Function -- the class of all functions

Types of function:

• CompiledFunction -- the class of all compiled functions
• CompiledFunctionClosure -- the class of all compiled function closures
• FunctionClosure -- the class of all function closures

Functions and methods returning a function:

• Function @@ Function -- composition of functions
• Function _ Thing -- attach the first argument to a function of two or more arguments
• Boolean >> Function -- see OptionTable >> Function -- attaching options to a function
• List >> Function -- see OptionTable >> Function -- attaching options to a function
• OptionTable >> Function -- attaching options to a function

Methods that use a function:

• ? Function -- see ? Symbol -- view brief documentation of a symbol
• about(Function) -- see about -- search the documentation
• accumulate(Function,Thing) -- see accumulate -- apply a binary operator repeatedly
• accumulate(Function,Thing,Thing) -- see accumulate -- apply a binary operator repeatedly
• accumulate(Function,Thing,VisibleList) -- see accumulate -- apply a binary operator repeatedly
• accumulate(Function,VisibleList) -- see accumulate -- apply a binary operator repeatedly
• accumulate(VisibleList,Function) -- see accumulate -- apply a binary operator repeatedly
• accumulate(VisibleList,Thing,Function) -- see accumulate -- apply a binary operator repeatedly
• addHook(MutableHashTable,Thing,Function) -- see addHook -- add a hook function to an object for later processing
• addHook(Sequence,Function) -- see addHook -- add a hook function to an object for later processing
• addHook(Symbol,Function) -- see addHook -- add a hook function to an object for later processing
• all(BasicList,BasicList,Function) -- whether all corresponding elements of a pair of lists satisfy a condition
• all(BasicList,Function) -- whether all elements of a list satisfy a specified condition
• all(ZZ,Function) -- see all(BasicList,Function) -- whether all elements of a list satisfy a specified condition
• all(HashTable,Function) -- whether all key/value pairs in a hash table satisfy a specified condition
• Function and Function -- see and -- conjunction
• any(BasicList,BasicList,Function) -- whether any corresponding elements of a pair of lists satisfy a condition
• any(BasicList,Function) -- whether any elements of a list satisfy a specified condition
• any(ZZ,Function) -- see any(BasicList,Function) -- whether any elements of a list satisfy a specified condition
• any(HashTable,Function) -- whether all key/value pairs in a hash table satisfy a specified condition
• apply(BasicList,BasicList,Function) -- apply a function to pairs of elements, one from each list
• apply(BasicList,String,Function) -- see apply(BasicList,BasicList,Function) -- apply a function to pairs of elements, one from each list
• apply(String,BasicList,Function) -- see apply(BasicList,BasicList,Function) -- apply a function to pairs of elements, one from each list
• apply(String,String,Function) -- see apply(BasicList,BasicList,Function) -- apply a function to pairs of elements, one from each list
• apply(BasicList,Function) -- apply a function to each element of a list
• apply(String,Function) -- see apply(BasicList,Function) -- apply a function to each element of a list
• apply(Thing,Function) -- apply a function to an object with an iterator
• apply(ZZ,Function) -- apply a function to {0,..., n-1}
• applyKeys(HashTable,Function) -- see applyKeys -- apply a function to each key in a hash table
• applyKeys(HashTable,Function,Function) -- see applyKeys -- apply a function to each key in a hash table
• applyPairs(BasicList,Function) -- see applyPairs -- apply a function to each pair in a hash table
• applyPairs(Dictionary,Function) -- see applyPairs -- apply a function to each pair in a hash table
• applyPairs(HashTable,Function) -- see applyPairs -- apply a function to each pair in a hash table
• applyPairs(Thing,Function) -- see applyPairs -- apply a function to each pair in a hash table
• applyValues(HashTable,Function) -- see applyValues -- apply a function to each value in a hash table
• code(Function) -- see code -- display source code
• createTask(Function) -- see createTask -- create a task
• createTask(Function,Thing) -- see createTask -- create a task
• fold(Function,Thing) -- see fold -- apply a binary operator repeatedly
• fold(Function,Thing,Thing) -- see fold -- apply a binary operator repeatedly
• fold(Function,VisibleList) -- see fold -- apply a binary operator repeatedly
• fold(VisibleList,Function) -- see fold -- apply a binary operator repeatedly
• fold(VisibleList,Thing,Function) -- see fold -- apply a binary operator repeatedly
• Function Thing -- function application
• hashTable(Function,BasicList) -- see hashTable -- make a hash table
• Function \ Ideal -- see Ideal / Function -- apply a function to generators of an ideal
• Ideal / Function -- apply a function to generators of an ideal
• installAssignmentMethod(Symbol,HashTable,Function) -- see installing assignment methods -- install methods assignment to the value of an operator
• installAssignmentMethod(Symbol,HashTable,HashTable,Function) -- see installing assignment methods -- install methods assignment to the value of an operator
• integrate(Function,InfiniteNumber,InfiniteNumber) -- see integrate -- numerical integration
• integrate(Function,InfiniteNumber,Number) -- see integrate -- numerical integration
• integrate(Function,Number,InfiniteNumber) -- see integrate -- numerical integration
• integrate(Function,Number,Number) -- see integrate -- numerical integration
• locate(Function) -- see locate -- locate source code
• new Manipulator from Function -- see Manipulator -- the class of all file manipulators
• map(Module,Module,Function) -- create a matrix by specifying a function that gives each entry
• map(Module,ZZ,Function) -- create a matrix from a free module by specifying a function that gives each entry
• memoize(Function) -- see memoize -- record results of function evaluation for future use
• memoize(Function,List) -- see memoize -- record results of function evaluation for future use
• merge(HashTable,HashTable,Function) -- see merge -- merge two hash tables
• mergePairs(BasicList,BasicList,Function) -- see mergePairs -- merge sorted lists of pairs
• methodOptions(Function) -- recover the options used when a method function was created
• not Function (missing documentation)
• options(Function) -- get the optional arguments and default values of a function or method
• Function or Function -- see or -- disjunction
• package(Function) -- see package -- get containing package
• parallelApply(BasicList,Function) -- see parallelApply -- apply a function to each element in parallel
• partition(Function,VirtualTally) -- see partition -- partition a set or list by values of a function
• partition(Function,VirtualTally,VisibleList) -- see partition -- partition a set or list by values of a function
• partition(Function,VisibleList) -- see partition -- partition a set or list by values of a function
• partition(Function,VisibleList,VisibleList) -- see partition -- partition a set or list by values of a function
• position(VisibleList,Function) -- see position -- the first element of a list satisfying a condition
• position(VisibleList,VisibleList,Function) -- see position -- the first element of a list satisfying a condition
• position(ZZ,Function) -- see position -- the first element of a list satisfying a condition
• positions(MutableList,Function) -- see positions -- which elements of a list satisfy a condition
• positions(VisibleList,Function) -- see positions -- which elements of a list satisfy a condition
• product(VisibleList,Function) -- product of values of a function
• product(VisibleList,VisibleList,Function) -- product of results of applying a function pairwise
• product(ZZ,Function) -- product of consecutive values of a function
• rsort(List,Function) -- see rsort -- sort a list or matrix in reverse order
• scan(BasicList,BasicList,Function) -- see scan -- apply a function to each element in a list or sequence
• scan(BasicList,Function) -- see scan -- apply a function to each element in a list or sequence
• scan(Thing,Function) -- see scan -- apply a function to each element in a list or sequence
• scan(ZZ,Function) -- see scan -- apply a function to each element in a list or sequence
• scanKeys(Database,Function) -- see scanKeys -- apply a function to each key in a hash table or database
• scanKeys(HashTable,Function) -- see scanKeys -- apply a function to each key in a hash table or database
• scanLines(Function,List) -- see scanLines -- apply a function to each line of a file
