append

append an object to a list

apply

apply homomorphism

ApproxSolve

Approximate real solutions for polynomial system

ArrBettiNumbers

Betti numbers of an arrangement of hyperplanes

ArrCharPoly

characteristic polynomial of an arrangement of hyperplanes

ArrCone

cone of an arrangement of hyperplanes

ArrDeletion

deletes a hyperplane from a list of hyperplanes

ArrFlats

list of flats of an arrangement of hyperplanes

ArrGraphical

graphical arrangement

ArrLattice

lattice of an arrangement of hyperplanes

ArrPoincarePoly

Poincare polynomial of an arrangement of hyperplanes

ArrRestriction

arrangement of hyperplanes A restricted to a hyperplane

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

ArrSignedGraphical

signed graphical arrangement

ArrToMultiArr

multiarrangement from an arrangement and a list of multiplicities

ArrTuttePoly

Tutte polynomial of an arrangement of hyperplanes

ArtinianOrlikTeraoIdeal

Artinian OrlikTerao ideal of an arrangement of hyperplanes

ascii

convert between characters and ascii code

BettiMatrix

the matrix of the graded Betti numbers

CartesianProduct, CartesianProductList

Cartesian product of lists

CheckArgTypes

Check types in a list

coefficients

list of coefficients of a polynomial

CoefficientsWRT

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

ColMat

single column matrix

CommonDenom

Common denominator of a polynomial with rational coefficients

concat

concatenate lists

ConcatHorList

create a simple block matrix

ConcatLists

concatenate a list of lists

ConcatVerList

create a simple block matrix

ContentWRT

content of a polynomial wrt and indet or a list of indets

ContFracToRat

convert continued fraction to rational

CoprimeFactorBasis

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

count

count the objects in a list

covers

a poset description from the list of the strict relations

DiagMat

matrix with given diagonal

diff

returns the difference between two lists

distrib

the distribution of objects in a list

DivAlg

division algorithm

elim

eliminate variables

ElimHomogMat

matrix for elimination ordering

ElimMat

matrix for elimination ordering

EqSet

checks if the set of elements in two lists are equal

eval

substitute numbers or polynomials for indeterminates

EvalQuasiPoly

Evaluate a quasipolynomial at an integer

Ext

presentation Ext modules as quotients of free modules

FGLM5

perform a FGLM Groebner Basis conversion

first

the first N elements of a list

flatten

flatten a list

foreach

loop command

FrobeniusMat

matrix of the Frobenius Map

FVector

fvector of a top simplices list

GBM

intersection of ideals for zerodimensional schemes

gcd

greatest common divisor

HGBM

intersection of ideals for zerodimensional schemes

HilbertSeriesShifts

the HilbertPoincare series

homog

homogenize wrt an indeterminate

ideal

ideal generated by list

IdealAndSeparatorsOfPoints

ideal and separators for affine points

IdealAndSeparatorsOfProjectivePoints

ideal and separators for points

implicit

implicitization

ImplicitHypersurface

implicitization of hypersurface

ImplicitPlot

outputs the zero locus of a bivariate polynomial to a file

ImplicitPlotOn

outputs the zero locus of a bivariate polynomial to a file

in

list element selector in list constructor

indent

prints in a more readable way

IndetsProd

(product of) indeterminates actually in a polynomial

InitialIdeal

Initial ideal

insert [OBSOLESCENT]

