# Code coverage report for build/MathLib.js

## Statements: 65.81% (2752 / 4182) Branches: 59.2% (1236 / 2088) Functions: 72.95% (577 / 791) Lines: 66.18% (2739 / 4139)

All files » build/ » MathLib.js

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    9299
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    9310
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    9321
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    9325
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    9330
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    9340
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    9350
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    9360
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    9364
    9365
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    9450
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    9460
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    9464
    9465
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    9594
    9595
    9596
    9597
    9598
    9599
    9600
    9601
    9602
    9603

    1
    1

    1
    1
    1

    1
    1
    1
    53

    1

    1
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    801
    801

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    1
    18

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    167
    13
    26

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    3
    1
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    2

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    18
    7

    11
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    133
    18
    2
    3

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    16
    27

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    3

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    2
    6
    18

    110
    86

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    16

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    4
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    1
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    1
    24

    24
    256
    72

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    16
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    1
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    1
    51

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    67
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    18

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    4

    93

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    83

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    51

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    30
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    22

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    83
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    9
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    19
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    36
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    30
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    54
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    1
    65
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    1
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    260

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    160

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    5
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    3
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    1

     /*!
     * MathLib JavaScript Library v0.6.1
     * http://mathlib.de/
     *
     * Copyright 2012 - 2013 Alexander Zeilmann
     * Released under the MIT license
     * http://mathlib.de/en/license
     *
     * build date: 2013-12-31
     */
    /// <reference path='reference.ts'/>
    var MathLib;
    (function (_MathLib) {

        _MathLib.version = '0.6.1';
        _MathLib.apery = 1.2020569031595942;
        _MathLib.e = Math.E;

        // Number.EPSILON is probably coming in ES6
        // (see section 20.1.2.1 in the current draft)
        _MathLib.epsilon = Number.EPSILON || (function () {
            var next, result;
            for (next = 1; 1 + next !== 1; next = next / 2) {
                result = next;
            }
            return result;
        }());
        _MathLib.eulerMascheroni = 0.5772156649015329;
        _MathLib.goldenRatio = 1.618033988749895;
        _MathLib.pi = Math.PI;

        _MathLib.isArrayLike = function (x) {
            return typeof x === 'object' && 'length' in x;
        };

        _MathLib.isNative = function (fn) {
            return fn && /^[^{]+\{\s*\[native \w/.test(fn.toString()) ? fn : false;
        };

        _MathLib.argToRgba = function (h) {
            var r, g, b;
            h = -h / (2 * Math.PI);

            function hue2rgb (t) {
                if (t < 0) {
                    t += 1;
                }
                if (t > 1) {
                    t -= 1;
                }
                if (t < 1 / 6) {
                    return 6 * t;
                }
                if (t < 1 / 2) {
                    return 1;
                }
                if (t < 2 / 3) {
                    return 4 - 6 * t;
                }
                return 0;
            }

            r = hue2rgb(h + 1 / 3);
            g = hue2rgb(h);
            b = hue2rgb(h - 1 / 3);

            return [r * 255, g * 255, b * 255, 255];
        };

        _MathLib.extendObject = function (dest, src) {
            for (var prop in src) {
                if (typeof dest[prop] === 'object' && typeof src[prop] === 'object') {
                    dest[prop] = _MathLib.extendObject(dest[prop], src[prop]);
                } else {
                    dest[prop] = src[prop];
                }
            }
            return dest;
        };

        _MathLib.colorConvert = function (n) {
            if (typeof n === 'number') {
                n = Math.max(Math.min(Math.floor(n), 0xffffff), 0);
                return '#' + ('00000' + n.toString(16)).slice(-6);
            }
            return n;
        };

        var flatten = function (a) {
            var flattendArray = [];
            a.forEach(function (x) {
                if (Array.isArray(x)) {
                    flattendArray = flattendArray.concat(flatten(x));
                } else {
                    flattendArray.push(x);
                }
            });
            return flattendArray;
        };

        var errors = [], warnings = [];

        // ### [MathLib.on()](http://mathlib.de/en/docs/on)
        // Binds an event handler to an event.
        //
        // *@param {string}* The name of the event.
        // *@param {function}* The callback function.
        _MathLib.on = function (type, callback) {
            if (type === 'error') {
                errors.push(callback);
            } else Eif (type === 'warning') {
                warnings.push(callback);
            }
        };

        // ### [MathLib.off()](http://mathlib.de/en/docs/off)
        // Unbinds an event handler from an event.
        //
        // *@param {string}* The name of the event.
        // *@param {function}* The callback function.
        _MathLib.off = function (type, callback) {
            if (type === 'error') {
                errors = errors.filter(function (x) {
                    return x !== callback;
                });
            } else Eif (type === 'warning') {
                warnings = warnings.filter(function (x) {
                    return x !== callback;
                });
            }
        };

        // ### MathLib.error()
        // Fires an error event.
        //
        // *@param {oject}* An object describing the error further.
        _MathLib.error = function (details) {
            errors.forEach(function (cb) {
                cb(details);
            });
        };

        // ### MathLib.warning()
        // Fires a waring event.
        //
        // *@param {object}* An object describing the warning further.
        _MathLib.warning = function (details) {
            warnings.forEach(function (cb) {
                cb(details);
            });
        };

        'export MathLib';
    })(MathLib || (MathLib = {}));

    /// <reference path='reference.ts'/>
    var MathLib;
    (function (MathLib) {
        // ## <a id="Expression" href="http://mathlib.de/en/docs/Expression">Expression</a>
        // MathLib.Expression is the MathLib implementation of symbolic expressions
        /// no import
        // There is no DOMParser in Node, so we have to require one (done via a regexp replace)
        /// DOMParser
        var Expression = (function () {
            function Expression(expr) {
                if (typeof expr === "undefined") { expr = {}; }
                this.type = 'expression';
                var prop;

                if (typeof expr === 'string') {
                    expr = MathLib.Expression.parse(expr);
                }
                for (prop in expr) {
                    if (expr.hasOwnProperty(prop)) {
                        this[prop] = expr[prop];
                    }
                }
            }
            // ### [Expression.prototype.compare()](http://mathlib.de/en/docs/Expression/compare)
            // Compares two expressions
            //
            // *@param {Expression}* The expression to compare
            // *@return {number}*
            Expression.prototype.compare = function (e) {
                return MathLib.sign(this.toString().localeCompare(e.toString()));
            };

            // ### Expression.constant
            // Constructs a constant expression.
            //
            // *@return {Expression}*
            Expression.constant = function (n) {
                return new MathLib.Expression({
                    subtype: 'constant',
                    value: n
                });
            };

            // ### <a href="http://mathlib.de/en/docs/Expression/evaluate">Expression.prototype.evaluate</a>
            // Evaluates the symbolic expression
            //
            // *@return {any}*
            Expression.prototype.evaluate = function () {
                if (this.subtype === 'binaryOperator') {
                    return MathLib[this.name].apply(null, this.content.map(function (x) {
                        return x.evaluate();
                    }));
                }
                Iif (this.subtype === 'brackets') {
                    return this.content.evaluate();
                }
                if (this.subtype === 'complexNumber') {
                    if (this.mode === 'cartesian') {
                        return new MathLib.Complex(this.value[0].evaluate(), this.value[1].evaluate());
                    } else Eif (this.mode === 'polar') {
                        return MathLib.Complex.polar(this.value[0].evaluate(), this.value[1].evaluate());
                    }
                }
                if (this.subtype === 'constant') {
                    if (this.value === 'false') {
                        return false;
                    }
                    if (this.value === 'pi') {
                        return Math.PI;
                    }
                    Eif (this.value === 'true') {
                        return true;
                    }
                }
                if (this.subtype === 'functionCall') {
                    if (this.isMethod) {
                        var args = this.content.map(function (x) {
                            return x.evaluate();
                        }), _this = args.shift();

                        return _this[this.value].apply(_this, args);
                    } else {
                        return MathLib[this.value].apply(null, this.content.map(function (x) {
                            return x.evaluate();
                        }));
                    }
                }
                if (this.subtype === 'functionDefinition') {
                    return MathLib.Functn(this.content[0].evaluate(), {
                        name: 'f',
                        expression: this.value
                    });
                }
                if (this.subtype === 'matrix') {
                    return new MathLib.Matrix(this.value.map(function (r) {
                        return r.map(function (c) {
                            return c.evaluate();
                        });
                    }));
                }
                if (this.subtype === 'number') {
                    return parseFloat(this.value);
                }
                if (this.subtype === 'naryOperator') {
                    return MathLib[this.name].apply(null, this.content.map(function (x) {
                        return x.evaluate();
                    }));
                }
                if (this.subtype === 'rationalNumber') {
                    return new MathLib.Rational(this.value[0].evaluate(), this.value[1].evaluate());
                }
                if (this.subtype === 'set') {
                    return new MathLib.Set(this.value.map(function (x) {
                        return x.evaluate();
                    }));
                }
                if (this.subtype === 'string') {
                    return this.value;
                }
                if (this.subtype === 'variable') {
                    if (this.value in MathLib.Expression.variables) {
                        return MathLib.Expression.variables[this.value];
                    }
                    return this;
                }
                if (this.subtype === 'vector') {
                    return new MathLib.Vector(this.value.map(function (x) {
                        return x.evaluate();
                    }));
                }
                Eif (this.subtype === 'unaryOperator') {
                    if (this.value === '-') {
                        return MathLib.negative(this.content.evaluate());
                    }
                    return this.content.evaluate();
                }
            };

            // ### Expression.prototype.map
            // Maps the expression tree over to an other expression tree.
            //
            // *@return {Expression}*
            Expression.prototype.map = function (f) {
                var prop, properties = {}, mappedProperties;

                for (prop in this) {
                    if (this.hasOwnProperty(prop) && prop !== 'content') {
                        properties[prop] = this[prop];
                    }
                }

                mappedProperties = f(properties);
                if (Array.isArray(this.content)) {
                    mappedProperties.content = this.content.map(function (expr) {
                        return expr.map(f);
                    });
                } else Iif (this.content) {
                    mappedProperties.content = this.content.map(f);
                }

                return new MathLib.Expression(mappedProperties);
            };

            // ### Expression.number
            // Constructs a number expression.
            //
            // *@return {Expression}*
            Expression.number = function (n) {
                return new MathLib.Expression({
                    subtype: 'number',
                    value: n
                });
            };

            // ### Expression.prototype.parseContentMathML
            // Parses a content MathML string and returns an Expression.
            //
            // *@return {Expression}*
            Expression.parseContentMathML = function (MathMLString) {
                var MathMLdoc, tokenizer = new DOMParser();

                // Whitespace normalization (see section 2.1.7 of the MathML 3 specification)
                // TODO: Find a better way of normalizing whitespace.
                MathMLString = MathMLString.split('cs>').map(function (x, i) {
                    // We are not in an cs element.
                    // 1. normalize multiple spaces to one space
                    // 		("whitespace internal to content of the element is collapsed canonically,
                    // 		i.e., each sequence of 1 or more whitespace characters is replaced with one space character")
                    // 2. Remove whitespace outside of token elements
                    // 		("MathML ignores whitespace occurring outside token elements.")
                    // 		and remove whitespace at the beginning and end of elements
                    // 		("All whitespace at the beginning and end of the content is removed").
                    if (i % 2 === 0) {
                        return x.replace(/\s+/g, ' ').replace(/ </g, '<').replace(/> /g, '>');
                    } else {
                        return x;
                    }
                }).join('cs>');

                // Gives an error in Firefox
                //* MathML = tokenizer.parseFromString(MathMLString, 'application/mathml+xml'); *
                MathMLdoc = tokenizer.parseFromString(MathMLString, 'application/xml');

                var handler = {
                    apply: function (node) {
                        var children = Array.prototype.slice.call(node.childNodes), functnName = children.shift().nodeName, isMethod = true, functnNames = {
                            ident: 'identity',
                            power: 'pow',
                            rem: 'mod',
                            setdifference: 'without'
                        };

                        // Change some function names for functions with different names in MathLib
                        if (functnName in functnNames) {
                            functnName = functnNames[functnName];
                        }

                        if (MathLib[functnName]) {
                            isMethod = false;
                        }

                        return new MathLib.Expression({
                            subtype: 'functionCall',
                            value: functnName,
                            isMethod: isMethod,
                            content: parser(children)
                        });
                    },
                    ci: function (node) {
                        return new MathLib.Expression({
                            subtype: 'variable',
                            value: node.textContent
                        });
                    },
                    cn: function (node) {
                        var type = node.getAttribute('type');

                        if (type === null || type === '') {
                            type = 'number';
                        }

                        if (type === 'number') {
                            /* TODO: base conversions
                            var base = node.getAttribute('base') !== null ? node.getAttributes('base') : '10'; */
                            return parser(node.childNodes[0]);
                        } else if (type === 'rational') {
                            return new MathLib.Expression({
                                value: [parser(node.childNodes[0]), parser(node.childNodes[2])],
                                subtype: 'rationalNumber'
                            });
                        } else if (type === 'complex-cartesian') {
                            return new MathLib.Expression({
                                value: [parser(node.childNodes[0]), parser(node.childNodes[2])],
                                subtype: 'complexNumber',
                                mode: 'cartesian'
                            });
                        } else Eif (type === 'complex-polar') {
                            return new MathLib.Expression({
                                value: [parser(node.childNodes[0]), parser(node.childNodes[2])],
                                subtype: 'complexNumber',
                                mode: 'polar'
                            });
                        }
                    },
                    cs: function (node) {
                        return new MathLib.Expression({
                            subtype: 'string',
                            value: node.textContent
                        });
                    },
                    lambda: function (node) {
                        var bvar = node.childNodes[0], doa = node.childNodes[1], apply = node.childNodes[2];

                        return new MathLib.Expression({
                            subtype: 'functionDefinition',
                            domain: doa.childNodes[0].nodeName,
                            arguments: Array.prototype.map.call(bvar.childNodes, function (variable) {
                                return MathLib.Expression.variable(variable.textContent);
                            }),
                            content: [parser(apply)]
                        });
                    },
                    math: function (node) {
                        return parser(node.childNodes[0]);
                    },
                    matrix: function (node) {
                        return new MathLib.Expression({
                            value: Array.prototype.slice.call(node.childNodes).map(handler.matrixrow),
                            subtype: 'matrix'
                        });
                    },
                    matrixrow: function (node) {
                        return Array.prototype.map.call(node.childNodes, parser);
                    },
                    set: function (node) {
                        return new MathLib.Expression({
                            value: parser(Array.prototype.slice.call(node.childNodes)),
                            subtype: 'set'
                        });
                    },
                    '#text': function (node) {
                        Eif (node.parentNode.nodeName === 'cn') {
                            return MathLib.Expression.number(node.nodeValue.trim());
                        }
                        return node.nodeValue;
                    },
                    vector: function (node) {
                        return new MathLib.Expression({
                            value: parser(Array.prototype.slice.call(node.childNodes)),
                            subtype: 'vector'
                        });
                    },
                    false: function () {
                        return MathLib.Expression.constant('false');
                    },
                    pi: function () {
                        return MathLib.Expression.constant('pi');
                    },
                    true: function () {
                        return MathLib.Expression.constant('true');
                    }
                };

                var parser = function (node) {
                    if (Array.isArray(node)) {
                        var nodes = node.map(parser);
                        return nodes;
                    }

                    return handler[node.nodeName](node);
                };

                return parser(MathMLdoc.childNodes[0]);
            };

            // ### <a href="http://mathlib.de/en/docs/Expression/toContentMathML">Expression.prototype.toContentMathML</a>
            // Convert the Expression to MathML.
            //
            // *@return {string}*
            Expression.prototype.toContentMathML = function () {
                if (this.subtype === 'binaryOperator') {
                    var op = this.name === 'pow' ? 'power' : this.name;

                    return '<apply><csymbol cd="arith1">' + op + '</csymbol>' + this.content[0].toContentMathML() + this.content[1].toContentMathML() + '</apply>';
                }
                if (this.subtype === 'brackets') {
                    return this.content.toContentMathML();
                }
                if (this.subtype === 'number') {
                    return '<cn>' + this.value + '</cn>';
                }
                if (this.subtype === 'variable') {
                    return '<ci>' + this.value + '</ci>';
                }
                if (this.subtype === 'naryOperator') {
                    return '<apply><csymbol cd="arith1">' + this.name + '</csymbol>' + this.content.map(function (expr) {
                        return expr.toContentMathML();
                    }).join('') + '</apply>';
                }
                Iif (this.subtype === 'unaryOperator') {
                    if (this.value === '-') {
                        return '<apply><csymbol cd="arith1">unary_minus</csymbol>' + this.content.toContentMathML() + '</apply>';
                    }
                    return this.content.toContentMathML();
                }

                /*
                var transc1 = ['arccos', 'arccosh', 'arccot', 'arccoth', 'arccsc', 'arccsch', 'arcsec',
                'arcsech', 'arcsin', 'arcsinh', 'arctan', 'arctanh', 'cos', 'cosh', 'cot', 'coth',
                'csc', 'csch', 'exp', 'ln', 'log', 'sec', 'sech', 'sin', 'sinh', 'tan', 'tanh'];
                */
                if (this.subtype === 'functionCall') {
                    // There are some functions which have different names in MathML
                    var conversion = {
                        arcosh: 'arccosh',
                        arcoth: 'arccoth',
                        arcsch: 'arccsch',
                        arsech: 'arcsech',
                        arsinh: 'arcsinh',
                        artanh: 'arctanh',
                        identity: 'ident'
                    }, funcName;

                    Iif (this.value in conversion) {
                        funcName = conversion[this.value];
                    } else {
                        funcName = this.value;
                    }

                    return '<apply><csymbol cd="transc1">' + funcName + '</csymbol>' + this.content.map(function (expr) {
                        return expr.toContentMathML();
                    }).join('') + '</apply>';
                }

                Eif (this.subtype === 'functionDefinition') {
                    return '<lambda><bvar><ci>' + this.arguments.join('</ci></bvar><bvar><ci>') + '</ci></bvar>' + this.content.map(function (expr) {
                        return expr.toContentMathML();
                    }) + '</lambda>';
                }
            };

