Alphabetical list of commands

ABCDEFGHIJKLMNOPQRSTUVWXZ

Special Characters

Shortcuts -- Special characters equivalent to commands

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A

Abs -- absolute value of a number
Adjoint -- adjoint matrix
AffHilbert -- the affine Hilbert function
AffHilbertFn -- the affine Hilbert function
AffHilbertSeries -- the affine Hilbert-Poincare series
AffPoincare -- the affine Hilbert-Poincare series
AlexanderDual_Frobby5 -- Alexander Dual of monomial ideals
Alias -- define aliases for package names
Alias In -- temporarily override global aliases
Aliases -- list of global aliases
AllIndetsCalled -- List of indeterminates of current ring with a given name
AlmostQR -- QR decomposition of a matrix
Append -- append an object to an existing list
Ascii -- convert between characters and ascii code

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B

BBasis5 -- Border Basis of zero dimensional ideal
BettiDiagram -- the diagram of the graded Betti numbers
BettiMatrix -- the matrix of the graded Betti numbers
Bin -- binomial coefficient
BinExp -- binomial expansion
Block -- group several commands into a single command
BlockMatrix -- create a block matrix
Break -- break out of a loop
BringIn -- bring in objects from another ring

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C

Call -- apply a function to given arguments
CartesianProduct, CartesianProductList -- Cartesian product of lists
Cast -- type conversion
Catch -- catch an error
CFApprox -- continued fractions
CFApproximants -- continued fractions
Characteristic -- the characteristic of a ring
CharPoly -- characteristic polynomial of a matrix
CheckArgTypes -- Check types in a list
Ciao -- quit CoCoA
Clear -- clear the working memory or a ring-bound memory
ClearDenom -- clear common denominator of a polynomial with rational coeffs
Close -- close a device
CloseLog -- close a log of a CoCoA session
CocoaLimits -- limits on exponents and ring characteristics
CocoaPackagePath -- returns the path to the CoCoA packages
Coefficients -- list of coefficients of a polynomial or vector
CoeffOfTerm -- coefficient of a term of a polynomial or vector
ColMat -- single column matrix
Colon -- ideal or module quotient
ColumnVectors -- the list of column vectors of a matrix
Comp -- the N-th component of a list
Comps -- list of components of a vector
Concat -- concatenate lists
ConcatLists -- concatenate a list of lists
Cond -- conditional expression
ContFrac -- continued fractions denominators
ContFracToRat -- convert continued fraction to rational
Count -- count the objects in a list
CurrentRing -- the current ring

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D

Dashes -- returns string of dashes
Date -- the date
DecimalStr -- convert rational number to decimal string
Define -- define a function
Deg -- the degree of a polynomial or vector
DegLexMat -- matrices for std. term-orderings
DegRevLexMat -- matrices for std. term-orderings
Delete -- delete variables from the working memory
Den -- denominator
DensePoly -- the sum of all power-products of a given degree
Depth -- Depth of a module
Der -- the derivative of a rational function
DerivationAction -- Action of a derivation
Describe -- information about an expression
Destroy -- delete rings
Det -- the determinant of a matrix
DiagonalMat -- matrix with given diagonal
Diff -- returns the difference between two lists
Dim -- the dimension of a ring or quotient object
Discriminant -- the discriminant of a polynomial
Distrib -- the distribution of objects in a list
Div -- quotient for integers
DivAlg -- division algorithm

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E

E_ -- canonical vector
Eigenvectors -- eigenvalues and eigenvectors of a matrix
Elim -- eliminate variables
EqSet -- checks if the set of elements in two lists are equal
Equals -- returns a string of equal signs
EquiIsoDec -- equidimensional isoradical decomposition
Error -- return an error message
Eval -- substitute numbers or polynomials for indeterminates
EvalBinExp -- binomial expansion functions
EvalHilbertFn -- evaluate the Hilbert function
Ext -- presentation Ext modules as quotients of free modules

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F

Fact -- factorial function
Factor -- factor a polynomial
FactorMultiplicity -- multiplicity of a factor of an integer
FGLM5 -- perform a FGLM Groebner Basis conversion
Fields -- list the fields of a record
First -- the first N elements of a list
FirstNonZero -- the first non-zero entry in a vector
FirstNonZeroPos -- the first non-zero entry in a vector
Flatten -- flatten a list
FloatApprox -- approx. of rational number of the form M*10^E
FloatStr -- convert rational number to a float string
For -- loop command
Foreach -- loop command
Format -- convert object to formatted string
Fraction -- returns the quotient of its arguments
Function -- return a function
Functions -- list the functions of a package

