<!-- Beginfunction reponse(form){for(var i=0;i<form.length;i++){if(form[i].checked){break}}var repondu=""if(i<form.length){repondu=form[i].value}return repondu;}function affiche(form){var auteur="Arnaud Saint-Martin de www.homeomath.com";var P=form.px.value;var fracine="";var racines=form.racines.value;var racine=Array();var facteur=Array();var ordre=Array();var multiplicite=0;var texte="";var k=0;var R="";var r=Array();var p=Array();var q=Array();var fac="";multiplicite=form.multiplicite.value;P=P.replace(/ /g,"");P=P.toLowerCase();if((P!="")&&(racines!="")){p=polysuite(P);q=polysuite(P);r=polysuite(P);racine=racines.split(",");for(var i=0;i<racine.length;i++){k=0;fac="x-"+racine[i];fac=fac.replace("--","+");facteur[i]=fac;q=polysuite(P);fracine=pimage(q,racine[i]);while((fracine=="0")&&(q.length!=1)&&(q[0]!="0")){k++;q=derivee(q);fracine=pimage(q,racine[i]);};ordre[i]=k;};if(multiplicite==0){for(var i=0;i<racine.length;i++){for(var j=1;j<=ordre[i];j++){r=divsuit(r,polysuite(""+facteur[i]+""),1);};if(ordre[i]!=0){if(ordre[i]!=1){texte="("+facteur[i]+")^"+ordre[i]+texte;}else{texte="("+facteur[i]+")"+texte;};};};}else{for(var i=0;i<racine.length;i++){if(ordre[i]!=0){r=divsuit(r,polysuite(""+facteur[i]+""),1);texte="("+facteur[i]+")"+texte;};};};R=ecritpol(r);if(r.length!=1){texte=texte+"("+R+")";}else{texte=R+texte;};document.formulaire.pfx.value=texte;};}function polysuite(POL){var POL1=POL;var POL2=Array();var MON=Array();var degpol=0;var POL1=POL.replace(/-/g,"+-");MON=POL1.split("+");for(var i=0;i<MON.length;i++){POL2[deg(MON[i])]=coef(MON[i]);};degpol=eval(POL2.length-1);;for(var i=0;i<=degpol;i++){if((POL2[i]=="")||(POL2[i]==null)){POL2[i]="0";};};return POL2;}function deg(mon){var degre=0;var pos=mon.indexOf("^");var long=mon.length;if(pos==-1){pos=mon.indexOf("x");if(pos==-1){degre=0;}else{degre=1;};}else{degre=eval(mon.substring(pos+1,long));};return degre;}function coef(mon){var coefficient="";var mon1="";var pos=0;pos=mon.indexOf("x");if(pos!=-1){mon1=mon.substring(0,pos);}else{mon1=mon;};if(mon1==""){coefficient="1";};if(mon1=="-"){coefficient="-1";};if((mon1!="")&&(mon1!="-")){coefficient=mon1;};return coefficient;}function somsuit(pola,polb){var da=eval(pola.length-1);var db=eval(polb.length-1);var pols=Array();if(da<db){for(var i=0;i<=da;i++){pols[i]=somme(""+pola[i]+"",""+polb[i]+"");};for(var i=eval(da+1);i<=db;i++){pols[i]=polb[i];};pols.length=eval(db+"+"+1);}else{for(var i=0;i<=db;i++){pols[i]=somme(""+pola[i]+"",""+polb[i]+"");};for(var i=eval(db+1);i<=da;i++){pols[i]=pola[i];};pols.length=eval(da+"+"+1);};pols=reducpol(pols);return pols;}function diffsuit(pola,polb){var da=eval(pola.length-1);var db=eval(polb.length-1);var pols=Array();if(da<db){for(var i=0;i<=da;i++){pols[i]=somme(""+pola[i]+"",produit("-1",""+polb[i]+""));};for(var i=eval(da+1);i<=db;i++){pols[i]=produit("-1",""+polb[i]+"");};pols.length=eval(db+"+"+1);}else{for(var i=0;i<=db;i++){pols[i]=somme(""+pola[i]+"",produit("-1",""+polb[i]+""));};for(var i=eval(db+1);i<=da;i++){pols[i]=pola[i];};pols.length=eval(da+"+"+1);};pols=reducpol(pols);return pols;}function prodsuit(pola,polb){var da=eval(pola.length-1);var db=eval(polb.length-1);var ds=eval(da+"+"+db);var aux="";var pols=Array();for(var i=0;i<=ds;i++){pols[i]="0";};for(var i=0;i<=ds;i++){for(var j=0;j<=i;j++){if((j>da)||(eval(i-j)>db)){aux="0";}else{aux=produit(pola[j],polb[i-j]);};if(aux!