KAS/test.html at master · Khan/KAS · GitHub

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<!DOCTYPE html>
<html>
<head>
    <meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
    <title>KAS Browser Tests</title>

    <!-- Include QUnit -->
    <link rel="stylesheet" href="node_modules/qunit/qunit/qunit.css" type="text/css" media="screen">
    <script src="node_modules/qunit/qunit/qunit.js"></script>
    <script src="node_modules/qunit-assert-close/qunit-assert-close.js"></script>

    <!-- Include Underscore -->
    <script src="node_modules/underscore/underscore.js"></script>

    <!-- Include KAS -->
    <script src="src/parser.js"></script>
    <script src="src/unitparser.js"></script>
    <script src="src/nodes.js"></script>
    <script src="src/compare.js"></script>
</head>
<body>

<h1 id="qunit-header">KAS Browser Tests</h1>
<h2 id="qunit-banner"></h2>
<div id="qunit-testrunner-toolbar"></div>
<h2 id="qunit-userAgent"></h2>
<ol id="qunit-tests"></ol>

<div id="qunit-fixture">
    <div id="solutionarea">
    </div>
    <div class="problem">
    </div>
</div>

<script type="text/javascript">
(function(KAS) {

    var parse = function(input, options) {
        return KAS.parse(input, options).expr;
    };


    QUnit.module("parsing");

    var print = function(assert, input, expected, options) {
        var message = input + " parses as " + expected;
        assert.close(parse(input, options).print(), expected, 1e-9, message);
    };

    QUnit.test("empty", function(assert) {
        print(assert, "", "");
    });

    QUnit.test("positive and negative primitives", function(assert) {
        print(assert, "0", "0");
        print(assert, "1.", "1");
        print(assert, "3.14", "3.14");
        print(assert, ".14", "0.14");
        print(assert, "pi", "pi");
        print(assert, "e", "e");
        print(assert, "x", "x");
        print(assert, "theta", "theta");

        print(assert, "-0", "-1*0");
        print(assert, "-1.", "-1");
        print(assert, "-3.14", "-3.14");
        print(assert, "-.14", "-0.14");
        print(assert, "-pi", "-1*pi");
        print(assert, "-e", "-1*e");
        print(assert, "-theta", "-1*theta");
    });

    QUnit.test("LaTeX constants", function(assert) {
        print(assert, "\\theta", "theta");
        print(assert, "\\pi", "pi");
        print(assert, "\\phi", "phi");
    });

    QUnit.test("ignore TeX spaces", function(assert) {
        print(assert, "a\\space b", "a*b");
        print(assert, "a\\ b", "a*b");
    });

    QUnit.test("positive and negative rationals", function(assert) {
        print(assert, "1/2", "1/2");
        print(assert, "-1/2", "-1/2");
        print(assert, "1/-2", "-1/2");
        print(assert, "-1/-2", "-1*-1/2");
        print(assert, "42/42", "42/42");
        print(assert, "42/1", "42/1");
        print(assert, "0/42", "0/42");

        print(assert, "2 (1/2)", "2*1/2");
        print(assert, "1/2 1/2", "1/2*1/2");
        print(assert, "-1/2", "-1/2");
        print(assert, "1/2 2", "1/2*2");
    });

    QUnit.test("rationals using \\frac", function(assert) {
        print(assert, "\\frac{1}{2}", "1/2");
        print(assert, "\\frac{-1}{2}", "-1/2");
        print(assert, "\\frac{1}{-2}", "-1/2");
        print(assert, "\\frac{-1}{-2}", "-1*-1/2");
        print(assert, "\\frac{42}{42}", "42/42");
        print(assert, "\\frac{42}{1}", "42/1");
        print(assert, "\\frac{0}{42}", "0/42");

        print(assert, "2\\frac{1}{2}", "2*1/2");
        print(assert, "\\frac{1}{2}\\frac{1}{2}", "1/2*1/2");
        print(assert, "-\\frac{1}{2}", "-1/2");
        print(assert, "\\frac{1}{2}2", "1/2*2");
    });

    QUnit.test("rationals using \\dfrac", function(assert) {
        print(assert, "\\dfrac{1}{2}", "1/2");
        print(assert, "\\dfrac{-1}{2}", "-1/2");
        print(assert, "\\dfrac{1}{-2}", "-1/2");
        print(assert, "\\dfrac{-1}{-2}", "-1*-1/2");
        print(assert, "\\dfrac{42}{42}", "42/42");
        print(assert, "\\dfrac{42}{1}", "42/1");
        print(assert, "\\dfrac{0}{42}", "0/42");

        print(assert, "2\\dfrac{1}{2}", "2*1/2");
        print(assert, "\\dfrac{1}{2}\\dfrac{1}{2}", "1/2*1/2");
        print(assert, "-\\dfrac{1}{2}", "-1/2");
        print(assert, "\\dfrac{1}{2}2", "1/2*2");
    });

    QUnit.test("parens", function(assert) {
        print(assert, "(0)", "0");
        print(assert, "(ab)", "a*b");
        print(assert, "(a/b)", "a*b^(-1)");
        print(assert, "(a^b)", "a^(b)");
        print(assert, "(ab)c", "a*b*c");
        print(assert, "a(bc)", "a*b*c");
        print(assert, "a+(b+c)", "a+b+c");
        print(assert, "(a+b)+c", "a+b+c");
        print(assert, "a(b+c)", "a*(b+c)");
        print(assert, "(a+b)^c", "(a+b)^(c)");
        print(assert, "(ab)^c", "(a*b)^(c)");
    });

