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 |
Shortcuts -- Special characters equivalent to commands
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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 |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
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 |
jacobian -- the Jacobian of a list of polynomials
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ker -- Kernel of a K-algebra homomorphism
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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 |
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 |
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 |
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 |
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 |
quit -- quit CoCoA
QuotientBasis -- vector space basis for zero-dimensional quotient rings QZP -- change field for polynomials and ideals |
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 |
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 |
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 |
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 |
ref -- function calls by reference
Vector -- create a vector |
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 |
XelMat -- matrices for std. term-orderings
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ZPQ -- change field for polynomials and ideals
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