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Recursion in SMath - Can we use recursion in SMath? - Messaggi

#1 Pubblicato: 24/10/2023 13:28:09
Valery Ochkov

Valery Ochkov

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Can we use recursion in SMath?
Fibo.png
#2 Pubblicato: 24/10/2023 14:53:19
Gerry_Bush

Gerry_Bush

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Yes, recursion is possible. Although I don't remember how many levels are allowed.

Here is your example in an smath file.

Fibo_recursion_example.sm (3,56 KiB) scaricato 1511 volta(e).
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Valery Ochkov 24/10/2023 16:48:00
#3 Pubblicato: 24/10/2023 17:13:18
Valery Ochkov

Valery Ochkov

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Wrote

Yes, recursion is possible. Although I don't remember how many levels are allowed.

Here is your example in an smath file.

Fibo_recursion_example.sm (3,56 KiB) scaricato 1511 volta(e).



Thanks! But I think it was not from me but from SMath error!
And the second!
Why 0!=1?
See
Factorial.sm (4,45 KiB) scaricato 1497 volta(e).
Factorial.png
#4 Pubblicato: 24/10/2023 18:23:19
Gerry_Bush

Gerry_Bush

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Here is the corrected Fibo recursive function...

Fibo_recursion_corrected.sm (4,21 KiB) scaricato 1453 volta(e).

As for 0!=1 the following page gives two explanations.

https://zero-factorial.com/whatis.html
#5 Pubblicato: 24/10/2023 20:21:01
Gerry_Bush

Gerry_Bush

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Here is a more streamlined version...

Fibonacci function
1 utenti hanno apprezzato questo post
Valery Ochkov 24/10/2023 20:50:00
#6 Pubblicato: 24/10/2023 20:49:36
Valery Ochkov

Valery Ochkov

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Wrote

Here is a more streamlined version...

Fibonacci function



Thanks!
And what about
https://en.wikipedia.org/wiki/Ackermann_function
#7 Pubblicato: 24/10/2023 21:16:47
Gerry_Bush

Gerry_Bush

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This seems to work for the Ackermann function...

Ackermann Function

Ackermann function.sm (4,49 KiB) scaricato 1449 volta(e).
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Valery Ochkov 24/10/2023 22:08:00
#8 Pubblicato: 25/10/2023 20:32:50
Jean Giraud

Jean Giraud

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Wrote

Yes, recursion is possible. Although I don't remember how many levels are allowed.


Typical, factorial(n) command-line is limited ...factorial(40)
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Valery Ochkov 25/10/2023 20:46:00
#9 Pubblicato: 25/10/2023 21:08:48
Jean Giraud

Jean Giraud

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Wrote

Originally Posted by: Gerry_Bush [url=/forum/yaf_postsm82817_Recursion-in-SMath.aspx#post82817][/url]Yes, recursion is possible. Although I don't remember how many levels are allowed.
Typical, factorial(n) command-line is limited ...factorial(40)


By same token, Fibonacci(n) command-line upper limit
Fibonacci(1473) ... 1.9069*10^307 ... Windows limit.
1 utenti hanno apprezzato questo post
Valery Ochkov 26/10/2023 00:49:00
#10 Pubblicato: 25/10/2023 21:15:33
overlord

overlord

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Wrote

Yes, recursion is possible. Although I don't remember how many levels are allowed.


Recursion in SMath has a limit of 50.
After that, it won't calculate.

Regards

2023-10-25_17-01.png
2 utenti hanno apprezzato questo post
ioan92 25/10/2023 21:26:00, Valery Ochkov 25/10/2023 21:46:00
#11 Pubblicato: 25/10/2023 22:37:39
Alvaro

Alvaro

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Hi. In this post you can see how to handle recursive formulas for more than 50 calls, with a small function rec()

Clipboard01.png

and in this other you can see the relationship between recursive and iterative algorithms, remembering that SMath is optimized for iterative ones.

Clipboard02.png

Best regards.
Alvaro
4 utenti hanno apprezzato questo post
ioan92 26/10/2023 00:28:00, Valery Ochkov 25/10/2023 23:27:00, NDTM Amarasekera 25/10/2023 23:53:00, Oscar Campo 26/10/2023 16:39:00
#12 Pubblicato: 26/10/2023 00:33:28
Jean Giraud

Jean Giraud

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Wrote

Typical, factorial(n) command-line is limited ...factorial(40)


The vectorized version n 170 ... 7.2574*10^306

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Valery Ochkov 26/10/2023 00:49:00
#13 Pubblicato: 26/10/2023 02:00:47
Valery Ochkov

Valery Ochkov

67 apprezzamenti in 713 post.

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Gamma.png

#14 Pubblicato: 26/10/2023 02:02:25
overlord

overlord

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Your RAM and OS is the limit.

Regards

fib_fact.sm (11,01 KiB) scaricato 1491 volta(e).

2023-10-25_22-00.png
2 utenti hanno apprezzato questo post
Valery Ochkov 26/10/2023 02:39:00, Oscar Campo 26/10/2023 16:40:00
#15 Pubblicato: 26/10/2023 04:07:27
Jean Giraud

Jean Giraud

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Valery, Smath Gamma(x) is known 4 decimals.
Reported years ago, ignored.
Alvaro Gamma(x) 15 decimals
#16 Pubblicato: 26/10/2023 09:07:36
Alvaro

Alvaro

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Wrote

... And what about
https://en.wikipedia.org/wiki/Ackermann_function



Ackermann function is not 'primitive recursive', which means that it can't be computed only with for loops. Here an iterative implementation with a stack and no recursion.

Ackermann-Iterative.sm (8,7 KiB) scaricato 1432 volta(e).

Clipboard01.png

Best regards.
Alvaro.
2 utenti hanno apprezzato questo post
Valery Ochkov 26/10/2023 12:04:00, Oscar Campo 26/10/2023 16:41:00
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