CoCoA-5.1.4 Manual


Part 1: Alphabetical list of commands
Part 2: CoCoA Language
Part 3: CoCoA Data Types

Part 1: 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

operators, shortcuts -- Special characters equivalent to commands

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A

abs -- absolute value of a number
adj -- classical adjoint matrix (also known as adjugate)
AffHilbert [OBSOLESCENT] -- [OBSOLESCENT] renamed AffHilbertFn
AffHilbertFn -- the affine Hilbert function
AffHilbertSeries -- the affine Hilbert-Poincare series
AffPoincare [OBSOLESCENT] -- [OBSOLESCENT] Renamed AffHilbertSeries
alias -- define aliases for package names
aliases -- list of global aliases
AllReducedGroebnerBases -- all reduced Groebner bases of an ideal
AlmostQR -- QR decomposition of a matrix
and -- boolean "and" operator
append -- append an object to a list
apply -- apply homomorphism
ApproxSolve -- Approximate real solutions for polynomial system
ascii -- convert between characters and ascii code
AsINT -- convert into an INT
AsRAT -- convert into a RAT

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B

BaseRing -- the base ring of a ring
BBasis5 -- Border Basis of zero dimensional ideal
BettiDiagram -- the diagram of the graded Betti numbers
BettiMatrix -- the matrix of the graded Betti numbers
binomial -- binomial coefficient
BinomialRepr, BinomialReprShift -- binomial representation of integers
block -- group several commands into a single command
BlockMat -- create a block matrix
BlockMat2x2 -- create a block matrix with 4 matrices
Bool01 -- Convert a boolean to an integer
break -- break out of a loop
BringIn -- bring in objects from another ring

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C

Call [OBSOLETE] -- [OBSOLETE] apply a function to given arguments
CanonicalHom -- canonical homomorphism
CanonicalRepr -- representative of a class in a quotient ring
CartesianProduct, CartesianProductList -- Cartesian product of lists
Cast [OBSOLETE] -- [OBSOLETE] type conversion
ceil -- round rational up to integer
CFApprox -- continued fraction approximation
CFApproximants -- continued fraction approximants
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
CoCoA-4 mode -- Backward compatibility mode for CoCoA-4
CocoaLimits -- limits on exponents and ring characteristics
CocoaPackagePath -- returns the path to the CoCoA packages
codomain -- codomain of a homomorphism
CoeffEmbeddingHom -- returns the coefficient embedding homomorphism of a polynomial ring
coefficients -- list of coefficients of a polynomial
CoefficientsWRT -- list of coeffs and PPs of a polynomial wrt an indet or a list of indets
CoeffListWRT -- list of coefficients of a polynomial wrt and indet
CoeffOfTerm -- coefficient of a term of a polynomial
CoeffRing -- the ring of coefficients of a polynomial ring
ColMat -- single column matrix
colon -- ideal or module quotient
ColumnVectors [OBSOLETE] -- [OBSOLETE] list of module elements
Comp [OBSOLETE] -- [OBSOLETE] access a component
Comparison Operators -- less than, greater than, ...
CompleteToOrd [OBSOLESCENT] -- [OBSOLESCENT] renamed MakeTermOrd
compts -- list of components of a ModuleElem
ComputeElimFirst -- ComputeElimFirst
concat -- concatenate lists
ConcatAntiDiag -- create a simple block matrix
ConcatDiag -- create a simple block matrix
ConcatHor -- create a simple block matrix
ConcatHorList -- create a simple block matrix
ConcatLists -- concatenate a list of lists
ConcatVer -- create a simple block matrix
ConcatVerList -- create a simple block matrix
content -- content of a polynomial
ContentFreeFactor -- factorization of multivariate polynomial into content-free factors
ContentWRT -- content of a polynomial wrt and indet or a list of indets
ContFrac -- continued fraction quotients
ContFracToRat -- convert continued fraction to rational
count -- count the objects in a list
CpuTime -- Counts cpu time
CRT -- Chinese Remainder Theorem
CRTPoly -- Chinese Remainder Theorem on polynomial coefficients
CurrentRing -- the current ring
CurrentTypes -- lists all data types
cyclotomic -- n-th cyclotomic polynomial