    QUnit.test("subscripts", function(assert) {
        print(assert, "a", "a");
        print(assert, "a_0", "a_(0)");
        print(assert, "a_i", "a_(i)");
        print(assert, "a_n", "a_(n)");
        print(assert, "a_n+1", "a_(n)+1");
        print(assert, "a_(n+1)", "a_(n+1)");
        print(assert, "a_{n+1}", "a_(n+1)");
    });

    QUnit.test("negation", function(assert) {
        print(assert, "-x", "-1*x");
        print(assert, "--x", "-1*-1*x");
        print(assert, "---x", "-1*-1*-1*x");
        print(assert, "-1", "-1");
        print(assert, "--1", "-1*-1");
        print(assert, "---1", "-1*-1*-1");
        print(assert, "-3x", "-3*x");
        print(assert, "--3x", "-1*-3*x");
        print(assert, "-x*3", "x*-3");
        print(assert, "--x*3", "-1*x*-3");
        print(assert, "\u2212x", "-1*x");
    });

    QUnit.test("addition and subtraction", function(assert) {
        print(assert, "a+b", "a+b");
        print(assert, "a-b", "a+-1*b");
        print(assert, "a--b", "a+-1*-1*b");
        print(assert, "a---b", "a+-1*-1*-1*b");
        print(assert, "2-4", "2+-4");
        print(assert, "2--4", "2+-1*-4");
        print(assert, "2---4", "2+-1*-1*-4");
        print(assert, "2-x*4", "2+x*-4");
        print(assert, "1-2+a-b+pi-e", "1+-2+a+-1*b+pi+-1*e");
        print(assert, "x+1", "x+1");
        print(assert, "x-1", "x+-1");
        print(assert, "(x-1)", "x+-1");
        print(assert, "a(x-1)", "a*(x+-1)");
        print(assert, "a\u2212b", "a+-1*b");
    });

    QUnit.test("multiplication", function(assert) {
        print(assert, "a*b", "a*b");
        print(assert, "-a*b", "-1*a*b");
        print(assert, "a*-b", "a*-1*b");
        print(assert, "-ab", "-1*a*b");
        print(assert, "-a*b", "-1*a*b");
        print(assert, "-(ab)", "-1*a*b");
        print(assert, "a\u00b7b", "a*b");
        print(assert, "a\u00d7b", "a*b");
        print(assert, "a\\cdotb", "a*b");
        print(assert, "a\\timesb", "a*b");
        print(assert, "a\\astb", "a*b");
    })

    QUnit.test("division", function(assert) {
        print(assert, "a/b", "a*b^(-1)");
        print(assert, "a/bc", "a*b^(-1)*c");
        print(assert, "(ab)/c", "a*b*c^(-1)");
        print(assert, "ab/c", "a*b*c^(-1)");
        print(assert, "ab/cd", "a*b*c^(-1)*d");
        print(assert, "a\\divb", "a*b^(-1)");
        print(assert, "a\u00F7b", "a*b^(-1)");
    });

    QUnit.test("exponentiation", function(assert) {
        print(assert, "x^y", "x^(y)");
        print(assert, "x^y^z", "x^(y^(z))");
        print(assert, "x^yz", "x^(y)*z");
        print(assert, "-x^2", "-1*x^(2)");
        print(assert, "-(x^2)", "-1*x^(2)");
        print(assert, "0-x^2", "0+-1*x^(2)");
        print(assert, "x^-y", "x^(-1*y)");
        print(assert, "x^(-y)", "x^(-1*y)");
        print(assert, "x^-(y)", "x^(-1*y)");
        print(assert, "x^-(-y)", "x^(-1*-1*y)");
        print(assert, "x^--y", "x^(-1*-1*y)");
        print(assert, "x^-yz", "x^(-1*y)*z");
        print(assert, "x^-y^z", "x^(-1*y^(z))");
        print(assert, "x**y", "x^(y)");

        print(assert, "x^{a}", "x^(a)");
        print(assert, "x^{ab}", "x^(a*b)");
    });

    QUnit.test("square root", function(assert) {
        print(assert, "sqrt(x)", "x^(1/2)");
        print(assert, "sqrt(x)y", "x^(1/2)*y");
        print(assert, "1/sqrt(x)", "x^(-1/2)");
        print(assert, "1/sqrt(x)y", "x^(-1/2)*y");

        print(assert, "sqrt(2)/2", "2^(1/2)*1/2");
        print(assert, "sqrt(2)^2", "(2^(1/2))^(2)");

        print(assert, "\\sqrt(x)", "x^(1/2)");
        print(assert, "\\sqrt(x)y", "x^(1/2)*y");
        print(assert, "1/\\sqrt(x)", "x^(-1/2)");
        print(assert, "1/\\sqrt(x)y", "x^(-1/2)*y");

        print(assert, "\\sqrt(2)/2", "2^(1/2)*1/2");
        print(assert, "\\sqrt(2)^2", "(2^(1/2))^(2)");

        print(assert, "\\sqrt{2}", "2^(1/2)");
        print(assert, "\\sqrt{2+2}", "(2+2)^(1/2)");
    });