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G

GB.Complete -- Complete an interactive Groebner-type calculation
GB.GetBettiMatrix -- returns the Betti matrix computed so far
GB.GetNthSyz -- returns the part of the Nth syzygy module computed so far
GB.GetNthSyzShifts -- shifts of the Nth syzygy module computed so far
GB.GetRes -- returns the resolution computed so far
GB.GetResLen -- returns the length of the resolution computed so far
GB.ResReport -- status of an interactive resolution calculation
GB.Start_GBasis -- start interactive Groebner basis computation
GB.Start_MinGens -- start interactive minimal generator calculation
GB.Start_MinSyzMinGens -- start interactive calc., min. syzs. of min. gens.
GB.Start_Res -- start interactive resolution computation
GB.Start_Syz -- start interactive syzygy computation
GB.Start_SyzMinGens -- start interactive calc. of syzygies of min. gens.
GB.Stats -- status of an interactive Groebner-type calculation
GB.Step -- take one step in an interactive Groebner-type calculation
GB.Steps -- take steps in an interactive Groebner-type calculation
GBasis -- calculate a Groebner basis
GBasis5, and more -- calculations using the CoCoAServer
GBasisTimeout -- compute a Groebner basis with a timeout
GBM -- intersection of ideals for zero-dimensional schemes
GCD -- greatest common divisor
GCDFreeBasis -- determine (minimal) GCD free basis of a set of integers
GenericPoints -- random projective points
GenRepr -- representation in terms of generators
Gens -- list of generators of an ideal
Get -- read characters from a device
GetEnv -- access shell variables
GetErrMesg -- returns the message associated with an error
Gin, Gin5 -- generic initial ideal
GlobalMemory -- contents of global memory

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H

H.Browse -- browse the online help system
H.Commands -- list commands according to type
H.Man -- search online help system
H.OutCommands -- print command descriptions to a file
H.OutManual -- print the online manual to a file
H.SetMore -- more-device for online help
H.Syntax -- display the syntax of a command
H.Tips -- quick tips for using online help
H.Toc -- display the Table Of Contents of the online manual
H.Tutorial -- run the CoCoA tutorial
H.UnSetMore -- more-device for online help
HColon -- ideal or module quotient
Head -- the first element of a list
Help -- extend online help for user-defined functions
HGBM -- intersection of ideals for zero-dimensional schemes
Hilbert -- the Hilbert-Poincare' function
HilbertBasis -- Hilbert basis for a monoid
HilbertFn -- the Hilbert function
HilbertPoly -- the Hilbert polynomial
HilbertSeries -- the Hilbert-Poincare series
HilbertSeriesMultiDeg -- the Hilbert-Poincare series wrt a multigrading
HilbertSeriesShifts -- the Hilbert-Poincare series
HIntersection -- intersection of ideals
HIntersectionList -- intersection of ideals
Homogenized -- homogenize with respect to an indeterminate
HSaturation -- saturation of ideals
HVector -- the h-vector of a module or quotient object

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I

Ideal -- convert an expression into an ideal
IdealAndSeparatorsOfPoints -- ideal and separators for affine points
IdealAndSeparatorsOfProjectivePoints -- ideal and separators for points
IdealOfPoints -- ideal of a set of affine points
IdealOfProjectivePoints -- ideal of a set of projective points
Identity -- the identity matrix
If -- conditional statement
ILogBase -- integer part of the logarithm
Image -- apply ring homomorphism
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 -- create a list satisfying given conditions
Indet -- individual indeterminates
IndetInd -- the index of an indeterminate
IndetIndex -- index of an indeterminate
IndetName -- the name of an indeterminate
Indets -- list of current indeterminates
Insert -- insert an object in a list
Interpolate -- interpolating polynomial
Interreduce, Interreduced -- interreduce a list of polynomials or vectors
Intersection -- intersect lists, ideals, or modules
IntersectionList -- intersect lists, ideals, or modules
Inverse -- multiplicative inverse
InverseSystem -- Inverse system of an ideal of derivations
IO.SprintTrunc -- convert to a string and truncate
Iroot -- integer part of r-th root of an integer
IrreducibleDecom_Frobby5 -- Irreducible decomposition of monomial ideals
IsAntiSymmetric -- checks if a matrix is anti-symmetric
IsDefined -- check if an expression has been defined
IsDiagonal -- checks if a matrix is diagonal
IsEven, IsOdd -- test whether an integer is even or odd
IsHomog -- test whether given polynomials are homogeneous
IsIn -- check if one object is contained in another
IsInRadical -- check if a polynomial (or ideal) is in a radical
IsInSubalgebra -- check if one polynomial is in a subalgebra
IsLexSegment -- checks if an ideal is lex-segment
IsNumber -- checks if the argument is a number
IsPositiveGrading -- check if a matrix defines a positive grading
IsPPrime -- checks if an integer is a probable prime
IsPrime -- prime integer test
Isqrt -- (truncated) square root of an integer
IsServerReady -- checks if CoCoAServer is running
IsStable -- checks if an ideal is stable
IsStronglyStable -- checks if an ideal is strongly stable
IsSubset -- checks if the elements of one list are a subset of another
IsSymmetric -- checks if a matrix is symmetric
IsTerm -- checks if the argument is a term
IsTermOrdering -- check if a matrix defines a term-ordering
IsTree5 -- checks if a facet complex is a tree
IsZero -- test whether an object is zero

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J

Jacobian -- the Jacobian of a list of polynomials

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K

Ker -- Kernel of a K-algebra homomorphism

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L

Last -- the last N elements of a list
Latex -- LaTeX formatting
LC -- the leading coefficient of a polynomial or vector
LCM -- least common multiple
Len -- the length of an object
LexMat -- matrices for std. term-orderings
LexSegmentIdeal -- lex-segment ideal containing L, or with the same Hilbert fn as I
LinearSimplify -- find simplifying substitution for a univariate polynomial over QQ
LinKer -- find the kernel of a matrix
LinKerModP -- find the kernel of a matrix
LinSol -- find a solution to a linear system
List -- convert an expression into a list
LM -- the leading monomial of a polynomial or vector
Log -- the list of exponents of the leading term of a polynomial
LogToTerm -- returns a monomial (power-product) with given exponents
LPos -- the position of the leading power-product in a vector
LPP -- the leading power-product of a polynomial or vector
LT -- the leading term of an object

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M

MakeCheck -- run a series of tests
MakeMatByRows, MakeMatByCols -- convert a list into a matrix
MakeSet -- remove duplicates from a list
Man -- search online help system
MantissaAndExponent -- convert rational number to a float
MapDown -- convert a constant polynomial to a number
Mat -- convert an expression into a matrix
MatConcatAntiDiag -- create a simple block matrix
MatConcatDiag -- create a simple block matrix
MatConcatHor -- create a simple block matrix
MatConcatVer -- create a simple block matrix
Max -- a maximum element of a sequence or list
MaximalStandardMonomials_Frobby5 -- Maximal standard monomials of monomial ideals
MayerVietorisTreeN1 -- N-1st Betti multidegrees of monomial ideals using Mayer-Vietoris trees
MDeg -- multi-degree of an polynomial
Memory -- contents of local memory or ring-bound memory
Min -- a minimum element of a sequence or list
MinGens -- list minimal generators
Minimalize -- remove redundant generators
Minimalized -- remove redundant generators
MinimalPresentation -- minimal presentation for a quotient
Minors -- list of minor determinants of a matrix
MinPowerInIdeal -- the mininum power of a polynomial is an ideal
MinSyzMinGens -- minimal generators of syzygies of minimal generators
Mod -- remainder for integers
Mod2Rat -- reconstructing rationals from modular integers
Module -- convert an expression into a module
Monic -- divide polynomials by their leading coefficients
Monomials -- the list of monomials of a polynomial or vector
MonsInIdeal -- ideal generated by the monomials in an ideal
More -- print a string, N lines at a time
Multiplicity -- the multiplicity (degree) of a ring or quotient object

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N

NewId -- create a new identifier
NewLine -- string containing a newline
NewList -- create a new list
NewMat -- create a new matrix
NewVector -- create a new vector
NextPPrime -- find the next largest probable prime number
NextPrime -- find the next largest prime number
NF -- normal form
NFsAreZero -- test if normal forms are zero
NonZero -- remove zeroes from a list
Not, And, Or -- boolean operators
NR -- normal reduction
Num -- numerator
NumCols -- number of columns in a matrix
NumComps -- the number of components of a vector
NumIndets -- number of indeterminates
NumRows -- number of rows in a matrix

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O

OpenIFile -- open input file
OpenIString -- open input string
OpenLog -- open a log of a CoCoA session
OpenOFile -- open output file
OpenOString -- open output string
OpenSocket -- open a socket connection
Option -- status of a panel option
Ord -- matrix defining a term-ordering