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D

dashes -- returns string of dashes
date -- the date
DecimalStr -- convert rational number to decimal string
define -- define a function
DefiningIdeal -- defining ideal of a quotient ring
deg -- the standard degree of a polynomial or moduleelem
den -- denominator
DensePoly -- the sum of all power-products of a given degree
depth -- Depth of a module
deriv -- the derivative of a polynomial or rational function
DerivationAction -- Action of a derivation
describe -- information about an object
det -- the determinant of a matrix
DF -- the degree form of a polynomial
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
domain -- domain of a homomorphism

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E

E_ [OBSOLETE] -- [OBSOLETE] vector of the canonical basis
eigenfactors -- eigenfactors of a matrix
eigenvectors -- eigenvalues and eigenvectors of a matrix
elim -- eliminate variables
ElimMat -- matrix for elimination ordering
EmbeddingHom -- returns the embedding homomorphism of a fraction field
EqSet -- checks if the set of elements in two lists are equal
Equality Test -- test whether two values are equal or not
EquiIsoDec -- equidimensional isoradical decomposition
error -- throw an error message
eval -- substitute numbers or polynomials for indeterminates
EvalHilbertFn -- evaluate the Hilbert function
EvalQuasiPoly -- Evaluate a quasi-polynomial at an integer
exponents -- the list of exponents of the leading term of a polynomial
Ext -- presentation Ext modules as quotients of free modules
ExternalLibs -- Linked external libraries

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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 MODULEELEM
FirstNonZeroPosn -- the first non-zero entry in a MODULEELEM
flatten -- flatten a list
FloatApprox -- approx. of rational number of the form M*2^E
FloatStr -- convert rational number to a decimal string
floor -- round rational down to integer
FloorLog2, FloorLog10, FloorLogBase -- integer part of the logarithm
FloorSqrt -- (truncated) square root of an integer
for -- loop command
foreach -- loop command
format -- convert object to formatted string
FrbAlexanderDual -- Alexander Dual of monomial ideals
FrbAssociatedPrimes -- Associated primes of monomial ideals
FrbIrreducibleDecomposition -- Irreducible decomposition of monomial ideals
FrbMaximalStandardMonomials -- Maximal standard monomials of monomial ideals
FrbPrimaryDecomposition -- Primary decomposition of monomial ideals
func -- Anonymous function
Function [OBSOLETE] -- [OBSOLETE]
functions [OBSOLETE] -- [OBSOLETE] replaced by describe
FVector -- compute the f-vector of a top simplices list

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G

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
GensAsCols, GensAsRows -- matrix of generators of a module
Get -- read characters from a device
GetCol -- convert a column of a matrix into a list
GetCols -- convert a matrix into a list of lists
GetEnv -- access shell variables
GetErrMesg -- returns the message associated with an error
GetRow -- convert a row of a matrix into a list
GetRows -- convert a matrix into a list of lists
GFanRelativeInteriorPoints -- relative interion point of a cone
gin -- generic initial ideal
GradingDim -- Number of components in weighted degree
GradingMat -- matrix of generalized weights for indeterminates

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H

HColon -- ideal or module quotient
HGBM -- intersection of ideals for zero-dimensional schemes
hilbert [OBSOLESCENT] -- the Hilbert-Poincare' function
HilbertBasisKer -- 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
homog -- homogenize with respect to an indeterminate
HomogElimMat -- matrix for elimination ordering
HSaturation -- saturation of ideals
HVector -- the h-vector of a module or quotient object

