FunctionClosure -- the class of all function closures

Types of function closure :

• CacheFunction -- the class of cache functions
• Iterator -- class for iterators
• MethodFunctionBinary -- a type of method function
• MethodFunctionSingle -- a type of method function
• MethodFunctionWithOptions -- a type of method function

Fixed objects of class FunctionClosure :

• about -- search the documentation
• addEndFunction -- add an ending function
• addHook -- add a hook function to an object for later processing
• addStartFunction -- add a startup function
• adjoint -- the tensor-Hom adjunction maps
• analyticSpread -- Compute the analytic spread of a module or ideal
• ancestors -- the ancestors of something
• annihilator -- the annihilator ideal
• applicationDirectory -- the path to the user's application directory
• applyTable -- apply a function to each element of a table
• associatedPrimes -- find associated primes
• baseFilename -- the base part of a filename or path
• basis -- basis or generating set of all or part of a ring, ideal or module
• beginDocumentation -- start documentation section of a package
• benchmark -- accurate timing of execution
• betti -- display or modify a Betti diagram
• cacheValue -- cache values of functions in their arguments
• canonicalBundle (missing documentation)
• capture -- evaluate Macaulay2 code and capture the output
• centerString -- center a string or net
• chainComplex -- make a chain complex
• check -- perform tests of a package
• checkDegrees -- compares the degrees of generators of two modules
• code -- display source code
• codim -- compute the codimension
• coefficients -- monomials and their coefficients
• cohomology -- general cohomology functor
• columnate -- arrange strings in columns
• commonest -- the most common elements of a list or tally
• compose -- composition as a pairing on Hom-modules
• conwayPolynomial -- provide a Conway polynomial
• copyDirectory -- see copyDirectory(String,String)
• copyFile -- see copyFile(String,String)
• cotangentSheaf -- cotangent sheaf of a projective variety
• currentPosition -- the current position in the current source file
• decompose
• demark -- insert a string between elements of a list of strings
• describe -- real description
• determinant -- determinant of a matrix
• directSum -- direct sum of modules or maps
• discriminant -- see discriminant(RingElement,RingElement)
• distinguished -- Compute the distinguished subvarieties of a pullback, intersection or cone
• document -- create a documentation node
• makeDocumentTag -- see DocumentTag -- the class of all document tags
• dual -- dual module or map
• eigenvalues -- find eigenvalues of a matrix
• eigenvectors -- find eigenvectors of a matrix over RR or CC
• End -- module of endomorphisms
• error -- deliver error message
• even -- tell whether an integer is even
• EXAMPLE -- hypertext EXAMPLE item
• examples -- list the examples in documentation
• export -- export symbols from a package
• exportMutable -- export mutable symbols from a package
• expression -- convert to an expression
• extend -- extend a module map to a chain map, if possible
• exteriorPower -- exterior power
• factor -- factor a ring element or a ZZ-module
• fillMatrix -- fill a mutable matrix with random numbers
• findFiles -- find files recursively
• findHeft -- find a heft vector for a list of degrees
• findProgram -- load external program
• first -- first element of a list
• flatten -- flatten a nested list or a matrix
• flattenRing -- write a ring as a (quotient of a) polynomial ring
• forceGB -- declare that the columns of a matrix are a Gröbner basis
• format -- format a string or a real number
• fromDual -- Ideal from inverse system
• gb -- compute a Gröbner basis
• gcd -- greatest common divisor
• gcdLLL -- compute the gcd of integers, and small multipliers
• generators -- provide matrix or list of generators
• getNonUnit -- retrieve a previously discovered non-unit
• getPrimeWithRootOfUnity -- find a prime p with a primitive n-th root of unity r in ZZ/p
• getSymbol -- make a global user symbol from a string
• GF -- make a finite field
• globalAssign -- global assignment, in function form
• globalAssignFunction -- the standard method for the global assignment hook
• globalAssignment -- install standard global assignment method
• globalReleaseFunction -- the standard method for the global variable release hook
• gradedModule -- make a graded module
• gradedModuleMap -- make a map of graded modules
• graphIdeal -- see graphIdeal(RingMap) -- the ideal of the graph of the regular map corresponding to a ring map
• graphRing -- see graphRing(RingMap) -- the coordinate ring of the graph of the regular map corresponding to a ring map
• Grassmannian -- see Grassmannian(ZZ,ZZ) -- the Grassmannian of linear subspaces of a vector space
• groebnerBasis -- Gröbner basis, as a matrix
