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Copy pathsimplex - Version 12 de Junio.html
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simplex - Version 12 de Junio.html
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<!DOCTYPE html>
<html>
<head>
<title>Simplex</title>
<script src="https://code.jquery.com/jquery-3.2.1.slim.min.js" integrity="sha384-KJ3o2DKtIkvYIK3UENzmM7KCkRr/rE9/Qpg6aAZGJwFDMVNA/GpGFF93hXpG5KkN" crossorigin="anonymous"></script>
<script src="https://cdnjs.cloudflare.com/ajax/libs/popper.js/1.12.9/umd/popper.min.js" integrity="sha384-ApNbgh9B+Y1QKtv3Rn7W3mgPxhU9K/ScQsAP7hUibX39j7fakFPskvXusvfa0b4Q" crossorigin="anonymous"></script>
<script src="https://maxcdn.bootstrapcdn.com/bootstrap/4.0.0/js/bootstrap.min.js" integrity="sha384-JZR6Spejh4U02d8jOt6vLEHfe/JQGiRRSQQxSfFWpi1MquVdAyjUar5+76PVCmYl" crossorigin="anonymous"></script>
<link rel="stylesheet" href="https://maxcdn.bootstrapcdn.com/bootstrap/4.0.0/css/bootstrap.min.css" integrity="sha384-Gn5384xqQ1aoWXA+058RXPxPg6fy4IWvTNh0E263XmFcJlSAwiGgFAW/dAiS6JXm" crossorigin="anonymous">
<script src="https://unpkg.com/[email protected]/dist/math.min.js"></script>
<script src="https://cdn.plot.ly/plotly-1.35.2.min.js"></script>
<meta name="viewport" content="width=device-width, user-scalable=no">
<style>
input[type=text] {
width: 300px;
}
input {
padding: 6px;
}
body, html, input {
font-family: sans-serif;
font-size: 11pt;
}
form {
margin: 20px 0;
}
label {
font-weight: bold;
}
.num {
width:100%;
}
</style>
<script type="text/javascript">
var M= 10000000000;//Number.MAX_VALUE/10000;
var MV = []
var RowName = []
var ColName = []
var criterial_second = false;
var rowIdent =function(pos,problem){
var len = problem.constraints.length+1
row = [];
MV = Object.values(problem.objective);
for (var i=0;i<len-1;i++){
var value=2;
if (problem.constraints[i].constraint == "="){
value = 0 // podria ser 1 si no estaria el continue en el siguiente for en esta misma
MV.push(0);
}
if (problem.constraints[i].constraint == "<="){
value = 1
MV.push(0);
}
if (problem.constraints[i].constraint == ">="){
value = -1
MV.push(0);
}
if (value == 2){
throw "Estructura Problem es invalida en sus constraints ["+i+"]. solo soporta '=','>=','<=' tiene '" + problem.constraints[i].constraint +"'" ;
}
row[i]=(i==pos?value:0)
}
for (var i=0;i<len-1;i++){
var value=2;
if (problem.constraints[i].constraint == "="){
value = 1
MV.push(-M);
}
if (problem.constraints[i].constraint == "<="){
continue;
}
if (problem.constraints[i].constraint == ">="){
value = 1
MV.push(-M);
}
if (value == 2){
throw "Estructura Problem es invalida en sus constraints ["+i+"]. solo soporta '=','>=','<=' tiene '" + problem.constraints[i].constraint +"'" ;
}
row.push((i==pos?value:0))
}
RowName.push("s"+pos)
return row
}
var initTable = function(problem){
var table = []
coeficientesEconomicos = Object.keys(problem.objective)
RowName = []
coeficientesEconomicos.forEach(function (k){
RowName.push(k)
})
if (problem.optimizationType == 'min'){
coeficientesEconomicos.forEach(function (k){
problem.objective[k] = (-1)*problem.objective[k]
}
)
}
var last = 0;
ColName = []
ColName[0] = []
for (var j in problem.constraints){
ColName[0].push("?")
