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352 lines
8.6 KiB
352 lines
8.6 KiB
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// -------------------- Etude de fonctions --------------------
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var etudeX = new Array()
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var etudeY = new Array()
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var etudeD = new Array()
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var limGauche = new Array()
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var limDroite = new Array()
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var listeIndefini = new Array()
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var listeZeros = new Array()
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var intervalEtudeGauche = -50
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var intervalEtudeDroite = 50
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var precisionEtude = 0.001
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function etudier(fct){
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if(check(fct)){
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prepareEtude(fct)
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pariteFct()
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signeFct(fct)
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asymptotes()
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courbure()
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ensembleDefinition()
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}
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}
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// Préparation à l'étude de fonction
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function prepareEtude(fct){
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listeIndefini = new Array()
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var f = function(x){
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return eval(fct)
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}
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// Calcul de tous les points de la fonction
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var i = 0
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for(var x=intervalEtudeGauche; x<=intervalEtudeDroite; x+=precisionEtude){
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etudeX[i] = x
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etudeY[i] = Math.round(f(x)*10000)/10000
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etudeD[i] = Math.round(1000000*(f(x+0.0001)-f(x-0.0001))/(2*0.0001))/1000000
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i++
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}
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// Calcul des extrémités de la fonction
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var x = -100000
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limGauche[0] = f(x)
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x = -10000
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limGauche[1] = f(x)
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x = 100000
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limDroite[0] = f(x)
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x = 10000
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limDroite[1] = f(x)
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}
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// Recherche de l'ensemble de définition
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function ensembleDefinition(){
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var fctDefinie = false
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var dejaDefinie = false
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var EDF = ""
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if(!isNaN(limGauche[0])){
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fctDefinie = true
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dejaDefinie = true
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EDF += "]-∞;"
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}
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if(!isNaN(limGauche[1]) && !fctDefinie){
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fctDefinie = true
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dejaDefinie = true
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EDF += "]-∞;"
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}
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for(var i=0; i<etudeX.length; i++){
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if(fctDefinie && isNaN(etudeY[i])){
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fctDefinie = false
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EDF += (parseInt(etudeX[i]/precisionEtude)*precisionEtude)+"["
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}
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else if(!fctDefinie && !isNaN(etudeY[i])){
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fctDefinie = true
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if(dejaDefinie){
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EDF += " u "
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}
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EDF += "["+(parseInt(etudeX[i]/precisionEtude)*precisionEtude)+";"
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dejaDefinie = true
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}
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}
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if(fctDefinie && !isNaN(limDroite[1])){
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fctDefinie = false
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EDF += "+∞["
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}
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if(fctDefinie && !isNaN(limDroite[0])){
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fctDefinie = false
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EDF += "+∞["
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}
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for(var i=0; i<listeIndefini.length; i++){
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if(i==0){
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EDF += " - {"
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}
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EDF += listeIndefini[i]
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if(i==listeIndefini.length-1){
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EDF += "}"
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}
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else
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EDF += ";"
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}
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document.getElementById('etudeEDF').innerHTML = EDF
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}
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// Etude de la parité
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function pariteFct(){
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var posZero
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var paire = true
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var impaire = true
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var positif, negatif
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var precisionParite = 1000
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for(var i=0;i<etudeX.length;i++){
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if(Math.round(etudeX[i]*precisionParite)/precisionParite==0){
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posZero = i
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}
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}
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for(var i=1; i<etudeX.length/2; i++){
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if(etudeY[posZero+i]>0){
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positif = Math.floor(etudeY[posZero+i])
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}
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else{
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positif = Math.ceil(etudeY[posZero+i])
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}
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if(etudeY[posZero-i]>0){
