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Timo Kuchheuser

Reason for difference between Nest and NestList

Timo Kuchheuser
Posted 1 year ago
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Hi!

Is there a reason that Nest[] applies a function n times but NestList[] applies a function 0 to n times?

Thank you!
POSTED BY: Timo Kuchheuser
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I was asking about the rational behind the decision to implement the parameter to both functions in different ways?!

There is no difference.

Can you show an example that demonstrates a difference?
POSTED BY: Szabolcs Horvát
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Look at it: NestList gives a list of the intermediate results, which may be useful for a bunch of reasons.

Nest[f, x, 3]
NestList[f, x, 3]
POSTED BY: Hans Dolhaine
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Mike Besso
Mike Besso
Posted 1 year ago

Great thinking Ahmed. That does make sense to me.
POSTED BY: Mike Besso
Answer

Hi Timo In my personal opinion, I think in Nest the user is only interested in the final answer and whether the step zero is included or not won't make a difference in the final result. However, in NestList, the user is interested to see all the steps of the operation so Wolfram staff thought that it would be useful to also include step zero in the list. Hope this makes sense to you.
POSTED BY: Ahmed Elbanna
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Mike Besso
Mike Besso
Posted 1 year ago

Timo:

That is a great question. But how is the implementation different? It seems to me they just described the function differently in the documentation.

But, I am still very new to all of this. I would really like to understand as well.

THANK YOU for the great question.
POSTED BY: Mike Besso
Answer

Hey Mike,

thank you for your answer! I think i phrased my question wrong.

I was asking about the rational behind the decision to implement the parameter to both functions in different ways?!

All the best, Timo
POSTED BY: Timo Kuchheuser
Answer
Mike Besso
Mike Besso
Posted 1 year ago

Timo:

From what I can tell, the documentation is perhaps a bit misleading one compared side by side.

Next[f, x, 0]

returns

x

While

Next[f, x, 1]

returns 

f[x]

So, I think Nest supports n = 0 and works as expected.

I hope that helps.

Have a great and safe rest of your weekend.
POSTED BY: Mike Besso
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