}
for (var j in problem.constraints){
table[j] = []
table[j][0]=0
if (problem.constraints[j].constraint == '='){
table[j][0]= -M;
}
if (problem.constraints[j].constraint == '>=' ){
table[j][0]= -M;
}
var i=1
coeficientesEconomicos.forEach(function (k){
e = problem.constraints[j].namedVector[k]
if (e== undefined) e = 0;
table[j][i] = e
i++;
})
var r = rowIdent(j,problem)
for (var k in r){
if (r[k] == 1){
ColName[0][j] = "s"+k
}
table[j][i] = r[k]
i++;
}
table[j][i] = problem.constraints[j].constant
last = j
}
last++
var i=1;
table[last]=[]
table[last][0]=1
type=-1
if (problem.optimizationType == 'min'){
table[last][0]=-1
}
var c=1;
coeficientesEconomicos.forEach(function (k){
var e = type*problem.objective[k]
for (var d in problem.constraints){
e=e-(table[d][c]*table[d][0])
}
table[last][i] = e
i++;
c++;
})
var r = rowIdent(last,problem)
for (var k in r){
table[last][i] = r[k]
i++;
}
table[last][i] = 0
for (var i = 1; i < table[0].length-1; i++){
var acum=0;
for (var j = 0; j < table.length-1; j++) {
acum = acum + (table[j][0]*table[j][i])
}
var r = Object.values(problem.objective)[i-1]
if (r == null) r = 0;
table[table.length-1][i]= acum - r;
}
return table
}
var buscarPivot = function(table){
var min = Number.MAX_VALUE;
var col = 0;
var row = 0;
var columnaModificada = []
var f = table.length-1;
for (var c = 1; c < table[f].length-1; c++) {
if (criterial_second){
if (min >= table[f][c]){
min = table[f][c]
col = c;
row= f;
}
}else{
if (min > table[f][c]){
min = table[f][c]
col = c;
row= f;
}
}
}
var minAux = Number.MAX_VALUE;
for (var i = 0; i < table.length-1; i++) {
if (table[i][col]>0) {
var data = table[i][table[i].length-1]/table[i][col]
if (minAux >= data){
minAux= data
row=i
}
}
}
return [col,row];
}
var operar = function(table, pivot, problem) {
var filaPivot = []
var pivotValue = table[pivot[1]][pivot[0]]
filaPivot[0] = (-1)*(table[pivot[1]][0] + table[ table.length-1][pivot[0]])
for (var i=1; i< table[0].length;i++){
filaPivot[i]= table[pivot[1]][i]/ pivotValue
}
for (var i = 0; i < table.length; i++) {
if (i != pivot[1]){
var coeficientePivotFila = table[i][pivot[0]]
for (var j = 1; j < table[i].length; j++) {
table[i][j] = table[i][j] - (coeficientePivotFila *filaPivot[j])
if (table[i][j] == Infinity){
table[i][j] = M;
}
}
}else{
table[i]=filaPivot
}
}
var r = MV[pivot[0]-1]
if (r == null) r = 0;
table[pivot[1]][0]= MV[pivot[0]-1]
for (var i = 1; i < table[0].length-1; i++){
var acum=0;
for (var j = 0; j < table.length-1; j++) {
acum = acum + (table[j][0]*table[j][i])
}
var r = MV[i-1]
if (r == null) r = 0;
table[table.length-1][i]= acum - r;
}
var z =0;
for (var i=0; i< table.length-1;i++){
z=z+ (table[i][0]* table[i][table[0].length-1])
}
table[table.length-1][table[0].length-1]=z
var len = ColName.length
ColName [len] = []
for (var i=0; i< ColName[len-1].length;i++){
ColName [len].push(ColName [len-1][i])
}
ColName [len] [pivot[1]] = RowName[pivot[0]-1]
return table
}
var verificarFin = function(table, problem){
var flag = false;
var filaZ = table[table.length-1];
var limite = filaZ.length; //Object.keys(problem.objective).length
for (var i = 1; i <= limite; i++) {
if (filaZ[i] < 0) {
flag = true;
break;
}
}
var pivot =buscarPivot(table);
var col = pivot[0];
var flagc = false;
for (var i=0; i <= table.length-1;i++){
if (table[i][col] > 0) {
flagc = true;
break
}
}
// console.log("Verifica si entra una variable de la base?")