• hermite (missing documentation)
• hilbertPolynomial -- compute the Hilbert polynomial
• hilbertSeries -- compute the Hilbert series
• hold -- hold something in a holder expression
• Hom -- module of homomorphisms
• homology -- general homology functor
• homomorphism' -- get the element of Hom from a homomorphism
• hooks -- list hooks attached to a key
• html -- convert to HTML format
• hypertext -- prepare hypertext for display
• icFracP -- compute the integral closure in prime characteristic
• ideal -- make an ideal
• idealizer -- compute Hom(I,I) as a quotient ring
• independentSets -- some size-maximal independent subsets of variables modulo an ideal
• inducedMap -- compute an induced map
• info -- convert hypertext to info format
• input -- read Macaulay2 commands and echo
• installedPackages
• installPackage -- load and install a package and its documentation
• integralClosure -- integral closure of an ideal or a domain
• intersect -- compute an intersection
• intersectInP -- Compute distinguished varieties for an intersection in A^n or P^n
• intersection -- compute an intersection
• interval -- construct an interval
• inversePermutation -- inverse permutation
• inverseSystem -- Inverse systems with equivariance
• isFinitePrimeField -- whether a ring is a finite prime field
• isIsomorphic -- Probabilistic test for isomorphism of modules
• isLinearType -- Determine whether module has linear type
• isLLL -- is a basis an LLL basis?
• isPrimary -- determine whether a submodule is primary
• isPrime -- whether a integer or polynomial is prime
• isPrimitive -- whether an element is a primitive element of a finite field
• isPseudoprime -- see isPseudoprime(ZZ) -- whether an integer is probably prime
• isReduction -- Determine whether an ideal is a reduction
• isSorted -- whether a list is sorted
• isTable -- whether something is a list of lists of equal length
• iterator -- get an iterator
• jacobianDual -- Computes the 'jacobian dual', part of a method of finding generators for Rees Algebra ideals
• kernel -- kernel of a ringmap, matrix, or chain complex
• kernelLLL (missing documentation)
• last -- last element of a list
• lcm -- least common multiple
• length -- length of an object
• lift -- lift to another ring
• lines -- split a string into lines
• LLL -- compute an LLL basis
• load -- read Macaulay2 commands
• loadPackage -- load a package
• localize -- localize an ideal at a prime ideal
• locate -- locate source code
• makePackageIndex -- create an index of installed packages
• makeS2 -- compute the S2ification of a reduced ring
• map -- make a map
• markedGB -- see markedGB(Matrix,Matrix) -- make a marked Gröbner basis
• match -- regular expression matching
• mathML -- convert to MathML format
• matrix -- make a matrix
• max -- yields the maximum element in a list or sequence
• maxPosition -- position of the largest element
• memoizeClear -- see memoize -- record results of function evaluation for future use
• memoizeValues -- see memoize -- record results of function evaluation for future use
• method -- make a new method function
• methods -- list methods
• min -- yields the minimum element in a list or sequence
• mingens -- minimal generator matrix
• minimalBetti -- minimal betti numbers of (the minimal free resolution of) a homogeneous ideal or module
• minimalPresentation -- compute a minimal presentation
• minimalPrimes -- minimal primes of an ideal
• minimalReduction -- Find a minimal reduction of an ideal
• minors -- see minors(ZZ,Matrix) -- ideal generated by minors
• minPosition -- position of the smallest element
• mod -- reduce modulo an integer
• modulo -- see modulo(Matrix,Matrix) -- find the pre-image (pullback) of image of a map (low level version)
• monoid -- make or retrieve a monoid
• monomialCurveIdeal -- make the ideal of a monomial curve
• monomialIdeal -- make a monomial ideal
• monomials -- matrix of monomials in a ring element or matrix
• moveFile -- see moveFile(String,String)
• multiplicity -- Compute the Hilbert-Samuel multiplicity of an ideal
• mutableIdentity -- see mutableIdentity(Ring,ZZ) -- make a mutable identity matrix
• mutableMatrix -- make a mutable matrix
• needs -- read Macaulay2 commands if necessary
• needsPackage -- load a package if not already loaded
• net -- format for printing, as a net
• netList -- see netList(VisibleList) -- a table of boxes
• newPackage -- the preamble of a package
• newRing -- make a copy of a ring, with some features changed
• normalCone -- The normal cone of a subscheme
• notImplemented -- print an 'not implemented' error message
• number -- count how many elements of a list satisfy a condition
• odd -- tell whether an integer is odd
• oeis -- OEIS lookup
• on -- trace a function each time it's run
• options -- get options
• package -- get containing package
• pager -- display with paging
• peek -- examine contents of an object
