File:EulerPhi.svg
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Size of this PNG preview of this SVG file: 731 × 551 pixels. Other resolutions: 319 × 240 pixels | 637 × 480 pixels | 1,019 × 768 pixels | 1,280 × 965 pixels | 2,560 × 1,930 pixels.
Original file (SVG file, nominally 731 × 551 pixels, file size: 232 KB)
Summary
| Description |
English: Plot of the first 1000 values of the en:Euler's totient function. Svg version of Image:EulerPhi.PNG
|
| Date | |
| Source |
Own work This W3C-unspecified plot was created with Matplotlib. |
| Author | Pietro Battiston (it:User:Toobaz) |
| Other versions | Image:EulerPhi.PNG |
Created with the following script, ran in "ipython -pylab":
xlabel('n')
ylabel('$\phi(n)$')
plot([None]+[fi(i) for i in range(1,1000)], 'b.')
"fi" is the Euler φ, defined for instance as:
def fattorizza(n):
c = 0
f = {}
for i in xrange( 2, int(sqrt(n))+1 ):
if not n%i:
f[i] = 1
n /= i
while not n%i:
f[i] += 1
vn = n
n /= i
if n == 1:
return f
f[n] = 1
return f
def fi(n):
if n == 1:
return 1
fi = 1
f = fattorizza(n)
for p in f:
k = f[p]
fi *= (p-1)*p**(k-1)
return fi
Licensing
I, the copyright holder of this work, hereby publish it under the following licenses:
|
Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled GNU Free Documentation License. |
This file is licensed under the Creative Commons Attribution-Share Alike 4.0 International, 3.0 Unported, 2.5 Generic, 2.0 Generic and 1.0 Generic license.
- You are free:
- to share – to copy, distribute and transmit the work
- to remix – to adapt the work
- Under the following conditions:
- attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
- share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.
You may select the license of your choice.
File history
Click on a date/time to view the file as it appeared at that time.
| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 17:07, 17 May 2012 | | 731 × 551 (232 KB) | wikimediacommons>Itzuvit | Reverted to version as of 09:29, 16 March 2010 |
File usage
The following page uses this file:
