure of a monomial ideal

NmzIntClosureToricRing

integral closure of a toric ring

NmzIntersectionValRings

intersection of ring of valuations

NmzNormalToricRing

normalization of a toric ring

NmzTorusInvariants

ring of invariants of torus action

NonZero

remove zeroes from a list

operators, shortcuts

Special characters equivalent to commands

packages

list of loaded packages

partitions

partitions of an integer

permutations

returns all permutations of the entries of a list

PosetDual

dual of a poset from the relations of the poset

PosetJoin

join between two elements of a poset from the relations of the poset

PosetMeet

meet between two elements of a poset from the relations of the poset

PrimaryDecomposition

primary decomposition of an ideal

PrimaryDecompositionGTZ0

primary decomposition of a 0dimensional ideal

QuotientBasis

vector space basis for zerodimensional quotient rings

QuotientBasisSorted

vector space basis for zerodimensional quotient rings

QZP

change field for polynomials and ideals

RandomPermutation

random permutation (of indices)

RandomSubset

random subset

RandomSubsetIndices

indices for random subset

RandomTuple

random tuple

RandomTupleIndices

indices for random tuples

RationalAffinePoints

Affine rational solutions

RationalProjectivePoints

Projective rational solutions

RationalSolve

Rational solutions for polynomial system

RealRoots

real roots of a univariate polynomial

RealRootsApprox

approximations to the real roots of a univariate poly

ReducedGBasis

reduced Groebner basis

res

free resolution

reverse, reversed

reverse a list

RingElems

convert an expression into a RINGELEM

RingsOf

list of the rings of an object

SeparatorsOfPoints

separators for affine points

SeparatorsOfProjectivePoints

separators for projective points

shape

extended list of types involved in an expression

sorted

sort a list

SortedBy

sort a list

starting

list functions starting with a given string

StdBasis

Standard basis

SturmSeq

Sturm sequence of a univariate polynomial

subsets

returns all sublists of a list

support

the list of terms of a polynomial or moduleelem

SymbolRange

range of symbols for the indeterminates of a PolyRing

SymmetricPolys

list of symmetric polynomials

tail

remove the first element of a list

TopLevelFunctions

returns the functions available at toplevel

tuples

Ntuples

TVecFromHF

Type vector from Hilbert Function

UniversalGBasis

universal Groebner basis of the input ideal

wdeg

multidegree of a polynomial

WithoutNth

removes the Nth component from a list

ZPQ

change field for polynomials and ideals