            // ### <a href="http://mathlib.de/en/docs/Expression/toLaTeX">Expression.prototype.toLaTeX</a>
            // Convert the expression to a LaTeX string
            //
            // *@return {string}*
            Expression.prototype.toLaTeX = function (opts) {
                if (typeof opts === "undefined") { opts = {}; }
                var op;

                if (this.subtype === 'binaryOperator') {
                    var str;

                    if (this.value === '/') {
                        str = '\\frac{' + this.content[0].toLaTeX() + '}';
                    } else {
                        str = this.content[0].toLaTeX() + this.value;
                    }

                    str += this.value !== '-' ? '{' : '';
                    str += this.content[1].toLaTeX();
                    str += this.value !== '-' ? '}' : '';

                    return str;
                }
                if (this.subtype === 'brackets') {
                    return '\\left(' + this.content.toLaTeX(opts) + '\\right)';
                }
                if (this.subtype === 'complexNumber') {
                    Eif (this.mode === 'cartesian') {
                        return this.value[0] + '+' + this.value[1] + 'i';
                    } else if (this.mode === 'polar') {
                        return this.value[0] + ' \\cdot e^{' + this.value[1] + 'i}';
                    }
                }
                Iif (this.subtype === 'constant') {
                    if (this.value === 'pi') {
                        return '\\pi';
                    }
                }
                if (this.subtype === 'matrix') {
                    return '\\begin{pmatrix}' + this.value.map(function (row) {
                        return row.map(function (col) {
                            return col.toLaTeX();
                        }).join('&');
                    }).join('\\\\') + '\\end{pmatrix}';
                }
                if (this.subtype === 'number' || this.subtype === 'variable') {
                    return this.value;
                }
                if (this.subtype === 'naryOperator') {
                    op = this.value === '*' ? '\\cdot' : this.value;
                    return this.content.reduce(function (old, cur, idx) {
                        return old + (idx ? op : '') + cur.toLaTeX(opts);
                    }, '');
                }
                if (this.subtype === 'rationalNumber') {
                    return '\\frac{' + this.value[0].toLaTeX() + '}{' + this.value[1].toLaTeX() + '}';
                }
                if (this.subtype === 'set') {
                    return '\\left{' + this.value.map(function (x) {
                        return x.toLaTeX();
                    }).join(', ') + '\\right}';
                }
                if (this.subtype === 'string') {
                    return '\\texttt{"{}' + this.value + '"}';
                }
                Iif (this.subtype === 'unaryOperator') {
                    if (this.value === '-') {
                        return '-' + this.content.toLaTeX(opts);
                    }
                    return this.content.toLaTeX(opts);
                }
                if (this.subtype === 'vector') {
                    return '\\begin{pmatrix}' + this.value.map(function (x) {
                        return x.toLaTeX();
                    }).join('\\\\') + '\\end{pmatrix}';
                }

                if (this.subtype === 'functionCall') {
                    // These operators are predefined by amsmath.
                    // (There are more predefined ones, but these are the useful ones.)
                    if ([
                        'arccos', 'arcsin', 'arctan', 'arg', 'cos', 'cosh', 'cot', 'coth', 'csc', 'deg', 'det', 'dim',
                        'gcd', 'lg', 'ln', 'log', 'max', 'min', 'sec', 'sin', 'sinh', 'tan', 'tanh'].indexOf(this.value) + 1) {
                        return '\\' + this.value + '\\left(' + (this.content.length ? this.content.reduce(function (old, cur, idx) {
                            return old + (idx ? ',' : '') + cur.toLaTeX(opts);
                        }, '') : 'x') + '\\right)';
                    } else if (this.value === 'exp') {
                        return 'e^{' + (this.content.length ? this.content[0].toLaTeX(opts) : 'x') + '}';
                    } else if (this.value === 'sqrt') {
                        return '\\' + this.value + '{' + (this.content.length ? this.content[0].toLaTeX(opts) : 'x') + '}';
                    } else {
                        return '\\operatorname{' + this.value + '}\\left(' + (this.content.length ? this.content.reduce(function (old, cur, idx) {
                            return old + (idx ? ',' : '') + cur.toLaTeX(opts);
                        }, '') : 'x') + '\\right)';
                    }
                }

                Eif (this.subtype === 'functionDefinition') {
                    return (this.arguments.length === 1 ? this.arguments[0] : '\\left(' + this.arguments.join(', ') + '\\right)') + ' \\longmapsto ' + (this.content.length === 1 ? this.content[0].toLaTeX() : '\\left(' + this.content.map(function (expr) {
                        return expr.toLaTeX();
                    }).join(', ') + '\\right)');
                }
            };

            // ### <a href="http://mathlib.de/en/docs/Expression/toMathML">Expression.prototype.toMathML</a>
            // Convert the Expression to MathML.
            //
            // *@return {string}*
            Expression.prototype.toMathML = function () {
                if (this.subtype === 'binaryOperator') {
                    if (this.value === '-') {
                        return this.content[0].toMathML() + '<mo>-</mo>' + this.content[1].toMathML();
                    }
                    if (this.value === '/') {
                        return '<mfrac>' + this.content[0].toMathML() + this.content[1].toMathML() + '</mfrac>';
                    }
                    Eif (this.value === '^') {
                        return '<msup>' + this.content[0].toMathML() + this.content[1].toMathML() + '</msup>';
                    }
                }
                if (this.subtype === 'brackets') {
                    return '<mrow><mo>(</mo>' + this.content.toMathML() + '<mo>)</mo></mrow>';
                }
                if (this.subtype === 'complexNumber') {
                    Eif (this.mode === 'cartesian') {
                        return '<mrow>' + this.value[0].toMathML() + '<mo>+</mo>' + this.value[1].toMathML() + '<mi>i</mi></mrow>';
                    } else if (this.mode === 'polar') {
                        return this.value[0].toMathML() + '<msup><mi>e</mi><mrow>' + this.value[1].toMathML() + '<mi>i</mi></mrow></msup>';
                    }
                }
                Iif (this.subtype === 'constant') {
                    if (this.value === 'pi') {
                        return '<mi>&pi;</mi>';
                    }
                }
                if (this.subtype === 'matrix') {
                    return '<mrow><mo>(</mo><mtable><mtr><mtd>' + this.value.map(function (row) {
                        return row.map(function (col) {
                            return col.toMathML();
                        }).join('</mtd><mtd>');
                    }).join('</mtd></mtr><mtr><mtd>') + '</mtd></mtr></mtable><mo>)</mo></mrow>';
                }
                if (this.subtype === 'number') {
                    return '<mn>' + this.value + '</mn>';
                }
                if (this.subtype === 'rationalNumber') {
                    return '<mfrac>' + this.value[0].toMathML() + this.value[1].toMathML() + '</mfrac>';
                }
                if (this.subtype === 'set') {
                    return '<mrow><mo>{</mo>' + this.value.map(function (x) {
                        return x.toMathML();
                    }).join('<mo>,</mo>') + '<mo>}</mo></mrow>';
                }
                if (this.subtype === 'string') {
                    return '<ms>' + this.value + '</ms>';
                }
                if (this.subtype === 'variable') {
                    return '<mi>' + this.value + '</mi>';
                }
                if (this.subtype === 'vector') {
                    return '<mrow><mo>(</mo><mtable><mtr><mtd>' + this.value.map(function (x) {
                        return x.toMathML();
                    }).join('</mtd></mtr><mtr><mtd>') + '</mtd></mtr></mtable><mo>)</mo></mrow>';
                }
                if (this.subtype === 'naryOperator') {
                    return '<mrow>' + this.content.map(function (expr) {
                        return expr.toMathML();
                    }).join('<mo>' + (this.value === '*' ? '&middot;' : this.value) + '</mo>') + '</mrow>';
                }
                Iif (this.subtype === 'unaryOperator') {
                    if (this.value === '-') {
                        return '<mo>-</mo>' + this.content.toMathML();
                    }
                    return this.content.toMathML();
                }
                if (this.subtype === 'functionCall') {
                    return '<mrow><mi>' + this.value + '</mi><mo>&af;</mo><mrow><mo>(</mo>' + (this.content.length ? this.content.map(function (expr) {
                        return expr.toMathML();
                    }).join('') : '<mi>x</mi>') + '<mo>)</mo></mrow></mrow>';
                }

                Eif (this.subtype === 'functionDefinition') {
                    return '<mrow>' + (this.arguments.length === 1 ? '<mi>' + this.arguments[0] + '</mi>' : '<mrow><mo>(</mo><mi>' + this.arguments.join('</mi><mo>,<mo><mi>') + '</mi><mo>)</mo></mrow>') + '<mo>&#x27FC;</mo>' + (this.content.length === 1 ? this.content[0].toMathML() : '<mrow><mo>(</mo>' + this.content.map(function (expr) {
                        return expr.toMathML();
                    }) + '<mo>)</mo></mrow>') + '</mrow>';
                }
            };

            // ### <a href="http://mathlib.de/en/docs/Expression/toString">Expression.prototype.toString</a>
            // A custom toString function
            //
            // *@return {string}*
            Expression.prototype.toString = function () {
                var _this = this;
                if (this.subtype === 'binaryOperator') {
                    return this.content[0].toString() + this.value + this.content[1].toString();
                }
                if (this.subtype === 'brackets') {
                    return '(' + this.content.toString() + ')';
                }
                if (this.subtype === 'complexNumber') {
                    Eif (this.mode === 'cartesian') {
                        return this.value[0] + '+' + this.value[1] + 'i';
                    } else if (this.mode === 'polar') {
                        return this.value[0] + '*e^' + this.value[1] + 'i';
                    }
                }
                Iif (this.subtype === 'constant') {
                    if (this.value === 'pi') {
                        return 'π';
                    }
                }
                if (this.subtype === 'matrix') {
                    var length = this.value.length;
                    return this.value.map(function (row) {
                        return row.map(function (col) {
                            return col.toString();
                        }).join('\t');
                    }).map(function (row, index) {
                        if (index === 0) {
                            return '⎛' + row + '⎞';
                        } else if (index === length - 1) {
                            return '⎝' + row + '⎠';
                        } else {
                            return '⎜' + row + '⎟';
                        }
                    }).join('\n');
                }
                if (this.subtype === 'number' || this.subtype === 'variable') {
                    return this.value;
                }
                if (this.subtype === 'naryOperator') {
                    return this.content.reduce(function (old, cur) {
                        return old + _this.value + cur;
                    });
                }
                if (this.subtype === 'rationalNumber') {
                    return this.value[0].toString() + '/' + this.value[1].toString();
                }
                if (this.subtype === 'set') {
                    return '{' + this.value.map(function (x) {
                        return x.toString();
                    }).join(', ') + '}';
                }
                if (this.subtype === 'string') {
                    return '"' + this.value + '"';
                }
                Iif (this.subtype === 'unaryOperator') {
                    if (this.value === '-') {
                        return '-' + this.content.toString();
                    }
                    return this.content.toString();
                }
                if (this.subtype === 'vector') {
                    return '(' + this.value.map(function (x) {
                        return x.toString();
                    }).join(', ') + ')';
                }
                if (this.subtype === 'functionCall') {
                    return this.value + '(' + (this.content.length ? this.content.map(function (expr) {
                        return expr.toString();
                    }).join(', ') : 'x') + ')';
                }
                Eif (this.subtype === 'functionDefinition') {
                    return (this.arguments.length === 1 ? this.arguments[0] : '(' + this.arguments.join(', ') + ')') + ' ⟼ ' + (this.content.length === 1 ? this.content[0].toString() : '(' + this.content.map(function (expr) {
                        return expr.toString();
                    }).join(', ') + ')');
                }
            };

            // ### Expression.variable
            // Constructs a variable expression.
            //
            // *@return {Expression}*
            Expression.variable = function (n) {
                return new MathLib.Expression({
                    subtype: 'variable',
                    value: n
                });
            };
            Expression.parse = function (str) {
                var Token, Lexer, Parser;

                Token = {
                    Operator: 'Operator',
                    Identifier: 'Identifier',
                    Number: 'Number'
                };

                Lexer = function () {
                    var expression = '', length = 0, index = 0, marker = 0, T = Token;

                    function peekNextChar () {
                        var idx = index;
                        return ((idx < length) ? expression.charAt(idx) : '\x00');
                    }

                    function getNextChar () {
                        var ch = '\x00', idx = index;
                        Eif (idx < length) {
                            ch = expression.charAt(idx);
                            index += 1;
                        }
                        return ch;
                    }

                    function isWhiteSpace (ch) {
                        return (ch === '\u0009') || (ch === ' ') || (ch === '\u00A0');
                    }

                    function isLetter (ch) {
                        return (ch >= 'a' && ch <= 'z') || (ch >= 'A' && ch <= 'Z');
                    }

                    function isDecimalDigit (ch) {
                        return (ch >= '0') && (ch <= '9');
                    }

                    function createToken (type, value) {
                        return {
                            type: type,
                            value: value,
                            start: marker,
                            end: index - 1
                        };
                    }

                    function skipSpaces () {
                        var ch;

                        while (index < length) {
                            ch = peekNextChar();
                            Eif (!isWhiteSpace(ch)) {
                                break;
                            }
                            getNextChar();
                        }
                    }

                    function scanOperator () {
                        var ch = peekNextChar();
                        if ('+-*/()^%=;,'.indexOf(ch) >= 0) {
                            return createToken(T.Operator, getNextChar());
                        }
                        return undefined;
                    }

                    function isIdentifierStart (ch) {
                        return (ch === '_') || isLetter(ch);
                    }

                    function isIdentifierPart (ch) {
                        return isIdentifierStart(ch) || isDecimalDigit(ch);
                    }

                    function scanIdentifier () {
                        var ch, id;

                        ch = peekNextChar();
                        Iif (!isIdentifierStart(ch)) {
                            return undefined;
                        }

                        id = getNextChar();
                        while (true) {
                            ch = peekNextChar();
                            if (!isIdentifierPart(ch)) {
                                break;
                            }
                            id += getNextChar();
                        }

                        return createToken(T.Identifier, id);
                    }

                    function scanNumber () {
                        var ch, number;

                        ch = peekNextChar();
                        if (!isDecimalDigit(ch) && (ch !== '.')) {
                            return undefined;
                        }

                        number = '';
                        if (ch !== '.') {
                            number = getNextChar();
                            while (true) {
                                ch = peekNextChar();
                                if (!isDecimalDigit(ch)) {
                                    break;
                                }
                                number += getNextChar();
                            }
                        }

                        if (ch === '.') {
                            number += getNextChar();
                            while (true) {
                                ch = peekNextChar();
                                if (!isDecimalDigit(ch)) {
                                    break;
                                }
                                number += getNextChar();
                            }
                        }

                        if (ch === 'e' || ch === 'E') {
                            number += getNextChar();
                            ch = peekNextChar();
                            Eif (ch === '+' || ch === '-' || isDecimalDigit(ch)) {
                                number += getNextChar();
                                while (true) {
                                    ch = peekNextChar();
                                    if (!isDecimalDigit(ch)) {
                                        break;
                                    }
                                    number += getNextChar();
                                }
                            } else {
                                ch = 'character ' + ch;
                                if (index >= length) {
                                    ch = '<end>';
                                }
                                throw new SyntaxError('Unexpected ' + ch + ' after the exponent sign');
                            }
                        }

                        Iif (number === '.') {
                            throw new SyntaxError('Expecting decimal digits after the dot sign');
                        }

                        return createToken(T.Number, number);
                    }

                    function reset (str) {
                        expression = str;
                        length = str.length;
                        index = 0;
                    }

                    function next () {
                        var token;

                        skipSpaces();
                        if (index >= length) {
                            return undefined;
                        }

                        marker = index;

                        token = scanNumber();
                        if (typeof token !== 'undefined') {
                            return token;
                        }

                        token = scanOperator();
                        if (typeof token !== 'undefined') {
                            return token;
                        }

                        token = scanIdentifier();
                        Eif (typeof token !== 'undefined') {
                            return token;
                        }

                        throw new SyntaxError('Unknown token from character ' + peekNextChar());
                    }

                    function peek () {
                        var token, idx;

                        idx = index;
                        try  {
                            token = next();
                            delete token.start;
                            delete token.end;
                        } catch (e) {
                            token = undefined;
                        }
                        index = idx;

                        return token;
                    }

                    return {
                        reset: reset,
                        next: next,
                        peek: peek
                    };
                };

                Parser = function () {
                    var lexer = new Lexer(), T = Token;

                    function matchOp (token, op) {
                        return (typeof token !== 'undefined') && token.type === T.Operator && token.value === op;
                    }

                    // ArgumentList := Expression |
                    //                 Expression ',' ArgumentList
                    function parseArgumentList () {
                        var token, expr, args = [];

                        while (true) {
                            expr = parseExpression();
                            Iif (typeof expr === 'undefined') {
                                break;
                            }
                            args.push(expr);
                            token = lexer.peek();
                            Eif (!matchOp(token, ',')) {
                                break;
                            }
                            lexer.next();
                        }

                        return args;
                    }

                    // FunctionCall ::= Identifier '(' ')' ||
                    //                  Identifier '(' ArgumentList ')'
                    function parseFunctionCall (name) {
                        var token, args = [];

                        token = lexer.next();
                        Iif (!matchOp(token, '(')) {
                            throw new SyntaxError('Expecting ( in a function call "' + name + '"');
                        }

                        token = lexer.peek();
                        Eif (!matchOp(token, ')')) {
                            args = parseArgumentList();
                        }

                        token = lexer.next();
                        Iif (!matchOp(token, ')')) {
                            throw new SyntaxError('Expecting ) in a function call "' + name + '"');
                        }

                        return new MathLib.Expression({
                            subtype: 'functionCall',
                            value: name,
                            content: args
                        });
                    }

                    // Primary ::= Identifier |
                    //             Number |
                    //             '(' Assignment ')' |
                    //             FunctionCall
                    function parsePrimary () {
                        var token, expr;

                        token = lexer.peek();

                        Iif (typeof token === 'undefined') {
                            throw new SyntaxError('Unexpected termination of expression');
                        }

                        if (token.type === T.Identifier) {
                            token = lexer.next();
                            Eif (matchOp(lexer.peek(), '(')) {
                                return parseFunctionCall(token.value);
                            } else {
                                return new MathLib.Expression({
                                    subtype: 'Identifier',
                                    value: token.value
                                });
                            }
                        }

                        if (token.type === T.Number) {
                            token = lexer.next();
                            return MathLib.Expression.number(token.value);
                        }

                        Eif (matchOp(token, '(')) {
                            lexer.next();
                            expr = parseAssignment();
                            token = lexer.next();
                            Iif (!matchOp(token, ')')) {
                                throw new SyntaxError('Expecting )');
                            }
                            return new MathLib.Expression({
                                subtype: 'brackets',
                                value: 'brackets',
                                content: expr
                            });
                        }

                        throw new SyntaxError('Parse error, can not process token ' + token.value);
                    }

                    // Unary ::= Primary |
                    //           '-' Unary
                    function parseUnary () {
                        var token, expr;

                        token = lexer.peek();
                        if (matchOp(token, '-') || matchOp(token, '+')) {
                            token = lexer.next();
                            expr = parseUnary();
                            return new MathLib.Expression({
                                subtype: 'unaryOperator',
                                value: token.value,
                                content: expr
                            });
                        }

                        return parsePrimary();
                    }

                    // Exponentiation ::= Unary |
                    //                    Exponentiation '^' Unary |
                    function parseExponentiation () {
                        var token, left, right;

                        left = parseUnary();
                        token = lexer.peek();
                        if (matchOp(token, '^')) {
                            token = lexer.next();

                            right = parseExponentiation();

                            // Exponentiation is right associative
                            // a^b^c should be a^(b^c) and not (a^b)^c
                            return new MathLib.Expression({
                                subtype: 'binaryOperator',
                                value: '^',
                                content: [left, right],
                                name: 'pow'
                            });
                        }
                        return left;
                    }

                    // Multiplicative ::= Exponentiation |
                    //                    Multiplicative '*' Exponentiation |
                    //                    Multiplicative '/' Exponentiation
                    function parseMultiplicative () {
                        var token, left, right, r;

                        left = parseExponentiation();
                        token = lexer.peek();
                        if (matchOp(token, '*') || matchOp(token, '/')) {
                            token = lexer.next();

                            right = parseMultiplicative();

                            // Multiplication and division is left associative:
                            // a/b/c should be (a/b)/c and not a/(b/c)
                            if (right.subtype === 'naryOperator' || right.subtype === 'binaryOperator') {
                                r = right;
                                while (r.content[0].subtype === 'naryOperator' || r.content[0].subtype === 'binaryOperator') {
                                    r = r.content[0];
                                }

                                r.content[0] = new MathLib.Expression({
                                    subtype: token.value === '*' ? 'naryOperator' : 'binaryOperator',
                                    content: [left, r.content[0]],
                                    value: token.value,
                                    name: token.value === '*' ? 'times' : 'divide'
                                });
                                return right;
                            } else {
                                return new MathLib.Expression({
                                    subtype: token.value === '*' ? 'naryOperator' : 'binaryOperator',
                                    value: token.value,
                                    name: token.value === '*' ? 'times' : 'divide',
                                    content: [left, right]
                                });
                            }
                        }
                        return left;
                    }