var entra = RowName[pivot[0]-1];
if (ColName[ColName.length-1].indexOf( entra) >=0){
flag = false
}
if (!flagc){
problem["result"] = "Solucion no acotada";
}
if (!(flag && flagc)){
for (var i=0; i <= table.length-1;i++){
if (table[i][0] == -M) {
problem["result"] = "No hay solucion";
break
}
}
}
return flag && flagc;
}
function ejercicioYuotube(){
var cc =[3,2];
var pp = [5,2,4,2,-3,5,5,4,10,-11,6];
var ss=['<=','<=']
var r = test(cc,pp,ss);
return (true)
}
function ejercicio1(){
var cc =[2,3];
var pp = [8,3,1,0,3,0,1,6,6,4,36];
var ss=['<=','<=','<=']
var r = test(cc,pp,ss);
console.log (r.result["z"]== 37.5 && r.result["x0"] == 3 && r.result["x1"]==4.5)
}
function ejercicio2(){
var cc =[2,3];
var pp = [5,2,-2,1,2,1,-1,2,1,1,5];
var ss=['<=','<=','<=']
var r = test(cc,pp,ss);
console.log (r.result["z"]== 20.5 && r.result["x0"] == 3.5 && r.result["x1"]==1.5)
}
function ejercicio3(){
var cc =[2,3];
var pp = [5,2,0,1,3,4,6,24,4,-3,12];
var ss=['<=','<=','<=']
var r = test(cc,pp,ss);
console.log (r.result["z"]== (68/3) && r.result["x0"] == 4 && r.result["x1"]==(4/3))
}
function ejercicio4(){
var cc =[2,3];
var pp = [5,8,6,5,30,0,1,1,-2,2,6];
var ss=['<=','>=','<=']
var r = test(cc,pp,ss);
console.log (r.result["z"]== (459/11) && r.result["x0"] == (15/11) && r.result["x1"]==(48/11))
}
function ejercicio5(){
var cc =[2,4];
var pp = [6,2,1,1,300,2.5,4,1000,0,1,200,1,0,200];
var ss=['<=','<=','=','<=']
var r = test(cc,pp,ss);
console.log (r.result["z"]== 880 && r.result["x0"] == 80 && r.result["x1"]==200)
}
function ejercicio6(){
var cc =[2,3];
var pp = [-2,4,0,1,3,4,5,24,2,2,0];
var ss=['<=','<=','>=']
var r = test(cc,pp,ss);
console.log (r.result["z"]== 12 && r.result["x0"] == 0 && r.result["x1"]==3)
}
function ejercicio7(){
var cc =[2,3];
var pp = [4,4,1,0,6,1,1,8,1,2,12];
var ss=['<=','<=','<=']
var r = test(cc,pp,ss);
console.log (r.result["z"]== 32 && r.result["x0"] == 6 && r.result["x1"]==2) // && r.result["x0"] == 4 && r.result["x1"]==4)
}
function ejercicio8(){
var cc =[2,3];
var pp = [6,4,2,4,48,4,2,60,3,0,45];
var ss=['<=','<=','<=']
var r = test(cc,pp,ss);
console.log (r.result["z"]== 96 && r.result["x0"] == 12 && r.result["x1"]==6)
