CompiledFunctionClosure -- the class of all compiled function closures

Types of compiled function closure :

• MethodFunction -- a type of method function

Fixed objects of class CompiledFunctionClosure :

• abs -- absolute value function
• accumulate -- apply a binary operator repeatedly
• acos -- arccosine
• acosh -- inverse hyperbolic cosine
• acot -- compute the inverse cotangent
• acoth -- compute the hyperbolic arctangent of a number
• adjoint' -- see adjoint -- the tensor-Hom adjunction maps
• agm -- arithmetic-geometric mean
• all -- whether all elements satisfy a specified condition
• ambient -- ambient free module of a subquotient, or ambient ring
• antipode -- antipode for skew commuting polynomial rings
• apropos -- symbols matching a pattern
• arXiv -- link to an arXiv article
• asin -- arcsine
• asinh -- inverse hyperbolic sine
• assert -- check whether something is true, raise an error if not
• atan -- compute the arctangent of a number
• atan2 -- compute an angle of a certain triangle
• atanh -- compute the hyperbolic arctangent of a number
• autoload -- arrange for a function to be loaded automatically
• baseName -- the base name of a generator
• baseRing -- produce the ring from which a ring was formed
• BesselJ -- Bessel function of the first kind
• BesselY -- Bessel function of the second kind
• Beta -- Beta function
• between -- insert something between elements of a list
• binomial -- binomial coefficient
• borel -- see borel(Matrix) -- make a Borel fixed submodule
• ceiling -- ceiling function
• changeBase -- change integer base
• char -- computes the characteristic of the ring or field
• chi
• clean -- Set to zero elements that are approximately zero
• coefficient -- coefficient of a monomial
• coefficientRing -- get the coefficient ring
• coimage -- coimage of a map
• cokernel -- cokernel of a map of modules, graded modules, or chaincomplexes
• columnAdd -- add a multiple of one column to another
• columnMult -- multiply a column by a ring element
• columnPermute -- permute some columns
• columnRankProfile -- find the column rank profile of a mutable matrix
• columnSwap -- interchange columns
• commonRing -- find smallest containing ring
• comodule -- submodule to quotient module
• compareExchange -- compares and possibly exchanges the value of an atomic integer
• complement -- see complement(Matrix) -- find the minimal generators for cokernel of a matrix (low level form)
• complete
• components -- list the components of a direct sum
• compositions -- list the compositions of an integer
• compress -- extract nonzero columns from a matrix
• conductor -- the conductor of a finite ring map
• cone -- mapping cone or polyhedral cone
• conjugate -- complex conjugate
• content -- the content of a polynomial
• contract -- contract one matrix by another
• contract' -- see contract'(Matrix,Matrix) -- contract a matrix by a matrix, the dual notion
• cos -- compute the cosine
• cosh -- compute the hyperbolic cosine
• cot -- cotangent
• coth -- hyperbolic cotangent
• cover -- get the covering free module
• coverMap -- see coverMap(Module) -- the surjective map from a free module to a module corresponding to the generators
• csc -- cosecant
• csch -- hyperbolic cosecant
• debug -- open the private dictionary of a package
• default -- default member of a family
• degree
• degreeGroup (missing documentation)
• degreeLength -- the length of the degree vector
• degrees -- degrees of generators
• degreesMonoid -- see degreesRing -- the ring or monoid of degrees
• degreesRing -- the ring or monoid of degrees
• delete -- delete some elements of a list
• denominator -- denominator of a fraction
• depth -- depth of a net
• diagonalMatrix -- make a diagonal matrix
• diameter -- diameter of an interval
• dictionary -- determine the dictionary to which a symbol belongs
• diff -- differentiate or take difference
• diff' -- see diff'(Matrix,Matrix) -- differentiate a matrix by a matrix, the dual notion
• Digamma -- Digamma function
• dim -- compute the Krull dimension
• dismiss -- dismiss a package
• divideByVariable -- divide all columns by a (power of a) variable
• doc -- a simple documentation function
• multidoc -- see doc -- a simple documentation function
• eagonNorthcott -- see eagonNorthcott(Matrix) -- Eagon-Northcott complex of a matrix of linear forms
• effCone (missing documentation)
• effGenerators (missing documentation)