    QUnit.test("nth root", function(assert) {
        print(assert, "sqrt[3]{x}", "x^(1/3)");
        print(assert, "sqrt[4]{x}y", "x^(1/4)*y");
        print(assert, "1/sqrt[5]{x}", "x^(-1/5)");
        print(assert, "1/sqrt[7]{x}y", "x^(-1/7)*y");

        print(assert, "sqrt[3]{2}/2", "2^(1/3)*1/2");
        print(assert, "sqrt[3]{2}^2", "(2^(1/3))^(2)");

        print(assert, "\\sqrt[4]{x}", "x^(1/4)");
        print(assert, "\\sqrt[4]{x}y", "x^(1/4)*y");
        print(assert, "1/\\sqrt[4]{x}", "x^(-1/4)");
        print(assert, "1/\\sqrt[4]{x}y", "x^(-1/4)*y");

        print(assert, "\\sqrt[5]{2}/2", "2^(1/5)*1/2");
        print(assert, "\\sqrt[5]{2}^2", "(2^(1/5))^(2)");

        print(assert, "\\sqrt[6]{2}", "2^(1/6)");
        print(assert, "\\sqrt[6]{2+2}", "(2+2)^(1/6)");

        print(assert, "\\sqrt[2]{2}", "2^(1/2)");
        print(assert, "\\sqrt[2]{2+2}", "(2+2)^(1/2)");
    });

    QUnit.test("absolute value", function(assert) {
        print(assert, "abs(x)", "abs(x)");
        print(assert, "abs(abs(x))", "abs(abs(x))");
        print(assert, "abs(x)abs(y)", "abs(x)*abs(y)");

        print(assert, "|x|", "abs(x)");
        print(assert, "||x||", "abs(abs(x))");
        // TODO(alex): fix the below so it doesn't require an *
        // may require own lexer/preprocessor
        print(assert, "|x|*|y|", "abs(x)*abs(y)");

        print(assert, "\\abs(x)", "abs(x)");
        print(assert, "\\abs(\\abs(x))", "abs(abs(x))");
        print(assert, "\\abs(x)\\abs(y)", "abs(x)*abs(y)");

        print(assert, "\\left|x\\right|", "abs(x)");
        print(assert, "\\left|\\left|x\\right|\\right|", "abs(abs(x))");
        print(assert, "\\left|x\\right|\\left|y\\right|", "abs(x)*abs(y)");
    });

    QUnit.test("logarithms", function(assert) {
        print(assert, "lnx", "ln(x)");
        print(assert, "ln x", "ln(x)");
        print(assert, "ln x^y", "ln(x^(y))");
        print(assert, "ln xy", "ln(x*y)");
        print(assert, "ln x/y", "ln(x*y^(-1))");
        print(assert, "ln x+y", "ln(x)+y");
        print(assert, "ln x-y", "ln(x)+-1*y");

        print(assert, "ln xyz", "ln(x*y*z)");
        print(assert, "ln xy/z", "ln(x*y*z^(-1))");
        print(assert, "ln xy/z+1", "ln(x*y*z^(-1))+1");

        print(assert, "ln x(y)", "ln(x)*y");

        print(assert, "logx", "log_(10) (x)");
        print(assert, "log x", "log_(10) (x)");
        print(assert, "log_2x", "log_(2) (x)");
        print(assert, "log _ 2 x", "log_(2) (x)");
        print(assert, "log_bx_0", "log_(b) (x_(0))");
        print(assert, "log_x_0b", "log_(x_(0)) (b)");

        print(assert, "log_2.5x", "log_(2.5) (x)");

        print(assert, "ln ln x", "ln(ln(x))");
        print(assert, "ln x ln y", "ln(x)*ln(y)");
        print(assert, "ln x/ln y", "ln(x)*ln(y)^(-1)");

        print(assert, "\\lnx", "ln(x)");
        print(assert, "\\ln x", "ln(x)");
        print(assert, "\\ln x^y", "ln(x^(y))");
        print(assert, "\\ln xy", "ln(x*y)");
        print(assert, "\\ln x/y", "ln(x*y^(-1))");
        print(assert, "\\ln x+y", "ln(x)+y");
        print(assert, "\\ln x-y", "ln(x)+-1*y");

        print(assert, "\\logx", "log_(10) (x)");
        print(assert, "\\log x", "log_(10) (x)");
        print(assert, "\\log_2x", "log_(2) (x)");
        print(assert, "\\log _ 2 x", "log_(2) (x)");
        print(assert, "\\log_bx_0", "log_(b) (x_(0))");
        print(assert, "\\log_x_0b", "log_(x_(0)) (b)");

        print(assert, "\\log_2.5x", "log_(2.5) (x)");

        print(assert, "\\frac{\\logx}{y}", "log_(10) (x)*y^(-1)");
        print(assert, "\\frac{\\log x}{y}", "log_(10) (x)*y^(-1)");
    });

    QUnit.test("trig functions", function(assert) {
        var functions = [
            "sin", "cos", "tan",
            "csc", "sec", "cot"
        ];

        var inverses = _.map(functions, function(func) {
            return "arc" + func;
        });

        _.each(functions.concat(inverses), function(func) {
            print(assert, func + "x", func + "(x)");
            print(assert, "\\" + func + "x", func + "(x)");
        });

        print(assert, "sin^-1 x", "arcsin(x)");
        print(assert, "\\sin^-1 x", "arcsin(x)");

        print(assert, "(sinx)^2", "sin(x)^(2)");
        print(assert, "sin^2x", "sin(x)^(2)");
        print(assert, "sin^2(x)", "sin(x)^(2)");
        print(assert, "sin^2 x", "sin(x)^(2)");
        print(assert, "(sin^2x)", "sin(x)^(2)");

        print(assert, "sin xy", "sin(x*y)");
        print(assert, "sin x(y)", "sin(x)*y");
        print(assert, "sin x/y", "sin(x*y^(-1))");
        print(assert, "(sin x)/y", "sin(x)*y^(-1)");

        print(assert, "sin sin x", "sin(sin(x))");
        print(assert, "sin x sin y", "sin(x)*sin(y)");
        print(assert, "sin x/sin y", "sin(x)*sin(y)^(-1)");

        print(assert, "1/(sinx)^2", "sin(x)^(-2)");
        print(assert, "1/sin^2x", "sin(x)^(-2)");
        print(assert, "1/sin^2(x)", "sin(x)^(-2)");
        print(assert, "1/(sin^2x)", "sin(x)^(-2)");

        print(assert, "sin(theta)", "sin(theta)");
        print(assert, "\\sin(\\theta)", "sin(theta)");
    });