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negatif = Math.floor(etudeY[posZero-i])
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}
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else{
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negatif = Math.ceil(etudeY[posZero-i])
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}
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if(positif<25000 && positif>-25000){
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if(positif != negatif){
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paire = false
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//alert(i+" ; "+posZero+" ; "+etudeX.length+" ; "+positif+" ; "+negatif)
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}
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if(positif != (-negatif)){
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impaire = false
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}
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}
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}
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if(paire){
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document.getElementById("etudeParite").innerHTML = "paire"
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}
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else if(impaire){
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document.getElementById("etudeParite").innerHTML = "impaire"
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}
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else{
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document.getElementById("etudeParite").innerHTML = "aucune"
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}
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}
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function zeroFct(){
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listeZeros = new Array()
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var listeZerosArr = new Array()
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var precZeros = 5
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for(var i=0; i<etudeX.length; i++){
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if(Math.round(etudeY[i]*1000)/1000==0){
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var nouveauZero = Math.round(etudeX[i]*precZeros)/precZeros
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if(listeZerosArr[listeZerosArr.length-1]!=nouveauZero){
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listeZeros.push(Math.round(etudeX[i]*10)/10)
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listeZerosArr.push(nouveauZero)
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}
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}
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}
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}
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function signeFct(fct){
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var signe = new Array()
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var signePlus = new Array()
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var signeMoins = new Array()
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var dernier = 0
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if(limGauche[0]>0){
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signe[0] = "+"
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signePlus[0] = limGauche[1]
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signeMoins[0] = limGauche[0]
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}
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else{
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signe[0] = "-"
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signePlus[0] = limGauche[1]
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signeMoins[0] = limGauche[0]
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}
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for(var i=0; i<etudeY.length; i++){
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if(signe[signe.length-1]=="+"){
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if(etudeY[i]<0){
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signe.push("-")
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signePlus.push(etudeX[i])
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signeMoins.push(etudeX[dernier])
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}
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else if(etudeY[i]>0){
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dernier = i
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}
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}
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if(signe[signe.length-1]=="-"){
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if(etudeY[i]>0){
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signe.push("+")
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signePlus.push(etudeX[i])
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signeMoins.push(etudeX[dernier])
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//alert(signe+" ; "+signePlus+'\n'+etudeY[i+1]+" ; "+etudeY[i]+" ; "+etudeY[i-1]+" ; "+etudeY[i-2]+'\n'+etudeX[i+1]+" ; "+etudeX[i]+" ; "+etudeX[i-1]+" ; "+etudeX[i-2])
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}
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else if(etudeY[i]<0){
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dernier = i
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}
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}
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}
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var valeurPlus, valeurMoins, millieu, precisionZero
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listeZeros = new Array()
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for(var i=1; i<signePlus.length; i++){
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valeurPlus = signePlus[i]
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valeurMoins = signeMoins[i]
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for(var k=0;k<10000;k++){
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millieu = (valeurPlus + valeurMoins)/2
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x = valeurPlus
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if(eval(fct)>0){
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x = millieu
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if(eval(fct)>0){
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valeurPlus=millieu
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}
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else if(eval(fct)<0){
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valeurMoins=millieu
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}
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else{
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break
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}
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}
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else if(eval(fct)<0){
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x = millieu
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if(eval(fct)<0){
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valeurPlus=millieu
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}
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else if(eval(fct)>0){
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valeurMoins=millieu
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}
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else{
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break
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}
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}
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else{
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millieu = valeurPlus
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break
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}
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x = valeurPlus
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precisionZero = eval(fct)
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x = valeurMoins
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precisionZero -= eval(fct)
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if(precisionZero>0.0001){
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break
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}
