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append
|
append an object to a list
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apply
|
apply homomorphism
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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
|
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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
|
|
concat
|
concatenate lists
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|
ConcatHorList
|
create a simple block matrix
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|
ConcatLists
|
concatenate a list of lists
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|
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
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|
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
|
compute a matrix of the Frobenius Map
|
|
FVector
|
compute the f-vector of a top simplices list
|
|
GBM
|
intersection of ideals for zero-dimensional schemes
|
|
gcd
|
greatest common divisor
|
|
GCDFreeBasis
|
determine (minimal) GCD free basis of a set of integers
|
|
HGBM
|
intersection of ideals for zero-dimensional schemes
|
|
HilbertSeriesShifts
|
the Hilbert-Poincare series
|
|
homog
|
homogenize with respect to an indeterminate
|
|
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
|
lex-segment ideal containing L, or with the same HilbertFn as I
|
|
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
|
|
min
|
a minimum element of a sequence or list
|
|
MinBy
|
a minimum element of a list
|
|
MinPolyModular
|
minimal polynomial with modular method
|
|
ModuleElem
|
create a module element
|
|
MultiplicationMat
|
the multiplication matrix of a ringelem
|
|
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
|
Stanley-Reisner ideal, AlexanderDual complex, ideal of top simplices
|
|
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
|
|
StagedTrees
|
staged trees from Statistics
|
|
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
|
N-tuples
|
|
WithoutNth
|
removes the N-th component from a list
|
|
ZPQ
|
change field for polynomials and ideals
|