Alphabetical list of commands
Commands and functions by type
Tutorial

Alphabetical list of commands

A B C D E F G H I J K L M N O P Q R S T U V W X Z

Special Characters

Shortcuts -- Special characters equivalent to commands

Back to the top --- Back to the alphabet

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
aliases -- list of global aliases
AlmostQR -- QR decomposition of a matrix
append -- append an object to an existing list
ascii -- convert between characters and ascii code
IndetsCalled -- List of indeterminates of current ring with a given name

Back to the top --- Back to the alphabet

B

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

Back to the top --- Back to the alphabet

C

CartesianProduct, CartesianProductList -- Cartesian product of lists
Cast -- type conversion
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
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
CoefficientsWRT -- list of coefficients and PPs of a polynomial wrt and indet or a list of indets
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
ContentWRT -- content of a polynomial wrt and indet or a list of indets
ContFrac -- continued fractions denominators
ContFracToRat -- convert continued fraction to rational
count -- count the objects in a list
CurrentRing -- the current ring
Try -- try and catch an error

Back to the top --- Back to the alphabet

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
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
det -- the determinant of a matrix
DiagMat -- 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
StdDegLexMat -- matrices for std. term-orderings
StdDegRevLexMat -- matrices for std. term-orderings

Back to the top --- Back to the alphabet

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

Back to the top --- Back to the alphabet

F

factor -- factor a polynomial
factorial -- factorial function
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

Back to the top --- Back to the alphabet

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_Res -- start interactive resolution computation
GB.Start_Syz -- start interactive syzygy computation
GB.Stats -- status of an interactive Groebner-type calculation
GB.Steps -- take steps in an interactive Groebner-type calculation
GBasis -- calculate a Groebner basis
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

Back to the top --- Back to the alphabet

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.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
HColon -- ideal or module quotient
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
homog -- homogenize with respect to an indeterminate
HSaturation -- saturation of ideals
HVector -- the h-vector of a module or quotient object

Back to the top --- Back to the alphabet

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
IdentityMat -- 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
IndetSymbols -- the names of the indeterminates in a PolyRing
insert -- insert an object in a list
Interpolate -- interpolating polynomial
interreduce, interreduced -- interreduce a list of polynomials or vectors
intersect -- 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
IsPrime -- prime integer test
IsProbPrime -- checks if an integer is a probable prime
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

Back to the top --- Back to the alphabet

J

jacobian -- the Jacobian of a list of polynomials

Back to the top --- Back to the alphabet

K

ker -- Kernel of a K-algebra homomorphism

Back to the top --- Back to the alphabet

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

Back to the top --- Back to the alphabet

M

ConcatAntiDiag -- create a simple block matrix
ConcatDiag -- create a simple block matrix
ConcatHor -- create a simple block matrix
ConcatVer -- create a simple block matrix
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
matrix -- convert an expression into a 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 of 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
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
multiplicity -- the multiplicity (degree) of a ring or quotient object

Back to the top --- Back to the alphabet

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
NextPrime -- find the next largest prime number
NextProbPrime -- find the next largest probable 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

Back to the top --- Back to the alphabet

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

Back to the top --- Back to the alphabet

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
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

Back to the top --- Back to the alphabet

Q

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

Back to the top --- Back to the alphabet

R

radical -- radical of an ideal
RadicalOfUnmixed -- radical of an unmixed ideal
random -- 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 function
reverse, reversed -- reverse a list
RevLexMat -- matrices for std. term-orderings
RingElem -- convert an expression into a RINGELEM
RingOf -- name of the ring of the object
RingSet -- list of the rings of an object
RMap -- define ring homomorphism
RootBound -- bound on roots of a polynomial over QQ
RowMat -- single row matrix

Back to the top --- Back to the alphabet

S

saturate -- saturation of ideals
ScalarProduct -- scalar product
Seed -- seed for Rand
SeparatorsOfPoints -- separators for affine points
SeparatorsOfProjectivePoints -- separators for projective points
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
SymbolRange -- range of symbols for the indeterminates of a PolyRing
Syz -- syzygy modules
SyzOfGens -- syzygy module for a given set of generators

Back to the top --- Back to the alphabet

T

CoeffRing -- the ring of coefficients of a polynomial ring
CurrentTypes -- lists all data types
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

Back to the top --- Back to the alphabet

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

Back to the top --- Back to the alphabet

V

ref -- function calls by reference
Vector -- create a vector

Back to the top --- Back to the alphabet

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

Back to the top --- Back to the alphabet

X

XelMat -- matrices for std. term-orderings

Back to the top --- Back to the alphabet

Z

ZPQ -- change field for polynomials and ideals

Back to the top --- Back to the alphabet