append

append an object to a list

apply

apply homomorphism

ApproxSolve

Approximate real solutions for polynomial system

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 polynomial wrt an indet or a list of indets

ColMat

single column matrix

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

count

count the objects in a list

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

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

FVector

compute the fvector of a top simplices list

GBM

intersection of ideals for zerodimensional schemes

gcd

greatest common divisor

GCDFreeBasis

determine (minimal) GCD free basis of a set of integers

HGBM

intersection of ideals for zerodimensional schemes

HilbertSeriesShifts

the HilbertPoincare series

homog

homogenize with respect to an indeterminate

HomogElimMat

matrix for elimination ordering

ideal

ideal generated by list

IdealAndSeparatorsOfPoints

ideal and separators for affine points

IdealAndSeparatorsOfProjectivePoints

ideal and separators for points

IdealOfProjectivePoints

ideal of a set of projective 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

InitialIdeal

Initial ideal

insert [OBSOLESCENT]

[OBSOLESCENT] insert an object in a list

Interpolate

interpolating polynomial

interreduce, interreduced

interreduce a list of polynomials

intersection

intersect lists, ideals, or modules

IntersectList

intersect lists, ideals, or modules

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

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 Hilbert fn as I

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

min

a minimum element of a sequence or list

MinBy

a minimum element of a list

ModuleElem

create a module element

NewPolyRing

create a new PolyRing

NmzComputation

flexible access to Normaliz

NmzEhrhartRing

Computes the 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

operators, shortcuts

Special characters equivalent to commands

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

PrintBettiDiagram

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

RefineGCDFreeBasis

refine an integer GCD free basis

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

SetRow

set a list as a row into a matrix

shape

extended list of types involved in an expression

SimplexInfo

compute the StanleyReisner ideal, the Alexander Dual complex And ideal of a top simplices list

SimplicialHomology

compute the simplicial homology of a top simplices list

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

StronglyStableIdeal

strongly stable ideal containing L

SubalgebraRepr

representation of a polynomial as a subalgebra element

submat

submatrix

submodule

submodule generated by list

subsets

returns all sublists of a list

sum

the sum of the elements of a list

SymbolRange

range of symbols for the indeterminates of a PolyRing

syz

syzygy modules

tail

remove the first element of a list

TmpNBM

Numerical Border Basis of ideal of points

toric

saturate toric ideals

tuples

Ntuples

WithoutNth

removes the Nth component from a list

ZPQ

change field for polynomials and ideals