=null){pols[i]=somme(pols[i],aux);};};};pols=reducpol(pols);return pols;}function ecritpol(pol){var dp=eval(pol.length-1);var polich="";polich=""+pol[0];for(var i=1;i<=dp;i++){if(pol[i]!=0){if(i!=1){polich=pol[i]+"x^"+i+"+"+polich;}else{polich=pol[i]+"x+"+polich;};};};polich=polich.replace(/\+-/g,"-");polich=polich.replace(/\+1x/g,"+x");polich=polich.replace(/\-1x/g,"-x");polich=polich.replace("x^0","");return polich;}function entier(x){var entier=Math.round(eval(x-0.5));return entier;}function pgcd(a,b){var p=0;var reste=b%a;var quot=eval(eval(b-reste)/a);var divis=eval(a);var divid=eval(b);var produit=eval(a*b);while(reste!=0){divid=eval(divis);divis=eval(reste);reste=divid%divis;quot=eval(eval(divid-reste)/divis);};p=divis;return p;}function sortcarre(x){var reste=0;var carre=1;for(var i=x;i>=2;i--){reste=eval(i*i);reste=eval(x%reste);if(reste==0){carre=i;break;};};return carre;}function racine(chaine){var ch="";ch="<span style=\"text-decoration: overline\">"+chaine+"</span>";ch="<img border=\"0\" src=\"images/racine.gif\" width=\"14\" height=\"18\">"+ch;return ch;}function chainetab(eles,ele){var long=0;var c="";var ch=eles.toString();var k=1;var j=0;long=eles.length+1;for(var i=1;i<=long;i++){ele[i]=""};while(j<=long-1){c=ch.charAt(j);if(c!=","){ele[k]=ele[k]+c}else{k=k+1};j=j+1;};return k;}function videspace(chaine){var long=0;var c="";var ch=chaine.toString();var k=1;var j=0;long=chaine.length+1;while(j<=long-1){c=ch.charAt(j);if(c==" "){k=k+1;};j=j+1;};for(var i=1;i<=k;i++){ch=ch.replace(" ","");};return ch;}function arrondi(x,choix){var retour=eval(x*choix);var tronc=Math.round(retour);tronc=eval(tronc/choix);return tronc;}function reduction(chaine){var nume=numerateur(chaine);var deno=denominateur(chaine);var reduc="";var pg=0;if((nume!=0)&&(deno!=0)){pg=Math.abs(pgcd(nume,deno));nume=Math.round(nume/pg);deno=Math.round(deno/pg);if(deno<0){deno=Math.abs(deno);nume=eval(-nume);};if(deno==1){reduc=nume;}else{reduc=nume+"/"+deno;};};if(deno==0){reduc="Erreur !";};if((nume==0)&&(deno!=0)){reduc="0";};return reduc;}function decimal(den){var de=den;var deci=true;var div2=eval(de%2==0);var div5=eval(de%5==0);while(div2){de=Math.round(de/2);div2=eval(de%2==0);};while(div5){de=Math.round(de/5);div5=eval(de%5==0);};if(de!=1){deci=false;};return deci;}function numerateur(chaine){var ch=chaine.toString();var pos=ch.indexOf("/");var num="";if(pos!=-1){num=eval(ch.substring(0,pos));}else{num=ch.replace(".","");};return num;}function denominateur(chaine){var ch=chaine.toString();var pos=ch.indexOf("/");var long=ch.length;var den="";if(pos!=-1){den=ch.substring(pos+1,long);}else{pos=ch.indexOf(".");if(pos!