File:Right Euclidean relation scheme.pdf
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[edit]DescriptionRight Euclidean relation scheme.pdf |
English: Shows a schematized right Euclidean relation. Each right Euclidean relation R on a set X necessarily obeys this scheme. — The restriction R|ran(R) is always an equivalence relation. Deeply-colored squares indicate its equivalence classes, assuming X’s elements are arranged in such a way that equivalent ones are adjacent. Pale-colored rectangles indicate possible relationships of elements in the set rest := X \ ran(R), again assuming them to be arranged in convenient order. In these rectangles, relationships may, or may not, hold. A light grey color indicates that the element corresponding to the row is unrelated to that corresponding to the column; in particular, the lighter grey right rectangle indicates that no element at all can be related to some in the set rest. The diagonal line indicates that xRx holds iff x∈ran(R). |
Date | |
Source | Own work |
Author | Jochen Burghardt |
Other versions | File:Right Euclidean relation scheme.pdf * File:Left Euclidean relation scheme.pdf * File:Right Euclidean relation scheme svg.svg * File:Left Euclidean relation scheme svg.svg |
LaTeX source code
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\documentclass[12pt]{article}
\setlength{\unitlength}{1mm}
\usepackage[pdftex]{color}
\usepackage[paperwidth=105\unitlength,paperheight=105\unitlength]{geometry}
\setlength{\topmargin}{-36mm}
\setlength{\textwidth}{105\unitlength}
\setlength{\textheight}{105\unitlength}
\setlength{\oddsidemargin}{-23mm}
\setlength{\parindent}{0cm}
\pagestyle{empty}
\definecolor{fEqcA} {rgb}{0.99,0.00,0.00}
\definecolor{fEqcB} {rgb}{0.00,0.99,0.00}
\definecolor{fEqcC} {rgb}{0.00,0.00,0.99}
\definecolor{fEqcD} {rgb}{0.99,0.99,0.00}
\definecolor{fEqcE} {rgb}{0.00,0.99,0.99}
\definecolor{bEqcA} {rgb}{0.99,0.50,0.50}
\definecolor{bEqcB} {rgb}{0.50,0.99,0.50}
\definecolor{bEqcC} {rgb}{0.50,0.50,0.99}
\definecolor{bEqcD} {rgb}{0.99,0.99,0.50}
\definecolor{bEqcE} {rgb}{0.50,0.99,0.99}
\definecolor{bDomXr} {rgb}{0.85,0.85,0.85}
\definecolor{bDomXi} {rgb}{0.97,0.97,0.97}
\begin{document}
\begin{picture}(100,100)
% dom,ran split
\textcolor{bDomXr}{\put(10,90){\makebox(0,0)[tl]{\rule{60mm}{90mm}}}}%
\textcolor{bDomXi}{\put(70,90){\makebox(0,0)[tl]{\rule{30mm}{90mm}}}}%
% equaivalence class backgrounds in X_r
\textcolor{fEqcA}{\put(10,90){\makebox(0,0)[tl]{\rule{20mm}{20mm}}}}%
\textcolor{fEqcB}{\put(30,70){\makebox(0,0)[tl]{\rule{10mm}{10mm}}}}%
\textcolor{fEqcC}{\put(40,60){\makebox(0,0)[tl]{\rule{10mm}{10mm}}}}%
\textcolor{fEqcD}{\put(50,50){\makebox(0,0)[tl]{\rule{15mm}{15mm}}}}%
\textcolor{fEqcE}{\put(65,35){\makebox(0,0)[tl]{\rule{05mm}{05mm}}}}%
% equaivalence class echo backgrounds in X_i
\textcolor{bEqcA}{\put(10,30){\makebox(0,0)[tl]{\rule{20mm}{06mm}}}}%
\textcolor{bEqcB}{\put(30,24){\makebox(0,0)[tl]{\rule{10mm}{06mm}}}}%
\textcolor{bEqcC}{\put(40,18){\makebox(0,0)[tl]{\rule{10mm}{06mm}}}}%
\textcolor{bEqcD}{\put(50,12){\makebox(0,0)[tl]{\rule{15mm}{06mm}}}}%
\textcolor{bEqcE}{\put(65,06){\makebox(0,0)[tl]{\rule{05mm}{06mm}}}}%
\thicklines%
% outer frame
\put(10,90){\line(1,0){90}}%
\put(10,0){\line(1,0){90}}%
\put(10,0){\line(0,1){90}}%
\put(100,0){\line(0,1){90}}%
% separation X_r,X_i
\put(70,0){\line(0,1){90}}%
\put(10,30){\line(1,0){90}}%
% reflexive diagonal in X_r
\put(10,90){\line(1,-1){60}}%
% equivalence class 1,2 in X_r
\put(10,70){\line(1,0){30}}%
\put(30,90){\line(0,-1){30}}%
% equivalence class 2,3 in X_r
\put(30,60){\line(1,0){20}}%
\put(40,70){\line(0,-1){20}}%
% equivalence class 3,4 in X_r
\put(40,50){\line(1,0){25}}%
\put(50,60){\line(0,-1){25}}%
% equivalence class 4,5 in X_r
\put(50,35){\line(1,0){20}}%
\put(65,50){\line(0,-1){20}}%
% equivalence class 1,2 echo in X_i
\put(10,24){\line(1,0){30}}
\put(30,30){\line(0,-1){12}}
% equivalence class 2,3 echo in X_i
\put(30,18){\line(1,0){20}}
\put(40,24){\line(0,-1){12}}
% equivalence class 3,4 echo in X_i
\put(40,12){\line(1,0){25}}
\put(50,18){\line(0,-1){12}}
% equivalence class 4,5 echo in X_i
\put(50,06){\line(1,0){20}}
\put(65,12){\line(0,-1){12}}
% captions X_r, X_i
\put(5,60){\makebox(0,0){ran}}
\put(5,15){\makebox(0,0){\it rest}}
\put(40,95){\makebox(0,0){ran}}
\put(85,95){\makebox(0,0){\it rest}}
% captions row,col = x,y
\put(0,100){\makebox(0,0)[tl]{$xRy$}}
\put(5,87){\makebox(0,0)[t]{$x$}}
\put(13,95){\makebox(0,0)[l]{$y$}}
\put(5,85){\vector(0,-1){5}}
\put(15,95){\vector(1,0){5}}
\end{picture}
\end{document}
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Licensing
[edit]I, the copyright holder of this work, hereby publish it under the following license:
This file is licensed under the Creative Commons Attribution-Share Alike 4.0 International license.
- 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.
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Date/Time | Thumbnail | Dimensions | User | Comment | |
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current | 17:00, 9 June 2018 | 618 × 618 (27 KB) | Jochen Burghardt (talk | contribs) | User created page with UploadWizard |
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Software used | TeX |
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Conversion program | pdfTeX-1.40.18 |
Encrypted | no |
Page size | 297.636 x 297.636 pts |
Version of PDF format | 1.5 |