    QUnit.test("hyperbolic functions", function(assert) {
        print(assert, "sinh xy", "sinh(x*y)");
        print(assert, "1/(sinhx)^2", "sinh(x)^(-2)");
        print(assert, "\\sinh(\\theta)", "sinh(theta)");
    });

    QUnit.test("formulas", function(assert) {
        print(assert, "mx+b", "m*x+b");
        print(assert, "v^2/r", "v^(2)*r^(-1)");
        print(assert, "4/3pir^3", "4/3*pi*r^(3)");
        print(assert, "4/3\u03C0r^3", "4/3*pi*r^(3)");
        print(assert, "sin^2 x + cos^2 x = 1", "sin(x)^(2)+cos(x)^(2)=1");
    });

    QUnit.test("factors", function(assert) {
        print(assert, "(6x+1)(x-1)", "(6*x+1)*(x+-1)");
    });

    QUnit.test("whitespace", function(assert) {
        print(assert, "12/3", "12/3");
        print(assert, "12 /3", "12/3");
        print(assert, "12/ 3", "12/3");
        print(assert, "xy", "x*y");
        print(assert, "x y", "x*y");
    });

    QUnit.test("equations", function(assert) {
        print(assert, "y=x", "y=x");
        print(assert, "y=x^2", "y=x^(2)");
        print(assert, "1<2", "1<2");
        print(assert, "1<=2", "1<=2");
        print(assert, "1\\le2", "1<=2");
        print(assert, "2>1", "2>1");
        print(assert, "2>=1", "2>=1");
        print(assert, "2\\ge1", "2>=1");
        print(assert, "1<>2", "1<>2");
        print(assert, "1=/=2", "1<>2");
        print(assert, "1\\ne2", "1<>2");
        print(assert, "1\\neq2", "1<>2");
        print(assert, "a\u2260b", "a<>b");
        print(assert, "a\u2264b", "a<=b");
        print(assert, "a\u2265b", "a>=b");
    });

    QUnit.test("function variables", function(assert) {
        print(assert, "f(x)", "f*x");
        print(assert, "f(x)", "f(x)", {functions: ["f"]});
        print(assert, "f(x+y)", "f(x+y)", {functions: ["f"]});
        print(assert, "f(x)g(x)", "f(x)*g(x)", {functions: ["f", "g"]});
        print(assert, "f(g(h(x)))", "f(g(h(x)))", {functions: ["f", "g", "h"]});

        print(assert, "f\\left(x\\right)", "f*x");
        print(assert, "f\\left(x\\right)", "f(x)", {functions: ["f"]});
        print(assert, "f\\left(x+y\\right)", "f(x+y)", {functions: ["f"]});
        print(assert, "f\\left(x\\right)g\\left(x\\right)", "f(x)*g(x)", {functions: ["f", "g"]});
        print(assert, "f\\left(g\\left(h\\left(x\\right)\\right)\\right)", "f(g(h(x)))", {functions: ["f", "g", "h"]});
    });

    var repr = function(assert, input, expected, options) {
        var message = input + " parses as " + expected;
        assert.strictEqual(parse(input, options).repr(), expected, message);
    };

    QUnit.test("structure", function(assert) {
        repr(assert, "", "Add()");
        repr(assert, "1.", "1");
        repr(assert, "1/2", "1/2");
        repr(assert, "1/-2", "-1/2");
        repr(assert, "x/-2", "Mul(Var(x),-1/2)");
        repr(assert, "a+b", "Add(Var(a),Var(b))");
        repr(assert, "a+b+c", "Add(Var(a),Var(b),Var(c))");
        repr(assert, "a-b", "Add(Var(a),Mul(-1,Var(b)))");
        repr(assert, "a-b+c", "Add(Var(a),Mul(-1,Var(b)),Var(c))");
        repr(assert, "abc", "Mul(Var(a),Var(b),Var(c))");
        repr(assert, "a/bc", "Mul(Var(a),Pow(Var(b),-1),Var(c))");
        repr(assert, "a*(b+c)", "Mul(Var(a),Add(Var(b),Var(c)))");
        repr(assert, "x--y", "Add(Var(x),Mul(-1,-1,Var(y)))");
        repr(assert, "--y", "Mul(-1,-1,Var(y))");
        repr(assert, "e", "Const(e)");
        repr(assert, "2e", "Mul(2,Const(e))");
        repr(assert, "2e^x", "Mul(2,Pow(Const(e),Var(x)))");
        repr(assert, "cdef", "Mul(Var(c),Var(d),Const(e),Var(f))");
        repr(assert, "pi", "Const(pi)");
        repr(assert, "pi^2", "Pow(Const(pi),2)")
        repr(assert, "pir", "Mul(Const(pi),Var(r))");
        repr(assert, "pir^2", "Mul(Const(pi),Pow(Var(r),2))");
        repr(assert, "y=x^2", "Eq(Var(y),=,Pow(Var(x),2))");
        repr(assert, "log_2x", "Log(2,Var(x))");
        repr(assert, "f(x+y)", "Mul(Var(f),Add(Var(x),Var(y)))");
        repr(assert, "f(x+y)", "Func(f,Add(Var(x),Var(y)))", {functions: ["f"]});
        repr(assert, "sin(theta)", "Trig(sin,Var(theta))");
        repr(assert, "tanh(theta)", "Trig(tanh,Var(theta))");

