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2.5.3 Commands and Functions for LIST

append	append an object to a list
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	Shi-Catalan arrangement of type A with multiplicities
ArrShiCatalanB	Shi-Catalan arrangement of type B with given multiplicities
ArrShiCatalanD	Shi-Catalan 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 Orlik-Terao 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
ConcatStrings	concatenate strings
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 quasi-polynomial 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	f-vector of a top simplices list
GBM	intersection of ideals for zero-dimensional schemes
gcd	greatest common divisor
HGBM	intersection of ideals for zero-dimensional schemes
HilbertSeriesShifts	the Hilbert-Poincare 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
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
IsEmpty	checks if a list is empty
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
JacobianMat	the Jacobian matrix of a list of polynomials
last	the last N elements of a list
lcm	least common multiple
len	the length of an object
LexSegmentIdeal	lex-segment 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 (power-product) 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	maximal chains of the poset (from its relations)
min	a minimum element of a sequence or list
MinBy	a minimum element of a list
MinGBoverZZ [PROTOTYPE]	[PROTOTYPE] minimal Groebner basis of polys over ZZ
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	Orlik-Terao 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
RationalSolve	Rational solutions for 0-dim polynomial system
RationalSolveHomog	Rational solutions for 0-dim 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
SAGBI, SAGBIHomog	SAGBI bases for subalgebra
SatSAGBI	SAGBI bases for subalgebra
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	Stanley-Reisner ideal, AlexanderDual complex, ideal of top simplices
SimplicialHomology	simplicial homology of a top simplices list
SolomonTeraoIdeal	Solomon-Terao 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
SubalgebraMinGens	list of minimal generators as subalgebra
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 Swinnerton-Dyer 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	N-tuples
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 N-th component from a list
ZPQ	change field for polynomials and ideals