                    // Additive ::= Multiplicative |
                    //              Additive '+' Multiplicative |
                    //              Additive '-' Multiplicative
                    function parseAdditive () {
                        var token, left, right, r;

                        left = parseMultiplicative();
                        token = lexer.peek();
                        if (matchOp(token, '+') || matchOp(token, '-')) {
                            token = lexer.next();
                            right = parseAdditive();

                            // Addition and subtractio is left associative:
                            // a-b-c should be (a-b)-c and not a-(b-c)
                            if (right.value === '+' || right.value === '-') {
                                r = right;
                                while (r.content[0].subtype === 'naryOperator') {
                                    r = r.content[0];
                                }

                                r.content[0] = new MathLib.Expression({
                                    subtype: token.value === '+' ? 'naryOperator' : 'binaryOperator',
                                    content: [left, r.content[0]],
                                    value: token.value,
                                    name: token.value === '+' ? 'plus' : 'minus'
                                });
                                return right;
                            } else {
                                return new MathLib.Expression({
                                    subtype: token.value === '+' ? 'naryOperator' : 'binaryOperator',
                                    value: token.value,
                                    name: token.value === '+' ? 'plus' : 'minus',
                                    content: [left, right]
                                });
                            }
                        }
                        return left;
                    }

                    // Assignment ::= Identifier '=' Assignment |
                    //                Additive
                    function parseAssignment () {
                        var expr;

                        expr = parseAdditive();

                        /*
                        TODO: support assignments
                        if (typeof expr !== 'undefined' && expr.Identifier) {
                        token = lexer.peek();
                        if (matchOp(token, '=')) {
                        lexer.next();
                        return new MathLib.Expression({
                        subtype: 'Assignment',
                        name: expr,
                        value: parseAssignment()
                        });
                        }
                        return expr;
                        }
                        */
                        return expr;
                    }

                    // Expression ::= Assignment
                    function parseExpression () {
                        return parseAssignment();
                    }

                    function parse (expression) {
                        var expr, token;

                        lexer.reset(expression);
                        expr = parseExpression();

                        token = lexer.next();
                        Iif (typeof token !== 'undefined') {
                            throw new SyntaxError('Unexpected token ' + token.value);
                        }

                        return new MathLib.Expression(expr);
                    }

                    return {
                        parse: parse
                    };
                };

                return Parser().parse(str);
            };

            Expression.variables = {};
            return Expression;
        })();
        MathLib.Expression = Expression;
    })(MathLib || (MathLib = {}));

    /// <reference path='reference.ts'/>
    var MathLib;
    (function (MathLib) {
        // ## <a id="Functn" href="http://mathlib.de/en/docs/Functn">Functn</a>
        //
        // Because 'Function' is a reserved word in JavaScript,
        // the module is called 'Functn'.
        /// import Expression
        var functnPrototype = {};

        MathLib.Functn = function (f, options) {
            options = options || {};

            var functn = function (x) {
                if (typeof x === 'number' || typeof x === 'boolean') {
                    return f.apply('', arguments);
                } else if (x.type === 'functn') {
                    // x -> f(x)
                    // y -> g(y)
                    // y -> f(g(y))
                    var bvar = options.expression.arguments[0].value, composition = options.expression.map(function (expr) {
                        if (expr.subtype === 'variable' && expr.value === bvar) {
                            expr = x.expression.content[0];
                        }
                        return expr;
                    });

                    return new MathLib.Functn(function (y) {
                        return f(x(y));
                    }, {
                        expression: new MathLib.Expression({
                            subtype: 'functionDefinition',
                            arguments: x.expression.arguments,
                            content: composition.content
                        })
                    });
                } else if (x.type === 'expression' && x.subtype === 'variable') {
                    return new MathLib.Functn(f, {
                        expression: new MathLib.Expression({
                            subtype: 'functionDefinition',
                            arguments: x,
                            content: x
                        })
                    });
                } else Iif (typeof x === 'function') {
                    return function (y) {
                        return f(x(y));
                    };
                } else if (x.type === 'complex') {
                    return x[options.name].apply(x, Array.prototype.slice.call(arguments, 1));
                } else Iif (x.type === 'rational') {
                    return f(x.toNumber());
                } else Iif (x.type === 'set') {
                    return x.map(f);
                } else Eif (MathLib.type(x) === 'array') {
                    return x.map(f);
                } else {
                    return x[options.name]();
                }
            };

            for (var name in functnPrototype) {
                Eif (functnPrototype.hasOwnProperty(name)) {
                    functn[name] = functnPrototype[name];
                }
            }
            functn.type = 'functn';
            functn.constructor = MathLib.Functn;

            Object.defineProperties(functn, {
                id: { value: options.name },
                expression: { value: options.expression }
            });

            return functn;
        };

        var exports = {};
        var binaryFunctions = {
            arctan2: Math.atan2,
            binomial: function (n, k) {
                // TODO: non integer values
                // What should be done with very big numbers?
                var binomial = 1, i, sign;

                // not finite means ±∞ or NaN
                if (MathLib.isNaN(n) || !MathLib.isFinite(k)) {
                    return NaN;
                }

                // Exit early for areas which return 0
                if ((n >= 0 && k <= -1) || (n >= 0 && k > n) || (k < 0 && k > n)) {
                    return 0;
                }

                if (n < 0) {
                    if (k < 0) {
                        // negative odd number % 2 = -1 and not +1
                        // This leads to the + 1 here.
                        return ((n + k) % 2 * 2 + 1) * MathLib.binomial(-k - 1, -n - 1);
                    } else {
                        if (k === 0) {
                            sign = 1;
                        } else {
                            sign = -(k % 2 * 2 - 1);
                        }
                        binomial = sign * MathLib.binomial(k - n - 1, k);
                    }
                }

                if (k > n / 2) {
                    k = n - k;
                }

                for (i = 1; i <= k; i++) {
                    binomial *= (n + 1 - i) / i;
                }
                return binomial;
            },
            divide: function (a, b) {
                return MathLib.times(a, MathLib.inverse(b));
            },
            log: function (base, x) {
                if (arguments.length === 1) {
                    x = base;
                    base = 10;
                }
                return Math.log(x) / Math.log(base);
            },
            minus: function (a, b) {
                return MathLib.plus(a, MathLib.negative(b));
            },
            mod: function (n, m) {
                var nm = n % m;
                return nm >= 0 ? nm : nm + m;
            },
            pow: function (x, y) {
                if (x === 1 || (x === -1 && (y === Infinity || y === -Infinity))) {
                    return 1;
                }
                return Math.pow(x, y);
            },
            root: function (x, root) {
                Iif (arguments.length === 1) {
                    return Math.sqrt(x);
                }
                return Math.pow(x, 1 / root);
            }
        };

        var createBinaryFunction = function (f, name) {
            return function (x) {
                if (typeof x === 'number') {
                    return f.apply('', arguments);
                } else Iif (typeof x === 'function') {
                    return function (y) {
                        return f(x(y));
                    };
                } else Iif (x.type === 'set') {
                    return new MathLib.Set(x.map(f));
                } else Eif (x.type === 'complex') {
                    return x[name].apply(x, Array.prototype.slice.call(arguments, 1));
                } else if (Array.isArray(x)) {
                    return x.map(f);
                } else {
                    return x[name]();
                }
            };
        };

        var func, cur;
        for (func in binaryFunctions) {
            Eif (binaryFunctions.hasOwnProperty(func)) {
                cur = binaryFunctions[func];
                Object.defineProperty(exports, func, {
                    value: createBinaryFunction(binaryFunctions[func], func)
                });
            }
        }

        // ### [Functn.prototype.diff()](http://mathlib.de/en/docs/Functn/diff)
        // Numeric derivative at a given point
        //
        // *@param {number}* The point
        // *@param {number}* Optional step size
        // *@return {number}*
        functnPrototype.diff = function (x, h) {
            Eif (typeof h === "undefined") { h = 1e-5; }
            return (this(x + h) - this(x - h)) / (2 * h);
        };

        // ### [Functn.prototype.draw()](http://mathlib.de/en/docs/Functn/draw)
        // Draws the function on the screen
        //
        // *@param {Screen}* The screen to draw the function onto.
        // *@param {object}* [options] Optional drawing options.
        // *@return {Functn}*
        functnPrototype.draw = function (screen, options) {
            if (typeof options === "undefined") { options = {}; }
            var functn = this;
            if (Array.isArray(screen)) {
                screen.forEach(function (x) {
                    x.path(functn, options);
                });
            } else {
                screen.path(functn, options);
            }

            return this;
        };

        // These functions will be added to the functn prototype soon.
        var functionList1 = {
            /*
            divisors: function (x) {
            var divisors = x === 1 ? [] : [1],
            i, ii;
            for (i = 2, ii = x / 2; i <= ii; i++) {
            if (x % i === 0) {
            divisors.push(i);
            }
            }
            divisors.push(x);
            return new MathLib.Set(divisors);
            },
            factor: function (n) {
            var factors = [],
            i;
            n = Math.abs(n);
            while (n % 2 === 0) {
            n = n / 2;
            factors.push(2);
            }

            i = 3;
            while (n !== 1) {
            while (n % i === 0) {
            n = n / i;
            factors.push(i);
            }
            i += 2;
            }
            return new MathLib.Set(factors, true);
            },
            */
            fallingFactorial: function (n, m, s) {
                var factorial = 1, j;
                s = s || 1;

                for (j = 0; j < m; j++) {
                    factorial *= (n - j * s);
                }
                return factorial;
            },
            fibonacci: function (n) {
                return Math.floor(Math.pow(MathLib.goldenRatio, n) / Math.sqrt(5));
            },
            random: Math.random,
            risingFactorial: function (n, m, s) {
                var factorial = 1, j;
                s = s || 1;

                for (j = 0; j < m; j++) {
                    factorial *= (n + j * s);
                }
                return factorial;
            },
            round: function (x) {
                // Some implementations have a bug where Math.round(-0) = +0 (instead of -0).
                if (x === 0) {
                    return x;
                }
                return Math.round(x);
            },
            trunc: function (x, n) {
                return x.toFixed(n || 0);
            },
            toContentMathML: function (x) {
                Eif (typeof x === 'number') {
                    return '<cn>' + x + '</cn>';
                } else {
                    return x.toContentMathML();
                }
            },
            toLaTeX: function (x, plus) {
                if (plus) {
                    return (x < 0 ? '-' : '+') + Math.abs(x);
                } else {
                    return (x < 0 ? '-' : '') + Math.abs(x);
                }
            },
            toMathML: function (x, plus) {
                if (plus) {
                    return '<mo>' + (x < 0 ? '-' : '+') + '</mo><mn>' + Math.abs(x) + '</mn>';
                } else {
                    return (x < 0 ? '<mo>-</mo>' : '') + '<mn>' + Math.abs(x) + '</mn>';
                }
            },
            toString: function (x, plus) {
                if (plus) {
                    return (x < 0 ? '-' : '+') + Math.abs(x);
                } else {
                    return (x < 0 ? '-' : '') + Math.abs(x);
                }
            }
        };

        var createFunction1 = function (f, name) {
            return function (x) {
                Eif (typeof x === 'number') {
                    return f.apply('', arguments);
                } else if (typeof x === 'function') {
                    return function (y) {
                        return f(x(y));
                    };
                } else if (x.type === 'set') {
                    return new MathLib.Set(x.map(f));
                } else if (x.type === 'complex') {
                    return x[name].apply(x, Array.prototype.slice.call(arguments, 1));
                } else if (Array.isArray(x)) {
                    return x.map(f);
                } else {
                    return x[name]();
                }
            };
        };

        for (func in functionList1) {
            Eif (functionList1.hasOwnProperty(func)) {
                cur = functionList1[func];
                Object.defineProperty(exports, func, {
                    value: createFunction1(functionList1[func], func)
                });
            }
        }

        MathLib.compare = function (a, b) {
            if (MathLib.type(a) !== MathLib.type(b)) {
                return MathLib.sign(MathLib.type(a).localeCompare(MathLib.type(b)));
            } else if (typeof a === 'number') {
                return MathLib.sign(a - b);
            } else if (typeof a === 'string') {
                return a.localeCompare(b);
            }
            return a.compare(b);
        };

        MathLib.type = function (x) {
            if (x === null) {
                return 'null';
            }
            if (x === undefined) {
                return 'undefined';
            }
            return x.type ? x.type : (x.constructor.name || Object.prototype.toString.call(x).slice(8, -1)).toLowerCase();
        };

        MathLib.is = function (obj, type) {
            var ucfirst = function (str) {
                return str.slice(0, 1).toUpperCase() + str.slice(1);
            }, global = global, window = window, glbl = {
                Object: Object,
                Function: Function,
                RegExp: RegExp,
                Array: Array
            };

            if (MathLib.type(obj) === type) {
                return true;
            } else if ([
                'circle', 'complex', 'expression', 'functn', 'line', 'matrix', 'permutation', 'point',
                'polynomial', 'rational', 'screen', 'screen2d', 'screen3d', 'set', 'vector'].indexOf(type) !== -1) {
                return obj instanceof MathLib[ucfirst(type)];
            } else {
                // if (window) {
                return obj instanceof glbl[ucfirst(type)];
                // }
                // if (global) {
                // 	return obj instanceof global[ucfirst(type)];
                // }
            }
        };

        // ### MathLib.isMathMLSupported()
        // Checks if MathML is supported by the browser.
        // Code stolen from [Modernizr](http://www.modernizr.com/)
        //
        // *@return {boolean}*
        MathLib.isMathMLSupported = function () {
            var hasMathML = false, ns, div, mfrac;

            // If document is undefined (e.g. in Node) we return false
            Eif (typeof document !== 'undefined' && document.createElementNS) {
                ns = 'http://www.w3.org/1998/Math/MathML';
                div = document.createElement('div');
                div.style.position = 'absolute';
                mfrac = div.appendChild(document.createElementNS(ns, 'math')).appendChild(document.createElementNS(ns, 'mfrac'));
                mfrac.appendChild(document.createElementNS(ns, 'mi')).appendChild(document.createTextNode('xx'));
                mfrac.appendChild(document.createElementNS(ns, 'mi')).appendChild(document.createTextNode('yy'));
                document.body.appendChild(div);
                hasMathML = div.offsetHeight > div.offsetWidth;
                document.body.removeChild(div);
            }
            return hasMathML;
        };

        // ### MathLib.writeMathML()
        // Writes MathML to an element.
        //
        // *@param {string}* The id of the element in which the MathML should be inserted.
        // *@param {string}* The MathML to be inserted.
        MathLib.writeMathML = function (id, math) {
            var formula;
            document.getElementById(id).innerHTML = '<math>' + math + '</math>';
            if (typeof MathJax !== 'undefined') {
                formula = MathJax.Hub.getAllJax(id)[0];
                MathJax.Hub.Queue(['Typeset', MathJax.Hub, id]);
            }
        };

        // ### MathLib.loadMathJax()
        // Loads MathJax dynamically.
        //
        // *@param {string}* [config] Optional config options
        MathLib.loadMathJax = function (config) {
            var script = document.createElement('script');
            script.type = 'text/javascript';
            script.src = 'http://cdn.mathjax.org/mathjax/latest/MathJax.js';

            config = config || 'MathJax.Hub.Config({' + 'config: ["MMLorHTML.js"],' + 'jax: ["input/TeX", "input/MathML", "output/HTML-CSS", "output/NativeMML"],' + 'extensions: ["tex2jax.js", "mml2jax.js", "MathMenu.js", "MathZoom.js"],' + 'TeX: {' + 'extensions: ["AMSmath.js", "AMSsymbols.js", "noErrors.js", "noUndefined.js"]' + '}' + '});';

            if (window.opera) {
                script.innerHTML = config;
            } else {
                script.text = config;
            }

            document.getElementsByTagName('head')[0].appendChild(script);
        };

        // Functions that act on set-like structures and return one single number/boolean...
        var nAryFunctions = {
            // ### MathLib.and()
            // Returns true iff all arguments are true.
            //
            // *@param {boolean}* Expects an arbitrary number of boolean arguments
            // *@return {boolean}*
            and: function (n) {
                return n.every(function (x) {
                    return !!x;
                });
            },
            arithMean: function (n) {
                return MathLib.plus(n) / n.length;
            },
            gcd: function (a) {
                var min, reduction = function (x) {
                    return x !== min ? x % min : x;
                }, isntZero = function (x) {
                    return x !== 0;
                };

                // remove zeros and make negative values positive
                a = a.filter(isntZero).map(Math.abs);

                if (a.length === 0) {
                    return 0;
                }

                while (a.length > 1) {
                    min = MathLib.min(a);
                    a = a.map(reduction).filter(isntZero);
                }
                return a[0] || min;
            },
            geoMean: function (n) {
                return MathLib.root(MathLib.times(n), n.length);
            },
            harmonicMean: function (n) {
                return n.length / MathLib.plus(n.map(MathLib.inverse));
            },
            hypot: function (n) {
                var a, b, max, min;

                if (n.length === 1) {
                    return Math.abs(n[0]);
                }

                if (n.length > 2) {
                    return n.reduce(function (a, b) {
                        return MathLib.hypot(a, b);
                    });
                }

                a = MathLib.abs(n[0]);
                b = MathLib.abs(n[1]);

                // Return Infinity if one value is infinite, even if the other value is NaN.
                // (see IEEE 754-2008, 9.2.1)
                if (a === Infinity || b === Infinity) {
                    return Infinity;
                }

                // Return +0 if both values are ±0 (see IEEE 754-2008, 9.2.1)
                if (a === 0 && b === 0) {
                    return 0;
                }

                max = Math.max(a, b);
                min = Math.min(a, b);

                return max * Math.sqrt(1 + Math.pow(min / max, 2));
            },
            hypot2: function (n) {
                // Return Infinity if one value is infinite
                if (n.some(function (x) {
                    return x === Infinity || x === -Infinity;
                })) {
                    return Infinity;
                }
                return n.reduce(function (old, cur) {
                    return old + cur * cur;
                }, 0);
            },
            // ### MathLib.isEqual()
            // Determines if all arguments are equal.
            //
            // *@param {number, MathLib object}* Expects an arbitrary number of numbers or MathLib objects
            // *@return {boolean}*
            isEqual: function (n) {
                return n.every(function (a, i, args) {
                    if (a === args[0]) {
                        return true;
                    } else if (typeof a === 'number' && typeof args[0] === 'number') {
                        return Math.abs(a - args[0]) <= 3e-15;
                    } else if (typeof a === 'object') {
                        return a.isEqual(args[0]);
                    } else if (typeof args[0] === 'object') {
                        return args[0].isEqual(a);
                    }
                    return false;
                });
            },
            lcm: function (n) {
                if (n.length === 0) {
                    return 0;
                }
                if (n.length === 1) {
                    return n[0];
                } else if (n.length === 2) {
                    return MathLib.times(n) / MathLib.gcd(n);
                } else Eif (n.length > 2) {
                    return n.reduce(function (x, y) {
                        return MathLib.lcm(x, y);
                    });
                }
            },
            max: function (n) {
                return Math.max.apply(null, n);
            },
            min: function (n) {
                return Math.min.apply(null, n);
            },
            // ### MathLib.or()
            // Returns true iff at least one argument is true.
            //
            // *@param {boolean}* Expects an arbitrary number of boolean arguments
            // *@return {boolean}*
            or: function (n) {
                return n.some(function (x) {
                    return !!x;
                });
            },
            plus: function (n) {
                if (n.length === 0) {
                    return 0;
                }
                return n.reduce(function (a, b) {
                    var f1, f2, aExpr, bExpr;
                    if (typeof a === 'number' && typeof b === 'number') {
                        return a + b;
                    } else if (a.type === 'functn' || b.type === 'functn') {
                        f1 = a;
                        f2 = b;
                        aExpr = a.expression ? a.expression.content[0] : {};
                        bExpr = b.expression ? b.expression.content[0] : {};

