File:CarmichaelLambda.svg

Original file(SVG file, nominally 575 × 431 pixels, file size: 232 KB)

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Description
Français : Graphe des 1000 premières valeurs de la fonction de Carmichael; en transparence les valeurs de la fonction phi d'Euler
English: PLot of the 1000 first values of the Carmichael's reduced totient function; in transparency values of Euler's phi function
Date
Source Own work
Author Proz
SVG development
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The SVG code is valid.
 
This vector image was created with Python.

Created with python 2.7.13, matplotlib 2.0.0, sympy 1.1:

from sympy import *
import matplotlib.pyplot as plt
nmin, nmax = 1, 1000
l = range(nmin,nmax)
plt.plot(l, [totient(n) for n in l], 'g.', alpha=0.2, markersize=4)
plt.plot(l, [reduced_totient(n) for n in l], 'b.', alpha=1, markersize=2)
plt.axis([nmin,nmax,nmin,nmax])
plt.xlabel('$n$', fontsize='x-large')
ax = plt.gca()
ax.xaxis.set_label_coords(1.03,0.03)
xticks = ax.xaxis.get_major_ticks()
xticks[0].label1.set_visible(False)
yticks = ax.yaxis.get_major_ticks()
yticks[0].label1.set_visible(False)
plt.figtext(0.2,0.8,'$\lambda(n)$', fontsize='x-large', color='b', alpha=1)
plt.figtext(0.2,0.74,'$\\varphi(n)$', fontsize='x-large', color='g', alpha=0.6)
plt.savefig('carmichaelLambda.svg')

See also : File:EulerPhi.svg

Licensing

I, the copyright holder of this work, hereby publish it under the following license:
Creative Commons CC-Zero This file is made available under the Creative Commons CC0 1.0 Universal Public Domain Dedication.
The person who associated a work with this deed has dedicated the work to the public domain by waiving all of their rights to the work worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law. You can copy, modify, distribute and perform the work, even for commercial purposes, all without asking permission.

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5 February 2018

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9158572d1efeb7ed37d6cdbe3aa9c78e49d6e52b

237,637 byte

431 pixel

575 pixel

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Date/TimeThumbnailDimensionsUserComment
current18:55, 5 February 2018Thumbnail for version as of 18:55, 5 February 2018575 × 431 (232 KB)Prozlarger font
18:31, 5 February 2018Thumbnail for version as of 18:31, 5 February 2018575 × 431 (232 KB)ProzUser created page with UploadWizard
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