[OBSOLESCENT] insert an object in a list

Interpolate

interpolating polynomial

interreduce

interreduce a list of polynomials

interreduced

interreduce a list of polynomials

intersection

intersect lists, ideals, or modules

IntersectionList

intersect lists, ideals, or modules

IsArrCentral

checks if the arrangement is central

IsFactorClosed

test whether a list of PPs is factor closed

IsHomog

test whether given polynomials are homogeneous

IsIn

check if one object is contained in another

IsLattice

checks if the poset is a lattice

IsMultiArrFree

checks if the multiarrangement is free

IsPosetGraded

checks if the poset is graded

IsSubset

checks if the elements of one list are a subset of another

IsTree5

checks if a facet complex is a tree

jacobian

the Jacobian of a list of polynomials

last

the last N elements of a list

lcm

least common multiple

len

the length of an object

LexSegmentIdeal

lexsegment ideal containing L, or with the same HilbertFn as I

LinKerBasis

find the kernel of a matrix

MakeMatByRows, MakeMatByCols

convert a list into a matrix

MakeSet

remove duplicates from a list

MakeTerm

returns a monomial (powerproduct) with given exponents

matrix

convert a list into a matrix

max

a maximum element of a sequence or list

MaxBy

a maximum element of a list

MaxChains

computes all the maximal chains from the relations of the poset

min

a minimum element of a sequence or list

MinBy

a minimum element of a list

ModuleElem

create a module element

moebius

Moebius function of a poset

MultiArrDerModule

set of generators of the module of logarithmic derivations of a multiarrangement of hyperplanes

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

MultiplicationMat

multiplication matrix of a ringelem

NewPolyRing

create a new PolyRing

NmzComputation

flexible access to Normaliz

NmzEhrhartRing

Ehrhart ring

NmzIntClosureMonIdeal

integral closure of a monomial ideal

NmzIntClosureToricRing

integral closure of a toric ring

NmzNormalToricRing

normalization of a toric ring

NonZero

remove zeroes from a list

NR

normal reduction

NumBChambers

number of bounded chambers of an arrangement of hyperplanes

NumChambers

number of chambers of an arrangement of hyperplanes

operators, shortcuts

Special characters equivalent to commands

OrlikTeraoIdeal

OrlikTerao ideal of an arrangement of hyperplanes

permutations

returns all permutations of the entries of a list

PlotPoints

outputs the coordinates of the points to a file

PlotPointsOn

outputs the coordinates of the points to a file

PolyAlgebraHom

homomorphism of polynomial algebras

PolyRingHom

homomorphism of polynomial rings

PosetCharPoly

characteristic polynomial of a poset from the relations of the poset

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

PosetNRank

rank of the node N from the relations of the graded poset

PosetPoincarePoly

Poincare polynomial of a poset from the relations of the poset

PosetRank

rank of the poset from its relations

PrintBettiDiagram

print the diagram of the graded Betti numbers

product

the product of the elements of a list

QZP

change field for polynomials and ideals

RandomSubset

random subset

RandomTuple

random tuple

RationalAffinePoints

Affine rational solutions

RationalProjectivePoints

Projective rational solutions

RationalSolve

Rational solutions for polynomial system

RatReconstructWithBounds

deterministic rational reconstruction from modular image

ReloadMan

Reload CoCoAManual/CoCoAHelp.xml

remove

remove an object in a list

reverse, reversed

reverse a list

RingsOf

list of the rings of an object

RMap [OBSOLESCENT]

[OBSOLESCENT] define ring homomorphism for function image

RowMat

single row matrix

ScalarProduct

scalar product

SeparatorsOfPoints

separators for affine points

SeparatorsOfProjectivePoints

separators for projective points

SetCol

set a list as a column into a matrix

SetRow

set a list as a row into a matrix

shape

extended list of types involved in an expression

SimplexInfo

StanleyReisner ideal, AlexanderDual complex, ideal of top simplices

SimplicialHomology

simplicial homology of a top simplices list

SolomonTeraoIdeal

SolomonTerao ideal of an arrangement of hyperplanes wrt a poly

sort

sort a list

SortBy

sort a list

sorted

sort a list

SortedBy

sort a list

StableBBasis5

Stable Border Basis of ideal of points

StableIdeal

stable ideal containing L

StagedTrees

staged trees from Statistics

StronglyStableIdeal

strongly stable ideal containing L

submat

submatrix

submodule

submodule generated by list

subsets

returns all sublists of a list

sum

the sum of the elements of a list

SwinnertonDyerPoly

compute SwinnertonDyer polynomial with given roots

SymbolRange

range of symbols for the indeterminates of a PolyRing

syz

syzygy modules

tail

remove the first element of a list

toric

saturate toric ideals

tuples

Ntuples

TVecFromHF

Type vector from Hilbert Function

TVecPoints

points associated to type vector

TVecPrintRes

resolution associated to type vector

TVecToHF

Hilbert Function of a type vector

WithoutNth

removes the Nth component from a list

ZPQ

change field for polynomials and ideals