• eint -- exponential integral
• elements -- list of elements
• eliminate
• endPackage -- end a new package
• entries -- lists the entries of a matrix
• erf -- error function
• erfc -- complementary error function
• euler -- Euler characteristic
• eulers -- list the sectional Euler characteristics
• exchange -- exchange the value of an atomic integer
• exp -- exponential function
• expectedReesIdeal -- symmetric algebra ideal plus jacobian dual
• expm1 -- exponential minus 1
• exponents -- the exponents of a polynomial
• exportFrom -- export symbols from a package's private dictionary
• Fano -- Fano scheme
• findSynonyms -- see findSynonyms(Symbol) -- find synonyms of symbols
• fittingIdeal -- Fitting ideal of a module
• flip -- isomorphism map of commutativity of tensor product
• floor -- floor function
• fold -- apply a binary operator repeatedly
• formation -- recover the methods used to make a module
• frac -- construct a fraction field
• fraction
• fromDividedPowers -- Translates from divided power monomial basis to ordinary monomial basis
• Gamma -- Gamma function
• gbRemove -- remove Gröbner basis
• gbSnapshot -- the Gröbner basis matrix as so far computed
• gcdCoefficients -- gcd with coefficients
• genera -- list of the successive linear sectional arithmetic genera
• generateAssertions -- generate assert statements from experimental input
• generator -- provide a single generator
• genericMatrix -- make a generic matrix of variables
• genericSkewMatrix -- make a generic skew symmetric matrix of variables
• genericSymmetricMatrix -- make a generic symmetric matrix
• genus -- arithmetic genus
• getChangeMatrix -- get the change of basis matrix
• getWWW -- get a web page
• gramm (missing documentation)
• heft -- heft vector of ring or monoid
• height -- height of a net
• hilbertFunction -- the Hilbert function
• homogenize -- homogenize with respect to a variable
• homomorphism -- get the homomorphism from element of Hom
• httpHeaders -- see httpHeaders(String) -- prepend http headers to a string
• icFractions -- fractions integral over an affine domain
• icMap -- natural map from an affine domain into its integral closure
• icPIdeal -- compute the integral closure in prime characteristic of a principal ideal
• image -- image of a map
• imaginaryPart -- imaginary part
• importFrom -- import symbols to the current private dictionary
• index -- numeric index of a ring variable
• indices -- indices of a polynomial; also components for a direct sum
• inducesWellDefinedMap -- whether a map is well defined
• insert -- copy a list, inserting an element
• installAssignmentMethod -- install methods assignment to the value of an operator
• instances -- see instances(Type)
• integrate -- numerical integration
• inverse -- compute the inverse
• inverseErf -- inverse error function
• inverseRegularizedBeta -- inverse of the regularized beta function
• inverseRegularizedGamma -- inverse of the upper regularized gamma function
• irreducibleCharacteristicSeries -- irreducible characteristic series of an ideal
• irreducibleDecomposition -- express a monomial ideal as an intersection of irreducible monomial ideals
• isAffineRing -- whether something is an affine ring
• isBorel -- whether an ideal is fixed by upper triangular changes of coordinates
• isc -- ISC lookup
• isCommutative -- whether a ring is commutative
• isConstant -- whether a ring element is constant
• isDirectSum -- whether something is a direct sum
• isEmpty
• isField -- whether something is a field
• isFreeModule -- whether something is a free module
• isHomogeneous -- whether something is homogeneous (graded)
• isIdeal -- whether something is an ideal
• isInfinite -- whether a number is infinite
• isInjective -- whether a map is injective
• isIsomorphism -- whether a map is an isomorphism
• isLiftable (missing documentation)
• isMember -- test membership in a list or set
• isModule -- whether something is a module
• isMonomialIdeal -- whether something is a monomial ideal
• isNormal -- determine if a reduced ring is normal
• isPolynomialRing -- whether something is a polynomial ring
• isProjective (missing documentation)
• isQuotientModule -- whether something is evidently a quotient of a free module
• isQuotientOf -- whether one thing is a quotient of another
• isQuotientRing -- whether something is a quotient ring
• isReal -- whether a number is real