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I

ID [OBSOLETE] -- [OBSOLETE] renamed RingID
ideal -- ideal generated by list
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 -- [OBSOLESCENT] renamed to FloorLogBase
image [OBSOLESCENT] -- [OBSOLESCENT] apply ring homomorphism
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
ImportByRef, ImportByValue -- import an external variable by reference or value
in -- list element selector in list constructor
incr, decr -- increment/decrement a counter
indent -- prints in a more readable way
indet -- individual indeterminates
IndetIndex -- index of an indeterminate
IndetName -- the name of an indeterminate
indets -- list of indetermiantes in a PolyRing
IndetSubscripts -- the index of an indeterminate
IndetSymbols -- the names of the indeterminates in a PolyRing
InducedHom -- homomorphism induced by a homomorphism
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
inverse -- multiplicative inverse of matrix
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
IsAntiSymmetric -- checks if a matrix is anti-symmetric
IsConstant -- checks if a ringelem is in the coefficient ring
IsContained -- checks if A is Contained in B
IsDefined -- check if an expression has been defined
IsDiagonal -- checks if a matrix is diagonal
IsDivisible -- checks if A is divisible by B
IsElem -- checks if A is an element of B
IsEven, IsOdd -- test whether an integer is even or odd
IsFactorClosed -- test whether a list of PPs is factor closed
IsField -- test whether a ring is a field
IsFiniteField -- test whether a ring is a finite field
IsFractionField -- test whether a ring is a fraction field
IsHomog -- test whether given polynomials are homogeneous
IsIn -- check if one object is contained in another
IsIndet -- checks argument is an indetermiante
IsInjective -- check if a RINGHOM is injective
IsInRadical -- check if a polynomial (or ideal) is in a radical
IsInSubalgebra [OBSOLETE] -- [OBSOLETE] check if one polynomial is in a subalgebra
IsInvertible -- check if a RINGELEM is invertible
IsIrred -- check if a RINGELEM is irreducible
IsLexSegment -- checks if an ideal is lex-segment
IsMaximal -- maximality test
IsNumber [OBSOLETE] -- [OBSOLETE] checks if the argument is a number
IsOne -- test whether an object is one
IsPolyRing -- test whether a ring is a polynomial ring
IsPositiveGrading -- check if a matrix defines a positive grading
IsPrimary -- primary test
IsPrime -- prime integer test
IsProbPrime -- checks if an integer is a probable prime
IsPthPower -- p-th power test
IsQQ -- test whether a ring is the ring of rationals
isqrt -- [OBSOLESCENT] renamed to FloorSqrt
IsQuotientRing -- test whether a ring is a quotient ring
IsStable -- checks if an ideal is stable
IsStdGraded -- checks if the grading is standard
IsStronglyStable -- checks if an ideal is strongly stable
IsSubset -- checks if the elements of one list are a subset of another
IsSurjective -- check if a RINGHOM is surjective
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
IsTrueGCDDomain -- test whether a ring is a true GCD domain
IsZero -- test whether an object is zero
IsZeroCol, IsZeroRow -- test whether a column(row) is zero
IsZeroDim -- test whether an ideal is zero-dimensional
IsZeroDivisor -- test whether a RINGELEM is a zero-divisor
IsZZ -- test whether a ring is the ring of integers
It -- variable containing the last result

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J

jacobian -- the Jacobian of a list of polynomials
JanetBasis -- the Janet basis of an ideal