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P

Packages -- list of loaded packages
Panel -- print status of a panel's options
Panels -- list of CoCoA panels
Partitions -- partitions of an integer
Permutations -- returns all permutations of the entries of a list
PerpIdealOfForm -- Ideal of derivations annihilating a form
Pfaffian -- the Pfaffian of a skew-symmetric matrix
PkgName -- returns the name of a package
PlotPoints -- outputs the coordinates of the points to a file
PlotPointsOn -- outputs the coordinates of the points to a file
Poincare -- the Hilbert-Poincare series
PoincareMultiDeg -- the Hilbert-Poincare series wrt a multigrading
PoincareShifts -- the Hilbert-Poincare series
Poly -- convert an expression into a polynomial
PositiveGrading4 -- extend a positive grading (for CoCoA-4 multigradings limitation)
PowerMod -- compute a modular power efficiently
PreprocessPts5 -- Reduce redundancy in a set of approximate points
PrimaryDecomposition -- primary decomposition of an ideal
Print -- print the value of an expression
Print On -- print to an output device
PrintLn -- print the value of an expression
Product -- the product of the elements of a list

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Q

Quit -- quit CoCoA
QuotientBasis -- vector space basis for zero-dimensional quotient rings
QZP -- change field for polynomials and ideals

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R

Radical -- radical of an ideal
RadicalOfUnmixed -- radical of an unmixed ideal
Rand -- random integer
Randomize -- randomize the coefficients of a given polynomial
Randomized -- randomize the coefficients of a given polynomial
Rank -- rank of a module
RealRootRefine -- refine a real root of a univariate polynomial
RealRoots -- computes the real roots of a univariate polynomial
RealRootsApprox -- computes approximations to the real roots of a univariate polynomial
Record -- create a record
ReducedGBasis -- compute reduced Groebner basis
RefineGCDFreeBasis -- refine an integer GCD free basis
Reg, Reg5 -- Castelnuovo-Mumford regularity of a module
RegularityIndex -- regularity index of a Hilbert function or series
RelNotes -- print the release notes
Remove -- remove an object in a list
Repeat -- loop command
Res -- free resolution
Reset -- reset panels and random number seed to defaults
ResetPanels -- reset panels to their default values
Resultant -- the resultant of two polynomials
Return -- exit from a structured command
Reverse, Reversed -- reverse a list
RevLexMat -- matrices for std. term-orderings
Ring -- returns the ring with a given name
RingEnv -- name of the current ring
RingEnvs -- names of all defined rings
RingEnvSet -- set of names of the ring environments
RMap -- define ring homomorphism
RootBound -- bound on roots of a polynomial over QQ
RowMat -- single row matrix

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S

Saturation -- saturation of ideals
ScalarProduct -- scalar product
Seed -- seed for Rand
SeparatorsOfPoints -- separators for affine points
SeparatorsOfProjectivePoints -- separators for projective points
Set, Unset -- set and unset panel options
Shape -- extended list of types involved in an expression
Sign -- the sign of a number
Size -- the amount of memory used by an object
Skip -- does nothing
SmoothFactor -- find small prime factors of an integer
Sort -- sort a list
SortBy -- sort a list
Sorted -- sort a list
SortedBy -- sort a list
Source -- read commands from a file or device
Spaces -- return a string of spaces
Sprint -- convert to a string
StableBBasis5 -- Stable Border Basis of ideal of points
StableBBasisNBM5 -- Numerical Border Basis of ideal of points
StableIdeal -- stable ideal containing L
StarPrint, StarSprint -- print polynomial with *'s for multiplications
Starting -- list functions starting with a given string
StronglyStableIdeal -- strongly stable ideal containing L
SubalgebraMap -- algebra homomorphism representing a subalgebra
SubalgebraRepr -- representation of a polynomial as a subalgebra element
Submat -- submatrix
Subsets -- returns all sublists of a list
Subst -- substitute values for indeterminates
Sum -- the sum of the elements of a list
Support -- the list of terms of a polynomial or vector
Sylvester -- the Sylvester matrix of two polynomials
Syz -- syzygy modules
SyzMinGens -- syzygy module for a set of minimal generators
SyzOfGens -- syzygy module for a given set of generators

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T

Tag -- returns the tag string of an object
Tagged -- tag an object for pretty printing
Tail -- remove the first element of a list
TensorMat -- returns the tensor product of two matrices
Toric -- saturate toric ideals
Transposed -- the transposition of a matrix
Tuples -- N-tuples
Type -- the data type of an expression
TypeOfCoeffs -- type of the coefficients of the current ring
Types -- lists all data types

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U

UnivariateIndetIndex -- the index of the indeterminate of a univariate polynomial
Unset -- set and unset panel options
Untagged -- untag an object
Use -- command for making a ring active
Using -- perform commands in non-active ring

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V

Var -- function calls by reference, other complex referencing
Vector -- create a vector

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W

WeightsList -- first row of the weights matrix
WeightsMatrix -- matrix of generalized weights for indeterminates
While -- loop command
WithoutNth -- removes the N-th component from a list
WLog -- weighted list of exponents

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X

XelMat -- matrices for std. term-orderings

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Z

ZPQ -- change field for polynomials and ideals

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