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Function -- the class of all functions
See also
using functions
using functions with optional inputs
making functions
local variables in a function
making functions with a variable number of arguments
making functions with multiple return values
making new functions with optional arguments
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
profile(Function)
-- see
profile
-- profile 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
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
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 \ 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,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(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
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
profile(String,Function)
-- see
profile
-- profile a function
rsort(List,Function)
(missing documentation)
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
selectValues(HashTable,Function)
-- see
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
selectValues(ZZ,HashTable,Function)
-- see
select(ZZ,HashTable,Function)
-- select a limited number of pairs from a hash table
select(Set,Function)
-- see
select(ZZ,Set,Function)
-- select a part of a set
select(ZZ,Set,Function)
-- select a part of a set
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(HashTable,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
Set / Function
(missing documentation)
setupLift(Function,Ring,Ring)
-- see
setupLift
-- set up lift from one ring to another
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
.