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K

ker -- Kernel of a 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 ModuleElem
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
LF -- the leading form of a polynomial or an ideal
LinearSimplify -- simplifying linear substitution for a univariate polynomial over QQ
LinKer -- find the kernel of a matrix
LinKerBasis -- find the kernel of a matrix
LinKerModP [OBSOLETE] -- [OBSOLETE] find the kernel of a matrix mod p
LinSol [OBSOLETE] -- [OBSOLETE] find a solution to a linear system
LinSolve -- find a solution to a linear system
LM -- the leading monomial of a polynomial or ModuleElem
log [OBSOLESCENT] -- [OBSOLESCENT] renamed to exponents
LogCardinality -- extension degree of a finite field
LPosn -- the position of the leading power-product in a ModuleElem
LPP -- the leading power-product of a polynomial or ModuleElem
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
MakeTerm -- returns a monomial (power-product) with given exponents
MakeTermOrd -- Make a term order matrix from a given matrix
MantissaAndExponent10 -- convert rational number to a float
MantissaAndExponent2 -- convert rational number to a binary float
Manual -- search online help system
MapDown [OBSOLETE] -- [OBSOLETE] convert a constant polynomial to a number
matrix -- convert a list into a matrix
max -- a maximum element of a sequence or list
MaxBy -- a maximum element of a list
MayerVietorisTreeN1 -- N-1st Betti multidegrees of monomial ideals using Mayer-Vietoris trees
min -- a minimum element of a sequence or list
MinBy -- a minimum element of a list
MinGens -- list of minimal generators
MinGensGeneral [OBSOLESCENT] -- [OBSOLESCENT] renamed MinSubsetOfGens
minimalize -- ideal, submodule with minimal generators
minimalized -- ideal, submodule with minimal generators
MinimalPresentation -- minimal presentation for a quotient
minors -- list of minor determinants of a matrix
MinPoly -- minimal polynomial of a matrix
MinPowerInIdeal -- the mininum power of a polynomial is an ideal
MinSubsetOfGens -- list of minimal generators
mod -- remainder for integers
Mod2Rat [OBSOLETE] -- [OBSOLETE] reconstruct rationals from modular integers
ModuleElem -- create a module element
ModuleOf -- the module environment of the object
monic -- divide polynomials by their leading coefficients
monomials -- the list of monomials of a polynomial
MonsInIdeal -- ideal generated by the monomials in an ideal
multiplicity -- the multiplicity (degree) of a ring or quotient object

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N

NewFractionField -- create a new fraction field
NewFreeModule -- create a new FreeModule
NewId [OBSOLETE] -- [OBSOLETE] create a new identifier
NewLine [OBSOLESCENT] -- [OBSOLESCENT] string containing a newline
NewList -- create a new list
NewMat -- Zero matrix
NewMatFilled -- matrix filled with value
NewPolyRing -- create a new PolyRing
NewQuotientRing -- create a new quotient ring
NewRingFp -- create a new finite field
NewRingTwinFloat -- create a new twin-float ring
NewWeylAlgebra -- create a new Weyl Algebra
NextPrime -- find the next largest prime number
NextProbPrime -- find the next largest probable prime number
NF -- normal form
NFsAreZero [OBSOLETE] -- [OBSOLETE]test if normal forms are zero
NmzComputation -- flexible access to Normaliz
NmzDiagInvariants -- ring of invariants of a diagonalizable group action
NmzEhrhartRing -- Computes the Ehrhart ring
NmzFiniteDiagInvariants -- ring of invariants of a finite group action
NmzHilbertBasis -- Hilbert Basis of a monoid
NmzIntClosureMonIdeal -- integral closure of a monomial ideal
NmzIntClosureToricRing -- integral closure of a toric ring
NmzIntersectionValRings -- intersection of ring of valuations
NmzNormalToricRing -- normalization of a toric ring
NmzSetVerboseDefault -- Set the verbosity state for Normaliz
NmzTorusInvariants -- ring of invariants of torus action
NonZero -- remove zeroes from a list
not -- boolean "not" operator
NR -- normal reduction
num -- numerator
NumCols -- number of columns in a matrix
NumCompts -- the number of components
NumGens -- number of generators
NumIndets -- number of indeterminates
NumPartitions -- number of partitions of an integer
NumRows -- number of rows in a matrix
NumTerms -- number of terms in a polynomial

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O

one -- one of a ring
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 [OBSOLETE] -- [OBSOLETE] status of a panel option
or -- boolean "or" operators
OrdMat -- matrix defining a term-ordering

