File:PlotDiscriminantsOfQuarticFields.svg

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File:PlotDiscriminantsOfQuarticFields.svg

PlotDiscriminantsOfQuarticFields.svg‎ (SVG file, nominally 600 × 480 pixels, file size: 84 KB)

[edit] Summary

Description	PlotDiscriminantsOfQuarticFields.svg 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	25 November 2007(2007-11-25)
Source	Own work
Author	RobHar
Permission (Reusing this image)	Public Domain

[edit] Data file

This image was created using gnuplot 4.2.2 with the following command file. It was subsequently edited with Inkscape and a text editor to fix display problems wikipedia has.

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

[edit] Licensing

I, the copyright holder of this work, hereby release it into the public domain. This applies worldwide.

In case this is not legally possible:
I grant anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law.

File history

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

	Date/Time	Thumbnail	Dimensions	User	Comment
current	16:03, 5 August 2009		600×480 (84 KB)	RobHar (talk \| contribs)	(Crossing fingers that this will work.)
	16:00, 5 August 2009		600×480 (85 KB)	RobHar (talk \| contribs)	(Display problems keep changing. Try again.)
	15:52, 5 August 2009		600×480 (84 KB)	RobHar (talk \| contribs)	(Fix further display problems. (note: added white background in previous edit))
	15:50, 5 August 2009		600×480 (49 KB)	RobHar (talk \| contribs)	(Fix display problems, fix inkscape compatibility problems.)
	02:57, 26 November 2007		600×480 (15 KB)	RobHar (talk \| contribs)	(Previous version looked fine by itself in firefox but otherwise looked bad.)
	02:25, 26 November 2007		600×480 (15 KB)	RobHar (talk \| contribs)	({{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.)