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Summary

Description Plot of the number of quartic fields of bounded discriminant up to 107, and the asymptotic distribution. Data from Cohen, Diaz y Diaz, and Olivier, Constructing Complete Tables of Quartic Fields using Kummer Theory, Math. Comp. 2003. Asymptotic from Bhargava, "The Density of Discriminants of Quartic Rings and Fields", Ann. Math. 2005.
Date
Source Own work
Author RobHar
Permission
(Reusing this file)
Public Domain
SVG development
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This chart was created with Gnuplot.
 
This chart uses translateable embedded text.
Source code
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Gnuplot code
set terminal svg enhanced fname "Helvetica" fsize 20
 set output "quartic.svg"
 
 #Axes
 set size square				#make the graph square
 set logscale				#loglog plot
 set xrange [ 100 : 10000000 ]		#adjust axis range
 set yrange [ 10 : 10000000 ]
 set xlabel "Bound on Discriminant"
 set ylabel "Quartic Number 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 2		#set marker style to black thick line
 
 plot "quarticdata" index 0 using 1:2 notitle with points linestyle 1 ,\
 	"quarticdata" index 1 using 1:2 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.

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25 November 2007

File history

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Date/TimeThumbnailDimensionsUserComment
current16:03, 5 August 2009Thumbnail for version as of 16:03, 5 August 2009600 × 480 (84 KB)RobHarCrossing fingers that this will work.
16:00, 5 August 2009Thumbnail for version as of 16:00, 5 August 2009600 × 480 (85 KB)RobHarDisplay problems keep changing. Try again.
15:52, 5 August 2009Thumbnail for version as of 15:52, 5 August 2009600 × 480 (84 KB)RobHarFix further display problems. (note: added white background in previous edit)
15:50, 5 August 2009Thumbnail for version as of 15:50, 5 August 2009600 × 480 (49 KB)RobHarFix display problems, fix inkscape compatibility problems.
02:57, 26 November 2007Thumbnail for version as of 02:57, 26 November 2007600 × 480 (15 KB)RobHarPrevious version looked fine by itself in firefox but otherwise looked bad.
02:25, 26 November 2007Thumbnail for version as of 02:25, 26 November 2007600 × 480 (15 KB)RobHar{{Information |Description=Plot of the number of quartic fields of bounded discriminant up to 10^7, and the asymptotic distribution. Data from Cohen, Diaz y Diaz, and Olivier, '''Constructing Complete Tables of Quartic Fields using Kummer Theory''', Math.

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