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P

Packages -- list of loaded packages
panel [OBSOLETE] -- [OBSOLETE] print status of a panel's options
panels [OBSOLETE] -- [OBSOLETE] 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 [OBSOLESCENT] -- [OBSOLESCENT] the Hilbert-Poincare series
PoincareMultiDeg [OBSOLETE] -- [OBSOLETE]
PoincareShifts [OBSOLETE] -- [OBSOLETE]
PolyAlgebraHom -- homomorphism of polynomial algebras
PolyRingHom -- homomorphism of polynomial rings
PowerMod -- compute a modular power efficiently
PreImage -- preimage of a RINGELEM
PreprocessPts -- Reduce redundancy in a set of approximate points
PrimaryDecomposition -- primary decomposition of an ideal
PrimaryDecomposition0 -- primary decomposition of a 0-dimensional ideal
PrimaryDecompositionGTZ0 -- primary decomposition of a 0-dimensional ideal
PrimaryHilbertSeries -- primary
PrimaryPoincare [OBSOLESCENT] -- [OBSOLESCENT] renamed PrimaryHilbertSeries
PrimitiveRoot -- find a primitive root modulo a prime
print -- print the value of an expression
print on -- print to an output device
PrintBettiDiagram -- the diagram of the graded Betti numbers
PrintBettiMatrix -- print the matrix of the graded Betti numbers
println -- print the value of an expression
PrintRes -- print free resolution
product -- the product of the elements of a list
protect -- protect a variable from being overwritten
PthRoot -- Compute p-th root

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Q

QQ -- the ring of rationals
quit -- quit CoCoA
QuotientBasis -- vector space basis for zero-dimensional quotient rings
QuotientingHom -- returns the projection homomorphism into a quotient ring
QZP -- change field for polynomials and ideals

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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
RandomSubset -- random subset
RandomSubsetIndices -- indices for random subset
RandomTuple -- random tuple
RandomTupleIndices -- indices for random tuples
rank [OBSOLESCENT] -- [OBSOLESCENT] rank
RationalAffinePoints -- Affine rational solutions
RationalProjectivePoints -- Projective rational solutions
RationalSolve -- Rational solutions for polynomial system
RatReconstructByContFrac, RatReconstructByLattice -- rational reconstruction from modular image
RatReconstructPoly -- Rational reconstruction of polynomial coefficents
RatReconstructWithBounds -- deterministic rational reconstruction from modular image
ReadExpr -- Read RINGELEM expression from string
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
record field selector -- select a field of a record
ReducedGBasis -- compute reduced Groebner basis
ref -- passing function parameters by reference
RefineGCDFreeBasis -- refine an integer GCD free basis
reg -- Castelnuovo-Mumford regularity of a module
RegularityIndex -- regularity index of a Hilbert function or series
RelNotes -- print the release notes
ReloadMan -- Reload CoCoAManual/CoCoAHelp.xml
remove -- remove an object in a list
repeat -- loop command
res -- free resolution
Reset [OBSOLETE] -- [OBSOLETE] reset panels and random number seed to defaults
ResetPanels [OBSOLETE] -- [OBSOLETE] 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
RingEnv [OBSOLETE] -- [OBSOLETE] name of the ring environment
RingID -- identification for ring
RingOf -- the ring of the object
RingQQ -- the ring of rationals
RingQQt -- pre-defined polynomial rings
RingSet [OBSOLETE] -- [OBSOLETE] renamed RingsOf
RingsOf -- list of the rings of an object
RingZZ -- the ring of integers
rk -- rank of a matrix or module
RMap [OBSOLESCENT] -- [OBSOLESCENT] define ring homomorphism for function image
RootBound -- bound on roots of a polynomial over QQ
round -- round to integer
RowMat -- single row matrix

