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#1 2014-03-03 17:16:14

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
Posts: 15,759
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Optimising Ackermann Recursions

How can I have a method that calculates Ackermann Functions very fast?


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Humanity is still kept intact. It remains within.' -Alokananda

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#2 2014-03-04 05:10:02

bobbym
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From: Bumpkinland
Registered: 2009-04-12
Posts: 84,079

Re: Optimising Ackermann Recursions

Hi;

It would be extremely fast because the numbers grow very large, very quickly, so even with M you could only compute the first few.

For instance:


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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#3 2014-03-04 15:02:03

Agnishom
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From: The Complex Plane
Registered: 2011-01-29
Posts: 15,759
Website

Re: Optimising Ackermann Recursions

Suppose I am interested in the last 4 digits of A(4,4)?


'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'Humanity is still kept intact. It remains within.' -Alokananda

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#4 2014-03-04 16:13:50

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,114

Re: Optimising Ackermann Recursions

Then I'd either find a very fast and powerful computer or do a lot of number theory.


“Here lies the reader who will never open this book. He is forever dead.

“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#5 2014-03-04 16:14:52

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 84,079

Re: Optimising Ackermann Recursions

You can probably get the last 4 digits.


In mathematics, you don't understand things. You just get used to them.
I have the result, but I do not yet know how to get it.
All physicists, and a good many quite respectable mathematicians are contemptuous about proof.

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