SequenceFold
SequenceFold [f,{x1,…,xn},{a1,a2,…}]
gives the last element of SequenceFoldList [f,{x1,…,xn},{a1,a2,…}].
SequenceFold [f,{x1,…,xn},{a1,a2,…},k]
applies f to k arguments at each step, with the first n coming from the xi or previous results, and the last k-n coming from the ai.
Details
- In SequenceFold [f,{x1,…,xn},{a1,a2,…}], the function f is assumed to have n+1 arguments.
- SequenceFold [f,{x},{a1,a2,…}] is equivalent to Fold [f,x,{a1,a2,…}].
- SequenceFold [f,{x1,…,xn},{a1,a2,…}] is equivalent to SequenceFold [f,{x1,…,xn},{a1,a2,…},n+1].
- In SequenceFold [f,{x1,…,xn},{a1,a2,…},k], the integer k must obey k≥n.
Examples
open allclose allBasic Examples (2)
Scope (2)
Take one element from the list in the third argument in each iteration:
Take several elements from the list in the third argument in each iteration:
Properties & Relations (5)
SequenceFold [f,xlist,alist] returns the last element of SequenceFoldList [f,xlist,alist]:
Starting with a seed sequence of length 1 makes SequenceFold equivalent to Fold :
An empty seed sequence makes SequenceFold apply the function to the last element of the final list:
If f has only one argument, then SequenceFold is equivalent to Nest :
The number of arguments of the function cannot be smaller than the length of the seed sequence:
If they are equal, then the actual elements of the list in the third argument are not used:
Possible Issues (1)
This case is not well defined, and hence it is left unevaluated:
See Also
Related Guides
History
Text
Wolfram Research (2015), SequenceFold, Wolfram Language function, https://reference.wolfram.com/language/ref/SequenceFold.html.
CMS
Wolfram Language. 2015. "SequenceFold." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/SequenceFold.html.
APA
Wolfram Language. (2015). SequenceFold. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/SequenceFold.html
BibTeX
@misc{reference.wolfram_2025_sequencefold, author="Wolfram Research", title="{SequenceFold}", year="2015", howpublished="\url{https://reference.wolfram.com/language/ref/SequenceFold.html}", note=[Accessed: 10-April-2025 ]}
BibLaTeX
@online{reference.wolfram_2025_sequencefold, organization={Wolfram Research}, title={SequenceFold}, year={2015}, url={https://reference.wolfram.com/language/ref/SequenceFold.html}, note=[Accessed: 10-April-2025 ]}