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}
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//alert(signePlus[i]+" et "+signeMoins[i]+" -> "+millieu)
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listeZeros.push(Math.round(millieu*100)/100)
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}
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var texteZeros = ""
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if(listeZeros==""){
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zeroFct()
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texteZeros = "~ "
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}
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var texte = "Signe : "
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var aSupprimer = new Array()
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for(var i=0; i<signe.length; i++){
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texte += "<td>"+signe[i]+"</td>"
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if(listeZeros[i]!=undefined){
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x = listeZeros[i]
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if(isFinite(eval(fct))){
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texte += "<td class='border'>"+listeZeros[i]+"</td>"
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}
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else{
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texte += "<td class='border infini'>"+listeZeros[i]+"</td>"
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listeIndefini.push(listeZeros[i])
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aSupprimer.push(i)
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}
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}
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}
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document.getElementById("etudeSigne").innerHTML = texte
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for(var i=0; i<aSupprimer.length; i++){
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listeZeros.splice((aSupprimer[i]-i), 1)
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}
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if(listeZeros==""){
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texteZeros = "aucuns"
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}
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document.getElementById("etudeZeros").innerHTML = texteZeros+listeZeros
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}
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function asymptotes(){
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// Horizontales
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if(Math.abs(limGauche[0])<1000){
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var limRound = Math.round(limGauche[0]*100)/100
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if(limGauche[0]<limRound){
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document.getElementById("etudeAHG").innerHTML = "y = "+limRound +" <span class='texteSecondaire'>(courbe au-dessous de l'AH)</span>"
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}
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else if(limGauche[0]>limRound){
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document.getElementById("etudeAHG").innerHTML = "y = "+limRound +" <span class='texteSecondaire'>(courbe au-dessus de l'AH)</span>"
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}
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else{
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document.getElementById("etudeAHG").innerHTML = "y = "+limRound
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}
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}
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else{
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document.getElementById("etudeAHG").innerHTML = "aucune"
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}
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if(Math.abs(limDroite[0])<1000){
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var limRound = Math.round(limDroite[0]*100)/100
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if(limDroite[0]<limRound){
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document.getElementById("etudeAHD").innerHTML = "y = "+limRound +" <span class='texteSecondaire'>(courbe au-dessous de l'AH)</span>"
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}
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else if(limDroite[0]>limRound){
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document.getElementById("etudeAHD").innerHTML = "y = "+limRound +" <span class='texteSecondaire'>(courbe au-dessus de l'AH)</span>"
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}
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else{
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document.getElementById("etudeAHD").innerHTML = "y = "+limRound
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}
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}
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else{
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document.getElementById("etudeAHD").innerHTML = "aucune"
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}
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// Verticales
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var texteAV = ""
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for(var i=0; i<listeIndefini.length; i++){
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texteAV += "x = "+listeIndefini[i]
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if(listeIndefini[i+1]!=undefined){
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texteAV += " ; "
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}
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}
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if(texteAV==""){
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texteAV = "aucune <br/>"
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}
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document.getElementById("etudeAV").innerHTML = texteAV
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}
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function courbure(){
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var texteMin = "";
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var texteMax = "";
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var texteI = "";
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var nbrI = 0;
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var i;
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for(i=0; i<etudeD.length; i++){
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if(etudeD[i]==0){
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if(etudeD[i-1]<0 && etudeD[i+1]>0){
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texteMin += "<br/>Min("+Math.round(etudeX[i]*10000)/10000+";"+etudeY[i]+")";
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}
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else if(etudeD[i-1]>0 && etudeD[i+1]<0){
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texteMax += "<br/>Max("+Math.round(etudeX[i]*10000)/10000+";"+etudeY[i]+")";
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}
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else{
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nbrI++;
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texteI += '<br/>I<span style="vertical-align:sub;font-size:50%;">'+nbrI+"</span>("+Math.round(etudeX[i]*10000)/10000+";"+etudeY[i]+")";
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}
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}
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}
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if(texteMin==""){texteMin = "<br/>Aucun Minimum";}
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if(texteMax==""){texteMax = "<br/>Aucun Maximum";}
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if(texteI==""){texteI = "<br/>Aucun I";}
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document.getElementById("etudeMin").innerHTML = texteMin;
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document.getElementById("etudeMax").innerHTML = texteMax;
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document.getElementById("etudeI").innerHTML = texteI;
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} |