• scanLines(Function,String) -- see scanLines -- apply a function to each line of a file
• scanPairs(HashTable,Function) -- see scanPairs -- apply a function to the pairs in a hash table
• scanPairs(Thing,Function) -- see scanPairs -- apply a function to the pairs in a hash table
• scanValues(HashTable,Function) -- see scanValues -- apply a function to each value in a hash table or database
• schedule(Function) -- see schedule -- schedule a task for execution
• schedule(Function,Thing) -- see schedule -- schedule a task for execution
• select(BasicList,Function) -- select elements from a list
• select(Set,Function) -- select a part of a set
• select(ZZ,Set,Function) -- see select(Set,Function) -- select a part of a set
• select(Thing,Function) -- select elements from an object with an iterator
• select(ZZ,BasicList,Function) -- select a limited number of elements from a list
• select(ZZ,Function) -- select integers
• selectKeys(HashTable,Function) -- see selectKeys -- select a part of a hash table by keys
• selectKeys(ZZ,HashTable,Function) -- see selectKeys -- select a part of a hash table by keys
• selectPairs(BasicList,Function) -- see selectPairs -- select a part of a hash table by pairs
• selectPairs(HashTable,Function) -- see selectPairs -- select a part of a hash table by pairs
• selectPairs(ZZ,BasicList,Function) -- see selectPairs -- select a part of a hash table by pairs
• selectPairs(ZZ,HashTable,Function) -- see selectPairs -- select a part of a hash table by pairs
• select(HashTable,Function) -- see selectValues -- select part of a hash table by values
• select(ZZ,HashTable,Function) -- see selectValues -- select part of a hash table by values
• selectValues(HashTable,Function) -- see selectValues -- select part of a hash table by values
• selectValues(ZZ,HashTable,Function) -- see selectValues -- select part of a hash table by values
• setupLift(Function,Ring,Ring) -- see setupLift -- set up lift from one ring to another
• sort(List,Function) -- see sort(List) -- sort a list
• sublists(VisibleList,Function) -- see sublists -- process interspersed subsequences of a visible list
• sublists(VisibleList,Function,Function) -- see sublists -- process interspersed subsequences of a visible list
• sublists(VisibleList,Function,Function,Function) -- see sublists -- process interspersed subsequences of a visible list
• sublists(VisibleList,Function,Function,Nothing) -- see sublists -- process interspersed subsequences of a visible list
• sublists(VisibleList,Function,Nothing) -- see sublists -- process interspersed subsequences of a visible list
• sublists(VisibleList,Function,Nothing,Function) -- see sublists -- process interspersed subsequences of a visible list
• sublists(VisibleList,Function,Nothing,Nothing) -- see sublists -- process interspersed subsequences of a visible list
• sum(VisibleList,Function) -- sum results of applying a function
• sum(VisibleList,VisibleList,Function) -- sum results of applying a function pairwise
• sum(ZZ,Function) -- sum consecutive values of a function
• ultimate(Function,Thing) -- see ultimate -- ultimate value for an iteration
• Function \ Set -- see VisibleList / Function -- apply a function to elements of a list
• Function \ String -- see VisibleList / Function -- apply a function to elements of a list
• Function \ VirtualTally -- see VisibleList / Function -- apply a function to elements of a list
• Function \ VisibleList -- see VisibleList / Function -- apply a function to elements of a list
• List / Function -- see VisibleList / Function -- apply a function to elements of a list
• Set / Function -- see VisibleList / Function -- apply a function to elements of a list
• String / Function -- see VisibleList / Function -- apply a function to elements of a list
• VirtualTally / Function -- see VisibleList / Function -- apply a function to elements of a list
• VisibleList / Function -- apply a function to elements of a list
• Function \\ Thing -- see VisibleList // Function -- apply a function
• Thing // Function -- see VisibleList // Function -- apply a function
• VisibleList // Function -- apply a function
• Function xor Function -- see xor -- exclusive disjunction

For the programmer

The object Function is a type, with ancestor class Thing.

The source of this document is in Macaulay2Doc/ov_methods.m2:283:0.