// Coordinates System :
SetCoords(438,282,40);


// Geometry :
u=Point("u",1.95,1.35);
w=Point("w",-1.75,1.8);
v=Point("v",-1.525,0.625);
E19=Expression("E19","Ainsi dans ce cas, <u+v,w> = <u,w> +<v,w>","","","2","-10.45","-6.45");
E18=Expression("E18","donc en g\u00e9n\u00e9ral <u+v,w> \u2260 <u,w> + <v,w>","","","1","-10.45","-6.45");
E13=Expression("E13","V\u00e9rifions que, pour cette norme, <|> n'est pas additif ","","","2","-10.45","-2.45");
E12=Expression("E12","4<u,v> = ||u+v||^2-||u-v||^2 ","","","1","-10.45","4.55");
O=Point("O","[0,0]","0");
E11=Expression("E11","Si la norme est euclidienne alors son produit scalaire <|> v\u00e9rifie : ","","","1","-10.45","5.3");
P1=Point("P1",-10,1.35);
P2=Point("P2",5.35,3.525);
E10=Expression("E10","Exploration sur la norme sup : ||u|| = sup(|x|,|y|) ","","","2","-10.45","6.3");
E1=ExpressionOn("E1","||u|| = ","","","max(abs(x(u)),abs(y(u)))",P1,[20,-20]);
E9=ExpressionOn("E9","||v-w|| = ","","","max(abs(x(v-w)),abs(y(v-w)))",P2,[20,30]);
E6=ExpressionOn("E6","||u+w|| = ","","","max(abs(x(u+w)),abs(y(u+w)))",P2,[20,-60]);
S3=Segment("S3",O,w);
S2=Segment("S2",O,v);
E7=ExpressionOn("E7","||u-w|| = ","","","max(abs(x(u-w)),abs(y(u-w)))",P2,[20,-30]);
S1=Segment("S1",O,u);
E2=ExpressionOn("E2","||v|| = ","","","max(abs(x(v)),abs(y(v)))",P1,[20,10]);
E8=ExpressionOn("E8","||v+w|| = ","","","max(abs(x(v+w)),abs(y(v+w)))",P2,[20,0]);
E3=ExpressionOn("E3","||w|| = ","","","max(abs(x(w)),abs(y(w)))",P1,[20,40]);
suv=Point("suv","u+v","0");
E16=Expression("E16","4<v,w>= ||v+w||^2-||v-w||^2 = ","","","E8^2-E9^2","-10.45","-4.7");
E15=Expression("E15","4<u,w> = ||u+w||^2-||u-w||^2 = ","","","E6^2-E7^2","-10.45","-3.95");
suvmw=Point("suvmw","suv-w","0");
suvw=Point("suvw","suv+w","0");
E17=Expression("E17","","","","\"Or (\"+E15+\")+(\"+E16+\") = \"+(E15+E16)","-10.45","-5.7");
E4=ExpressionOn("E4","||u+v+w|| = ","","","max(abs(x(suvw)),abs(y(suvw)))",P2,[20,60]);
E5=ExpressionOn("E5","||u+v-w|| = ","","","max(abs(x(suvmw)),abs(y(suvmw)))",P2,[20,90]);
E14=Expression("E14","4<u+v,w>=||u+v+w||^2-||u+v-w||^2 = ","","","E4^2-E5^2","-10.45","-3.2");
Egal=Expression("Egal","","","","abs(E14-E15-E16)<0.000000001","4.55","-4.7");
E20=Expression("E20","","","","E18.setHidden(Egal==1);E19.setHidden(Egal==0);\"gestion commentaire\"","-9.7","2.3");