                        if (a.type !== 'functn') {
                            f1 = function () {
                                return a;
                            };
                            aExpr = new MathLib.Expression({
                                value: a,
                                subtype: 'number'
                            });
                        } else if (b.type !== 'functn') {
                            f2 = function () {
                                return b;
                            };
                            bExpr = new MathLib.Expression({
                                value: b,
                                subtype: 'number'
                            });
                        }
                        return MathLib.Functn(function (x) {
                            return MathLib.plus(f1(x), f2(x));
                        }, {
                            expression: new MathLib.Expression({
                                subtype: 'functionDefinition',
                                arguments: ['x'],
                                content: [
                                    new MathLib.Expression({
                                        content: [aExpr, bExpr],
                                        subtype: 'naryOperator',
                                        value: '+',
                                        name: 'plus'
                                    })
                                ]
                            })
                        });
                    } else if (typeof a === 'object') {
                        return a.plus(b);
                    } else Eif (typeof b === 'object') {
                        return b.plus(a);
                    }
                });
            },
            times: function (n) {
                if (n.length === 0) {
                    return 1;
                }
                return n.reduce(function (a, b) {
                    var f1, f2, aExpr, bExpr;
                    if (typeof a === 'number' && typeof b === 'number') {
                        return a * b;
                    } else if (a.type === 'functn' || b.type === 'functn') {
                        f1 = a;
                        f2 = b;
                        aExpr = a.expression ? a.expression.content[0] : {};
                        bExpr = b.expression ? b.expression.content[0] : {};

                        if (a.type !== 'functn') {
                            f1 = function () {
                                return a;
                            };
                            aExpr = new MathLib.Expression({
                                value: a,
                                subtype: 'number'
                            });
                        } else Iif (b.type !== 'functn') {
                            f2 = function () {
                                return b;
                            };
                            bExpr = new MathLib.Expression({
                                value: b,
                                subtype: 'number'
                            });
                        }
                        return MathLib.Functn(function (x) {
                            return MathLib.times(f1(x), f2(x));
                        }, {
                            expression: new MathLib.Expression({
                                subtype: 'functionDefinition',
                                arguments: ['x'],
                                content: [
                                    new MathLib.Expression({
                                        content: [aExpr, bExpr],
                                        subtype: 'naryOperator',
                                        value: '*',
                                        name: 'times'
                                    })
                                ]
                            })
                        });
                    } else if (typeof a === 'object') {
                        return a.times(b);
                    } else Eif (typeof b === 'object') {
                        return b.times(a);
                    }
                });
            },
            // ### MathLib.xor()
            // Returns true iff an odd number of the arguments is true.
            //
            // *@param {boolean}* Expects an arbitrary number of boolean arguments
            // *@return {boolean}*
            xor: function (n) {
                return n.reduce(function (x, y) {
                    return x + !!y;
                }, 0) % 2 !== 0;
            }
        };

        var createNaryFunction = function (f) {
            return function (n) {
                if (MathLib.type(n) === 'set') {
                    return f(n.slice());
                } else if (MathLib.type(n) !== 'array') {
                    n = Array.prototype.slice.apply(arguments);
                }
                return f(n);
            };
        };

        for (func in nAryFunctions) {
            Eif (nAryFunctions.hasOwnProperty(func)) {
                Object.defineProperty(exports, func, {
                    value: createNaryFunction(nAryFunctions[func])
                });
            }
        }

        // ### [Functn.prototype.quad()](http://mathlib.de/en/docs/Functn/quad)
        // Numeric evaluation of an integral using an adative simpson approach.
        //
        // Inspired by "adaptsim.m" by Walter Gander
        // and MatLab's "quad.m"
        //
        // *@param {number}* The starting point
        // *@param {number}* The end point
        // *@param {number}* The tolerance
        // *@return {number}*
        functnPrototype.quad = function (a, b, options) {
            Eif (typeof options === "undefined") { options = {}; }
            var f = this, warnMessage = [
                'Calculation succeded',
                'Minimum step size reached',
                'Maximum function count exceeded',
                'Infinite or NaN function value encountered'
            ], Q;

            options.calls = 3;
            options.warn = 0;

            Iif (a === -Infinity) {
                a = -Number.MAX_VALUE;
            }

            Iif (b === Infinity) {
                b = Number.MAX_VALUE;
            }

            Eif (!('minStep' in options)) {
                options.minStep = 1e-15;
            }

            Eif (!('maxCalls' in options)) {
                options.maxCalls = 10000;
            }

            Eif (!('tolerance' in options)) {
                options.tolerance = 1e-5;
            }

            Q = quadstep(f, a, b, f(a), f((a + b) / 2), f(b), options);

            options.warnMessage = warnMessage[options.warn];

            return Q;
        };

        // Recursive function for the quad method
        var quadstep = function (f, a, b, fa, fc, fb, options) {
            var h = b - a, c = (a + b) / 2, fd = f((a + c) / 2), fe = f((c + b) / 2), Q1 = (h / 6) * (fa + 4 * fc + fb), Q2 = (h / 12) * (fa + 4 * fd + 2 * fc + 4 * fe + fb), Q = Q2 + (Q2 - Q1) / 15;

            options.calls = options.calls + 2;

            // Infinite or Not-a-Number function value encountered
            Iif (!MathLib.isFinite(Q)) {
                options.warn = Math.max(options.warn, 3);
                return Q;
            }

            // Maximum function count exceeded; singularity likely
            Iif (options.calls > options.maxCalls) {
                options.warn = Math.max(options.warn, 2);
                return Q;
            }

            // Accuracy over this subinterval is acceptable
            if (Math.abs(Q2 - Q) <= options.tolerance) {
                return Q;
            }

            // Minimum step size reached; singularity possible
            Iif (Math.abs(h) < options.minStep || c === a || c === b) {
                options.warn = Math.max(options.warn, 1);
                return Q;
            }

            // Otherwise, divide the interval into two subintervals
            return quadstep(f, a, c, fa, fd, fc, options) + quadstep(f, c, b, fc, fe, fb, options);
        };

        // ### Functn.prototype.toContentMathML()
        // Returns a content MathML representation of the function
        //
        // *@return {MathML}*
        functnPrototype.toContentMathML = function () {
            return this.expression.toContentMathML();
        };

        // ### [Functn.prototype.toLaTeX()](http://mathlib.de/en/docs/Functn/toLaTeX)
        // Returns a LaTeX representation of the function
        //
        // *@return {string}*
        functnPrototype.toLaTeX = function () {
            return this.expression.toLaTeX();
            /*
            / / List of functions to be executed on the specified node type
            var handlers = {
            apply: function (n) {
            var f = n.childNodes[0],
            args = n.childNodes.slice(1).map(function (x) {
            return handlers[x.nodeName](x);
            }),
            str = '';

            if (f.nodeName === 'plus') {
            str = args.join('+');
            }
            else if (f.nodeName === 'times') {
            str = args.join('*');
            }
            else if (f.nodeName === 'power') {
            str = args[0] + '^{' + args[1] + '}';
            }
            else {
            / / TODO: not all functions can be written like \sin some have to be written like \operatorname{argmax}
            str = '\\' + f.nodeName + '(' + args.join(', ') + ')';
            }
            return str;
            },
            bvar: function () {return '';},
            ci: function (n) {return bvar || n.innerMathML;},
            cn: function (n) {return n.innerMathML;},
            cs: function (n) {return n.innerMathML;},
            domainofapplication: function () {return '';},
            lambda: function (n) {
            return n.childNodes.reduce(function (old, cur) {
            return old + handlers[cur.nodeName](cur);
            }, '');
            },
            '#text': function (n) {return n.innerMathML;}
            };

            / / Start the node handling with the first real element (not the <math> element)
            return handlers[this.contentMathML.childNodes[0].nodeName](this.contentMathML.childNodes[0]);
            */
        };

        // ### Functn.prototype.toMathML()
        // Returns a MathML representation of the function
        //
        // *@return {string}*
        functnPrototype.toMathML = function () {
            return this.expression.toMathML();
        };

        // ### Functn.prototype.toMathMLString
        // Returns a MathML representation of the function
        //
        // *@return {string}*
        /*functnPrototype.toMathMLString = function () {
        return this.contentMathML.toMathMLString();
        };*/
        // ### [Functn.prototype.toString()](http://mathlib.de/en/docs/Functn/toString)
        // Returns a string representation of the function
        //
        // *@return {string}*
        functnPrototype.toString = function () {
            return this.expression.toString();
            /*
            / / List of functions to be executed on the specified node type
            var handlers = {
            apply: function (n) {
            var f = n.childNodes[0],
            args = n.childNodes.slice(1).map(function (x) {
            return handlers[x.nodeName](x);
            }),
            str = '';

            if (f.nodeName === 'plus') {
            str = args.join('+');
            }
            else if (f.nodeName === 'times') {
            str = args.join('*');
            }
            else if (f.nodeName === 'power') {
            str = args[0] + '^' + args[1];
            }
            else {
            str = f.nodeName + '(' + args.join(', ') + ')';
            }
            return str;
            },
            bvar: function () {return '';},
            ci: function (n) {return bvar || n.innerMathML;},
            cn: function (n) {return n.innerMathML;},
            cs: function (n) {return n.innerMathML;},
            domainofapplication: function () {return '';},
            lambda: function (n) {
            return n.childNodes.reduce(function (old, cur) {
            return old + handlers[cur.nodeName](cur);
            }, '');
            },
            '#text': function (n) {return n.innerMathML;}
            };

            / / Start the node handling with the first real element (not the <math> element)
            return handlers[this.contentMathML.childNodes[0].nodeName](this.contentMathML.childNodes[0]);
            */
        };

        // ## unary functions
        // Some functions for the functn prototype
        var unaryFunctions = {
            abs: Math.abs,
            arccos: Math.acos,
            arccot: function (x) {
                return 1.5707963267948966 - Math.atan(x);
            },
            arccsc: function (x) {
                return Math.asin(1 / x);
            },
            arcosh: MathLib.isNative(Math.acosh) || function (x) {
                return Math.log(x + Math.sqrt(x * x - 1));
            },
            arcoth: function (x) {
                // Handle ±∞
                if (!MathLib.isFinite(x)) {
                    return 1 / x;
                }
                return 0.5 * Math.log((x + 1) / (x - 1));
            },
            arcsch: function (x) {
                // Handle ±0 and ±∞ separately
                if (x === 0 || !MathLib.isFinite(x)) {
                    return 1 / x;
                }
                return Math.log(1 / x + Math.sqrt(1 / (x * x) + 1));
            },
            arcsec: function (x) {
                return Math.acos(1 / x);
            },
            arcsin: Math.asin,
            arctan: Math.atan,
            arsech: function (x) {
                return Math.log((1 + Math.sqrt(1 - x * x)) / x);
            },
            arsinh: MathLib.isNative(Math.asinh) || function (x) {
                // Handle ±0 and ±∞ separately
                if (x === 0 || !MathLib.isFinite(x)) {
                    return x;
                }
                return Math.log(x + Math.sqrt(x * x + 1));
            },
            artanh: MathLib.isNative(Math.atanh) || function (x) {
                // Handle ±0
                if (x === 0) {
                    return x;
                }
                return 0.5 * Math.log((1 + x) / (1 - x));
            },
            ceil: function (x) {
                // Some implementations have a bug where Math.ceil(-0) = +0 (instead of -0)
                if (x === 0) {
                    return x;
                }
                return Math.ceil(x);
            },
            cbrt: function (x) {
                var a3, a3x, an, a;

                // Handle ±0, NaN, ±∞
                if (x === 0 || x !== x || x === Infinity || x === -Infinity) {
                    return x;
                }

                // Get an approximation
                a = MathLib.sign(x) * Math.pow(Math.abs(x), 1 / 3);

                while (true) {
                    a3 = Math.pow(a, 3);
                    a3x = a3 + x;
                    an = a * (a3x + x) / (a3x + a3);
                    Eif (MathLib.isZero(an - a)) {
                        break;
                    }
                    a = an;
                }
                return an;
            },
            conjugate: function (x) {
                return x;
            },
            copy: function (x) {
                return x;
            },
            cos: Math.cos,
            cosh: MathLib.isNative(Math.cosh) || function (x) {
                return (Math.exp(x) + Math.exp(-x)) / 2;
            },
            cot: function (x) {
                // Handle ±0 separate, because tan(pi/2 ± 0) is not ±∞
                if (x === 0) {
                    return 1 / x;
                }

                // cot(x) = tan(pi/2 - x) is better than 1/tan(x)
                return Math.tan(1.5707963267948966 - x);
            },
            coth: function (x) {
                // Handle ±0
                if (x === 0) {
                    return 1 / x;
                }

                // Handle ±∞
                if (!MathLib.isFinite(x)) {
                    return MathLib.sign(x);
                }

                return (Math.exp(x) + Math.exp(-x)) / (Math.exp(x) - Math.exp(-x));
            },
            csc: function (x) {
                return 1 / Math.sin(x);
            },
            csch: function (x) {
                // csch(-0) should be -∞ not ∞
                if (x === 0) {
                    return 1 / x;
                }
                return 2 / (Math.exp(x) - Math.exp(-x));
            },
            degToRad: function (x) {
                // Math.PI / 180 = 0.017453292519943295
                return x * 0.017453292519943295;
            },
            digitsum: function (x) {
                var out = 0;
                while (x > 9) {
                    out += x % 10;
                    x = Math.floor(x / 10);
                }
                return out + x;
            },
            exp: Math.exp,
            factorial: function (x) {
                var factorial = 1, i;
                if ((x > 170 && MathLib.isInt(x)) || x === Infinity) {
                    return Infinity;
                }
                if (x < 0 || !MathLib.isInt(x) || MathLib.isNaN(x)) {
                    return NaN;
                }
                for (i = 1; i <= x; i++) {
                    factorial *= i;
                }
                return factorial;
            },
            floor: Math.floor,
            identity: function (x) {
                return x;
            },
            inverse: function (x) {
                return 1 / x;
            },
            isFinite: function (x) {
                return Math.abs(x) < Infinity;
            },
            isInt: function (x) {
                return x % 1 === 0;
            },
            isNaN: function (x) {
                return x !== x;
            },
            isNegZero: function (x) {
                return 1 / x === -Infinity;
            },
            isOne: function (a) {
                return Math.abs(a - 1) < MathLib.epsilon;
            },
            isPosZero: function (x) {
                return 1 / x === Infinity;
            },
            isPrime: function (x) {
                var sqrt = Math.sqrt(x), i;
                Eif (x % 1 === 0 && x > 1) {
                    Iif (x === 2) {
                        return true;
                    }
                    if (x % 2 === 0) {
                        return false;
                    }
                    for (i = 3; i <= sqrt; i += 2) {
                        Iif (x % i === 0) {
                            return false;
                        }
                    }
                    return true;
                }
                return false;
            },
            isReal: function (x) {
                return Math.abs(x) < Infinity;
            },
            isZero: function (x) {
                return Math.abs(x) < MathLib.epsilon;
            },
            lg: function (x) {
                return Math.log(x) / Math.LN10;
            },
            ln: Math.log,
            // Algorithm based on [Numerical Recipes Vol. 3, p. 257](www.nr.com)
            logGamma: function (x) {
                var j, tmp, y, ser, cof = [
                    57.1562356658629235, -59.5979603554754912, 14.1360979747417471, -0.491913816097620199,
                    0.339946499848118887e-4, 0.465236289270485756e-4, -0.983744753048795646e-4, 0.158088703224912494e-3,
                    -0.210264441724104883e-3, 0.217439618115212643e-3, -0.164318106536763890e-3, 0.844182239838527433e-4,
                    -0.261908384015814087e-4, 0.368991826595316234e-5];

                y = x;
                tmp = x + 5.24218750000000000; // Rational 671/128.
                tmp = (x + 0.5) * Math.log(tmp) - tmp;
                ser = 0.999999999999997092;
                for (j = 0; j < 14; j++) {
                    ser += cof[j] / ++y;
                }
                return tmp + Math.log(2.5066282746310005 * ser / x);
            },
            negative: function (x) {
                return -x;
            },
            not: function (x) {
                return !x;
            },
            radToDeg: function (x) {
                // 180 / Math.PI = 57.29577951308232
                return x * 57.29577951308232;
            },
            sec: function (x) {
                return 1 / Math.cos(x);
            },
            sech: function (x) {
                return 2 / (Math.exp(x) + Math.exp(-x));
            },
            sign: function (x) {
                return x && (x < 0 ? -1 : 1);
            },
            sin: Math.sin,
            sinh: MathLib.isNative(Math.sinh) || function (x) {
                // sinh(-0) should be -0
                if (x === 0) {
                    return x;
                }
                return (Math.exp(x) - Math.exp(-x)) / 2;
            },
            sqrt: Math.sqrt,
            tan: Math.tan,
            tanh: MathLib.isNative(Math.tanh) || function (x) {
                var p;

                // Handle ±0 and ±∞ separately
                // Their values happen to coincide with sign
                if (x === 0 || !MathLib.isFinite(x)) {
                    return MathLib.sign(x);
                }

                p = Math.exp(x);
                return (p * p - 1) / (p * p + 1);
            }
        };

        for (var elemfn in unaryFunctions) {
            Eif (unaryFunctions.hasOwnProperty(elemfn)) {
                Object.defineProperty(exports, elemfn, {
                    value: MathLib.Functn(unaryFunctions[elemfn], {
                        name: elemfn,
                        expression: new MathLib.Expression({
                            subtype: 'functionDefinition',
                            arguments: [
                                new MathLib.Expression({
                                    subtype: 'variable',
                                    value: 'x'
                                })
                            ],
                            content: [
                                new MathLib.Expression({
                                    subtype: 'functionCall',
                                    content: [
                                        new MathLib.Expression({
                                            subtype: 'variable',
                                            value: 'x'
                                        })
                                    ],
                                    value: elemfn
                                })
                            ]
                        })
                    }),
                    writable: true,
                    enumerable: true,
                    configurable: true
                });
            }
        }

        MathLib.abs = exports.abs;
        MathLib.arccos = exports.arccos;
        MathLib.arccot = exports.arccot;
        MathLib.arccsc = exports.arccsc;
        MathLib.arcosh = exports.arcosh;
        MathLib.arcoth = exports.arcoth;
        MathLib.arcsch = exports.arcsch;
        MathLib.arcsec = exports.arcsec;
        MathLib.arcsin = exports.arcsin;
        MathLib.arctan = exports.arctan;
        MathLib.arsech = exports.arsech;
        MathLib.arsinh = exports.arsinh;
        MathLib.artanh = exports.artanh;
        MathLib.ceil = exports.ceil;
        MathLib.cbrt = exports.cbrt;
        MathLib.conjugate = exports.conjugate;
        MathLib.copy = exports.copy;
        MathLib.cos = exports.cos;
        MathLib.cosh = exports.cosh;
        MathLib.cot = exports.cot;
        MathLib.coth = exports.coth;
        MathLib.csc = exports.csc;
        MathLib.csch = exports.csch;
        MathLib.degToRad = exports.degToRad;
        MathLib.digitsum = exports.digitsum;
        MathLib.exp = exports.exp;
        MathLib.factorial = exports.factorial;
        MathLib.floor = exports.floor;
        MathLib.identity = exports.identity;
        MathLib.inverse = exports.inverse;
        MathLib.isFinite = exports.isFinite;
        MathLib.isInt = exports.isInt;
        MathLib.isNaN = exports.isNaN;
        MathLib.isNegZero = exports.isNegZero;
        MathLib.isOne = exports.isOne;
        MathLib.isPosZero = exports.isPosZero;
        MathLib.isPrime = exports.isPrime;
        MathLib.isReal = exports.isReal;
        MathLib.isZero = exports.isZero;
        MathLib.lg = exports.lg;
        MathLib.ln = exports.ln;
        MathLib.logGamma = exports.logGamma;
        MathLib.negative = exports.negative;
        MathLib.not = exports.not;
        MathLib.radToDeg = exports.radToDeg;
        MathLib.sec = exports.sec;
        MathLib.sech = exports.sech;
        MathLib.sign = exports.sign;
        MathLib.sin = exports.sin;
        MathLib.sinh = exports.sinh;
        MathLib.sqrt = exports.sqrt;
        MathLib.tan = exports.tan;
        MathLib.tanh = exports.tanh;

