/**
 * @license Fraction.js v2.7.0 01/06/2015
 * http://www.xarg.org/2014/03/rational-numbers-in-javascript/
 *
 * Copyright (c) 2015, Robert Eisele (robert@xarg.org)
 * Dual licensed under the MIT or GPL Version 2 licenses.
 **/

// NOTE: This is a nice example, but a stable version of this is served with Polynomial.js: 
// https://github.com/infusion/Polynomial.js

var Fraction = require('../fraction.min.js');

function integrate(poly) {

    poly = poly.replace(/\s+/g, "");

    var regex = /(\([+-]?[0-9/]+\)|[+-]?[0-9/]+)x(?:\^(\([+-]?[0-9/]+\)|[+-]?[0-9]+))?/g;
    var arr;
    var res = {};
    while (null !== (arr = regex.exec(poly))) {

        var a = (arr[1] || "1").replace("(", "").replace(")", "").split("/");
        var b = (arr[2] || "1").replace("(", "").replace(")", "").split("/");

        var exp = new Fraction(b).add(1);
        var key = "" + exp;

        if (res[key] !== undefined) {
            res[key] = {x: new Fraction(a).div(exp).add(res[key].x), e: exp};
        } else {
            res[key] = {x: new Fraction(a).div(exp), e: exp};
        }
    }

    var str = "";
    var c = 0;
    for (var i in res) {
        if (res[i].x.s !== -1 && c > 0) {
            str += ("+");
        } else if (res[i].x.s === -1) {
            str += ("-");
        }
        if (res[i].x.n / res[i].x.d !== 1) {
            if (res[i].x.d !== 1) {
                str += ("" + res[i].x.n + "/" + res[i].x.d + "");
            } else {
                str += ("" + res[i].x.n);
            }
        }
        str += ("x");
        if (res[i].e.n / res[i].e.d !== 1) {
            str += ("^");
            if (res[i].e.d !== 1) {
                str += ("(" + res[i].e.n + "/" + res[i].e.d + ")");
            } else {
                str += ("" + res[i].e.n);
            }
        }
        c++;
    }
    return str;
}

var poly = "-2/3x^3-2x^2+3x+8x^3-1/3x^(4/8)";

console.log("f(x): " + poly);
console.log("F(x): " + integrate(poly));