• isRing -- whether something is a ring
• isSkewCommutative -- whether a ring has skew commuting variables
• isSquareFree -- whether something is square free monomial ideal
• isStandardGradedPolynomialRing -- Checks whether a ring is a polynomial ring over a field with variables of degree 1
• isSubmodule -- whether a module is evidently a submodule of a free module
• isSubquotient -- see isSubquotient(Module,Module) -- check whether a module is a subquotient of another
• isSubset -- whether one object is a subset of another
• isSupportedInZeroLocus -- whether support of a module is contained in the zero locus of the (irrelevant) ideal
• isSurjective -- whether a map is surjective
• isUnit -- whether a ring element is a unit
• isWellDefined -- whether a map is well defined
• jacobian -- the Jacobian matrix of partial derivatives
• kernelOfLocalization -- the kernel of the localization map
• koszul -- Koszul complex or specific matrix in the Koszul complex
• leadCoefficient -- the coefficient of the leading term
• leadComponent -- the leading component(s) of a vector or matrix
• leadMonomial -- the leading monomial of a ring element
• leadTerm -- get the greatest term
• liftable -- whether lifting to another ring is possible
• listForm -- convert to list form
• listSymbols -- compact display of symbols and their values
• lngamma -- logarithm of the Gamma function
• log -- logarithm function
• log1p -- logarithm of 1+x
• LUdecomposition -- LU decomposition
• makeDirectory -- see makeDirectory(String) -- make a directory
• memoize -- record results of function evaluation for future use
• methodOptions -- see methodOptions(Function) -- recover the options used when a method function was created
• minimize
• module -- make or get a module
• monomialSubideal -- find the largest monomial ideal in an ideal
• multidegree -- multidegree
• multigraded -- convert a Betti tally into a multigraded Betti tally
• nefCone (missing documentation)
• nefGenerators (missing documentation)
• newCoordinateSystem -- change variables
• next -- get the next object from an iterator
• nextPrime -- compute the smallest prime greater than or equal to a given number
• norm
• nullhomotopy -- make a null homotopy
• nullSpace -- find the null space of a mutable matrix
• numColumns -- see numColumns(Matrix) -- number of columns in a matrix or mutable matrix
• numerator -- numerator of a fraction
• numeric -- convert to floating point
• numericInterval -- converts to an interval
• numgens -- the number of generators
• numRows -- see numRows(Matrix) -- number of rows in a matrix or mutable matrix
• ofClass -- English phrases for types
• packageTemplate -- a template for a package
• pad -- pad a string or net with spaces
• part -- select terms of a polynomial by degree(s) or weight(s)
• partition -- partition a set or list by values of a function
• partitions -- list the partitions of an integer
• parts -- display terms of a polynomial degree by degree
• pdim -- calculate the projective dimension
• peek' -- examine contents of an object
• permanents -- ideal generated by square permanents of a matrix
• permutations -- produce all permutations of a list
• pfaffians -- ideal generated by Pfaffians
• pivots -- see pivots(Matrix) -- list of pivot locations of a matrix
• installHilbertFunction -- see poincare -- assemble degrees of a ring, module, or ideal into a polynomial
• poincare -- assemble degrees of a ring, module, or ideal into a polynomial
• poincareN -- assemble degrees into polynomial
• poly -- see poly(String) -- make a polynomial using classic Macaulay syntax
• positions -- which elements of a list satisfy a condition
• precision
• preimage -- preimage of a map
• presentation -- presentation of a module or ring
• product
• profile -- profile a function
• Proj -- make a projective variety
• projectiveHilbertPolynomial -- Hilbert polynomial of projective space
• promote -- promote to another ring
• pseudoRemainder -- compute the pseudo-remainder
• pushout -- compute the pushout morphism
• QRDecomposition -- compute a QR decomposition of a real matrix
• quotient' -- matrix quotient (opposite)
• quotientRemainder -- matrix quotient and remainder
• quotientRemainder' -- matrix quotient and remainder (opposite)
• randomKRationalPoint -- Pick a random K rational point on the scheme X defined by I
• rank -- compute the rank
• rays -- 1-dimensional cones of a fan or polyhedral object