// Styles :
STL(u,"c:#006633;s:6;sn:true;f:20;sp:1");
STL(w,"c:#966400;s:6;sn:true;f:20;sp:1;np:1.5707963267948966");
STL(v,"c:#2c69cf;s:6;sn:true;f:20;sp:1;np:3.486594830796898");
STL(E19,"c:#ea15e4;h:1;s:7;f:18;p:-1;cL:200;cPT:YzojNzgwMDEzO2g6MTtzOjEwO2Y6MzA=");
STL(E18,"c:#cf0928;s:7;f:18;p:-1;cL:200;cPT:YzojNzgwMDEzO3M6MTA7ZjozMA==");
STL(E13,"c:#883884;s:7;f:16;p:-1;cL:200;cPT:YzojNzgwMDEzO3M6MTA7ZjozMA==");
STL(E12,"c:#0000b2;s:7;f:16;p:-1;cL:200;cPT:YzojNzgwMDEzO3M6MTA7ZjozMA==");
STL(O,"c:#cf0928;s:6;sn:true;f:11;sp:1");
STL(E11,"c:#0000b2;s:7;f:16;p:-1;cL:200;cPT:YzojNzgwMDEzO3M6MTA7ZjozMA==");
STL(P1,"c:#007c7c;s:6;f:30;sp:1");
STL(P2,"c:#0000b2;s:6;f:30;sp:1");
STL(E10,"c:#760012;s:7;f:18;p:-1;cL:200;cPT:YzojNzgwMDEzO3M6MTA7ZjozMA==");
STL(E1,"c:#007c7c;s:7;f:16;p:6;cL:200;cPT:YzojNzgwMDEzO3M6MTA7ZjozMA==");
STL(E9,"c:#966400;s:7;f:16;p:6;cL:200;cPT:YzojNzgwMDEzO3M6MTA7ZjozMA==");
STL(E6,"c:#2c69cf;s:7;f:16;p:6;cL:200;cPT:YzojNzgwMDEzO3M6MTA7ZjozMA==");
STL(S3,"c:#966400;s:1;f:24");
STL(S2,"c:#2c69cf;s:1;f:24");
STL(E7,"c:#2c69cf;s:7;f:16;p:6;cL:200;cPT:YzojNzgwMDEzO3M6MTA7ZjozMA==");
STL(S1,"c:#006633;s:1;f:24");
STL(E2,"c:#007c7c;s:7;f:16;p:6;cL:200;cPT:YzojNzgwMDEzO3M6MTA7ZjozMA==");
STL(E8,"c:#966400;s:7;f:16;p:6;cL:200;cPT:YzojNzgwMDEzO3M6MTA7ZjozMA==");
STL(E3,"c:#007c7c;s:7;f:16;p:6;cL:200;cPT:YzojNzgwMDEzO3M6MTA7ZjozMA==");
STL(suv,"c:#0000b2;h:1;s:6;sn:true;f:30");
STL(E16,"c:#966400;s:7;f:15;p:6;cL:200;cPT:YzojNzgwMDEzO3M6MTA7ZjozMA==");
STL(E15,"c:#2c69cf;s:7;f:16;p:6;cL:200;cPT:YzojNzgwMDEzO3M6MTA7ZjozMA==");
STL(suvmw,"c:#0000b2;h:1;s:6;sn:true;f:30");
STL(suvw,"c:#0000b2;h:1;s:6;sn:true;f:30");
STL(E17,"c:#cf0928;s:7;f:18;p:4;cL:200;cPT:YzojNzgwMDEzO3M6MTA7ZjozMA==");
STL(E4,"c:#39aa44;s:7;f:16;p:6;cL:200;cPT:YzojNzgwMDEzO3M6MTA7ZjozMA==");
STL(E5,"c:#39aa44;s:7;f:16;p:6;cL:200;cPT:YzojNzgwMDEzO3M6MTA7ZjozMA==");
STL(E14,"c:#39aa44;s:7;f:16;p:6;cL:200;cPT:YzojNzgwMDEzO3M6MTA7ZjozMA==");
STL(Egal,"c:#2f0449;h:1;s:7;sn:true;f:24;p:4;cL:200;cPT:YzojNzgwMDEzO2g6MTtzOjEwO2Y6MzA=");
STL(E20,"c:#790379;h:1;s:7;f:24;p:4;cL:200;cPT:YzojNzgwMDEzO2g6MTtzOjEwO2Y6MzA=");
SetCoordsStyle("isAxis:false;isGrid:true;isOx:true;isOy:true;isLockOx:false;isLockOy:false;centerZoom:false;color:#111111;fontSize:18;axisWidth:1;gridWidth:0.1");
SetGeneralStyle("background-color:#FFFFFF");