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S

saturate -- saturation of ideals
ScalarProduct -- scalar product
ScientificStr -- convert integer/rational to a floating-point string
seed -- seed for random
SeparatorsOfPoints -- separators for affine points
SeparatorsOfProjectivePoints -- separators for projective points
SetRow -- set a list as a row into a matrix
SetStackSize -- secret ;-)
shape -- extended list of types involved in an expression
sign -- the sign of a number
SimplestBinaryRatBetween -- find simplest binary rational in a closed interval
SimplestRatBetween -- find simplest rational in a closed interval
SimplexInfo -- compute the Stanley-Reisner ideal, the Alexander Dual complex And ideal of a top simplices list
SimplicialHomology -- compute the simplicial homology of a top simplices list
size [OBSOLETE] -- [OBSOLETE]
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
SourceRegion -- read commands from a region in a file
spaces -- return a string of spaces
sprint -- convert to a string
SqFreeFactor -- compute a squarefree factorization
StableBBasis5 -- Stable 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
StdDegLexMat -- matrices for std. term-orderings
StdDegRevLexMat -- matrices for std. term-orderings
StronglyStableIdeal -- strongly stable ideal containing L
SubalgebraMap [OBSOLETE] -- [OBSOLETE] algebra homomorphism representing a subalgebra
SubalgebraRepr -- representation of a polynomial as a subalgebra element
submat -- submatrix
submodule -- submodule generated by list
SubmoduleCols, SubmoduleRows -- convert a matrix into a module
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 moduleelem
swap -- swap two values
SwapRows -- swap two rows in a matrix
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

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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
TgCone -- tangent cone
TimeFrom -- time elapsed since a given moment
TimeOfDay -- the current time
TmpChainCanonicalHom -- canonical homomorphism
TmpNBM -- Numerical Border Basis of ideal of points
TopLevel -- make a top level variable accessible
TopLevelFunctions -- returns the functions available at top-level
toric -- saturate toric ideals
transposed -- the transposition of a matrix
try -- try and catch an error
tuples -- N-tuples
type -- the data type of an expression

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U

UnivariateIndetIndex -- the index of the indeterminate of a univariate polynomial
UniversalGroebnerBasis -- universal Groebner basis of the input ideal
unprotect -- remove protection from a variable
Unset [OBSOLETE] -- [OBSOLETE] set and unset panel options
untagged -- untag an object
use -- command for making a ring active

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V

valuation [OBSOLETE] -- [OBSOLETE]
VersionInfo -- version and info about CoCoA

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W

wdeg -- multi-degree of an polynomial
WeightsMatrix [OBSOLESCENT] -- [OBSOLESCENT] matrix of generalized weights for indeterminates
while -- loop command
WithoutNth -- removes the N-th component from a list
WLog [OBSOLETE] -- [OBSOLETE]weighted list of exponents

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X

XelMat -- matrices for std. term-orderings

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Z

zero -- zero of a ring
ZeroMat -- matrix filled with 0
ZPQ -- change field for polynomials and ideals
ZZ -- the ring of integers

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Part 2: The CoCoA Programming Language

Part 2 - Chapter 1 - Introduction to CoCoA Programming
2.1.1. An Overview of CoCoA Programming
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Part 2 - Chapter 2 - Language Elements
2.2.1. Character Set and Special Symbols
2.2.2. Identifiers
2.2.3. Reserved Names
2.2.4. Comments
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Part 2 - Chapter 3 - Operators
2.3.1. CoCoA Operators
2.3.2. Algebraic Operators
2.3.3. Relational Operators
2.3.4. Selection Operators
2.3.5. Range Operator
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Part 2 - Chapter 4 - Evaluation and Assignment
2.4.1. Evaluation
2.4.2. Assignment
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Part 2 - Chapter 5 - Flow Control: Conditional Statements and Loops
2.5.1. All CoCoA commands
2.5.2. Commands and Functions for Branching
2.5.3. Commands and Functions for Loops
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Part 2 - Chapter 6 - Input/Output
2.6.1. Introduction to IO
2.6.2. Standard IO
2.6.3. File IO
2.6.4. String IO
2.6.5. Commands and Functions for IO
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Part 2 - Chapter 7 - CoCoA Packages
2.7.1. Introduction to Packages
2.7.2. First Example of a Package
2.7.3. Package Essentials
2.7.4. Global Aliases
2.7.5. Sharing Your Package
2.7.6. Commands and Functions for Packages
2.7.7. Supported Packages
2.7.8. Galois Package
2.7.9. Integer Programming
2.7.10. Algebra of Invariants
2.7.11. Special Varieties
2.7.12. Statistics
2.7.13. Geometrical Theorem-Proving
2.7.14. Typevectors
2.7.15. Conductor
2.7.16. Matrix Normal Form
2.7.17. CantStop
2.7.18. Control
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Part 2 - Chapter 8 - Linked libraries
2.8.1. CoCoALib
2.8.2. GMP
2.8.3. GSL
2.8.4. Frobby
2.8.5. Normaliz
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Part 2 - Chapter 9 - Migrating from CoCoA-4 and keeping up-to-date
2.9.1. Changes in the CoCoA language
2.9.2. Recent changes in the CoCoA-5 language
2.9.3. Obsolete and obsolescent functions
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Part 3: CoCoA datatypes