        MathLib.arctan2 = exports.arctan2;
        MathLib.binomial = exports.binomial;
        MathLib.divide = exports.divide;
        MathLib.log = exports.log;
        MathLib.minus = exports.minus;
        MathLib.mod = exports.mod;
        MathLib.pow = exports.pow;
        MathLib.root = exports.root;

        MathLib.divisors = exports.divisors;
        MathLib.factor = exports.factor;
        MathLib.fallingFactorial = exports.fallingFactorial;
        MathLib.fibonacci = exports.fibonacci;
        MathLib.risingFactorial = exports.risingFactorial;
        MathLib.round = exports.round;
        MathLib.trunc = exports.trunc;
        MathLib.toContentMathML = exports.toContentMathML;
        MathLib.toLaTeX = exports.toLaTeX;
        MathLib.toMathML = exports.toMathML;
        MathLib.toString = exports.toString;

        MathLib.and = exports.and;
        MathLib.arithMean = exports.arithMean;
        MathLib.gcd = exports.gcd;
        MathLib.geoMean = exports.geoMean;
        MathLib.harmonicMean = exports.harmonicMean;
        MathLib.hypot = exports.hypot;
        MathLib.hypot2 = exports.hypot2;
        MathLib.isEqual = exports.isEqual;
        MathLib.lcm = exports.lcm;
        MathLib.max = exports.max;
        MathLib.min = exports.min;
        MathLib.or = exports.or;
        MathLib.plus = exports.plus;
        MathLib.times = exports.times;
        MathLib.xor = exports.xor;
    })(MathLib || (MathLib = {}));

    /// <reference path='reference.ts'/>
    var MathLib;
    (function (MathLib) {
        var template = function (data) {
            var p = [];
            p.push(' <figure class="MathLib_figure">     <div class="MathLib_wrapper" style="width: ');
            p.push(data.width);
            p.push('px; height: ');
            p.push(data.height);
            p.push('px">   <div class="MathLib_info_message">Your browser does not seem to support WebGL.<br>   Please update your browser to see the plot.</div>  </div>      ');
            Iif (data.figcaption) {
                p.push('   <figcaption class="MathLib_figcaption">');
                p.push(data.figcaption);
                p.push('</figcaption>  ');
            }
            p.push('  </figure>  ');
            Eif (data.contextMenu) {
                p.push('  <div class="MathLib_contextMenuOverlay">   <menu class="MathLib_menu MathLib_mainmenu">          ');
                Eif (data.contextMenu.screenshot) {
                    p.push('     <div class="MathLib_screenshot MathLib_menuItem">Save Screenshot</div>    ');
                }
                p.push('      ');
                Eif (data.contextMenu.fullscreen) {
                    p.push('     <div class="MathLib_fullscreen MathLib_menuItem">      <span class="needs-nofullscreen">Enter Fullscreen</span>      <span class="needs-fullscreen">Exit Fullscreen</span>     </div>    ');
                }
                p.push('      ');
                Eif (data.contextMenu.grid) {
                    p.push('     <div class="MathLib_menuItem MathLib_hasSubmenu">      Grid      <menu class="MathLib_menu MathLib_submenu">       <div class="MathLib_needs2D">        <label class="MathLib_menuItem">         <input type="radio" name="MathLib_grid_type_');
                    p.push(data.uuid);
                    p.push('" class="MathLib_radio MathLib_grid_type" value="cartesian">cartesian        </label>        <label class="MathLib_menuItem">         <input type="radio" name="MathLib_grid_type_');
                    p.push(data.uuid);
                    p.push('" class="MathLib_radio MathLib_grid_type" value="polar">polar        </label>        <label class="MathLib_menuItem">         <input type="radio" name="MathLib_grid_type_');
                    p.push(data.uuid);
                    p.push('" class="MathLib_radio MathLib_grid_type" value="none">none        </label>       </div>        <div class="MathLib_needs3D MathLib_menuItem MathLib_is_disabled" style="font-size: 0.7em">        Gridoptions for 3D are coming soon.       </div>      </menu>     </div>    ');
                }
                p.push('      <hr class="MathLib_separator">    <div class="MathLib_is_disabled MathLib_menuItem MathLib_is_centered" style="font-size:0.83em">     Plot generated by MathLib.js    </div>   </menu>  </div> ');
            }
            p.push('');
            return p.join("");
        };

        // ## <a id="Screen"></a>Screen
        // This module contains the common methods of all drawing modules.
        /// no import
        var Screen = (function () {
            function Screen(id, options) {
                Iif (typeof options === "undefined") { options = {}; }
                var _this = this;
                this.type = 'screen';
                var that = this, defaults = {
                    height: 500,
                    width: 500,
                    contextMenu: {
                        screenshot: true,
                        fullscreen: true,
                        grid: true
                    },
                    figcaption: ''
                }, opts = MathLib.extendObject(defaults, options), container = document.getElementById(id), innerHTMLContextMenu = '', uuid = +Date.now(), fullscreenchange, innerHTML;

                container.innerHTML = template(opts);
                container.classList.add('MathLib_container');

                this.height = opts.height;
                this.width = opts.width;
                this.options = opts;
                this.container = container;
                this.figure = container.getElementsByClassName('MathLib_figure')[0];
                this.wrapper = container.getElementsByClassName('MathLib_wrapper')[0];
                this.contextMenu = container.getElementsByClassName('MathLib_mainmenu')[0];
                this.contextMenuOverlay = container.getElementsByClassName('MathLib_contextMenuOverlay')[0];
                this.innerHTMLContextMenu = innerHTMLContextMenu;

                Iif (options.contextMenu) {
                    this.wrapper.oncontextmenu = function (evt) {
                        return _this.oncontextmenu(evt);
                    };

                    if (opts.contextMenu.screenshot && !('opera' in window)) {
                        this.contextMenu.getElementsByClassName('MathLib_screenshot')[0].onclick = function () {
                            var dataURI, a = document.createElement('a');

                            if (that.options.renderer === 'Canvas' && that.type === 'screen2D') {
                                var canvas = document.createElement('canvas'), ctx = canvas.getContext('2d');

                                canvas.height = that.height;
                                canvas.width = that.width;

                                ctx.drawImage(that.layer.back.element, 0, 0);
                                ctx.drawImage(that.layer.grid.element, 0, 0);
                                ctx.drawImage(that.layer.axes.element, 0, 0);
                                ctx.drawImage(that.layer.main.element, 0, 0);

                                dataURI = canvas.toDataURL('image/png');
                                if ('download' in a) {
                                    a.href = dataURI;
                                    a.download = 'plot.png';
                                    a.click();
                                } else {
                                    window.location.href = dataURI.replace('image/png', 'image/octet-stream');
                                }
                            }

                            if (that.options.renderer === 'WebGL' && that.type === 'screen3D') {
                                dataURI = that.element.toDataURL('image/png');
                                if ('download' in a) {
                                    a.href = dataURI;
                                    a.download = 'plot.png';
                                    a.click();
                                } else {
                                    window.location.href = dataURI.replace('image/png', 'image/octet-stream');
                                }
                            } else if (that.options.renderer === 'SVG') {
                                dataURI = 'data:image/svg+xml,' + that.element.parentElement.innerHTML;

                                if ('download' in a) {
                                    a.href = dataURI;
                                    a.download = 'plot.svg';
                                    a.click();
                                } else {
                                    window.location.href = dataURI.replace('image/svg+xml', 'image/octet-stream');
                                }
                            }
                        };
                    }

                    if (opts.contextMenu.fullscreen && 'requestFullScreen' in document.body) {
                        this.contextMenu.getElementsByClassName('MathLib_fullscreen')[0].onclick = function () {
                            if (document.fullscreenElement) {
                                document.exitFullScreen();
                            } else {
                                that.container.requestFullScreen();
                            }
                        };
                    }

                    if (opts.contextMenu.grid) {
                        this.contextMenu.getElementsByClassName('MathLib_grid_type')[0].onchange = function () {
                            that.options.grid.type = 'cartesian';
                            that.draw();
                        };
                        this.contextMenu.getElementsByClassName('MathLib_grid_type')[1].onchange = function () {
                            that.options.grid.type = 'polar';
                            that.draw();
                        };
                        this.contextMenu.getElementsByClassName('MathLib_grid_type')[2].onchange = function () {
                            that.options.grid.type = false;
                            that.draw();
                        };
                    }
                }

                fullscreenchange = function () {
                    if (document.fullscreenElement) {
                        that.origWidth = that.width;
                        that.origHeight = that.height;
                        that.resize(window.outerWidth, window.outerHeight);
                    } else {
                        that.resize(that.origWidth, that.origHeight);
                        delete that.origWidth;
                        delete that.origHeight;
                    }
                };

                Iif ('onfullscreenchange' in this.container) {
                    this.container.addEventListener('fullscreenchange', fullscreenchange);
                } else Iif ('onmozfullscreenchange' in this.container) {
                    this.container.addEventListener('mozfullscreenchange', fullscreenchange);
                } else Iif ('onwebkitfullscreenchange' in this.container) {
                    this.container.addEventListener('webkitfullscreenchange', fullscreenchange);
                }
            }
            // ### Screen.prototype.contextmenu()
            // Handles the contextmenu event
            //
            // *@param {event}*
            Screen.prototype.oncontextmenu = function (evt) {
                var listener, _this = this, menu = this.contextMenu, overlay = this.contextMenuOverlay;

                if (evt.preventDefault) {
                    evt.preventDefault();
                }
                evt.returnValue = false;

                menu.style.setProperty('top', (evt.clientY - 20) + 'px');
                menu.style.setProperty('left', evt.clientX + 'px');
                overlay.style.setProperty('display', 'block');

                listener = function () {
                    overlay.style.setProperty('display', 'none');

                    Array.prototype.forEach.call(_this.contextMenu.getElementsByClassName('MathLib_temporaryMenuItem'), function (x) {
                        _this.contextMenu.removeChild(x);
                    });

                    overlay.removeEventListener('click', listener);
                };

                overlay.addEventListener('click', listener);
            };
            return Screen;
        })();
        MathLib.Screen = Screen;
    })(MathLib || (MathLib = {}));

    /// <reference path='reference.ts'/>
    var MathLib;
    (function (MathLib) {
        // ## <a id="Layers"></a>Layers
        // Layers for two dimensional plotting
        /// import Screen2D
        var Layer = (function () {
            function Layer(screen, id, zIndex) {
                var _this = this;
                this.screen = screen;
                this.id = id;
                this.zIndex = zIndex;

                this.stack = [];
                this.transformation = screen.transformation;

                var element;

                if (screen.options.renderer === 'Canvas') {
                    // Create the canvas
                    element = document.createElement('canvas');
                    element.classList.add('MathLib_screen');
                    element.width = screen.width;
                    element.height = screen.height;
                    screen.wrapper.appendChild(element);
                    this.element = element;

                    // Get the context and apply the transformations
                    this.ctx = element.getContext('2d');
                    this.applyTransformation = function () {
                        var m = _this.transformation;
                        _this.ctx.setTransform(m[0][0], m[1][0], m[0][1], m[1][1], m[0][2], m[1][2]);
                    };
                    this.applyTransformation();

                    // Set the drawing functions
                    if (id === 'back') {
                        this.draw = function () {
                            var top = (-screen.translation.y) / screen.scale.y, bottom = (screen.height - screen.translation.y) / screen.scale.y, left = (-screen.translation.x) / screen.scale.x, right = (screen.width - screen.translation.x) / screen.scale.x;

                            // Draw the background
                            this.ctx.fillStyle = MathLib.colorConvert(screen.options.background);
                            this.ctx.fillRect(left, bottom, right - left, top - bottom);

                            this.stack.forEach(function (x) {
                                if (x.type === 'conic') {
                                    x.object.draw(_this, x.options, true);
                                } else if (x.type === 'text') {
                                    _this.text(x.object, x.x, x.y, x.options, true);
                                } else if (x.type === 'pixel') {
                                    _this.pixel(x.object, x.t, x.r, x.b, x.l, x.options, true);
                                } else {
                                    _this[x.type](x.object, x.options, true);
                                }
                            });
                        };
                    } else if (id === 'grid') {
                        this.ctx.strokeStyle = MathLib.colorConvert(screen.options.grid.color) || '#cccccc';
                        this.ctx.fillStyle = 'rgba(255, 255, 255, 0)';

                        this.draw = function () {
                            //					_this.ctx.lineWidth = (screen.options.grid.lineWidth || 4) / (screen.scale.x - screen.scale.y);
                            _this.screen.drawGrid();
                        };
                    } else if (id === 'axes') {
                        this.ctx.strokeStyle = MathLib.colorConvert(screen.options.axes.color) || '#000000';

                        this.draw = function () {
                            _this.ctx.lineWidth = 4 / (screen.scale.x - screen.scale.y);
                            _this.screen.drawAxes();
                        };
                    } else {
                        this.ctx.strokeStyle = '#000000';
                        this.ctx.fillStyle = 'rgba(255, 255, 255, 0)';

                        this.draw = function () {
                            _this.ctx.lineWidth = 4 / (screen.scale.x - screen.scale.y);

                            this.stack.forEach(function (x) {
                                if (x.type === 'conic') {
                                    x.object.draw(_this, x.options, true);
                                } else if (x.type === 'text') {
                                    _this.text(x.object, x.x, x.y, x.options, true);
                                } else if (x.type === 'pixel') {
                                    _this.pixel(x.object, x.t, x.r, x.b, x.l, x.options, true);
                                } else {
                                    _this[x.type](x.object, x.options, true);
                                }
                            });
                        };
                    }

                    this.circle = MathLib.Canvas.circle;
                    this.line = MathLib.Canvas.line;
                    this.path = MathLib.Canvas.path;
                    this.pixel = MathLib.Canvas.pixel;
                    this.point = MathLib.Canvas.point;
                    this.text = MathLib.Canvas.text;
                } else if (screen.options.renderer === 'SVG') {
                    var ctx = document.createElementNS('http://www.w3.org/2000/svg', 'g'), m = screen.transformation;

                    ctx.className.baseVal = 'MathLib_layer_' + id;
                    ctx.setAttribute('transform', 'matrix(' + m[0][0] + ', ' + m[1][0] + ', ' + m[0][1] + ', ' + m[1][1] + ', ' + m[0][2] + ', ' + m[1][2] + ')');
                    screen.element.appendChild(ctx);
                    this.ctx = ctx;

                    // Set the drawing functions
                    if (id === 'back') {
                        this.draw = function () {
                            this.stack.forEach(function (x) {
                                if (x.type === 'conic') {
                                    x.object.draw(_this, x.options, true);
                                } else if (x.type === 'text') {
                                    _this.text(x.object, x.x, x.y, x.options, true);
                                } else if (x.type === 'pixel') {
                                    _this.pixel(x.object, x.t, x.r, x.b, x.l, x.options, true);
                                } else {
                                    _this[x.type](x.object, x.options, true);
                                }
                            });
                        };
                    } else if (id === 'grid') {
                        ctx.setAttribute('stroke', MathLib.colorConvert(screen.options.grid.color) || '#cccccc');

                        this.draw = function () {
                            ctx.setAttribute('stroke-width', 4 / (screen.scale.x - screen.scale.y) + '');
                            _this.screen.drawGrid();
                        };
                    } else if (id === 'axes') {
                        ctx.setAttribute('stroke', MathLib.colorConvert(screen.options.axes.color) || '#000000');

                        this.draw = function () {
                            ctx.setAttribute('stroke-width', 4 / (screen.scale.x - screen.scale.y) + '');
                            _this.screen.drawAxes();
                        };
                    } else {
                        this.draw = function () {
                            this.stack.forEach(function (x) {
                                if (x.type === 'conic') {
                                    x.object.draw(_this, x.options, true);
                                } else if (x.type === 'text') {
                                    _this.text(x.object, x.x, x.y, x.options, true);
                                } else if (x.type === 'pixel') {
                                    _this.pixel(x.object, x.t, x.r, x.b, x.l, x.options, true);
                                } else {
                                    _this[x.type](x.object, x.options, true);
                                }
                            });
                        };
                    }

                    this.circle = MathLib.SVG.circle;
                    this.line = MathLib.SVG.line;
                    this.path = MathLib.SVG.path;
                    this.pixel = MathLib.SVG.pixel;
                    this.point = MathLib.SVG.point;
                    this.text = MathLib.SVG.text;
                }

                // Insert the layer into the layer array of the screen object.
                screen.layer.splice(zIndex, 0, this);
            }
            // ### Layer.prototype.clear()
            // Clears the Layer
            //
            // *@return {Layer}* Returns the current Layer
            Layer.prototype.clear = function () {
                this.screen.renderer.clear(this);
                return this;
            };
            return Layer;
        })();
        MathLib.Layer = Layer;
    })(MathLib || (MathLib = {}));

    /// <reference path='reference.ts'/>
    var MathLib;
    (function (MathLib) {
        // ## Canvas
        // The Canvas renderer for 2D plotting
        /// import screen2d
        MathLib.Canvas = {
            // ### Canvas.applyTransformation
            // Applies the current transformations to the screen
            //
            applyTransformation: function () {
                var m = this.transformation;
                this.layer.forEach(function (l) {
                    l.ctx.setTransform(m[0][0], m[1][0], m[0][1], m[1][1], m[0][2], m[1][2]);
                });
            },
            // ### Canvas.circle
            // Draws a circle on the screen.
            //
            // *@param {Circle}* The circle to be drawn
            // *@param {object}* [options] Optional drawing options
            // *@return {Screen}* Returns the screen
            circle: function (circle, options, redraw) {
                if (typeof options === "undefined") { options = {}; }
                if (typeof redraw === "undefined") { redraw = false; }
                var screen = this.screen, ctx = this.ctx, prop, opts;

                ctx.save();
                ctx.lineWidth = (options.lineWidth || 4) / (screen.scale.x - screen.scale.y);

                // Set the drawing options
                if (options) {
                    opts = MathLib.Canvas.convertOptions(options);
                    for (prop in opts) {
                        if (opts.hasOwnProperty(prop)) {
                            ctx[prop] = opts[prop];
                        }
                    }

                    if ('setLineDash' in ctx) {
                        ctx.setLineDash(('dash' in options ? options.dash : []));
                    }
                    if ('lineDashOffset' in ctx) {
                        ctx.lineDashOffset = ('dashOffset' in options ? options.dashOffset : 0);
                    }
                }

