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
|