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File:Relative numbers representation.svg

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Summary

DescriptionRelative numbers representation.svg
English: A figure representing the equivalence classes of the relative numbers constructed as a pair of natural numbers. Any relative number (eg. -5) has an infinity of equivalent possible representation, eg. (2,7), (0,5), ... The equivalent representations (in red) are on the same blue dotted line, and the number in blue at the end on the line is the corresponding relative number
Francais : Une figure representant les classes d'equivalences entres les paire d'entiers construisant les nombre relatifs.

Chaque nombre relatif (par exemple -5) a une infinite de paire qui le representent de maniere equivalente, (par exemple (2,7), (0,5).

Toutes ces representation equivalente sont sur la meme pointille bleu, et le nombre relatif qu'elle representent est au bout de la ligne.
Date
Source Own work
Author TomdFr
Other versions File:Relatives Numbers Representation.png
SVG development
InfoField
The SVG code is valid.
This diagram was created with Asymptote.

Licensing

Public domainPublic domainfalsefalse
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.

Generation code

In asymptote programming language (w:Asymptote (vector graphics language))

// import settings;
import graph;

// pdfviewer="evince";
// psviewer="evince";

// returns a pair representation of a relative number of the equivalent class
pair pairRepresentation(int n){
if(n>0){
return(n,0);
}else{
return(0,-n);
}
}

string nullString(real r){
return "";
}

void drawCoordinates(pair point, align align=NoAlign){
label("$("+string(point.x)+","+string(point.y)+")$",point,align);
}

unitsize(50,50);

int num = 10;
int i;

for (i=-1*num ; i<=num ; ++i) {
pair point = pairRepresentation(i) ;
dot(point,red);

// equivalence classes labelled with usual names, in blue
label("$\mathbf{"+string(i)+"}$",point,5SW,fontsize(17)+blue);

int j;
for(j=abs(i);j<num;++j) {
drawCoordinates(point,E);
pair nextpoint = point + (1,1);

draw(point -- nextpoint,blue+Dotted+linewidth(2));
dot(point,red+linewidth(5));

point=nextpoint;
}
dot(point,red);
draw(point -- point+(0.5,0.5),blue+Dotted+linewidth(2));
dot(point,red+linewidth(5));
drawCoordinates(point,E);
}

// axes

real decay=-0.2;

ticks tick=RightTicks(N=0,n=1,end=false,nullString);
xaxis("$n_1$",YEquals(decay),decay,num+1.0,tick,Arrow);
yaxis("$n_2$",XEquals(decay),decay,num+1.0,LeftTicks(N=0,n=1,end=false,nullString),Arrow);

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depicts

25 November 2009

File history

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Date/TimeThumbnailDimensionsUserComment
current03:00, 31 January 2018512 x 494 (11 KB)Perhelionfix librsvg bug phab:T35245
21:57, 25 November 2009429 x 414 (81 KB)TomdFrUploaded a version from -5 to 5, -10 to 10 was uselessly too big.
20:05, 25 November 2009754 x 727 (244 KB)TomdFr{{Information |Description={{en|1=A figure representing the equivalence classes of the relative numbers constructed as a pair of natural numbers. Any relative number (eg. -5) has an infinity of equivalent possible representation, eg. (2,7), (0,5), ... The

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