Utilisateur:TomT0m/OppositeAddition.asy

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 "";
}

string pairToString(pair point){
	return "("+string(point.x)+","+string(point.y)+")";
}

void drawCoordinates(pair point, align align=NoAlign){
	label("$"+pairToString(point)+"$",point,align,mediumgray+opacity(0.2)+fontsize(8));
}

string latexBold(real r){
	return "$\mathbf{"+string(r)+"}$";
}

string latexBold(string s){
	return "$\mathbf{"+s+"}$";
}

// schema representing the addition of N1 + N2

int N1=-2 ;
int N2= 2 ;
int num = 5; // size of the grid, num * num

pen[] Colors=new pen[2*num+1];
Colors.cyclic=true;
int i;

for (i=-1*num ; i<=num ; ++i) {
	Colors[i] = blue;
}

Colors[N1]=brown;
Colors[N2]=green;
Colors[N1+N2]=orange;

unitsize(50,50);




// drawing the equivalent classes



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

	// choosing the color of the numbers, blue by default
	pen numberColor = Colors[i];

	// equivalence classes labelled with usual names, in blue
	label(latexBold(i),point,5SW,fontsize(17)+numberColor);

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

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

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


void drawAdd(int n1, int n2, pair decalN1, pair decalN2, align alignN1=NoAlign,align alignN2=NoAlign){
	pair n1pair = pairRepresentation(n1);
	pair n2pair = pairRepresentation(n2);

	pair n1rep = n1pair + decalN1;
	pair n2rep = n2pair + decalN2;

	draw (/*pairToString(n2rep),*/n1rep -- n1rep+n2rep,alignN1,Colors[N2],Arrow,Margins);
	draw (/*pairToString(n1rep),*/n2rep -- n1rep+n2rep,alignN2,Colors[N1],Arrow,Margins);

}


for(int decalage=0; decalage<4;++decalage){
	for(int i=decalage;i+decalage<4;++i){
		drawAdd(N1,N2,(i,i),(decalage,decalage),alignN1=3SW,alignN2=4SW);
		drawAdd(N1,N2,(decalage,decalage),(i,i),alignN1=5W,alignN2=3E);
	}
}
// Vectors



// 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);


path legend = (num * .1, -1) -- (num*.9, -1);


label( Label(latexBold(N1),position=Relative(0.1)), Colors[N1]+fontsize(17),g=legend);
label( Label(latexBold("+"),position=Relative(0.2)) ,fontsize(17),g=legend);
label( Label(latexBold(N2),position=Relative(0.3)),Colors[N2]+fontsize(17),g=legend);
label( shift(0,-3.5)*Label(latexBold("{=}"),position=Relative(0.4)),fontsize(17),g=legend);
label( Label(latexBold(N2),position=Relative(0.5)),Colors[N2]+fontsize(17),g=legend);
label( Label(latexBold("+"),position=Relative(0.6)) ,fontsize(17),g=legend);
label( Label(latexBold(N1),position=Relative(0.7)),Colors[N1]+fontsize(17),g=legend);
label( shift(0,-3.5)*Label(latexBold("="),position=Relative(0.8)),fontsize(17),g=legend);
label( Label(latexBold(N1+N2),position=Relative(0.9)),Colors[N1+N2]+fontsize(17),g=legend);