}
function ejercicio9(){
var cc =[2,3];
var pp = [2,1,-5,3,5,1,1,4,2,1,10];
var ss=['>=','<=','>=']
var r = test(cc,pp,ss);
console.log (r.message== "No hay solucion")
}
function ejercicio10(){
var cc =[2,3];
var pp = [1,8,0,1,2,4,4,24,10,-30,30];
var ss=['>=','>=','>=']
var r = test(cc,pp,ss);
console.log (r.message== "Solucion no acotada")
}
function ejercicio11(){
var cc =[2,4];
var pp = [1,-2,1,0,2,2,1,10,1,2,8,0,1,1];
var ss=['>=','<=','<=','>=']
var r = test(cc,pp,ss,'Min');
console.log (r.result["z"]== -4 && r.result["x0"] == 2 && r.result["x1"]==3)
}
function ejercicio12(){
var cc =[2,3];
var pp = [3,1,1,1,6,2,1,1,-1,2,8];
var ss=['>=','<=','>=']
var r = test(cc,pp,ss,'Min');
console.log (r.message== "No hay solucion")
}
function ejercicio13(){
var cc =[2,3];
var pp = [8,30,10,12,60,3,-4,12,-3,2,8];
var ss=['>=','<=','<=']
var r = test(cc,pp,ss,'Max');
console.log (r.message== "Solucion no acotada")
}
function ejercicio14(){
var cc =[2,3];
var pp = [14,10,5,2,30,6,3,24,0,1,5];
var ss=['<=','>=','>=']
var r = test(cc,pp,ss,'Min');
console.log (r.result["z"]== 71 && r.result["x0"] == 1.5 && r.result["x1"]==5)
}
function caso1(){
var cc =[2,4];
var pp = [6,2,1,1,300,2.5,4,1000,0,1,200,1,0,200];
var ss=[]
test(cc,pp,ss);
}
function caso2(){
var cc =[2,3]
var pp = [1,8,0,1,2,4,6,24,10,-30,30];
var ss=[]
test(cc,pp,ss);
}
function caso3(){
var cc =[2,3]
var pp = [1,8,0,1,2,4,6,24,10,-30,30];
var ss=[]
test(cc,pp,ss);
}
function caso4(){
var cc =[2,3]
var pp = [5,8,6,5,30,0,1,1,-2,2,6];
var ss=[]
test(cc,pp,ss);
}
function caso5(){
var cc =[2,4]
var pp = [1,-2,1,0,2,2,1,10,1,2,8,0,1,1];
var ss=[]
test(cc,pp,ss);
}
function test(cc,pp,ss, t){
if (t == undefined) t= "Max";
// cc = [3,3]
// pp = [6300,10800,11340,3,6,6,150,1,1,1,30,80000,130000,150000,4000000];
$("#numberV").val(cc[0])
$("#numberR").val(cc[1])
carga();
for (var i in pp){$(".num")[i].value=pp[i]}
for (var i in ss){
$("#o"+i).val(ss[i])
}
$("#otype").val(t)
return calcular()
}
var resultados = function(tables,pivots, problem){
var r = {}
r = {result:{}, tables:tables, pivotsColRowVal: pivots, message:"ok"}
if (tables.length > 100){
r.message="Error!!"