                // Draw the circle
                ctx.beginPath();
                ctx.arc(circle.center[0], circle.center[1], circle.radius, 0, 2 * Math.PI);
                ctx.closePath();
                ctx.fill();
                ctx.stroke();
                ctx.restore();

                if (!redraw) {
                    this.stack.push({
                        type: 'circle',
                        object: circle,
                        options: options
                    });
                }

                return this;
            },
            // ### Canvas.clear
            // Clears a given Layer.
            //
            // *@param {Layer}* The layer to be cleared
            clear: function (layer) {
                var screen = layer.screen, left = -screen.translation.x / screen.scale.x, top = -screen.translation.y / screen.scale.y, width = screen.width / screen.scale.x, height = screen.height / screen.scale.y;

                layer.ctx.clearRect(left, top, width, height);
            },
            // ### Canvas.convertOptions
            // Converts the options to the Canvas options format
            //
            // *@param {object}* The drawing options
            // *@return {object}* The converted options
            convertOptions: function (opt) {
                var convertedOptions = {};
                if ('fillColor' in opt) {
                    convertedOptions.fillStyle = MathLib.colorConvert(opt.fillColor);
                } else if ('color' in opt) {
                    convertedOptions.fillStyle = MathLib.colorConvert(opt.color);
                }

                if ('font' in opt) {
                    convertedOptions.font = opt.font;
                }

                if ('fontSize' in opt) {
                    convertedOptions.fontSize = opt.fontSize;
                }

                if ('lineColor' in opt) {
                    convertedOptions.strokeStyle = MathLib.colorConvert(opt.lineColor);
                } else if ('color' in opt) {
                    convertedOptions.strokeStyle = MathLib.colorConvert(opt.color);
                }

                return convertedOptions;
            },
            // ### Canvas.line
            // Draws a line on the screen.
            //
            // *@param {Line}* The line to be drawn
            // *@param {object}* [options] Optional drawing options
            // *@return {Screen}* Returns the screen
            line: function (line, options, redraw) {
                if (typeof options === "undefined") { options = {}; }
                if (typeof redraw === "undefined") { redraw = false; }
                var screen = this.screen, points, ctx = this.ctx, prop, opts;

                ctx.save();
                ctx.lineWidth = (options.lineWidth || 4) / (screen.scale.x - screen.scale.y);

                // Don't try to draw the line at infinity
                if (line.type === 'line' && MathLib.isZero(line[0]) && MathLib.isZero(line[1])) {
                    return this;
                } else {
                    points = this.screen.getLineEndPoints(line);
                }

                // Set the drawing options
                if (options) {
                    opts = MathLib.Canvas.convertOptions(options);
                    for (prop in opts) {
                        if (opts.hasOwnProperty(prop)) {
                            ctx[prop] = opts[prop];
                        }
                    }

                    if ('setLineDash' in ctx) {
                        ctx.setLineDash(('dash' in options ? options.dash : []));
                    }
                    if ('lineDashOffset' in ctx) {
                        ctx.lineDashOffset = ('dashOffset' in options ? options.dashOffset : 0);
                    }
                }

                // Draw the line
                ctx.beginPath();
                ctx.moveTo(points[0][0], points[0][1]);
                ctx.lineTo(points[1][0], points[1][1]);
                ctx.stroke();
                ctx.closePath();
                ctx.restore();

                if (!redraw) {
                    this.stack.push({
                        type: 'line',
                        object: line,
                        options: options
                    });
                }

                return this;
            },
            // ### Canvas.path
            // Draws a path on the screen.
            //
            // *@param {Path}* The path to be drawn
            // *@param {object}* [options] Optional drawing options
            // *@return {Screen}* Returns the scren
            path: function (curve, options, redraw) {
                if (typeof options === "undefined") { options = {}; }
                if (typeof redraw === "undefined") { redraw = false; }
                var screen = this.screen, ctx = this.ctx, prop, opts, path, paths = [], x, y, i, fx, fxold, step = 2 / (screen.scale.x - screen.scale.y), from, to;

                ctx.save();
                ctx.lineWidth = (options.lineWidth || 4) / (screen.scale.x - screen.scale.y);

                // Set the drawing options
                if (options) {
                    opts = MathLib.Canvas.convertOptions(options);
                    for (prop in opts) {
                        if (opts.hasOwnProperty(prop)) {
                            ctx[prop] = opts[prop];
                        }
                    }

                    if ('setLineDash' in ctx) {
                        ctx.setLineDash(('dash' in options ? options.dash : []));
                    }
                    if ('lineDashOffset' in ctx) {
                        ctx.lineDashOffset = ('dashOffset' in options ? options.dashOffset : 0);
                    }
                }

                // If curve is a function f, the path will be (x, f(x))
                if (typeof curve === 'function') {
                    path = [];
                    from = ('from' in options ? options.from : (-screen.translation.x) / screen.scale.x) - step;
                    to = ('to' in options ? options.to : (screen.width - screen.translation.x) / screen.scale.x) + step;

                    for (i = from; i <= to; i += step) {
                        fx = curve(i);

                        // Inline NaN test and disontinuity test
                        // Check if we are drawing a (nearly) vertical line, which should not be there.
                        // i.e the vertical lines at π/2 for the tangent function
                        // TODO: Find a better check if there is a discontinuity.
                        if (fx !== fx || (MathLib.abs((fxold - fx) / step) >= 1e2 && (fx - curve(i - step / 2)) * (fxold - curve(i - step / 2)) >= 0)) {
                            // Don't add empty subpaths
                            if (path.length) {
                                paths.push(path);
                                path = [];
                            }
                        } else {
                            path.push([i, fx]);
                        }

                        fxold = fx;
                    }
                    if (path.length) {
                        paths.push(path);
                    }
                } else if (typeof curve[0] === 'function') {
                    path = [];
                    x = curve[0];
                    y = curve[1];
                    from = ('from' in options ? options.from : 0) - step;
                    to = ('to' in options ? options.to : 2 * Math.PI) + step;
                    for (i = from; i <= to; i += step) {
                        path.push([x(i), y(i)]);
                    }
                    paths.push(path);
                } else {
                    path = curve;
                }

                // Draw the path
                // Till now I haven't found a way to stroke and fill the path in one go.
                // The problem is basically, that moveTo creates a new subpath
                // and every subpath is filled on its own.
                if (options.fillColor || options.fillColor !== 'transparent') {
                    ctx.beginPath();
                    ctx.lineTo(from, 0);
                    paths.forEach(function (path) {
                        // The following line (and the line four lines afterwards) fixes the fill at holes in the path.
                        ctx.lineTo(path[0][0], 0);
                        path.forEach(function (x) {
                            ctx.lineTo(x[0], x[1]);
                        });
                        ctx.lineTo(path[path.length - 1][0], 0);
                    });
                    ctx.fill();
                    //		ctx.closePath();
                }

                if (options.lineColor || options.lineColor !== 'transparent') {
                    ctx.beginPath();
                    paths.forEach(function (path) {
                        ctx.moveTo(path[0][0], path[0][1]);
                        path.forEach(function (x) {
                            ctx.lineTo(x[0], x[1]);
                        });
                    });
                    ctx.stroke();
                    //		ctx.closePath();
                }

                ctx.restore();

                if (!redraw) {
                    if (options.conic) {
                        this.stack.push({
                            type: 'conic',
                            object: options.conic,
                            options: options
                        });
                    } else {
                        this.stack.push({
                            type: 'path',
                            object: curve,
                            options: options
                        });
                    }
                }

                return this;
            },
            // ### Canvas.pixel
            // Draws pixel on the screen.
            //
            // *@param {function}* The pixel function
            // *@param {number}* The top coordinate of the draw rectangle
            // *@param {number}* The right coordinate of the draw rectangle
            // *@param {number}* The bottom coordinate of the draw rectangle
            // *@param {number}* The left coordinate of the draw rectangle
            // *@param {object}* [options] Optional drawing options
            // *@return {Screen}* Returns the screen
            pixel: function (f, t, r, b, l, options, redraw) {
                if (typeof options === "undefined") { options = {}; }
                if (typeof redraw === "undefined") { redraw = false; }
                var screen = this.screen, top = (-screen.translation.y) / screen.scale.y, bottom = (screen.height - screen.translation.y) / screen.scale.y, left = (-screen.translation.x) / screen.scale.x, right = (screen.width - screen.translation.x) / screen.scale.x, ctx = this.ctx, x, y, i;

                t = Math.min(top, t);
                r = Math.min(right, r);
                b = Math.max(bottom, b);
                l = Math.max(left, l);

                var tPxl = Math.floor(-t * screen.scale.y), rPxl = Math.floor(r * screen.scale.x), bPxl = Math.floor(-b * screen.scale.y), lPxl = Math.floor(l * screen.scale.x), w = (rPxl - lPxl), h = (bPxl - tPxl), imgData = ctx.createImageData(w, h), pxl;

                for (y = tPxl, i = 0; y > bPxl; y--) {
                    for (x = lPxl; x < rPxl; x++, i++) {
                        pxl = f(x / screen.scale.x, y / screen.scale.y);
                        imgData.data[4 * i] = pxl[0];
                        imgData.data[4 * i + 1] = pxl[1];
                        imgData.data[4 * i + 2] = pxl[2];
                        imgData.data[4 * i + 3] = pxl[3];
                    }
                }

                ctx.putImageData(imgData, (left - l) * screen.scale.x, (t - top) * screen.scale.y);

                if (!redraw) {
                    this.stack.push({
                        type: 'pixel',
                        object: f,
                        t: t,
                        r: r,
                        b: b,
                        l: l,
                        options: options
                    });
                }

                return this;
            },
            // ### Canvas.point
            // Draws a point on the screen.
            //
            // *@param {Point}* The point to be drawn
            // *@param {object}* [options] Optional drawing options
            // *@return {Screen}* Returns the screen
            point: function (point, options, redraw) {
                if (typeof options === "undefined") { options = {}; }
                if (typeof redraw === "undefined") { redraw = false; }
                var screen = this.screen, ctx = this.ctx, prop, opts, dist;

                ctx.save();
                ctx.lineWidth = (options.lineWidth || 4) / (screen.scale.x - screen.scale.y);

                // Set the drawing options
                if (options) {
                    opts = MathLib.Canvas.convertOptions(options);

                    if (!('fillColor' in options) && !('color' in options)) {
                        opts.fillStyle = 'black';
                    }

                    for (prop in opts) {
                        if (opts.hasOwnProperty(prop)) {
                            ctx[prop] = opts[prop];
                        }
                    }

                    if ('setLineDash' in ctx) {
                        ctx.setLineDash(('dash' in options ? options.dash : []));
                    }
                    if ('lineDashOffset' in ctx) {
                        ctx.lineDashOffset = ('dashOffset' in options ? options.dashOffset : 0);
                    }
                }

                // Draw the point
                ctx.beginPath();
                ctx.arc(point[0] / point[2], point[1] / point[2], (options.size || 10) / (screen.scale.x - screen.scale.y), 0, 2 * Math.PI);
                ctx.closePath();
                ctx.fill();
                ctx.stroke();
                ctx.restore();

                if (options.label) {
                    dist = 1.75 * (options.size || 10) + 0.75 * (options.lineWidth || 4);
                    screen.text(options.label, point[0] / point[2] + dist / (screen.scale.x - screen.scale.y), point[1] / point[2] + dist / (screen.scale.x - screen.scale.y), options, true);
                }

                if (!redraw) {
                    this.stack.push({
                        type: 'point',
                        object: point,
                        options: options
                    });
                }

                return this;
            },
            // ### Canvas.text
            // Writes text on the screen.
            //
            // *@param {str}* The string to be drawn
            // *@param {x}* The x coordinate
            // *@param {y}* The y coordinate
            // *@param {object}* [options] Optional drawing options
            // *@return {Screen}* Returns the screen
            text: function (str, x, y, options, redraw) {
                if (typeof options === "undefined") { options = {}; }
                if (typeof redraw === "undefined") { redraw = false; }
                var defaults = {
                    font: 'Helvetica',
                    fontSize: 12,
                    //				lineWidth:  0.05,
                    textColor: 'rgba(0, 0, 0, 1)'
                }, ctx, prop, opts;

                ctx = this.ctx;

                opts = MathLib.Canvas.convertOptions(MathLib.extendObject(defaults, options));

                for (prop in opts) {
                    if (opts.hasOwnProperty(prop)) {
                        ctx[prop] = opts[prop];
                    }
                }

                ctx.fillStyle = MathLib.colorConvert(options.textColor || options.color || defaults.textColor);
                ctx.strokeStyle = MathLib.colorConvert(options.textColor || options.color || defaults.textColor);

                ctx.font = opts.fontSize + 'px ' + opts.font;
                ctx.textAlign = 'center';
                ctx.textBaseline = 'middle';

                var tf = this.screen.transformation;

                ctx.save();
                ctx.transform(1 / tf[0][0], 0, 0, 1 / tf[1][1], 0, 0);
                ctx.fillText(str, tf[0][0] * x, tf[1][1] * y);
                ctx.restore();

                if (!redraw) {
                    this.stack.push({
                        type: 'text',
                        object: str,
                        x: x,
                        y: y,
                        options: options
                    });
                }

                return this;
            }
        };
    })(MathLib || (MathLib = {}));

    /// <reference path='reference.ts'/>
    var MathLib;
    (function (MathLib) {
        // ## SVG
        // The SVG renderer for 2D plotting
        //
        /// import screen2D
        MathLib.SVG = {
            // ### SVG.applyTransformation
            // Applies the current transformations to the screen
            //
            applyTransformation: function () {
                var m = this.transformation;
                this.layer.forEach(function (l) {
                    l.ctx.setAttribute('transform', 'matrix(' + m[0][0] + ', ' + m[1][0] + ', ' + m[0][1] + ', ' + m[1][1] + ', ' + m[0][2] + ', ' + m[1][2] + ')');
                });
            },
            // ### SVG circle
            // Draws a circle on the screen.
            //
            // *@param {Circle}* The circle to be drawn
            // *@param {object}* [options] Optional drawing options
            // *@return {Screen}* Returns the screen
            circle: function (circle, options, redraw) {
                if (typeof options === "undefined") { options = {}; }
                if (typeof redraw === "undefined") { redraw = false; }
                var screen = this.screen, prop, opts, svgCircle = document.createElementNS('http://www.w3.org/2000/svg', 'circle');

                svgCircle.setAttribute('cx', circle.center[0]);
                svgCircle.setAttribute('cy', circle.center[1]);
                svgCircle.setAttribute('r', circle.radius);

                if (options) {
                    svgCircle.setAttribute('stroke-width', (options.lineWidth || 4) / (screen.scale.x - screen.scale.y) + '');
                    opts = MathLib.SVG.convertOptions(options);
                    for (prop in opts) {
                        if (opts.hasOwnProperty(prop)) {
                            svgCircle.setAttribute(prop, opts[prop]);
                        }
                    }
                }

                this.ctx.appendChild(svgCircle);

                if (!redraw) {
                    this.stack.push({
                        type: 'circle',
                        object: circle,
                        options: options
                    });
                }

                return this;
            },
            // ### SVG.clear
            // Clears a given Layer.
            //
            // *@param {Layer}* The layer to be cleared
            clear: function (layer) {
                layer.ctx.textContent = '';
            },
            // ### SVG.convertOptions
            // Converts the options to the SVG options format
            //
            // *@param {object}* The drawing options
            // *@return {object}* The converted options
            convertOptions: function (opt) {
                var convertedOptions = {};
                if ('fillColor' in opt) {
                    convertedOptions.fill = MathLib.colorConvert(opt.fillColor);
                } else if ('color' in opt) {
                    convertedOptions.fill = MathLib.colorConvert(opt.color);
                }

                if ('font' in opt) {
                    convertedOptions.font = opt.font;
                }

                if ('fontSize' in opt) {
                    convertedOptions.fontSize = opt.fontSize;
                }

                if ('lineColor' in opt) {
                    convertedOptions.stroke = MathLib.colorConvert(opt.lineColor);
                } else if ('color' in opt) {
                    convertedOptions.stroke = MathLib.colorConvert(opt.color);
                }

                if ('dash' in opt && opt.dash.length !== 0) {
                    convertedOptions['stroke-dasharray'] = opt.dash;
                }

                if ('dashOffset' in opt && opt.dashOffset !== 0) {
                    convertedOptions['stroke-dashoffset'] = opt.dashOffset;
                }

                return convertedOptions;
            },
            // ### SVG line
            // Draws a line on the screen.
            //
            // *@param {Line}* The line to be drawn
            // *@param {object}* [options] Optional drawing options
            // *@return {Canvas}* Returns the screen
            line: function (line, options, redraw) {
                if (typeof options === "undefined") { options = {}; }
                if (typeof redraw === "undefined") { redraw = false; }
                var screen = this.screen, points, prop, opts, svgLine = document.createElementNS('http://www.w3.org/2000/svg', 'line');

                // Don't try to draw the line at infinity
                if (line.type === 'line' && MathLib.isZero(line[0]) && MathLib.isZero(line[1])) {
                    return this;
                } else {
                    points = this.screen.getLineEndPoints(line);
                }

                svgLine.setAttribute('x1', points[0][0]);
                svgLine.setAttribute('y1', points[0][1]);
                svgLine.setAttribute('x2', points[1][0]);
                svgLine.setAttribute('y2', points[1][1]);

                if (options) {
                    svgLine.setAttribute('stroke-width', (options.lineWidth || 4) / (screen.scale.x - screen.scale.y) + '');
                    opts = MathLib.SVG.convertOptions(options);
                    for (prop in opts) {
                        if (opts.hasOwnProperty(prop)) {
                            svgLine.setAttribute(prop, opts[prop]);
                        }
                    }
                }

                this.ctx.appendChild(svgLine);

                if (!redraw) {
                    this.stack.push({
                        type: 'line',
                        object: line,
                        options: options
                    });
                }

                return this;
            },
            // ### SVG path
            // Draws a path on the screen.
            //
            // *@param {curve}* The path to be drawn
            // *@param {object}* [options] Optional drawing options
            // *@return {Screen}* Returns the screen
            path: function (curve, options, redraw) {
                if (typeof options === "undefined") { options = {}; }
                if (typeof redraw === "undefined") { redraw = false; }
                var screen = this.screen, svgPathStroke = document.createElementNS('http://www.w3.org/2000/svg', 'path'), svgPathFill = document.createElementNS('http://www.w3.org/2000/svg', 'path'), step = 2 / (screen.scale.x - screen.scale.y), pathStringFill, pathStringStroke, from, to, prop, opts, x, y, i, path, paths = [], fx, fxold;

                // If curve is a function f, the path will be (x, f(x))
                if (typeof curve === 'function') {
                    path = [];
                    from = ('from' in options ? options.from : -screen.translation.x / screen.scale.x) - step;
                    to = ('to' in options ? options.to : (screen.width - screen.translation.x) / screen.scale.x) + step;
                    for (i = from; i <= to; i += step) {
                        fx = curve(i);

                        // Inline NaN test and disontinuity test
                        // For more info see the corresponding function for canvas
                        if (fx !== fx || (MathLib.abs((fxold - fx) / step) >= 1e2 && (fx - curve(i - step / 2)) * (fxold - curve(i - step / 2)) >= 0)) {
                            // Don't add empty subpaths
                            if (path.length) {
                                paths.push(path);
                                path = [];
                            }
                        } else {
                            path.push([i, fx]);
                        }

