# Function -- the class of all functions

## Methods that use a function :

• "? Function" -- see ? Symbol -- view brief documentation of a symbol
• "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
• 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
• 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(HashTable,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
• "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
• "frames(Function)" -- see frames -- get the frames associated to a closure
• Function \ Set (missing documentation)
• Function Thing -- function application
• hashTable(Function,List) (missing documentation)
• /// 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 installAssignmentMethod -- install methods assignment to the value of an operator
• "installAssignmentMethod(Symbol,HashTable,HashTable,Function)" -- see installAssignmentMethod -- install methods assignment to the value of an operator
• "integrate(Function,Constant,Constant)" -- see integrate -- numerical integration
• "integrate(Function,Constant,InfiniteNumber)" -- see integrate -- numerical integration
• "integrate(Function,Constant,Number)" -- see integrate -- numerical integration
• "integrate(Function,InfiniteNumber,Constant)" -- see integrate -- numerical integration
• "integrate(Function,InfiniteNumber,InfiniteNumber)" -- see integrate -- numerical integration
• "integrate(Function,InfiniteNumber,Number)" -- see integrate -- numerical integration
• "integrate(Function,Number,Constant)" -- see integrate -- numerical integration
• "integrate(Function,Number,InfiniteNumber)" -- see integrate -- numerical integration
• "integrate(Function,Number,Number)" -- see integrate -- numerical integration
• "localDictionaries(Function)" -- see localDictionaries -- get local dictionaries
• "locate(Function)" -- see locate -- locate source code
• "new Manipulator from Function" -- see Manipulator -- the class of all file manipulators
• map(ChainComplex,ChainComplex,Function) -- make a map of chain complexes
• "map(GradedModule,GradedModule,Function)" -- see map(ChainComplex,ChainComplex,Function) -- make a map of chain complexes
• 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
• "options(Function)" -- see options(Command) -- get optional arguments and default values of functions and methods
• "package(Function)" -- see package -- get containing package
• "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
• "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
• "profile(String,Function)" -- see profile -- profile a function
• "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
• "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(HashTable,Function) -- select part of a hash table
• 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
• select(ZZ,HashTable,Function) -- select a limited number of pairs from a hash table
• Set / Function (missing documentation)
• sort(List,Function) (missing documentation)
• "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
• /// Function \\ Thing /// -- see Thing // Function -- apply a function
• Thing // Function -- apply a function
• "ultimate(Function,Thing)" -- see ultimate -- ultimate value for an iteration
• /// 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
• "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

## For the programmer

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