File:Abstract interpretation of integers by signs svg.svg
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Size of this PNG preview of this SVG file: 800 × 544 pixels. Other resolutions: 320 × 217 pixels | 640 × 435 pixels | 1,024 × 696 pixels | 1,280 × 870 pixels | 2,560 × 1,739 pixels | 886 × 602 pixels.
Original file (SVG file, nominally 886 × 602 pixels, file size: 134 KB)
Summary
| Description |
English: Shows the lattice of all integer sets (red), the lattice of sign sets (green), and the usual abstraction function α between them. |
| Date | |
| Source |
Own work based on: Abstract interpretation of integers by signs.pdf:  |
| Author | Jochen Burghardt |
| SVG development |
LaTeX source code
|
|---|
\documentclass{article}
\usepackage[paperwidth=250mm,paperheight=170mm]{geometry}
\usepackage[pdftex]{color}
\usepackage{amssymb}
\setlength{\textwidth}{28cm}
\setlength{\textheight}{25cm}
\setlength{\oddsidemargin}{-3cm}
\setlength{\topmargin}{-2cm}
\setlength{\unitlength}{1cm}
\definecolor{grey} {rgb}{0.50, 0.50, 0.50}
\definecolor{bRed} {rgb}{1.00, 0.90, 0.90}
\definecolor{bGreen} {rgb}{0.90, 1.00, 0.90}
\newcommand{\set}[1]{\{#1\}}
\newcommand{\Z}{Z\!\!\!\!Z}
\pagestyle{empty}
\begin{document}
\begin{picture}(25,15)(0,-2.5)
% concrete lattice
\color{bRed}
\thicklines
\multiput(5.400,-1.600)(0.010,0.030){81}{\line(3,1){2.400}}
%\thinlines
\color{red}
\put(5.000,10.000){\makebox(0.000,0.000){$\scriptstyle \Z$}}
\put(4.600,9.600){\line(-1,-1){3.200}}
\put(5.000,9.600){\line(0,-1){3.200}}
\put(5.400,9.600){\line(1,-1){3.200}}
\put(1.000,6.000){\makebox(0.000,0.000){%
$\scriptstyle \set{\ldots,\mbox-2,\mbox-1,0}$}}
\put(5.000,6.000){\makebox(0.000,0.000){%
$\scriptstyle \set{\ldots,\mbox-2,\mbox-1,1,2,\ldots}$}}
\put(9.000,6.000){\makebox(0.000,0.000){%
$\scriptstyle \set{0,1,2,\ldots}$}}
\put(1.000,5.600){\line(0,-1){3.200}}
\put(1.400,5.600){\line(1,-1){3.200}}
\put(4.600,5.600){\line(-1,-1){3.200}}
\put(5.400,5.600){\line(1,-1){3.200}}
\put(8.600,5.600){\line(-1,-1){3.200}}
\put(9.000,5.600){\line(0,-1){3.200}}
\put(1.000,2.000){\makebox(0.000,0.000){%
$\scriptstyle \set{\ldots,\mbox-2,\mbox-1}$}}
\put(5.000,2.000){\makebox(0.000,0.000){$\scriptstyle \set{0}$}}
\put(9.000,2.000){\makebox(0.000,0.000){%
$\scriptstyle \set{1,2,\ldots}$}}
\put(1.400,1.600){\line(1,-1){3.200}}
\put(5.000,1.600){\line(0,-1){3.200}}
\put(8.600,1.600){\line(-1,-1){3.200}}
\put(5.000,-2.000){\makebox(0.000,0.000){$\scriptstyle \set{}$}}
\put(5.900,-0.800){\makebox(0.000,0.000){$\scriptstyle \set{1}$}}
\put(6.900,-0.800){\makebox(0.000,0.000){$\scriptstyle \set{3}$}}
\put(6.400,0.200){\makebox(0.000,0.000){$\scriptstyle \set{1,3}$}}
% abstract lattice
\color{green}
\put(20.000,13.750){\makebox(0.000,0.000){$\scriptstyle \set{-,0,+}$}}
\put(19.600,13.350){\line(-1,-1){3.200}}
\put(20.000,13.350){\line(0,-1){3.200}}
\put(20.400,13.350){\line(1,-1){3.200}}
\put(16.000,9.750){\makebox(0.000,0.000){$\scriptstyle \set{-,0}$}}
\put(20.000,9.750){\makebox(0.000,0.000){$\scriptstyle \set{-,+}$}}
\put(24.000,9.750){\makebox(0.000,0.000){$\scriptstyle \set{0,+}$}}
\put(16.000,9.350){\line(0,-1){3.200}}
\put(16.400,9.350){\line(1,-1){3.200}}
\put(19.600,9.350){\line(-1,-1){3.200}}
\put(20.400,9.350){\line(1,-1){3.200}}
\put(23.600,9.350){\line(-1,-1){3.200}}
\put(24.000,9.350){\line(0,-1){3.200}}
\put(16.000,5.750){\makebox(0.000,0.000){$\scriptstyle \set{-}$}}
\put(20.000,5.750){\makebox(0.000,0.000){$\scriptstyle \set{0}$}}
\put(24.000,5.750){\makebox(0.000,0.000){$\scriptstyle \set{+}$}}
\put(16.400,5.350){\line(1,-1){3.200}}
\put(20.000,5.350){\line(0,-1){3.200}}
\put(23.600,5.350){\line(-1,-1){3.200}}
\put(20.000,1.750){\makebox(0.000,0.000){$\scriptstyle \set{}$}}
% galois mapping
\color{grey}
\thinlines
\put(10.000,2.250){\vector(4,1){13.000}}
\put(12.500,3.000){\makebox(0.000,0.000)[b]{$\alpha$}}
\put(6.000,-1.750){\vector(4,1){13.000}}
\put(12.500,0.000){\makebox(0.000,0.000)[b]{$\alpha$}}
\put(7.200,0.167){\vector(3,1){15.800}}
\put(7.500,-0.800){\line(5,2){15.500}}
\put(6.000,10.250){\vector(4,1){13.000}}
\put(12.500,12.000){\makebox(0.000,0.000)[b]{$\alpha$}}
\end{picture}
\end{document}
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Licensing
Jochen Burghardt, the copyright holder of this work, hereby publishes it under the following license:
This file is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license.
Attribution:
- 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.
File history
Click on a date/time to view the file as it appeared at that time.
| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 14:26, 30 December 2013 | | 886 × 602 (134 KB) | wikimediacommons>Jochen Burghardt | User created page with UploadWizard |
File usage
The following page uses this file:
