CoCoA-5.1.5 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 [OBSOLESCENT] -- 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 AreGensMonomial -- checks if given gens are monomial AreGensSqFreeMonomial -- checks if given gens are squarefree monomial 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 CallOnGroebnerFanIdeals -- apply a function to Groebner fan ideals 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 poly wrt indet or 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 ElimHomogMat -- matrix for elimination ordering 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 exit -- quit CoCoA 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 FrobeniusMat -- compute a matrix of the Frobenius Map 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 GFanContainsPositiveVector -- ... GFanGeneratorsOfLinealitySpace -- ... GFanGeneratorsOfSpan -- ... GFanGetAmbientDimension -- ... GFanGetCodimension -- ... GFanGetDimension -- ... GFanGetDimensionOfLinealitySpace -- ... GFanGetFacets -- ... GFanGetImpliedEquations -- ... GFanGetUniquePoint -- ... GFanRelativeInteriorPoints -- relative interior point of a cone gin -- generic initial ideal GradingDim -- Number of components in weighted degree GradingMat -- matrix of generalized weights for indeterminates GraverBasis -- Graver basis GroebnerFanIdeals -- all reduced Groebner bases of an ideal

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H

 HasGBasis -- checks if the argument has a pre-computed GBasis 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 [OBSOLESCENT] -- [OBSOLESCENT] renamed to ElimHomogMat 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 IsInteger -- check if a RINGELEM is integer 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 IsRadical -- check if an IDEAL is radical IsRational -- check if a RINGELEM is rational IsSqFree -- check if an INT or RINGELEM is square-free 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 HilbertFn as I LF -- the leading form of a polynomial or an ideal LinearSimplify -- simplifying linear substitution for a univariate poly 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 MinPolyModular -- minimal polynomial with modular method MinPolyQuotDef, MinPolyQuotElim, MinPolyQuotMat -- compute a minimal polynomial 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 MultiplicationMat -- the multiplication matrix of a ringelem 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 QQEmbeddingHom -- returns the homomorphism QQ --> R 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 RandomUnimodularMat -- random unimodular matrix 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 -- approximations to the real roots of a univariate poly 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 -- Stanley-Reisner ideal, AlexanderDual complex, ideal of top simplices 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 StagedTrees -- staged trees from Statistics StarPrint, StarSprint -- print polynomial with *'s for multiplications starting -- list functions starting with a given string StdBasis -- Standard basis 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 SymmetricPolys -- list of symmetric polynomials 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 Tutorial -- Tutorial Tutorial: manual -- Tutorial-1 type -- the data type of an expression

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U

 UnivariateIndetIndex -- the index of the indeterminate of a univariate polynomial UniversalGBasis -- 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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