        // verify that negative signs get folded into numbers
        repr(assert, "-x*3", "Mul(Var(x),-3)");
        repr(assert, "sin -x*3", "Trig(sin,Mul(Var(x),-3))");
    });


    QUnit.module("rendering");

    var tex = function(assert, input, expected, options) {
        var message = input + " renders as " + expected;
        assert.strictEqual(parse(input, options).tex(), expected, message);
    };

    QUnit.test("positive and negative primitives", function(assert) {
        tex(assert, "0", "0");
        tex(assert, "-1", "-1");
        tex(assert, "--1", "--1");
        tex(assert, "-2", "-2");
        tex(assert, "--2", "--2");
        tex(assert, "x", "x");
        tex(assert, "theta", "\\theta");
        tex(assert, "1/2", "\\frac{1}{2}");
        tex(assert, "-1/2", "-\\frac{1}{2}");
        tex(assert, "1/-2", "-\\frac{1}{2}");
        tex(assert, "-1/-2", "--\\frac{1}{2}");
    });

    QUnit.test("addition", function(assert) {
        tex(assert, "1-2", "1-2");
        tex(assert, "a+b", "a+b");
        tex(assert, "a-b", "a-b");
        tex(assert, "a-1b", "a-1b");
        tex(assert, "a+-b", "a+-b");
        tex(assert, "a+-1b", "a+-1b");
    });

    QUnit.test("multiplication", function(assert) {
        tex(assert, "ab", "ab");
        tex(assert, "a*b", "ab");
        tex(assert, "a/b", "\\frac{a}{b}");
        tex(assert, "a/bc/d", "\\frac{ac}{bd}");

        tex(assert, "1/(x+y)", "\\frac{1}{x+y}");
        tex(assert, "2/(x+y)", "\\frac{2}{x+y}");
        tex(assert, "(z+2)/(x+y)", "\\frac{z+2}{x+y}");
        tex(assert, "(z+2)/4", "\\frac{z+2}{4}");
    });

    QUnit.test("rational expressions", function(assert) {
        tex(assert, "x+1/2", "x+\\frac{1}{2}");
        tex(assert, "x-1/2", "x-\\frac{1}{2}");

        tex(assert, "1/2x", "\\frac{1}{2}x");
        tex(assert, "1/2x/y", "\\frac{1}{2}\\frac{x}{y}");
        tex(assert, "5*1/2x/y", "\\frac{1}{2}\\frac{5x}{y}");
        tex(assert, "1/2*4*x/y", "\\frac{1}{2}\\frac{4x}{y}");
        tex(assert, "-1/2x", "-\\frac{1}{2}x");
        tex(assert, "a-1/2x", "a-\\frac{1}{2}x");

        tex(assert, "1/(2x)", "\\frac{1}{2x}");
        tex(assert, "8/(7p^4)", "\\frac{8}{7p^{4}}");

        tex(assert, "x/2", "\\frac{x}{2}");
        tex(assert, "1x/2", "\\frac{1x}{2}");
        tex(assert, "-x/2", "-\\frac{x}{2}");
        tex(assert, "x/-2", "-\\frac{x}{2}");
        tex(assert, "x/-2/-3", "--\\frac{x}{2 \\cdot 3}");
        tex(assert, "--x/2/3", "--\\frac{x}{2 \\cdot 3}");
        tex(assert, "a-x/2", "a-\\frac{x}{2}");

        tex(assert, "1*-2", "1 \\cdot -2");
        tex(assert, "1*-2*3", "1 \\cdot -2 \\cdot 3");
        tex(assert, "1*-2*3/4", "1 \\cdot -2 \\cdot \\frac{3}{4}");
        tex(assert, "1*-2*3/4/5", "1 \\cdot -2 \\cdot \\frac{3}{4} \\cdot \\frac{1}{5}");
        tex(assert, "1/2*1/2", "\\frac{1}{2} \\cdot \\frac{1}{2}");
    });

    QUnit.test("exponentiation", function(assert) {
        tex(assert, "x^y", "x^{y}");
        tex(assert, "xy^z", "xy^{z}");
        tex(assert, "(xy)^z", "(xy)^{z}");
        tex(assert, "(x+y)^z", "(x+y)^{z}");
        tex(assert, "x^(yz)", "x^{yz}");
        tex(assert, "x^-(yz)", "x^{-yz}");
        tex(assert, "x^(y+z)", "x^{y+z}");
        tex(assert, "x^-(y+z)", "x^{-(y+z)}");
        tex(assert, "(x^y)^z", "(x^{y})^{z}");
        tex(assert, "pir^2", "\\pi r^{2}");
    });

    QUnit.test("square root", function(assert) {
        tex(assert, "sqrt(x)", "\\sqrt{x}");
        tex(assert, "sqrt(x)y", "\\sqrt{x}y");
        tex(assert, "1/sqrt(x)", "\\frac{1}{\\sqrt{x}}");
        tex(assert, "1/sqrt(x)y", "\\frac{y}{\\sqrt{x}}");

        tex(assert, "sqrt(2)/2", "\\frac{\\sqrt{2}}{2}");
        tex(assert, "sqrt(2)^2", "(\\sqrt{2})^{2}");
    });

    QUnit.test("nth root", function(assert) {
        // This is an unfortunate case, but only nth degree roots with integer
        // n's get nicely printed as tex.
        tex(assert, "sqrt[z]{x}", "x^{\\frac{1}{z}}");

        tex(assert, "sqrt[3]{x}", "\\sqrt[3]{x}");
        tex(assert, "sqrt[3]{x}z", "\\sqrt[3]{x}z");
        tex(assert, "1/sqrt[4]{x}", "\\frac{1}{\\sqrt[4]{x}}");
        tex(assert, "1/sqrt[4]{x}y", "\\frac{y}{\\sqrt[4]{x}}");

        tex(assert, "sqrt[9]{2}/2", "\\frac{\\sqrt[9]{2}}{2}");
        tex(assert, "sqrt[9]{2}^2", "(\\sqrt[9]{2})^{2}");
    });

    QUnit.test("absolute value", function(assert) {
        tex(assert, "|x|", "\\left|x\\right|");
        tex(assert, "|x|y", "\\left|x\\right|y");
    })

    QUnit.test("logarithms", function(assert) {
        tex(assert, "lnx", "\\ln(x)");
        tex(assert, "logx", "\\log_{10}(x)");
        tex(assert, "lnx^y", "\\ln(x^{y})");
        tex(assert, "logx^y", "\\log_{10}(x^{y})");
        tex(assert, "(lnx)^y", "[\\ln(x)]^{y}");
        tex(assert, "(logx)^y", "[\\log_{10}(x)]^{y}");
    });

    QUnit.test("trig functions", function(assert) {
        tex(assert, "sinx", "\\sin(x)");

        tex(assert, "arcsin x", "\\arcsin(x)");
        tex(assert, "sin^-1 x", "\\arcsin(x)");

        tex(assert, "(sinx)^2", "\\sin^{2}(x)");
        tex(assert, "sin^2 x", "\\sin^{2}(x)");

        tex(assert, "1/(sinx)^2", "\\frac{1}{\\sin^{2}(x)}");
        tex(assert, "1/sin^2x", "\\frac{1}{\\sin^{2}(x)}");

        tex(assert, "sin^2 x + cos^2 x = 1", "\\sin^{2}(x)+\\cos^{2}(x) = 1");
    });

    QUnit.test("hyperbolic functions", function(assert) {
        tex(assert, "sinhx", "\\sinh(x)");
        tex(assert, "sinh^2 x", "\\sinh^{2}(x)");
    });

    QUnit.test("multiplication with numbers", function(assert) {
        tex(assert, "4*10", "4 \\cdot 10");
        tex(assert, "10^5", "10^{5}");
        tex(assert, "4*10^5", "4 \\cdot 10^{5}");
        tex(assert, "10^5x", "10^{5}x");
        tex(assert, "4*10^5x", "4 \\cdot 10^{5}x");
        tex(assert, "x*(10+4)^5", "x(10+4)^{5}");

        tex(assert, "-1*2", "-1 \\cdot 2");
        tex(assert, "1*-2", "1 \\cdot -2");
        tex(assert, "-1*-2", "-1 \\cdot -2");
        tex(assert, "-1*2*3", "-1 \\cdot 2 \\cdot 3");
    });

    QUnit.test("inverses and division", function(assert) {
        tex(assert, "x^-1", "x^{-1}");
        tex(assert, "2x^-1", "2x^{-1}");
        tex(assert, "1/x", "\\frac{1}{x}");
        tex(assert, "-1/x", "\\frac{-1}{x}");
        tex(assert, "2/x", "\\frac{2}{x}");
        tex(assert, "1/x^2", "\\frac{1}{x^{2}}");
        tex(assert, "2/x^2", "\\frac{2}{x^{2}}");
        tex(assert, "1/1/x", "\\frac{1}{x}");
        tex(assert, "1/(1/x)", "\\frac{1}{\\frac{1}{x}}");
        tex(assert, "1/x/x", "\\frac{1}{xx}");
        tex(assert, "1/(x/x)", "\\frac{1}{\\frac{x}{x}}");
        tex(assert, "-1/1/x", "\\frac{-1}{x}");
        tex(assert, "-1/(1/x)", "\\frac{-1}{\\frac{1}{x}}");
        tex(assert, "-1/x/x", "\\frac{-1}{xx}");
        tex(assert, "-1/(x/x)", "\\frac{-1}{\\frac{x}{x}}");
    });

    QUnit.test("distributive property", function(assert) {
        tex(assert, "ab+c", "ab+c");
        tex(assert, "ab+ac", "ab+ac");
        tex(assert, "a(b+c)", "a(b+c)");
    });

    QUnit.test("numerical exponents", function(assert) {
        tex(assert, "9^4", "9^{4}");
        tex(assert, "-9^4", "-9^{4}");
        tex(assert, "1-9^4", "1-9^{4}");
    });

    QUnit.test("negating a Mul", function(assert) {
        tex(assert, "-3x", "-3x");
        tex(assert, "--3x", "--3x");
        tex(assert, "-x*3", "-3x");
        tex(assert, "--x*3", "--3x");
    });

    QUnit.test("equations", function(assert) {
        tex(assert, "y=x", "y = x");
        tex(assert, "y<x", "y < x");
        tex(assert, "y>x", "y > x");
        tex(assert, "y<>x", "y \\ne x");
        tex(assert, "y=/=x", "y \\ne x");
        tex(assert, "y<=x", "y \\le x");
        tex(assert, "y>=x", "y \\ge x");
        print(assert, "y \\le x", "y<=x");
        print(assert, "y \\leq x", "y<=x");
        print(assert, "y \\ge x", "y>=x");
        print(assert, "y \\geq x", "y>=x");
    });

    QUnit.test("function variables", function(assert) {
        tex(assert, "f(x)", "fx");
        tex(assert, "f(x)", "f(x)", {functions: ["f"]});
        tex(assert, "f(sin x)", "f(\\sin(x))", {functions: ["f"]});
        tex(assert, "sin f(x)", "\\sin(f(x))", {functions: ["f"]});
    });

    var texopt = function(assert, input, expected) {
        var options = {
            display: false,
            dynamic: false,
            times: false
        };
        var optlist = _.toArray(arguments).slice(2);
        _.each(optlist, function(opt) { options[opt] = true; });

        var message = input + " renders with options as " + expected;
        assert.strictEqual(parse(input).asTex(options), expected, message);
    };

    QUnit.test("options", function(assert) {
        texopt(assert, "x", "x");
        texopt(assert, "x", "\\displaystyle x", "display");
        texopt(assert, "a(b+c(d+e))", "a(b+c(d+e))");
        texopt(assert, "a(b+c(d+e))", "a\\left(b+c\\left(d+e\\right)\\right)", "dynamic");
        texopt(assert, "2*2", "2 \\cdot 2");
        texopt(assert, "2*2", "2 \\times 2", "times");

        texopt(assert, "1*2(3+4)", "\\displaystyle 1 \\times 2\\left(3+4\\right)",
            "display", "dynamic", "times");
    });


    QUnit.module("evaluating");

    var val = function(assert, input, expected, vars, functions) {
        if (vars === undefined) vars = {};
        var message = input + " evaluates as " + expected;
        assert.strictEqual(parse(input, {functions: functions}).eval(vars, {functions: functions}), expected, message);
    };

    QUnit.test("empty", function(assert) {
        val(assert, "", 0);
    });

    QUnit.test("simple expressions", function(assert) {
        val(assert, "1+2+3+4", 10);
        val(assert, "1+2-3+4", 4);
        val(assert, "1*2*3*4", 24);
        val(assert, "1*2/3*4", 2 + 2/3);
        val(assert, "4^3^2^1", 262144);
        val(assert, "-1", -1);
        val(assert, "--1", 1);
        val(assert, "---1", -1);
        val(assert, "2^-2", .25);
        val(assert, "8^(1/3)", 2);
        val(assert, "0^0", 1);
        val(assert, ".25*4", 1);
        val(assert, "ln e", 1);
        val(assert, "log 10", 1);
        val(assert, "log_2 2", 1);
    });

    QUnit.test("hyperbolic expressions", function(assert) {
        val(assert, "cosh(0.2)", 1.020066755619076);
        val(assert, "coth(0.2)", 5.066489563439473);
        val(assert, "csch(3 * 2)", 0.00495753481347936);
    });

    QUnit.test("variable expressions", function(assert) {
        val(assert, "x", 3, {x: 3});
        val(assert, "x^2", 9, {x: 3});
        val(assert, "(x^2+y^2)^.5", 5, {x: 3, y: 4});
        val(assert, "log x_0", 1, {x_0: 10});
        val(assert, "log x_0 + log x_1", 3, {x_0: 10, x_1: 100});
        val(assert, "log x_42", 1, {x_42: 10});
        val(assert, "x_a + x_bc", 7, {x_a: 1, x_b: 2, c: 3});
    });

    QUnit.test("function expressions", function(assert) {
        val(assert, "f(2)", 4, {"f": "2x"}, ["f"]);
        val(assert, "f(4+8)", 48, {"f": "4x"}, ["f"]);
        val(assert, "f(x-1)-f(x)", -7, {"f": "x^3", "x": 2}, ["f"]);
        val(assert, "g(1)", -1, {f: "x", g: "-f(x)"}, ["f", "g"]);
    });

    QUnit.module("compilation");

    var compile = function(assert, input, expected, vars, functions) {
        if (vars === undefined) vars = {};
        var func = parse(input, {functions: functions}).compile();
        var result;
        try {
            result = func(vars);
        } catch (e) {
            throw new Error("invalid function: " + func.toString());
        }
        var message = input + " should evaluate to " + expected +
			", was " + result + "; by func: " + func.toString();
        assert.ok(Math.abs(result - expected) < 1e-9, message);
    };

    QUnit.test("empty", function(assert) {
        compile(assert, "", 0);
    });

    QUnit.test("simple expressions", function(assert) {
        compile(assert, "1+2+3+4", 10);
        compile(assert, "1+2-3+4", 4);
        compile(assert, "1*2*3*4", 24);
        compile(assert, "1*2/3*4", 2 + 2/3);
        compile(assert, "4^3^2^1", 262144);
        compile(assert, "-1", -1);
        compile(assert, "--1", 1);
        compile(assert, "---1", -1);
        compile(assert, "2^-2", .25);
        compile(assert, "8^(1/3)", 2);
        compile(assert, "0^0", 1);
        compile(assert, ".25*4", 1);
        compile(assert, "ln e", 1);
        compile(assert, "log 10", 1);
        compile(assert, "log_2 2", 1);
    });

    QUnit.test("variable expressions", function(assert) {
        compile(assert, "x", 3, {x: 3});
        compile(assert, "x^2", 9, {x: 3});
        compile(assert, "(x^2+y^2)^.5", 5, {x: 3, y: 4});
        compile(assert, "log x_0", 1, {x_0: 10});
        compile(assert, "log x_0 + log x_1", 3, {x_0: 10, x_1: 100});
        compile(assert, "log x_42", 1, {x_42: 10});
        compile(assert, "x_a + x_bc", 7, {x_a: 1, x_b: 2, c: 3});
    });

    QUnit.test("function expressions", function(assert) {
        compile(assert, "f(2)", 4, {"f": function(x) { return 2 * x; }}, ["f"]);
        compile(assert, "f(4+8)", 48, {"f": function(x) { return 4 * x; }}, ["f"]);
        compile(assert, "f(x-1)-f(x)", -7, {"f": function(x) { return Math.pow(x, 3); }, "x": 2}, ["f"]);
    });

    QUnit.test("trig expressions", function(assert) {
        compile(assert, "-2sin(pi x) + 4", 4, {x: 32});
        compile(assert, "sin(pi x)", 0, {x: 6});
        compile(assert, "sin(x)", 1, {x: Math.PI / 2});
        compile(assert, "sin(pi x)", -1, {x: 3/2});
        compile(assert, "cos(x)", 1, {x: 0});
        compile(assert, "cos x", -1, {x: Math.PI});
        compile(assert, "tan(x)", 0, {x: 0});
        compile(assert, "tan x", 1, {x: Math.PI / 4});
    });

    QUnit.module("checking form");

    var norm = function(assert, input, reference) {
        var actual = parse(input).normalize().print();
        var expected = parse(reference).normalize().print();
        var message = input + " is the same as " + reference;
        assert.strictEqual(actual, expected, message);
    };

    QUnit.test("normalize", function(assert) {
        norm(assert, "ab", "ba");
        norm(assert, "(ab)c", "(cb)a");

        var forms = [
            "(6x+1)(x-1)",
            "(1+6x)(x-1)",
            "(6x+1)(-1+x)",
            "(1+6x)(-1+x)",
            "(x-1)(6x+1)",
            "(x-1)(1+6x)",
            "(-1+x)(6x+1)",
            "(-1+x)(1+6x)"
        ];

        _.each(forms, function(form) {
            norm(assert, forms[0], form);
        });
    });

    var stripnorm = function(assert, input, reference) {
        var actual = parse(input).strip().normalize().print();
        var expected = parse(reference).strip().normalize().print();
        var message = input + " is the same as " + reference;
        assert.strictEqual(actual, expected, message);
    };

    QUnit.test("strip then normalize", function(assert) {
        stripnorm(assert, "ab", "ba");
        stripnorm(assert, "(ab)c", "(cb)a");

        var forms = [
            "(6x+1)(x-1)",
            "(1+6x)(x-1)",
            "(6x+1)(-1+x)",
            "(1+6x)(-1+x)",
            "(-6x-1)(-x+1)",
            "(-1-6x)(-x+1)",
            "(-6x-1)(1-x)",
            "(-1-6x)(1-x)",
            "(x-1)(6x+1)",
            "(x-1)(1+6x)",
            "(-1+x)(6x+1)",
            "(-1+x)(1+6x)",
            "(-x+1)(-6x-1)",
            "(-x+1)(-1-6x)",
            "(1-x)(-6x-1)",
            "(1-x)(-1-6x)",
            "-(6x+1)(1-x)",
            "-(-6x-1)(x-1)"
        ];

        _.each(forms, function(form) {
            stripnorm(assert, forms[0], form);
        });
    })


    QUnit.module("equation to expression");

    var asExpr = function(assert, input, reference) {
        var actual = parse(input).asExpr().simplify().normalize().print();
        var expected = parse(reference).normalize().print();
        var message = input + " as an expression is " + reference;
        assert.strictEqual(actual, expected, message);
    };

    QUnit.test("", function(assert) {
        var forms = [
            "y=2x-5",
            "-2x+5=-y",
            "2x-5<>y",
            "2x-y<>5",
            "(y+5)/2=x",
            "(y+5)/x=2",
            "1/2(y+5)=x",
            ".5(y+5)=x",
            "y-3=2(x-4)",
            "2y=4x-10",
            "yz=2xz-5z"
        ];

        _.each(forms, function(form) {
            if (form.indexOf("<>") !== -1) {
                asExpr(assert, form, "-y+2x-5");
            } else {
                asExpr(assert, form, "y-2x+5");
            }
        });

        var forms2 = [
            "1/3p-3=114",
            "1/3p=117",
            "p=351",
            "p-351=0",
        ];

        _.each(forms2, function(form) {
            asExpr(assert, form, "p-351");
        });
    });


    QUnit.module("comparing");

    var compare = function(assert, options, input, reference, expectedResult) {
        var actual = parse(input, {functions: ["f", "g", "h"]});
        var expected = parse(reference, {functions: ["f", "g", "h"]});
        var result = KAS.compare(actual, expected, options);
        if (expectedResult === undefined) expectedResult = true;
        var message = input + " is " + (expectedResult ? "" : "NOT ") + "the same as " + reference;
        assert.equal(result.equal, expectedResult, message);
    };

    QUnit.test("evaluate only", function(assert) {
        var comp = _.partial(compare, assert, {form: false});

        comp("2+2", "4");
        comp("a(b+c)", "ab+ac");
        comp("a/b", "a*b^-1");

        comp("1.2^2", "1.44");
        comp("1.3^2", "1.69");
        comp("1.4^2", "1.96");
        comp("1.5^2", "2.25");

        comp("1.2345^2", "1.52399025");
        comp("1.2345*1.2345", "1.52399025");
        comp("(1+.2345)^2", "1.52399025");
        comp("(-5)^(1/3)", "-1.709975946");
        comp("(-5)^(2/6)", "-1.709975946");
        comp("(-5)^(4/3)", "8.549879733");
        comp("(-5)^(-1/3)", "-0.584803547");

        comp("(-5)^(1/5)",  "-1.379729661");
        comp("(-5)^(0.2)",  "-1.379729661");

        comp("x^(1/5)", "x^(0.2)");
        comp("x^(8/5)", "x^(1.6)");

        comp("(1-x)(-1-6x)", "(6x+1)(x-1)");
        comp("y=x", "x", false);
        comp("x", "y=x", false);
        comp("y=x", "y=x");
        comp("y=x", "x=y");
        comp("y=x", "-y=-x");
        comp("y=x", "-x=-y");
        comp("y=x", "y=-x", false);
        comp("y=x", "-y=x", false);
        comp("y=x", "y=/=x", false);