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DOCUMENTATION CENTER SEARCH
New to
Mathematica
?
Find your learning path
»
Mathematica
>
Core Language
>
Functional Programming
>
Functional Iteration
>
Fold
>
Mathematica
>
Core Language
>
Procedural Programming
>
Looping Constructs
>
Functional Iteration
>
Fold
>
BUILT-IN MATHEMATICA SYMBOL
Applying Functions Repeatedly
Tutorials »
|
Nest
FoldList
ParallelCombine
See Also »
|
Functional Iteration
Functional Programming
Looping Constructs
Math & Counting Operations on Lists
More About »
Fold
Fold
gives the last element of
FoldList
.
MORE INFORMATION
You can use
Throw
to exit from
Fold
before it is finished.
EXAMPLES
CLOSE ALL
Basic Examples
(4)
In[1]:=
Out[1]=
In[1]:=
Out[1]=
In[1]:=
Out[1]=
In[1]:=
Out[1]=
Generalizations & Extensions
(3)
The head need not be
List
:
Use
Throw
to exit a
Fold
:
Fold to the right:
Applications
(9)
Create a nested polynomial (Horner form):
HornerForm
directly produces this output:
Form a continued fraction:
Form a number from digits:
Form an alternating sum:
Form a binary tree:
Form a left-branching binary tree:
Form a function composition:
Apply an indexed sequence of functions:
Successively partition a list:
Properties & Relations
(3)
Folding with an empty list does not apply the function at all:
Fold
returns the last element of
FoldList
:
Functions that ignore their second argument give the same result as in
Nest
:
Neat Examples
(3)
An explicit form of the primitive recursive function
[]:
Generate all subsets of a set:
Find all possible sums of any of the elements of a list of numbers:
The fourth Swinnerton-Dyer polynomial []:
SEE ALSO
Nest
FoldList
ParallelCombine
TUTORIALS
Applying Functions Repeatedly
MORE ABOUT
Functional Iteration
Functional Programming
Looping Constructs
Math & Counting Operations on Lists
RELATED LINKS
NKS|Online
(
A New Kind of Science
)
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