}
if (problem.result != undefined){
r.message = problem.result;
return r;
}
var table = tables[tables.length-1]
var coeficientesEconomicos = ['z']
coeficientesEconomicos = coeficientesEconomicos.concat( Object.keys(problem.objective))
var last = 0;
var name = "z"
for (var i in coeficientesEconomicos){
//cuento los unos
var coutUnos=0;
var sumaCol=0;
var pos=0;
for (var j=0; j < table.length; j++){
sumaCol=sumaCol+table[j][i];
if (table[j][i] == 1){
coutUnos++;
pos = j
}
}
r["result"][coeficientesEconomicos[i]] =0
if (coutUnos==1 && sumaCol == 1){
r["result"][coeficientesEconomicos[i]] = table[pos][table[pos].length-1]
}
}
r["result"]["z"]=0;
for (var i in problem.objective){
r["result"]["z"] = r["result"]["z"] + problem.objective[i]*r["result"][i];
}
r["result"]["z"] = table[table.length-1][0]*r["result"]["z"]
return r
}
var simplex = function (problem){
var table = initTable(problem);
var pivot =0;
tables = []
pivots = []
tables.push(JSON.parse(JSON.stringify(table)))
var n=0;
while( verificarFin(table,problem) && n < 100){
pivot =buscarPivot(table)
pivots.push (JSON.parse(JSON.stringify([pivot[1],pivot[0], table[pivot[1]][pivot[0]] ])))
table = operar(table, pivot, problem)
tables.push(JSON.parse(JSON.stringify(table)))
n++;
}
r = resultados(tables, pivots,problem)
return r
}
var problem = {
objective: {
a: 3,
b: 2,
c: 5
},
constraints: [
{
namedVector: { a: 1, b: 2, c: 1 },
constraint: '=',
constant: 430,
},
{
namedVector: { a: 3, b: 0, c: 2 },
constraint: '<=',
constant: 460,
},
{
namedVector: { a: 1, b: 4, c: 0 },
constraint: '<=',
constant: 420,
},
],
optimizationType: 'max',
}
function carga(){
document.getElementById("resultado").innerHTML = ""
var carga = document.getElementById("carga");
cargaHtml = "<hr/><div class='form-group mt-2 ml-3 mr-2 mb-2'><div class='row'> <div class='col-sm-12 ' ><center><table> "
var col = Number.parseInt(document.getElementById("numberV").value)
var row = Number.parseInt(document.getElementById("numberR").value)
var rowHtml = "<tr><td>Z</td>"
for (var j =0; j < col ; j++){
rowHtml += "<td><input type='number' class='num' id='z"+j+"' value=0 /> </td>"
}
rowHtml += "<td> <select id='otype'> <option>Max</option> <option de>Min</option> </td></tr>"
cargaHtml+=rowHtml;
cargaHtml += "<td>Regla </td>"
for (var j =0; j < col ; j++){
cargaHtml += "<td>X"+j+" </td>"
}
cargaHtml += "<td>M </td>"
cargaHtml += "<td> C</td>"
for (var i =0; i < row ; i++){
var rowHtml = "<tr><td>R"+i+"</td>"
for (var j =0; j < col ; j++){
rowHtml += "<td><input type='number' class='num' id='x"+i+j+"' value=0 maxlength='3'/> </td>"
}
rowHtml += "<td> <select id='o"+i+"' > <option><=</option> <option de>>=</option> <option>=</option> </select></td>"
rowHtml += "<td><input type='number' class='num' id='r"+i+"' value=0 /> </td></tr>"
cargaHtml+=rowHtml;
}
cargaHtml += "</table></center> </div></div><div class='row'> <div class='col-sm-12' ><input type='button' class='form-control btn-success' value='Primal <-> Dual' onclick='primal2daul()' /> <br></div></div><div class='row'> <div class='col-sm-12' ><input type='button' class='form-control btn-success' value='Calcular' onclick='calcular()' /> </div></div></div><hr/>"
carga.innerHTML = cargaHtml
$("#graph").hide()
//document.getElementById("graph").style.display = "none";
}
