Jump to content

File:PlotDiscriminantsOfRealCubicFields.svg

Page contents not supported in other languages.
This is a file from the Wikimedia Commons
From Wikipedia, the free encyclopedia

Original file (SVG file, nominally 510 × 480 pixels, file size: 86 KB)

Summary

Description
English: Plot of the number of real cubic fields of bounded discriminant up to 106, and the asymptotic distribution. Black line is the first order term of the asymptotic, green line includes the second order term, and blue crosses are the exact counts. Data by Michel Olivier available at [1]. Asymptotics from Bhargava–Shankar–Tsimerman, "On the Davenport–Heilbronn theorem and second order terms", arXiv:1005.0672.
Date
Source Own work
Author RobHar
SVG development
InfoField
 
The SVG code is valid.
 
This chart was created with Gnuplot.
 
This chart uses translateable embedded text.
Source code
InfoField
Gnuplot code
set terminal svg enhanced fname "Helvetica" fsize 20
 set output "cubicreal.svg"
 
 #Axes
 set size square				#make the graph square
 set logscale				#loglog plot
 set xrange [ 100 : 1000000 ]		#adjust axis range
 set yrange [ 1 : 200000 ]
 set xlabel "Bound on Discriminant"
 set ylabel "Totally Real Cubic Fields"
 set xlabel 0.0, 0.5			#adjust positioning of axis label
 set ylabel -2.1, 0.0
 
 #tics
 set format "@{10}&{m}^{%L}"		#adjust format of tic labels
 set xtics offset 1.0,0.45 nomirror	#adjust placement of tic labels, and nomirror tics
 set ytics offset 3.0,0.0 nomirror
 set mxtics 10				#set number of minor tics
 set mytics 10
 
 set grid xtics ytics lt rgb "gray" lw 1	#set grid
 
 set style line 1 lt 3 pt 1 ps 0.9	#set marker style to blue cross, adjust size
 set style line 2 lt -1 lw 1		#set marker style to black line
 set style line 3 lt 2 lw 1		#set marker style to green thick line
 
 f(x) = 0.069325614381725*x - 0.147685261030334*(x**(0.83333333333333333))
 g(x) = 0.069325614381725*x
 
 plot "cubicrealdata" index 0 using 1:2 notitle with points linestyle 1 ,\
 	f(x) notitle with lines linestyle 3 ,\
 	g(x) notitle with lines linestyle 2

Licensing

Public domain I, the copyright holder of this work, release this work into the public domain. This applies worldwide.
In some countries this may not be legally possible; if so:
I grant anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law.

Captions

Add a one-line explanation of what this file represents

Items portrayed in this file

depicts

6 June 2010

File history

Click on a date/time to view the file as it appeared at that time.

Date/TimeThumbnailDimensionsUserComment
current19:36, 6 June 2010Thumbnail for version as of 19:36, 6 June 2010510 × 480 (86 KB)RobHarFrom original: add white background, manually add thin non-break space (&#8239), convert text to path, and move axis tick labels
19:21, 6 June 2010Thumbnail for version as of 19:21, 6 June 2010510 × 480 (86 KB)RobHarconvert text to path
18:58, 6 June 2010Thumbnail for version as of 18:58, 6 June 2010510 × 480 (22 KB)RobHaradd thin no-break space to exponents 2,3,4, and 5
18:55, 6 June 2010Thumbnail for version as of 18:55, 6 June 2010510 × 480 (22 KB)RobHaradd more non-breaking space
18:52, 6 June 2010Thumbnail for version as of 18:52, 6 June 2010510 × 480 (22 KB)RobHarAdd unicode 160 (non-break space) to superscripts to fix display problems
18:43, 6 June 2010Thumbnail for version as of 18:43, 6 June 2010510 × 480 (22 KB)RobHarAdd white background
18:31, 6 June 2010Thumbnail for version as of 18:31, 6 June 2010600 × 480 (16 KB)RobHar{{Information |Description={{en|1=Plot of the number of real cubic fields of bounded discriminant up to 10<sup>6</sup>, and the asymptotic distribution. Black line is the first order term of the asymptotic, green line includes the second order term, and b

The following page uses this file:

Metadata