• realPart -- real part
• reducedRowEchelonForm -- compute the reduced row echelon form of a matrix or mutable matrix over a field
• reduceHilbert -- reduce a Hilbert series expression
• reductionNumber -- Reduction number of one ideal with respect to another
• registerFinalizer -- register a string that will be displayed when an object is garbage collected
• regularizedBeta -- regularized beta function
• regularizedGamma -- upper regularized gamma function
• relations -- the defining relations
• remainder -- matrix remainder
• remainder' -- matrix quotient and remainder (opposite)
• removeLowestDimension -- remove components of lowest dimension
• reshape -- reshape a matrix
• ring -- get the associated ring of an object
• rotate -- see rotate(ZZ,VisibleList) -- rotate a list
• round -- round a number
• rowAdd -- add a multiple of one row to another
• rowMult -- multiply a row by a ring element
• rowPermute -- permute some rows
• rowRankProfile -- find the row rank profile of a mutable matrix
• rowSwap -- interchange rows
• scanKeys -- apply a function to each key in a hash table or database
• scanLines -- apply a function to each line of a file
• scanValues -- apply a function to each value in a hash table or database
• schreyerOrder -- create or obtain free modules with Schreyer monomial orders
• searchPath -- see searchPath(List,String) -- search a path for a file
• sec -- secant
• sech -- hyperbolic secant
• selectInSubring -- select columns in a subring
• selectVariables -- see selectVariables(List,PolynomialRing) -- make a subring of a polynomial ring generated by selected variables
• setup
• setupEmacs
• sheaf -- make a coherent sheaf
• sheafMap (missing documentation)
• show -- display various objects in an external viewer
• sin -- compute the sine
• singularLocus -- singular locus
• sinh -- compute the hyperbolic sine
• size -- the size of an object
• someTerms -- select some terms of a polynomial
• source -- source of a map
• Spec -- make an affine variety
• splitWWW -- separate an http response into header and body
• sqrt -- square root function
• stacksProject -- link to a Stacks Project tag
• standardForm -- convert to standard form
• standardPairs -- find the standard pairs of a monomial ideal
• store -- store the value of an atomic integer
• sublists -- process interspersed subsequences of a visible list
• submatrix
• submatrix' -- exclude rows and/or columns of a matrix
• submatrixByDegrees -- submatrix consisting of rows and columns in an interval or box of degrees
• subquotient -- make a subquotient module
• subsets -- produce the subsets of a set or list
• substitute -- substituting values for variables
• sum -- compute the sum
• super -- get the ambient module
• support -- list of variables occurring in a polynomial or matrix
• switch -- copy a list, switching two elements
• sylvesterMatrix -- see sylvesterMatrix(RingElement,RingElement,RingElement)
• symmetricPower -- symmetric power
• tan -- compute the tangent
• tanh -- compute the hyperbolic tangent
• target -- target of a map
• tensorAssociativity -- associativity isomorphisms for tensor products
• terms -- provide a list of terms of a polynomial
• testHunekeQuestion -- tests a conjecture on integral closures strengthening the Eisenbud-Mazur conjecture
• tests -- locate a package's tests
• toDividedPowers -- Translates to divided power monomial basis from ordinary monomial basis
• toField -- see toField(Ring) -- declare that a ring is a field
• topCoefficients -- first variable and its coefficient of a polynomial or matrix
• topComponents -- compute top dimensional component of an ideal or module
• trace -- see trace(Matrix) -- trace of a matrix
• truncateOutput
• ultimate -- ultimate value for an iteration
• unbag -- see unbag(Bag)
• uniquePermutations -- produce all unique permutations of a list
• urlEncode -- URL encoding
• value -- evaluate
• variety -- get the variety
• vector -- make a vector
• versalEmbedding -- Compute a versal embedding
• wedgeProduct -- see wedgeProduct(ZZ,ZZ,Module) -- the exterior multiplication map
• weightRange -- the pair of lowest and highest weights of the monomials
• isWeylAlgebra -- see Weyl algebras
• whichGm -- Largest Gm satisfied by an ideal
• width -- width of a file or net
• wikipedia -- link to a Wikipedia article
• zeta -- Riemann zeta function

For the programmer

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