                        fxold = fx;
                    }
                    if (path.length) {
                        paths.push(path);
                    }
                } else if (typeof curve[0] === 'function') {
                    path = [];
                    x = curve[0];
                    y = curve[1];
                    from = ('from' in options ? options.from : 0) - step;
                    to = ('to' in options ? options.to : 2 * Math.PI) + step;
                    for (i = from; i <= to; i += step) {
                        path.push([x(i), y(i)]);
                    }
                    paths.push(path);
                } else {
                    path = curve;
                }

                pathStringFill = 'M' + from + ' 0 ' + paths.reduce(function (previ, path) {
                    return previ + ' L ' + path[0][0] + ' 0 ' + path.reduce(function (prev, cur) {
                        return prev + ' L ' + cur.join(' ');
                    }, '') + ' L ' + path[path.length - 1][0] + ' 0 ';
                }, '');

                pathStringStroke = paths.reduce(function (previ, path) {
                    return previ + ' M ' + path[0].join(' ') + path.reduce(function (prev, cur) {
                        return prev + ' L ' + cur.join(' ');
                    }, '');
                }, '');

                if (pathStringFill !== '') {
                    svgPathFill.setAttribute('d', pathStringFill);
                }
                if (pathStringStroke) {
                    svgPathStroke.setAttribute('d', pathStringStroke);
                }

                svgPathStroke.setAttribute('stroke-width', (options.lineWidth || 4) / (screen.scale.x - screen.scale.y) + '');

                if (options) {
                    opts = MathLib.SVG.convertOptions(options);
                    for (prop in opts) {
                        if (opts.hasOwnProperty(prop)) {
                            svgPathFill.setAttribute(prop, opts[prop]);
                            svgPathStroke.setAttribute(prop, opts[prop]);
                        }
                    }
                }

                svgPathFill.setAttribute('stroke', 'transparent');
                svgPathStroke.setAttribute('fill', 'transparent');

                this.ctx.appendChild(svgPathFill);
                this.ctx.appendChild(svgPathStroke);

                if (!redraw) {
                    if (options.conic) {
                        this.stack.push({
                            type: 'conic',
                            object: options.conic,
                            options: options
                        });
                    } else {
                        this.stack.push({
                            type: 'path',
                            object: curve,
                            options: options
                        });
                    }
                }

                return this;
            },
            // ### SVG pixel
            // Draws pixel on the screen.
            //
            // *@param {function}* The pixel function
            // *@param {number}* The top coordinate of the draw rectangle
            // *@param {number}* The right coordinate of the draw rectangle
            // *@param {number}* The bottom coordinate of the draw rectangle
            // *@param {number}* The left coordinate of the draw rectangle
            // *@param {object}* [options] Optional drawing options
            // *@return {Screen}* Returns the screen
            pixel: function (f, t, r, b, l, options, redraw) {
                if (typeof options === "undefined") { options = {}; }
                if (typeof redraw === "undefined") { redraw = false; }
                var screen = this.screen, top = (-screen.translation.y) / screen.scale.y, bottom = (screen.height - screen.translation.y) / screen.scale.y, left = (-screen.translation.x) / screen.scale.x, right = (screen.width - screen.translation.x) / screen.scale.x, canvas = document.createElement('canvas'), canvasCtx = canvas.getContext('2d'), svgImage = document.createElementNS('http://www.w3.org/2000/svg', 'image'), svgContainer = document.createElementNS('http://www.w3.org/2000/svg', 'g'), x, y, i, pxl, m = screen.transformation;

                canvas.width = screen.width;
                canvas.height = screen.height;
                canvasCtx.setTransform(m[0][0], m[1][0], m[0][1], m[1][1], m[0][2], m[1][2]);

                svgContainer.setAttribute('transform', 'matrix(' + 1 / m[0][0] + ', 0, 0, ' + 1 / m[1][1] + ', -' + m[0][2] / m[0][0] + ', ' + -m[1][2] / m[1][1] + ')');
                svgImage.setAttribute('width', screen.width + 'px');
                svgImage.setAttribute('height', screen.height + 'px');
                svgImage.setAttribute('x', '0');
                svgImage.setAttribute('y', '0');

                t = Math.min(top, t);
                r = Math.min(right, r);
                b = Math.max(bottom, b);
                l = Math.max(left, l);

                var tPxl = Math.floor(-t * screen.scale.y), rPxl = Math.floor(r * screen.scale.x), bPxl = Math.floor(-b * screen.scale.y), lPxl = Math.floor(l * screen.scale.x), w = (rPxl - lPxl), h = (tPxl - bPxl), imgData = canvasCtx.createImageData(w, h);

                for (y = tPxl, i = 0; y > bPxl; y--) {
                    for (x = lPxl; x < rPxl; x++, i++) {
                        pxl = f(x / screen.scale.x, y / screen.scale.y);
                        imgData.data[4 * i] = pxl[0];
                        imgData.data[4 * i + 1] = pxl[1];
                        imgData.data[4 * i + 2] = pxl[2];
                        imgData.data[4 * i + 3] = pxl[3];
                    }
                }

                canvasCtx.putImageData(imgData, 0, 0);

                svgImage.setAttributeNS('http://www.w3.org/1999/xlink', 'xlink:href', canvas.toDataURL());

                svgContainer.appendChild(svgImage);
                this.ctx.appendChild(svgContainer);

                if (!redraw) {
                    this.stack.push({
                        type: 'pixel',
                        object: f,
                        t: t,
                        r: r,
                        b: b,
                        l: l,
                        options: options
                    });
                }

                return this;
            },
            // ### SVG point
            // Draws a point on the screen.
            //
            // *@param {Point}* The point to be drawn
            // *@param {object}* [options] Optional drawing options
            // *@return {Screen}* Returns the screen
            point: function (point, options, redraw) {
                if (typeof options === "undefined") { options = {}; }
                if (typeof redraw === "undefined") { redraw = false; }
                var screen = this.screen, prop, opts, dist, svgPoint = document.createElementNS('http://www.w3.org/2000/svg', 'circle');

                svgPoint.setAttribute('cx', point[0] / point[2] + '');
                svgPoint.setAttribute('cy', point[1] / point[2] + '');
                svgPoint.setAttribute('r', (options.size || 10) / (screen.scale.x - screen.scale.y) + '');

                if (options) {
                    svgPoint.setAttribute('stroke-width', (options.lineWidth || 4) / (screen.scale.x - screen.scale.y) + '');
                    opts = MathLib.SVG.convertOptions(options);

                    if (!('fillOpacity' in options)) {
                        opts['fill-opacity'] = '1';
                    }

                    if (!('fillColor' in options) && !('color' in options)) {
                        opts.fill = 'black';
                    }

                    for (prop in opts) {
                        if (opts.hasOwnProperty(prop)) {
                            svgPoint.setAttribute(prop, opts[prop]);
                        }
                    }
                }

                if (options.moveable) {
                    svgPoint.setAttribute('cursor', 'move');

                    // mousedown
                    svgPoint.addEventListener('mousedown', function () {
                        screen.options.interaction.type = 'move';
                        var invTransformation = screen.transformation.inverse();

                        var move = function (evt) {
                            evt.stopPropagation();

                            var evtPoint = invTransformation.times(screen.getEventPoint(evt));
                            point[0] = evtPoint[0];
                            point[1] = evtPoint[1];
                            screen.draw();
                        }, up = function () {
                            screen.options.interaction.type = '';

                            document.body.removeEventListener('mousemove', move);
                            document.body.removeEventListener('mouseup', up);
                        };

                        // mousemove
                        document.body.addEventListener('mousemove', move);

                        // mouseup
                        document.body.addEventListener('mouseup', up);
                    });
                }

                this.ctx.appendChild(svgPoint);

                if (options.label) {
                    dist = 1.75 * (options.size || 10) + 0.75 * (options.lineWidth || 4);
                    screen.text(options.label, point[0] / point[2] + dist / (screen.scale.x - screen.scale.y), point[1] / point[2] + dist / (screen.scale.x - screen.scale.y), options, true);
                }

                svgPoint.addEventListener('contextmenu', function () {
                    screen.options.interaction.type = 'contextmenu';
                    var x = svgPoint.cx.baseVal.value, y = svgPoint.cy.baseVal.value;

                    screen.contextMenu.innerHTML = '<div class="MathLib_menuItem MathLib_temporaryMenuItem MathLib_is_disabled MathLib_is_centered">Point</div>' + '<div class="MathLib_menuItem MathLib_temporaryMenuItem MathLib_hasSubmenu">Coordinates' + '<menu class="MathLib_menu MathLib_submenu">' + '<div class="MathLib_menuItem">cartesian: <span class="MathLib_is_selectable MathLib_is_right">(' + x.toFixed(3) + ', ' + y.toFixed(3) + ')</span></div>' + '<div class="MathLib_menuItem">polar: <span class="MathLib_is_selectable MathLib_is_right">(' + MathLib.hypot(x, y).toFixed(3) + ', ' + Math.atan2(y, x).toFixed(3) + ')</span></div>' + '</menu>' + '</div>' + '<div class="MathLib_menuItem MathLib_temporaryMenuItem MathLib_hasSubmenu">Options' + '<menu class="MathLib_menu MathLib_submenu">' + '<div class="MathLib_menuItem">Moveable:' + '<input type="checkbox" class="MathLib_is_right">' + '</div>' + '<div class="MathLib_menuItem">Size:' + '<input type="spinner" class="MathLib_is_right">' + '</div>' + '<div class="MathLib_menuItem">Fill color:' + '<input type="color" class="MathLib_is_right">' + '</div>' + '<div class="MathLib_menuItem">Line color:' + '<input type="color" class="MathLib_is_right">' + '</div>' + '</menu>' + '</div>' + '<hr class="MathLib_separator MathLib_temporaryMenuItem">' + screen.contextMenu.innerHTML;
                });

                if (!redraw) {
                    this.stack.push({
                        type: 'point',
                        object: point,
                        options: options
                    });
                }

                return this;
            },
            // ### SVG text
            // Writes text on the screen.
            //
            // *@param {str}* The string to be drawn
            // *@param {x}* The x coordinate
            // *@param {y}* The y coordinate
            // *@param {object}* [options] Optional drawing options
            // *@return {Screen}* Returns the screen
            text: function (str, x, y, options, redraw) {
                if (typeof options === "undefined") { options = {}; }
                if (typeof redraw === "undefined") { redraw = false; }
                var defaults = {
                    font: 'Helvetica',
                    fontSize: 12,
                    //				lineWidth:  0.05,
                    textColor: 'rgba(0, 0, 0, 1)'
                }, opts, screen = this.screen, svgText = document.createElementNS('http://www.w3.org/2000/svg', 'text'), svgTspan = document.createElementNS('http://www.w3.org/2000/svg', 'tspan');

                opts = MathLib.SVG.convertOptions(MathLib.extendObject(defaults, options));

                svgTspan.textContent = str;
                svgTspan.setAttribute('x', x * screen.scale.x + '');
                svgTspan.setAttribute('y', y * screen.scale.y + '');
                svgText.setAttribute('transform', 'matrix(' + 1 / screen.scale.x + ', 0, 0, ' + 1 / screen.scale.y + ', 0, 0)');
                svgText.setAttribute('font-family', opts.font);
                svgText.setAttribute('font-size', opts.fontSize);
                svgText.setAttribute('fill', MathLib.colorConvert(options.textColor || options.color) || defaults.textColor);
                svgText.setAttribute('fill-opacity', '1');
                svgText.setAttribute('stroke', MathLib.colorConvert(options.textColor || options.color) || defaults.textColor);
                svgText.setAttribute('text-anchor', 'middle');

                // alignment-baseline isn't defined for text elements,
                // only for ‘tspan’, ‘tref’, ‘altGlyph’, ‘textPath’ elements.
                // see the [Specification](http://www.w3.org/TR/SVG/text.html#AlignmentBaselineProperty)
                // But it works for text elements, so we don't need an additional tspan element.
                svgTspan.setAttribute('alignment-baseline', 'middle');

                svgText.appendChild(svgTspan);
                this.ctx.appendChild(svgText);

                if (!redraw) {
                    this.stack.push({
                        type: 'text',
                        object: str,
                        x: x,
                        y: y,
                        options: options
                    });
                }

                return this;
            }
        };
    })(MathLib || (MathLib = {}));

    var __extends = this.__extends || function (d, b) {
        for (var p in b) {
          Eif (b.hasOwnProperty(p)) {
            d[p] = b[p];
          }
        }
        function __() {
          this.constructor = d;
        }
        __.prototype = b.prototype;
        d.prototype = new __();
    };
    /// <reference path='reference.ts'/>
    var MathLib;
    (function (MathLib) {
        // ## <a id="Screen2D"></a>Screen2D
        // Two dimensional plotting
        /// import Screen
        var Screen2D = (function (_super) {
            __extends(Screen2D, _super);
            function Screen2D(id, options) {
                if (typeof options === "undefined") { options = {}; }
                var _this = this;
                _super.call(this, id, options);
                this.type = 'screen2D';
                var defaults = {
                    axes: {
                        color: 0x000000,
                        lineColor: 0x000000,
                        textColor: 0x000000,
                        /*						label: true
                        label: false
                        label: {
                        x: true,
                        y: false
                        }
                        */
                        label: {
                            fontSize: 12,
                            font: 'Helvetica',
                            x: true,
                            y: true
                        },
                        x: true,
                        y: true
                    },
                    grid: {
                        // angle: Math.PI / 8,
                        type: 'cartesian',
                        lineColor: 0xcccccc,
                        lineWidth: 4,
                        dash: [],
                        dashOffset: 0,
                        //tick: {x: 1, y: 1, r: 1}
                        x: { tick: 1, lineColor: 0xcccccc, lineWidth: 4, dash: [], dashOffset: 0 },
                        y: { tick: 1, lineColor: 0xcccccc, lineWidth: 4, dash: [], dashOffset: 0 },
                        r: { tick: 1, lineColor: 0xcccccc, lineWidth: 4, dash: [], dashOffset: 0 },
                        angle: { tick: Math.PI / 8, lineColor: 0xcccccc, lineWidth: 4, dash: [], dashOffset: 0 }
                    },
                    interaction: {
                        allowPan: true,
                        allowZoom: true,
                        zoomSpeed: 1
                    },
                    background: 0xffffff,
                    lookAt: { x: 0, y: 0 },
                    range: { x: 1, y: 1 },
                    figcaption: '',
                    renderer: 'Canvas',
                    transformation: new MathLib.Matrix([
                        [Math.min(this.height, this.width) / 2, 0, this.width / 2],
                        [0, -Math.min(this.height, this.width) / 2, this.height / 2],
                        [0, 0, 1]])
                }, opts = MathLib.extendObject(defaults, options), element, transformation = opts.transformation, that = this;

                this.options = opts;
                this.renderer = MathLib[opts.renderer];

                this.circle = function () {
                    var args = [];
                    for (var _i = 0; _i < (arguments.length - 0); _i++) {
                        args[_i] = arguments[_i + 0];
                    }
                    return _this.renderer.circle.apply(_this.layer.main, args);
                };
                this.line = function () {
                    var args = [];
                    for (var _i = 0; _i < (arguments.length - 0); _i++) {
                        args[_i] = arguments[_i + 0];
                    }
                    return _this.renderer.line.apply(_this.layer.main, args);
                };
                this.path = function () {
                    var args = [];
                    for (var _i = 0; _i < (arguments.length - 0); _i++) {
                        args[_i] = arguments[_i + 0];
                    }
                    return _this.renderer.path.apply(_this.layer.main, args);
                };

                // Should the pixel method default to the main layer or to the back layer?
                this.pixel = function () {
                    var args = [];
                    for (var _i = 0; _i < (arguments.length - 0); _i++) {
                        args[_i] = arguments[_i + 0];
                    }
                    return _this.renderer.pixel.apply(_this.layer.main, args);
                };
                this.point = function () {
                    var args = [];
                    for (var _i = 0; _i < (arguments.length - 0); _i++) {
                        args[_i] = arguments[_i + 0];
                    }
                    return _this.renderer.point.apply(_this.layer.main, args);
                };
                this.text = function () {
                    var args = [];
                    for (var _i = 0; _i < (arguments.length - 0); _i++) {
                        args[_i] = arguments[_i + 0];
                    }
                    return _this.renderer.text.apply(_this.layer.main, args);
                };

                // Remove the warning message.
                this.wrapper.innerHTML = '';

                this.container.classList.add('MathLib_screen2D');

                // This is just a dummy method for the following few lines.
                // The real applyTransformation method is specified after the creation of the layers.
                this.applyTransformation = function () {
                };

                // The interaction methods
                this.translation = {};
                this.scale = {};
                this.transformation = transformation;

                Object.defineProperty(this.translation, 'x', {
                    get: function () {
                        return that.transformation[0][2];
                    },
                    set: function (x) {
                        that.transformation[0][2] = x;
                        that.applyTransformation();
                    }
                });

                Object.defineProperty(this.translation, 'y', {
                    get: function () {
                        return that.transformation[1][2];
                    },
                    set: function (y) {
                        that.transformation[1][2] = y;
                        that.applyTransformation();
                    }
                });

                Object.defineProperty(this.scale, 'x', {
                    get: function () {
                        return that.transformation[0][0];
                    },
                    set: function (x) {
                        that.transformation[0][0] = x;
                        that.applyTransformation();
                    }
                });

                Object.defineProperty(this.scale, 'y', {
                    get: function () {
                        return that.transformation[1][1];
                    },
                    set: function (y) {
                        that.transformation[1][1] = y;
                        that.applyTransformation();
                    }
                });

                this.lookAt = {};
                this.range = {};
                Object.defineProperty(this.lookAt, 'x', {
                    get: function () {
                        return (that.width / 2 - that.transformation[0][2]) / that.transformation[0][0];
                    },
                    set: function (x) {
                        that.transformation[0][2] = that.width / 2 - x * that.transformation[0][0];
                        that.applyTransformation();
                    }
                });

                Object.defineProperty(this.lookAt, 'y', {
                    get: function () {
                        return (that.height / 2 - that.transformation[1][2]) / that.transformation[1][1];
                    },
                    set: function (y) {
                        that.transformation[1][2] = that.height / 2 - y * that.transformation[1][1];
                        that.applyTransformation();
                    }
                });

                Object.defineProperty(this.range, 'x', {
                    get: function () {
                        return that.width / (2 * that.transformation[0][0]);
                    },
                    set: function (x) {
                        that.transformation[0][0] = 0.5 * that.width / x;
                        that.applyTransformation();
                    }
                });

                Object.defineProperty(this.range, 'y', {
                    get: function () {
                        return -that.height / (2 * that.transformation[1][1]);
                    },
                    set: function (y) {
                        that.transformation[1][1] = -0.5 * that.height / y;
                        that.applyTransformation();
                    }
                });

                this.range.x = opts.range.x;
                this.range.y = opts.range.y;
                this.lookAt.x = opts.lookAt.x;
                this.lookAt.y = opts.lookAt.y;

                // Create the SVG element which contains the layers
                if (opts.renderer === 'SVG') {
                    // Create the canvas
                    element = document.createElementNS('http://www.w3.org/2000/svg', 'svg');

                    // Safari does not support .classList on SVG elements
                    // This feature has be in webkit since [08/02/12](http://trac.webkit.org/changeset/124499)
                    /* element.classList.add('MathLib_screen'); */
                    element.className.baseVal = 'MathLib_screen';
                    element.setAttribute('xmlns', 'http://www.w3.org/2000/svg');
                    element.setAttribute('xmlns:xlink', 'http://www.w3.org/1999/xlink');
                    element.setAttribute('height', this.height + 'px');
                    element.setAttribute('width', this.width + 'px');
                    element.setAttribute('version', '1.1');

                    element.setAttribute('stroke', '#000000');
                    element.setAttribute('stroke-opacity', '1');
                    element.setAttribute('fill', 'transparent');

                    this.element = element;
                    this.wrapper.appendChild(element);

                    //			if ('background' in options) {
                    var background = document.createElementNS('http://www.w3.org/2000/svg', 'rect');

                    background.setAttribute('x', '0px');
                    background.setAttribute('y', '0px');
                    background.setAttribute('width', this.width + 'px');
                    background.setAttribute('height', this.height + 'px');
                    background.setAttribute('stroke', 'transparent');
                    background.setAttribute('fill', 'background' in options ? MathLib.colorConvert(options.background) : 'white');
                    background.setAttribute('fill-opacity', '1');
                    this.element.appendChild(background);
                    //			}
                }