function find_rational(value, maxdenom) {
var best = { numer: 1, denom: 1, err: Math.abs(value - 1) }
if (!maxdenom) maxdenom = 10000;
for (var denom = 1; best.err > 0 && denom <= maxdenom; denom++) {
var numer = Math.round(value * denom);
var err = Math.abs(value - numer / denom);
if (err >= best.err) continue;
best.numer = numer;
best.denom = denom;
best.err = err;
}
return best;
}
function calcular (){
document.getElementById("resultado").innerHTML = ""
var col = Number.parseInt(document.getElementById("numberV").value)
var row = Number.parseInt(document.getElementById("numberR").value);
var problem = {objective: {}, constraints: [], optimizationType: document.getElementById("otype").value.toLowerCase()}
var col = Number.parseInt(document.getElementById("numberV").value)
var row = Number.parseInt(document.getElementById("numberR").value);
for (var i =0; i< col; i++){
problem.objective["x"+i] = Number.parseFloat(document.getElementById("z"+i).value)
}
for (var i =0; i< row; i++){
problem.constraints[i]={}
problem.constraints[i]["namedVector"]={}
problem.constraints[i]["constraint"]=document.getElementById("o"+i).value
problem.constraints[i]["constant"]=Number.parseFloat(document.getElementById("r"+i).value)
for (var j =0; j< col; j++){
problem.constraints[i].namedVector["x"+j] = Number.parseFloat(document.getElementById("x"+i+j).value)
}
}
var coeficientesEconomicos = ['Z']
coeficientesEconomicos = coeficientesEconomicos.concat( Object.keys(problem.objective))
criterial_second = false;
var r = simplex(problem)
//console.log(r)
criterial_second = true;
var r1 =simplex(problem)
//console.log(r1)
var multi_Result_flag = false
if (r.result.z == r1.result.z){
for (var k in r.result){
if( r.result[k] != r1.result[k]){
multi_Result_flag = true
break;
}
}
}
var html = " <div class='ml-3'>";
html += "<span><b>Resultados:</b>"+ r.message +"<br/>"
if (multi_Result_flag) html += "<b>Solucion 1</b><br/>";
for (var k in r.result){
html += "<span><b> "+ k +":</b><span class='fraccionable'>"+ r.result[k] +"</span></span><br/>"
}
if (multi_Result_flag){
html += "<b>Solucion 2</b><br/>";
for (var k in r1.result){
html += "<span><b> "+ k +":</b><span class='fraccionable'>"+ r1.result[k] +"</span></span><br/>"
}
}
html += "<br/><center><input type='button' id='btnFrac' class=' btn-success' value='Pasar a fraccion' onclick='toFraction()' /></center></span> </div>"
html += "</tr></table><hr/>";
for (var n=0; n< r.tables.length;n++){
html += "<div style='float: left;padding: 7px;' ><b>Tabla Nº"+(n+1) + "<br/></b><table border=1>"
html += "<tr>"
html += "<td rowspan=2 colspan=2 >Ci/Cj</td>"
for (var j=1; j< coeficientesEconomicos.length; j++ ){
html += "<td>"+ MV[j-1] +"</td>"
}
for (var j=coeficientesEconomicos.length; j< (r.tables[n][0].length-1); j++ ){
html += "<td>"+ MV[j-1] +"</td>"
}
html += "<td colspan=2>-</td>"
html += "</tr>";
html += "<tr>"
for (var j=1; j< coeficientesEconomicos.length; j++ ){
html += "<td>"+ coeficientesEconomicos[j] +"</td>"
}
for (var j=coeficientesEconomicos.length; j< (r.tables[n][0].length-1); j++ ){
html += "<td>s"+ (j-coeficientesEconomicos.length) +"</td>"
}
html += "<td>Xj</td>"
html += "</tr>";
for (var i=0; i< r.tables[n].length; i++ ){
html += "<tr>"
if (ColName[n][i] != undefined){
html += "<td>"+ ColName[n][i]+ "</td>"