=-1){den=Math.pow(10,eval(long-pos-1));}else{den=1;};};return den;}function produit(fraca,fracb){var numa=numerateur(fraca);var numb=numerateur(fracb);var dena=denominateur(fraca);var denb=denominateur(fracb);var fracp="";var nump=eval(numa*numb);var denp=eval(dena*denb);if(denp<0){denp=Math.abs(denp);nump=eval(-nump);};fracp=nump+"/"+denp;fracp=reduction(fracp);return fracp;}function somme(fraca,fracb){var numa=numerateur(fraca);var numb=numerateur(fracb);var dena=denominateur(fraca);var denb=denominateur(fracb);var fracs="";var nums=eval(numa*denb+numb*dena);var dens=eval(dena*denb);if(dens<0){dens=Math.abs(dens);nums=eval(-nums);};fracs=nums+"/"+dens;fracs=reduction(fracs);return fracs;}function division(fraca,fracb){var numa=numerateur(fraca);var numb=numerateur(fracb);var dena=denominateur(fraca);var denb=denominateur(fracb);var fracp="";var nump=eval(numa*denb);var denp=eval(dena*numb);if(denp<0){denp=Math.abs(denp);nump=eval(-nump);};fracp=nump+"/"+denp;fracp=reduction(fracp);return fracp;}function puissance(frac,p){var pu="1";for(var i=1;i<=p;i++){pu=produit(frac,pu);};return pu;}function derivee(pol){var dp=eval(pol.length-1);var pold=Array();for(var i=0;i<=dp;i++){pold[i]=produit(pol[i],""+i+"");};for(var i=0;i<=dp;i++){pold[i]=pold[i+1];};if(dp==0){pold[0]="0";dp=1;};pold.length=eval(dp);return pold;}function pimage(pol,a){var dp=eval(pol.length-1);var puis="";var som=pol[0];for(var i=1;i<=dp;i++){puis=puissance(a,i);puis=produit(puis,pol[i]);som=somme(som,puis);};return som;}function puisuit(pol,k){var ins=Array();ins=polysuite("1");for(var i=1;i<=k;i++){ins=prodsuit(ins,pol);};return ins;}function compose(pol1,pol2){var comp=Array();var terme=Array();var coeffi=Array();var dp1=eval(pol1.length-1);comp=polysuite(""+pol1[0]+"");for(var i=1;i<=dp1;i++){terme=puisuit(pol2,i);coeffi=polysuite(""+pol1[i]+"");terme=prodsuit(terme,coeffi);comp=somsuit(comp,terme);};return comp;}function deriveen(pol,n){var poldd=Array();poldd=pol;for(var i=1;i<=n;i++){poldd=derivee(poldd);};return poldd;}function divsuit(pol1,pol2,option){var deg1=eval(pol1.length-1);var deg2=eval(pol2.length-1);var degq=eval(deg1-deg2);var degr=deg1;var qu=Array();var sous=Array();var reste=Array();var monome="";if(deg2!=0){if(degq>=0){monome=division(pol1[deg1],pol2[deg2]);qu[degq]=monome;for(var i=0;i<degq;i++){qu[i]="0";sous[i]="0";};reste=pol1;while(degr>=deg2){for(var i=0;i<=deg2;i++){sous[i+degq]=produit(monome,pol2[i]);};reste=diffsuit(reste,sous);degr=eval(reste.length-1);degq=eval(degr-deg2);monome=division(reste[degr],pol2[deg2]);qu[degq]=monome;sous.length=0;for(var i=0;i<=degq;i++){sous[i]="0";};};}else{qu[0]="0";reste=pol1;};}else{if(pol2[deg2]!="0"){for(var i=0;i<=deg1;i++){qu[i]=division(pol1[i],pol2[deg2]);};reste=polysuite("0");}else{alert("Division par 0 !");};};if(option==1){return qu;}else{return reste;};}function reducpol(pol){var poltab=Array();var poltexte="";poltexte=ecritpol(pol);poltab=polysuite(poltexte);return poltab;}function pgcdpol(pol1,pol2){var apol=Array();var bpol=Array();var rpol=Array();var da=0;var db=0;var dr=0;da=eval(pol1.length-1);db=eval(pol2.length-1);if(da>db){apol=pol1;bpol=pol2;}else{apol=pol2;bpol=pol1;};rpol=divsuit(apol,bpol,2);while(ecritpol(rpol)!="0"){dr=eval(rpol.length-1);da=eval(bpol.length-1);if(dr>da){apol=rpol;}else{apol=bpol;bpol=rpol;};rpol=divsuit(apol,bpol,2);};if(bpol.length==1){bpol[0]="1";alert("Ces deux polynômes sont premiers entre eux !");}else{for(var i=0;i<=eval(bpol.length-1);i++){bpol[i]=division(bpol[i],bpol[eval(bpol.length-1)]);};};return bpol;}
