Built-in Mathematica Symbol

FoldList

FoldList[f, x, {a, b, ...}]
gives {x, f[x, a], f[f[x, a], b], ...}.

MORE INFORMATION

FoldList[Plus, 0, list] generates cumulative sums of the elements in list.

With a length n list, FoldList generates a list of length . »

The head of list in FoldList[f, x, list] need not be List.

EXAMPLES

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Basic Examples (3)

Cumulative sums of the elements of the list:

Cumulative powers:

In[1]:=

Out[1]=

Cumulative sums of the elements of the list:

Cumulative powers:

Generalizations & Extensions (2)

The head need not be List:

Fold to the right:

Applications (15)

Compute successive factorials:

Compute products of successive primes:

Cumulative sums:

Build up a continued fraction:

Build up a nested polynomial (Horner form):

Build up a number from digits:

Form alternating sums:

Generate a random walk:

Find the running maximum of a list:

Find successively deeper parts in an expression:

Successively append to a list:

Build up a binary tree:

Build up a left-branching binary tree:

Make function compositions:

Compute a power using a power tree with successive squaring:

Properties & Relations (5)

FoldList makes a list of length

:

Rest gives a result of length

:

Folding with an empty list does not apply the function at all:

Fold gives the last element of FoldList:

Functions that ignore their second argument give the same result as in NestList:

Accumulate is equivalent to FoldList with Plus:

Neat Examples (1)

Compute the minimum number of coins of different value needed to make up an amount

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