Part 3 - Chapter 1 - BOOL
3.1.1. Introduction to BOOL
3.1.2. Commands and Functions for BOOL
3.1.3. Commands and Functions returning BOOL
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Part 3 - Chapter 2 - INT
3.2.1. Introduction to INT
3.2.2. Commands and Functions for INT
3.2.3. Commands and Functions returning INT
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Part 3 - Chapter 3 - RAT
3.3.1. Introduction to RAT
3.3.2. Commands and Functions for RAT
3.3.3. Commands and Functions returning RAT
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Part 3 - Chapter 4 - STRING
3.4.1. String Literals
3.4.2. String Operations
3.4.3. Commands and Functions for STRING
3.4.4. Commands and Functions returning STRING
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Part 3 - Chapter 5 - LIST
3.5.1. Introduction to LIST
3.5.2. List Constructors
3.5.3. Commands and Functions for LIST
3.5.4. Commands and Functions returning LIST
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Part 3 - Chapter 6 - RECORD
3.6.1. Introduction to RECORD
3.6.2. Commands and Functions for RECORD
3.6.3. Commands and Functions returning RECORD
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Part 3 - Chapter 7 - FUNCTION
3.7.1. Introduction to FUNCTION
3.7.2. FUNCTIONs are first class objects
3.7.3. Commands and Functions for FUNCTION
3.7.4. Commands and Functions returning FUNCTION
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Part 3 - Chapter 8 - TYPE
3.8.1. Commands and Functions for TYPE
3.8.2. Commands and Functions returning TYPE
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Part 3 - Chapter 9 - RING
3.9.1. Introduction to RING
3.9.2. Polynomial Rings
3.9.3. Coefficient Rings
3.9.4. Indeterminates
3.9.5. Orderings
3.9.6. Module Orderings
3.9.7. Quotient Rings
3.9.8. Commands and Functions for RING
3.9.9. Commands and Functions returning RING
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Part 3 - Chapter 10 - RINGHOM
3.10.1. Introduction to RINGHOM
3.10.2. Composition of RINGHOM
3.10.3. Commands and Functions for RINGHOM
3.10.4. Commands and Functions returning RINGHOM
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Part 3 - Chapter 11 - RINGELEM
3.11.1. Introduction to RINGELEM
3.11.2. Evaluation of Polynomials
3.11.3. Commands and Functions for RINGELEM
3.11.4. Commands and Functions returning RINGELEM
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Part 3 - Chapter 12 - IDEAL
3.12.1. Commands and Functions for IDEAL
3.12.2. Commands and Functions returning IDEAL
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Part 3 - Chapter 13 - MAT
3.13.1. Introduction to MAT
3.13.2. Commands and Functions for MAT
3.13.3. Commands and Functions returning MAT
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Part 3 - Chapter 14 - MODULE
3.14.1. Commands and Functions for MODULE
3.14.2. Commands and Functions returning MODULE
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Part 3 - Chapter 15 - MODULEELEM
3.15.1. Introduction to MODULEELEM
3.15.2. Commands and Functions for MODULEELEM
3.15.3. Commands and Functions returning MODULEELEM
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Part 3 - Chapter 16 - Creating new types
3.16.1. Tagging an Object
3.16.2. Printing a Tagged Object
3.16.3. Commands and Functions for Tags
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