Number Theory

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Number Theory

Postby oliver » Sat Mar 26, 2011 4:12 am

The beginnings of a folder containing functions used in Number Theory.

p
Computes the number of partitions of n. (See http://en.wikipedia.org/wiki/Partition_(number_theory).)
A BigInt result is returned. Be prepared for long compute times if you get into 4-digit integers as your input.
This is a JavaScript adaptation of original Java code copyrighted 2002 by Henry Bottomley (http://www.btinternet.com/~se16/js/partitions.htm)
Can someone implement the new (2011) method by Ken Ono et al.? (http://esciencecommons.blogspot.com/2011/01/new-theories-reveal-nature-of-numbers.html)

Examples:
p(4) = 5
p(100) = 190569292
oliver
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Added ϕ

Postby oliver » Mon Jul 18, 2011 5:37 pm

Added ϕ, Euler's totient (phi) function.
http://en.wikipedia.org/wiki/Euler%27s_totient_function

Example:
ϕ(88) = 40

(There's a built-in function, phi, which does the same and is faster.)
oliver
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Re: Number Theory

Postby oliver » Mon Oct 21, 2013 10:14 pm

Added plot μ in addition to plot ϕ (which was added silently some time ago).
These functions use the functions integers and points from the Plot folder, so you need to have that one downloaded.

The moebius function itself is new in v1.5 (Integer menu) and is one of the most advanced functions ND1 offers.
If you're interested: [url]http://en.wikipedia.org/wiki/Möbius_function[/url]
oliver
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