}else{
html += "<td>-</td>"
}
for (var j=0; j< tables[n][i].length; j++ ){
html += "<td class='fraccionable' name='data"+i+j+"'"
if (r.pivotsColRowVal[n] != undefined){
if (r.pivotsColRowVal[n][0] == (i) && r.pivotsColRowVal[n][1] != (j)){
html += " bgcolor='#00FF00' "
}
if (r.pivotsColRowVal[n][1] == (j) && r.pivotsColRowVal[n][0] != (i)){
html += " bgcolor='#00FFFF' "
}
if (r.pivotsColRowVal[n][1] == (j) && r.pivotsColRowVal[n][0] == (i)){
html += " bgcolor='#FFFF00' "
}
}
html +=">"+r.tables[n][i][j]+"</td>"
}
html += "</tr>"
}
html += "</table></div>"
}
html += "<br/> "
p=problem;
document.getElementById("resultado").innerHTML = html;
if (Object.keys(problem.objective).length == 2){
graph(problem, r)
}
return r;
}
function primal2daul(){
var numberV = $("#numberV").val();
var numberR = $("#numberR").val();
var op = $("#otype").val();
var objective = []
for (var i=0; i< numberV; i++){
objective.push($("#z"+i).val())
}
var constants = []
var rules = []
//TODO: desdoble del signo igual
for (var i=0; i< numberR; i++){
rules.push([]);
var signo = 1;
if ($("#otype").val() == "Max" && $("#o"+i).val()==">="){
signo = -1;
}
if ($("#otype").val() == "Min" && $("#o"+i).val()=="<="){
signo = -1;
}
constants.push(signo * $("#r"+i).val())
for (var j=0; j< numberV; j++){
rules[i][j]= signo * $("#x"+i+j).val()
}
}
for (var i=0; i< numberR; i++){
if ($("#o"+i).val()=="="){
rules.push([]);
var signo = -1;
constants.push(signo * $("#r"+i).val())
numberR++
for (var j=0; j< numberV; j++){
rules[rules.length-1][j]= signo * $("#x"+i+j).val()
}
}
}
$("#numberV").val(numberR);
$("#numberR").val(numberV);
carga();
if (op == "Max") $("#otype").val("Min")
for (var i=0; i< numberR; i++){
$("#z"+i).val(constants[i])
}
for (var i=0; i< numberV; i++){
$("#o"+i).val(">=")
if ($("#otype").val() == "Max"){
$("#o"+i).val("<=")
}
var signo = 1;
if (objective[i] < 0){
signo = -1
if ($("#o"+i).val() =="<="){
$("#o"+i).val(">=")
}else{
$("#o"+i).val("<=")
}
}
$("#r"+i).val(signo* objective[i])
for (var j=0; j< numberR; j++){
$("#x"+i+j).val(signo*rules[j][i])
}
}
}
function toFraction(){
$(".fraccionable").each(function(e){
var num = find_rational($(this).text(),10000)
if (num.denom != 1){
$(this).text((num.numer + "/" + num.denom))
}else{
$(this).text(num.numer )
}
})
$("#btnFrac").hide()
}
function intersect_rect(r1,r2){
var a1 = r1[0];
var b1 = r1[1];
var c1 = r1[2];
var a2 = r2[0];
var b2 = r2[1];
var c2 = r2[2];
if (a1 == 0 && a2 != 0 && b1 != 0){
y = c1/b1;
x = (c2 - b2*y)/a2;
return [x,y]
}
if (a1 != 0 && a2 == 0 && b2 != 0 ){
y = c2/b2;
x = (c1 - b1*y)/a1;
return [x,y]
}
if (b1 == 0 && b2 != 0 && a1 !=0){
x = c1/a1;
y = (c2 - a2*x)/b2;
return [x,y]
}
if (b1 != 0 && b2 == 0 && a2 != 0){
x = c2/a2;
y = (c1 - a1*x)/b1;
return [x,y]
}
if (a1 == 0 && a2 == 0 && b1 != 0 && b2 != 0){
if ( (c1/b1) == (c2/b2) ) {
return [undefined, (c2/b2)]
}
return [undefined,undefined]
}
if (b1 == 0 && b2 == 0 && a1 != 0 && a2 != 0){
if ( (c1/a1) == (c2/a2) ) {
return [undefined, (c2/a2)]
}
return [undefined,undefined]
}
if (a1 != 0 && a2 != 0){
if (b1 != (a1*b2/a2)){
y = (c1-(a1*c2/a2))/(b1-(a1*b2/a2));
x = (c1 - b1*y)/a1;
return [x,y]
}
if (b2 != (a2*b1/a1)){
y = (c2-(a2*c1/a1))/(b2-(a2*b1/a1));
x = (c2 - b2*y)/a2;
return [x,y]
}
}
return [undefined,undefined];
}
var p