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Alphabetic 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 Y Z
.. -- range operator
: -- See "Colon, :, HColon"
<< -- See "Source, <<"
>< -- Cartesian product
?, Man -- search online help system
@ -- See "Tagged, Untagged, @"
A Top
Abs -- absolute value of a number
Adjoint -- adjoint matrix
Alias -- define aliases for package names
Alias In -- temporarily override global aliases
Aliases -- list of global aliases
And -- See "Not, And, Or"
Append -- append an object to an existing list
Ascii -- convert between characters and ascii code
B Top
Bin -- binomial coefficient
BinExp, EvalBinExp -- 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
C Top
Call -- apply a function to given arguments
Cast -- type conversion
Catch -- catch an error
CFApprox, CFApproximants, ContFrac -- continued fractions
Characteristic -- the characteristic of a ring
Ciao -- quit CoCoA
Clear -- clear the working memory or a ring-bound memory
Close -- close a device
CloseLog -- See "OpenLog, CloseLog"
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
Colon, :, HColon -- 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, ConcatLists -- concatenate lists or lists of lists, respectively
Cond -- conditional expression
ContFrac -- See "CFApprox, CFApproximants, ContFrac"
Contrib -- list of contributors to CoCoA
Count -- count the objects in a list
CurrentRing -- the current ring
D Top
Dashes -- returns string of dashes
Date -- the date
DecimalStr -- convert rational number to decimal string
Define -- define a function
Defined -- check if an expression has been defined
Deg -- the degree of a polynomial or vector
DegLexMat, DegRevLexMat, LexMat, XelMat -- matrices for std. term-orderings
DegRevLexMat -- See "DegLexMat, DegRevLexMat, LexMat, XelMat"
Delete -- delete variables from the working memory
Den -- See "Num, Den"
DensePoly -- the sum of all power-products of a given degree
Der -- the derivative of a rational function
Describe -- information about an expression
Destroy -- delete rings
Det -- the determinant of a matrix
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, Mod -- quotient and remainder for integers
DivAlg -- division algorithm
E Top
E_ -- canonical vector
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 -- See "BinExp, EvalBinExp"
EvalHilbertFn -- evaluate the Hilbert function
F Top
Fact -- factorial function
Factor -- factor a polynomial
Fields -- list the fields of a record
First -- the first N elements of a list
FirstNonZero, 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, MantissaAndExponent -- 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
G Top
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, GB.Steps -- take steps in an interactive Groebner-type calculation
GBasis -- calculate a Groebner basis
GBM, HGBM -- intersection of ideals for zero-dimensional schemes
GCD, LCM -- greatest common divisor, least common multiple
GenericPoints -- random projective points
GenRepr -- representation in terms of generators
Gens -- list of generators of an ideal
Get -- read characters from a device
GetErrMesg -- returns the message associated with an error
Gin -- generic initial ideal
GlobalMemory -- contents of global memory
H Top
H.Browse -- browse the online help system
H.Commands -- list commands according to type
H.Man -- search online help system (see '?, Man')
H.OutCommands -- print command descriptions to a file
H.OutManual -- print the online manual to a file
H.SetMore, H.UnSetMore -- 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 -- See "H.SetMore, H.UnSetMore"
HColon -- See "Colon, :, HColon"
Head -- the first element of a list
Help -- extend online help for user-defined functions
HGBM -- See "GBM, HGBM"
Hilbert -- the Hilbert function
HilbertBasis -- Hilbert basis for a monoid
HilbertPoly -- the Hilbert polynomial
HilbertSeries -- See "Poincare, HilbertSeries"
HIntersection, HIntersectionList -- intersection of ideals
Homogenized -- homogenize with respect to an indeterminate
HSaturation -- See "Saturation, HSaturation"
HVector -- the h-vector of a ring or quotient object
I Top
Ideal -- convert an expression into an ideal
IdealAndSeparatorsOfPoints -- ideal & separators for affine points
IdealAndSeparatorsOfProjectivePoints -- ideal & 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 -- ring homomorphism
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, Remove -- insert or remove an object in a list
Interpolate -- interpolating polynomial
Interreduce, Interreduced -- interreduce a list of polynomials or vectors
Intersection, IntersectionList -- intersect lists, ideals, or modules
Inverse -- multiplicative inverse
IO.SprintTrunc -- convert to a string and truncate
Iroot -- integer part of r-th root of an integer
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
IsLexSegment -- See "IsStable, IsStronglyStable, IsLexSegment"
IsNumber -- checks if the argument is a number
IsOdd -- See "IsEven, IsOdd"
IsPosTo, IsToPos -- checks the module term-ordering of a ring
IsPrime -- prime integer test
Isqrt -- computes the (truncated) square root of an integer
IsStable, IsStronglyStable, IsLexSegment -- checks if an ideal is stable (resp. strongly stable or a lex-segment)
IsStronglyStable -- See "IsStable, IsStronglyStable, IsLexSegment"
IsSubset -- See "SubSet, IsSubset"
IsTerm -- checks if the argument is a term
IsToPos -- See "IsPosTo, IsToPos"
IsZero -- test whether an object is zero
J Top
Jacobian -- the Jacobian of a list of polynomials
K Top
L Top
Last -- the last N elements of a list
Latex -- LaTeX formatting
LC -- the leading coefficient of a polynomial or vector
LCM -- See "GCD, LCM"
Len -- the length of an object
LexMat -- See "DegLexMat, DegRevLexMat, LexMat, XelMat"
LinKer -- 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
M Top
Man -- See "?, Man"
MantissaAndExponent -- See "FloatStr, MantissaAndExponent"
MapDown -- convert a constant polynomial to a number
Mat -- convert an expression into a matrix
Max, Min -- a maximum or minimum element of a sequence or list
MDeg -- multi-degree of an polynomial
Memory -- contents of local memory or ring-bound memory
Min -- See "Max, Min"
MinGens -- list minimal generators
Minimalize, Minimalized -- remove redundant generators
Minors -- list of minor determinants of a matrix
MinSyzMinGens -- minimal generators of syzygies of minimal generators
Mod -- See "Div, Mod"
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
N Top
NewId -- create a new identifier
NewList -- create a new list
NewMat -- create a new matrix
NewVector -- create a new vector
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, Den -- numerator, denominator
NumComps -- the number of components of a vector
NumIndets -- number of indeterminates
O Top
OpenIFile, OpenOFile -- open input or output file
OpenIString, OpenOString -- open input or output string
OpenLog, CloseLog -- open or close a log of a CoCoA session
OpenOFile -- See "OpenIFile, OpenOFile"
OpenOString -- See "OpenIString, OpenOString"
Option -- status of a panel option
Or -- See "Not, And, Or"
Ord -- matrix defining a term-ordering
P Top
Packages -- list of loaded packages
Panel -- print status of a panel's options
Panels -- list of CoCoA panels
Partitions -- partitions of an integer
Pfaffian -- the Pfaffian of a skew-symmetric matrix
PkgName -- returns the name of a package
Poincare, HilbertSeries -- the Poincare series
Poly -- convert an expression into a polynomial
PrimaryDecomposition -- primary decomposition of an ideal
Print On -- print to an output device
Print, PrintLn -- print the value of an expression
Product, Sum -- the product or sum of the elements of a list
Q Top
Quit -- quit CoCoA
QuotientBasis -- vector space basis for zero-dimensional quotient rings
QZP, ZPQ -- change field for polynomials and ideals
R Top
Radical -- radical of an ideal
RadicalOfUnmixed -- radical of an unmixed ideal
Rand -- random integer
Randomize, Randomized -- randomize the coefficients of a given polynomial
Rank -- rank of a module
RealRootRefine -- refine a root of a univariate polynomial over Q
RealRoots -- computes a root of a univariate polynomial over Q
Record -- create a record
ReducedGBasis -- compute a reduced Groebner basis
Remove -- See "Insert, Remove"
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
Ring -- returns the ring with a given name
RingEnv -- name of the current ring
RingEnvs -- names of all defined rings
RootBound -- bound on roots of a polynomial over Q
S Top
Saturation, HSaturation -- saturation of ideals
ScalarProduct -- scalar product
Seed -- seed for 'Rand'
SeparatorsOfPoints -- separators for affine points
SeparatorsOfProjectivePoints -- separators for projective points
Set -- remove duplicates from a list
Set, Unset -- set and unset panel options
Shape -- extended list of types involved in an expression
Size -- the amount of memory used by an object
Skip -- does nothing
Sort, Sorted -- sort a list
SortBy, SortedBy -- sort a list
Sorted -- See "Sort, Sorted"
SortedBy -- See "SortBy, SortedBy"
Source, << -- read commands from a file or device
Spaces -- return a string of spaces
Sprint -- convert to a string
StarPrint -- print polynomial with *'s for multiplications
Starting -- list functions starting with a given string
Submat -- submatrix
SubSet, IsSubset -- checks if the elements of one list are a subset of another
Subsets -- returns all sublists of a list
Subst -- substitute values for indeterminates
Sum -- See "Product, Sum"
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
T Top
Tag -- returns the tag string of an object
Tagged, Untagged, @ -- tag or untag 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
Toric.CheckInput -- check input to 'Toric'
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
U Top
Unset -- See "Set, Unset"
Untagged -- See "Tagged, Untagged, @"
Use -- command for making a ring active
Using -- perform commands in non-active ring
V Top
Var -- function calls by reference, other complex referencing
Vector -- create a vector
W Top
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
X Top
XelMat -- See "DegLexMat, DegRevLexMat, LexMat, XelMat"
Y Top
Z Top
ZPQ -- See "QZP, ZPQ"