• polarize -- given a monomial ideal, computes the squarefree monomial ideal obtained via polarization
• position -- the first element of a list satisfying a condition
• pretty -- a pretty printer
• primaryComponent -- find a primary component corresponding to an associated prime
• primaryDecomposition -- irredundant primary decomposition of an ideal
• print -- print something
• printerr -- print something to stderr
• prune -- prune, e.g., compute a minimal presentation
• pullback -- compute the pullback morphism
• pushForward -- see pushForward(RingMap,Module)
• quotient -- quotient or division
• radical -- the radical of an ideal
• radicalContainment -- whether an element is contained in the radical of an ideal
• random -- get a random object
• randomMutableMatrix -- see randomMutableMatrix(ZZ,ZZ,RR,ZZ) -- a random mutable matrix of integers
• readPackage -- read the package preamble
• reesAlgebra -- Compute the defining ideal of the Rees Algebra
• reesIdeal -- Compute the defining ideal of the Rees Algebra
• regex -- evaluate a regular expression search
• regexQuote -- escape special characters in regular expressions
• regSeqInIdeal -- a regular sequence contained in an ideal
• regularity -- compute the Castelnuovo-Mumford regularity
• replace -- replacement in strings and lists
• resolution -- projective resolution
• resultant -- see resultant(RingElement,RingElement,RingElement)
• ringFromFractions -- find presentation for f.g. ring
• roots -- see roots(RingElement) -- compute the roots of a polynomial
• rsort -- sort a list or matrix in reverse order
• runHooks -- run the hook functions stored in an object
• runLengthEncode -- see runLengthEncode(VisibleList) -- run length encoding
• runProgram -- run an external program
• same -- whether everything in a list is the same
• saturate -- saturation of ideal or submodule
• Schubert -- see Schubert(ZZ,ZZ,VisibleList) -- find the Plücker ideal of a Schubert variety
• seeParsing -- display parsing precedence table for Macaulay2 operators
• select -- select from a list, hash table, or string
• separate -- split a string into substrings using a regular expression
• separateRegexp -- see separate -- split a string into substrings using a regular expression
• setRandomSeed -- set starting point for random number generator
• sheafHom -- sheaf Hom
• showHtml -- see show -- display various objects in an external viewer
• showTex -- see show -- display various objects in an external viewer
• simpleDocFrob -- a sample documentation node
• smithNormalForm -- see smithNormalForm(Matrix) -- smith normal form for a matrix over ZZ or a PID
• solve -- solve linear equation(s)
• sort -- sort a list or columns of a matrix
• sortColumns -- permutation giving sort order
• span -- construct smallest interval
• specialFiber -- Special fiber of a blowup
• specialFiberIdeal -- Special fiber of a blowup
• stashValue -- stash values of functions in their arguments
• status -- status of a resolution computation
• subtable -- extract a subtable from a table
• SVD -- singular value decomposition of a matrix
• symlinkDirectory -- see symlinkDirectory(String,String) -- make symbolic links for all files in a directory tree
• symmetricAlgebra -- the symmetric algebra of a module
• symmetricAlgebraIdeal -- Ideal of the symmetric algebra of an ideal or module
• symmetricKernel -- Compute the Rees ring of the image of a matrix
• synonym -- synonym for members of a class
• SYNOPSIS -- a standardized synopsis for use in documentation nodes
• syz -- the syzygy matrix
• syzygyScheme -- construct a syzygy scheme
• table -- make a table from a binary function
• tangentCone -- see tangentCone(Ideal)
• tangentSheaf -- tangent sheaf of a projective variety
• temporaryFileName -- make a temporary file name
• tensor -- tensor product
• TEST -- add a test for a package
• tex -- convert to $\TeX$ format
• texMath -- convert to TeX math format
• toAbsolutePath -- the absolute path version of a file name
• toDual -- finds the inverse system to an ideal up to a given degree
• toExternalString -- convert to a readable string
• toList -- create a list
• toLower -- convert to lower case
• toString -- convert to a string
• toUpper -- convert to upper case
• transpose -- transpose a table or a matrix
• trim -- minimize generators and relations
• truncate
• tutorial -- convert documentation from tutorial format
• undocumented -- declare that something need not be documented
• uniform -- whether all elements of a list are the same class
• uninstallAllPackages
• uninstallPackage -- uninstall a package and remove its documentation
• unique -- eliminate duplicates from a list
• use -- install or activate object
• userSymbols -- a list of the user's symbols
• vars -- variables
• zero -- whether something is zero

For the programmer

The object FunctionClosure is a type, with ancestor classes Function < Thing.