                // Create the Layers
                // =================
                this.layer = [];
                this.layer.back = new MathLib.Layer(this, 'back', 0);
                this.layer.grid = new MathLib.Layer(this, 'grid', 1);
                this.layer.axes = new MathLib.Layer(this, 'axes', 2);
                this.layer.main = new MathLib.Layer(this, 'main', 3);

                this.wrapper.addEventListener('mouseup', function (evt) {
                    return _this.onmouseup(evt);
                }, false);
                this.wrapper.addEventListener('mousedown', function (evt) {
                    return _this.onmousedown(evt);
                }, false);
                this.wrapper.addEventListener('mousemove', function (evt) {
                    return _this.onmousemove(evt);
                }, false);
                this.wrapper.addEventListener('mousewheel', function (evt) {
                    return _this.onmousewheel(evt);
                }, false);

                // For Firefox: [Bug report for the missing onmousewheel method](https://bugzilla.mozilla.org/show_bug.cgi?id=111647)
                this.wrapper.addEventListener('DOMMouseScroll', function (evt) {
                    return _this.onmousewheel(evt);
                }, false);

                this.applyTransformation = this.renderer.applyTransformation;

                this.draw = function (x, options) {
                    if (typeof options === "undefined") { options = {}; }
                    var _this = this;
                    // Clear and redraw the screen
                    if (arguments.length === 0) {
                        this.layer.forEach(function (l) {
                            l.clear().draw();
                        });
                    } else if (x.type === 'circle') {
                        this.circle(x, options);
                    } else if (x.type === 'line') {
                        this.line(x, options);
                    } else if (Array.isArray(x)) {
                        x.forEach(function (y) {
                            return _this[y.type](y, options);
                        });
                    }
                };

                if (this.options.contextMenu) {
                    var gridType = opts.grid.type ? opts.grid.type : 'none';
                    this.contextMenu.querySelectorAll('.MathLib_grid_type[value=' + gridType + ']')[0].checked = true;
                }

                this.draw();
            }
            // ### Screen.prototype.drawAxes
            // Draws the axes.
            //
            // *@return {Screen2D}*
            Screen2D.prototype.drawAxes = function () {
                var _this = this;
                var line = function () {
                    var args = [];
                    for (var _i = 0; _i < (arguments.length - 0); _i++) {
                        args[_i] = arguments[_i + 0];
                    }
                    return _this.renderer.line.apply(_this.layer.axes, args);
                }, text = function () {
                    var args = [];
                    for (var _i = 0; _i < (arguments.length - 0); _i++) {
                        args[_i] = arguments[_i + 0];
                    }
                    return _this.renderer.text.apply(_this.layer.axes, args);
                }, options = {
                    lineColor: MathLib.colorConvert(this.options.axes.color),
                    'stroke-width': -1 / this.transformation[1][1]
                }, textOptions = {
                    font: this.options.axes && 'label' in this.options.axes ? this.options.axes.label.font : '',
                    fontSize: this.options.axes && 'label' in this.options.axes ? this.options.axes.label.fontSize : '',
                    //				fontSize: this.options.axes.label.fontSize,
                    strokeStyle: MathLib.colorConvert(this.options.axes.textColor),
                    fillStyle: MathLib.colorConvert(this.options.axes.textColor)
                }, top = (-this.translation.y) / this.scale.y, bottom = (this.height - this.translation.y) / this.scale.y, left = (-this.translation.x) / this.scale.x, right = (this.width - this.translation.x) / this.scale.x, lengthX = 10 / this.transformation[0][0], lengthY = -10 / this.transformation[1][1], yExp = 1 - Math.floor(Math.log(-this.transformation[1][1]) / Math.LN10 - 0.3), xExp = 1 - Math.floor(Math.log(this.transformation[0][0]) / Math.LN10 - 0.3), yTick = Math.pow(10, yExp), xTick = Math.pow(10, xExp), i;

                if (!this.options.axes) {
                    return this;
                }

                // The axes
                if (this.options.axes.x) {
                    line([[left, 0], [right, 0]], options, true);
                }
                if (this.options.axes.y) {
                    line([[0, bottom], [0, top]], options, true);
                }

                // The ticks on the axes
                // The x axes
                if (this.options.axes.x) {
                    for (i = left; i <= right; i += yTick) {
                        line([[i, -lengthY], [i, lengthY]], options, true);
                    }
                }

                // The y axes
                if (this.options.axes.y) {
                    for (i = bottom; i <= top; i += xTick) {
                        line([[-lengthX, i], [lengthX, i]], options, true);
                    }
                }

                // The labels
                // The x axes
                // .toFixed() is necessary to display 0.3 as "0.3" and not as "0.30000000000000004".
                // .toFixed expects arguments between 0 and 20.
                var xLen = Math.max(0, Math.min(20, -xExp)), yLen = Math.max(0, Math.min(20, -yExp));

                if (this.options.axes.label) {
                    if (this.options.axes.x) {
                        for (i = -yTick; i >= left; i -= yTick) {
                            text(i.toFixed(yLen), i, -2 * lengthY, textOptions, true);
                        }
                        for (i = yTick; i <= right; i += yTick) {
                            text(i.toFixed(yLen), i, -2 * lengthY, textOptions, true);
                        }
                    }

                    // The y axes
                    if (this.options.axes.y) {
                        for (i = -xTick; i >= bottom; i -= xTick) {
                            text(i.toFixed(xLen), -2 * lengthX, i, textOptions, true);
                        }
                        for (i = xTick; i <= top; i += xTick) {
                            text(i.toFixed(xLen), -2 * lengthX, i, textOptions, true);
                        }
                    } else {
                        text(0..toFixed(yLen), 0, -2 * lengthY, textOptions, true);
                    }
                }

                return this;
            };

            // ### Screen2D.prototype.drawGrid
            // Draws the grid.
            //
            // *@return {Screen2D}*
            Screen2D.prototype.drawGrid = function () {
                var _this = this;
                if (!this.options.grid) {
                    return this;
                }

                var i, ii, line = function () {
                    var args = [];
                    for (var _i = 0; _i < (arguments.length - 0); _i++) {
                        args[_i] = arguments[_i + 0];
                    }
                    return _this.renderer.line.apply(_this.layer.grid, args);
                }, circle = function () {
                    var args = [];
                    for (var _i = 0; _i < (arguments.length - 0); _i++) {
                        args[_i] = arguments[_i + 0];
                    }
                    return _this.renderer.circle.apply(_this.layer.grid, args);
                }, top = (-this.translation.y) / this.scale.y, bottom = (this.height - this.translation.y) / this.scale.y, left = (-this.translation.x) / this.scale.x, right = (this.width - this.translation.x) / this.scale.x, yTick = Math.pow(10, 1 - Math.floor(Math.log(-this.transformation[1][1]) / Math.LN10 - 0.3)), xTick = Math.pow(10, 1 - Math.floor(Math.log(this.transformation[0][0]) / Math.LN10 - 0.3));

                if (this.options.grid.type === 'cartesian') {
                    // The vertical lines
                    if (this.options.grid.x) {
                        for (i = left - (left % xTick); i <= right; i += xTick) {
                            line([[i, bottom], [i, top]], MathLib.extendObject(this.options.grid, this.options.grid.x), true);
                        }
                    }

                    // The horizontal lines
                    if (this.options.grid.y) {
                        for (i = bottom - (bottom % yTick); i <= top; i += yTick) {
                            line([[left, i], [right, i]], MathLib.extendObject(this.options.grid, this.options.grid.y), true);
                        }
                    }
                    // Test for logarithmic plots
                    /*for (i = left - (left % this.axes.tick.x); i <= right; i += this.axes.tick.x) {
                    for (var j = 1; j <= 10; j++ ) {
                    this.line([[i * Math.log(10) + Math.log(j), bottom], [i * Math.log(10) + Math.log(j), top]], options);
                    }
                    }*/
                } else if (this.options.grid.type === 'polar') {
                    var max = Math.sqrt(Math.max(top * top, bottom * bottom) + Math.max(left * left, right * right)), min = 0;

                    if (this.options.grid.angle) {
                        for (i = 0, ii = 2 * Math.PI; i < ii; i += this.options.grid.angle.tick) {
                            line([[0, 0], [max * Math.cos(i), max * Math.sin(i)]], MathLib.extendObject(this.options.grid, this.options.grid.angle), true);
                        }
                    }

                    if (this.options.grid.r) {
                        for (i = min; i <= max; i += Math.min(xTick, yTick)) {
                            circle(new MathLib.Circle([0, 0, 1], i), MathLib.extendObject(this.options.grid, this.options.grid.r), true);
                        }
                    }
                }

                return this;
            };

            // ### Screen.prototype.getEventPoint
            // Creates a point based on the coordinates of an event.
            //
            // *@param {event}*
            // *@return {Point}*
            Screen2D.prototype.getEventPoint = function (evt) {
                var x, y;
                if (evt.offsetX) {
                    x = evt.offsetX;
                    y = evt.offsetY;
                } else {
                    x = evt.layerX;
                    y = evt.layerY;
                }
                return new MathLib.Point([x, y, 1]);
            };

            // ### Screen2D.prototype.getineEndPoint()
            // Calculates the both endpoints for the line
            // for drawing purposes
            //
            // *@param {Line|array}*
            // *@return {array}* The array has the format [[x1, y1], [x2, y2]]
            Screen2D.prototype.getLineEndPoints = function (l) {
                if (l.type === 'line') {
                    var top = (-this.translation.y) / this.scale.y, bottom = (this.height - this.translation.y) / this.scale.y, left = (-this.translation.x) / this.scale.x, right = (this.width - this.translation.x) / this.scale.x, lineRight = -(l[2] + l[0] * right) / l[1], lineTop = -(l[2] + l[1] * top) / l[0], lineLeft = -(l[2] + l[0] * left) / l[1], lineBottom = -(l[2] + l[1] * bottom) / l[0], points = [];

                    if (lineRight <= top && lineRight >= bottom) {
                        points.push([right, lineRight]);
                    }
                    if (lineLeft <= top && lineLeft >= bottom) {
                        points.push([left, lineLeft]);
                    }
                    if (lineTop < right && lineTop > left) {
                        points.push([lineTop, top]);
                    }
                    if (lineBottom < right && lineBottom > left) {
                        points.push([lineBottom, bottom]);
                    }
                    return points;
                } else {
                    return l;
                }
            };

            // ### Screen2D.prototype.onmousedown()
            // Handles the mousedown event
            //
            // *@param {event}*
            Screen2D.prototype.onmousedown = function (evt) {
                // Only start the action if the left mouse button was clicked
                if (evt.button !== 0) {
                    return;
                }

                if (evt.preventDefault) {
                    evt.preventDefault();
                }

                evt.returnValue = false;

                // Pan mode
                if (this.options.interaction.allowPan && !this.options.interaction.type) {
                    this.options.interaction.type = 'pan';
                    this.options.interaction.startPoint = this.getEventPoint(evt);
                    this.options.interaction.startTransformation = this.transformation.copy();
                }
            };

            // ### Screen.prototype.onmousemove()
            // Handles the mousemove event
            //
            // *@param {event}*
            Screen2D.prototype.onmousemove = function (evt) {
                var p;

                if (evt.preventDefault) {
                    evt.preventDefault();
                }

                evt.returnValue = false;

                // Pan mode
                if (this.options.interaction.type === 'pan') {
                    p = this.getEventPoint(evt).minus(this.options.interaction.startPoint);
                    this.translation.x = this.options.interaction.startTransformation[0][2] + p[0];
                    this.translation.y = this.options.interaction.startTransformation[1][2] + p[1];
                    this.draw();
                }
            };

            // ### Screen.prototype.onmouseup()
            // Handles the mouseup event
            //
            // *@param {event}*
            Screen2D.prototype.onmouseup = function (evt) {
                if (evt.preventDefault) {
                    evt.preventDefault();
                }

                evt.returnValue = false;

                // Go back to normal mode
                if (this.options.interaction.type === 'pan') {
                    delete this.options.interaction.type;
                    delete this.options.interaction.startPoint;
                    delete this.options.interaction.startTransformation;
                }
            };

            // ### Screen.prototype.onmousewheel()
            // Handles the mousewheel event
            //
            // *@param {event}*
            Screen2D.prototype.onmousewheel = function (evt) {
                var delta, s, p, z;

                if (this.options.interaction.allowZoom) {
                    if (evt.preventDefault) {
                        evt.preventDefault();
                    }
                    evt.returnValue = false;

                    // Chrome/Safari
                    if (evt.wheelDelta) {
                        delta = evt.wheelDelta / 360;
                    } else {
                        delta = evt.detail / -9;
                    }

                    // The amount of zoom is determined by the zoom speed
                    // and the amount how much the scrollwheel has been moved
                    z = Math.pow(1 + this.options.interaction.zoomSpeed, delta);

                    // Transform the (computer-)screen coordinates of the mouse to the internal coordinates
                    p = this.transformation.inverse().times(this.getEventPoint(evt));

                    // Compute new scale matrix in current mouse position
                    s = new MathLib.Matrix([[z, 0, p[0] - p[0] * z], [0, z, p[1] - p[1] * z], [0, 0, 1]]);

                    this.transformation = this.transformation.times(s);

                    this.applyTransformation();
                    this.draw();
                }
            };

            // ### Screen2D.prototype.resize()
            // Adjust the rendering if the screen is resized
            //
            // *@param {number}* The new width
            // *@param {number}* The new height
            // *@return {Screen2D}*
            Screen2D.prototype.resize = function (width, height) {
                this.height = height;
                this.width = width;

                if (this.options.renderer === 'Canvas') {
                    this.layer.back.element.width = width;
                    this.layer.back.element.height = height;
                    this.layer.back.ctx.fillStyle = 'rgba(255, 255, 255, 0)';

                    this.layer.grid.element.width = width;
                    this.layer.grid.element.height = height;
                    this.layer.grid.ctx.fillStyle = 'rgba(255, 255, 255, 0)';
                    this.layer.grid.ctx.strokeStyle = MathLib.colorConvert(this.options.grid.color) || '#cccccc';

                    this.layer.axes.element.width = width;
                    this.layer.axes.element.height = height;
                    this.layer.axes.ctx.fillStyle = 'rgba(255, 255, 255, 0)';
                    this.layer.axes.ctx.strokeStyle = MathLib.colorConvert(this.options.axes.color) || '#000000';

                    this.layer.main.element.width = width;
                    this.layer.main.element.height = height;
                    this.layer.main.ctx.fillStyle = 'rgba(255, 255, 255, 0)';
                } else if (this.options.renderer === 'SVG') {
                    this.element.setAttribute('width', width + 'px');
                    this.element.setAttribute('height', height + 'px');
                }

                this.applyTransformation();
                this.draw();

                return this;
            };
            return Screen2D;
        })(MathLib.Screen);
        MathLib.Screen2D = Screen2D;
    })(MathLib || (MathLib = {}));

    var __extends = this.__extends || function (d, b) {
        for (var p in b) {
          if (b.hasOwnProperty(p)) {
            d[p] = b[p];
          }
        }
        function __() {
          this.constructor = d;
        }
        __.prototype = b.prototype;
        d.prototype = new __();
    };
    /// <reference path='reference.ts'/>
    var MathLib;
    (function (MathLib) {

        // A function converting arrays to THREE.js vectors
        var to3js = function (x) {
            if (x.length === 2) {
                return new THREE.Vector2(x[0], x[1]);
            } else if (x.length === 3) {
                return new THREE.Vector3(x[0], x[1], x[2]);
            }
        };

        /// import Screen
        var Screen3D = (function (_super) {
            __extends(Screen3D, _super);
            function Screen3D(id, options) {
                if (typeof options === "undefined") { options = {}; }
                _super.call(this, id, options);
                this.type = 'screen3D';

                var defaults = {
                    anaglyphMode: false,
                    axes: true,
                    background: 0xffffff,
                    camera: {
                        lookAt: [0, 0, 0],
                        position: [10, 10, 10]
                    },
                    controls: 'Trackball',
                    grid: {
                        xy: {
                            angle: Math.PI / 8,
                            color: 0xcccccc,
                            type: 'none',
                            tick: { x: 1, y: 1, r: 1 }
                        },
                        xz: {
                            angle: Math.PI / 8,
                            color: 0xcccccc,
                            type: 'none',
                            tick: { x: 1, z: 1, r: 1 }
                        },
                        yz: {
                            angle: Math.PI / 8,
                            color: 0xcccccc,
                            type: 'none',
                            tick: { y: 1, z: 1, r: 1 }
                        }
                    },
                    height: 500,
                    renderer: 'WebGL',
                    width: 500
                }, opts = MathLib.extendObject(defaults, options), scene = new THREE.Scene(), camera, renderer, controls, viewAngle, aspect, near, far;

                this.options = opts;
                this.scene = scene;

                // Camera
                // ======
                viewAngle = 45;
                aspect = opts.width / opts.height;
                near = 0.1;
                far = 20000;

                camera = new THREE.PerspectiveCamera(viewAngle, aspect, near, far);
                camera.position = to3js(opts.camera.position);
                camera.lookAt(to3js(opts.camera.lookAt));
                camera.up = new THREE.Vector3(0, 0, 1);
                scene.add(camera);

                // Renderer
                // ========
                renderer = new THREE[opts.renderer + 'Renderer']({ antialias: true, preserveDrawingBuffer: true });

                // Remove the warning message.
                this.wrapper.innerHTML = '';
                this.wrapper.appendChild(renderer.domElement);

                // Storing the the original renderer to recover it easily when leaving anaglyph mode
                var origRenderer = renderer;

                // Overwrite the renderer with the anaglyph mode renderer
                if (opts.anaglyphMode) {
                    renderer = new THREE.AnaglyphEffect(renderer);
                }

                renderer.setSize(opts.width, opts.height);

                // Controls
                // ========
                // Other possible values are: 'FirstPerson', 'Fly', 'Orbit', 'Path', 'Roll', 'Trackback' or false
                // MathLib defaults to the TrackballControls
                // move mouse and left   click (or hold 'A') to rotate
                //                middle click (or hold 'S') to zoom
                //                right  click (or hold 'D') to pan
                if (opts.controls) {
                    controls = new THREE[opts.controls + 'Controls'](camera, renderer.domElement);
                } else {
                    controls = {
                        update: function () {
                        }
                    };
                }

                // Light
                // =====
                var light1 = new THREE.PointLight(0xffffff);
                light1.position.set(0, 0, 200);
                scene.add(light1);
                var light2 = new THREE.PointLight(0xffffff);
                light2.position.set(0, 0, -200);
                scene.add(light2);

                // Background
                // ==========
                renderer.setClearColorHex(opts.background, 1);
                renderer.clear();

                // Grid
                // ====
                if (opts.grid) {
                    this.drawGrid();
                }

                // Axes
                // ====
                if (opts.axes) {
                    var axes = new THREE.AxisHelper(10);
                    scene.add(axes);
                }

                // Animate the scene
                // =================
                function animate () {
                    requestAnimationFrame(animate);
                    render();
                    update();
                }

                function update () {
                    //var delta = clock.getDelta();
                    controls.update();
                }

                // Render the scene
                function render () {
                    renderer.render(scene, camera);
                }

                // kick of the animation loop
                animate();

                this.options = opts;
                this.element = renderer.domElement;
                this.renderer = renderer;
                this.camera = camera;

                this.container.classList.add('MathLib_screen3D');
            }
            // ### Screen3D.prototype.drawGrid
            // Draws the grid.
            //
            // *@return {Screen3D}*
            Screen3D.prototype.drawGrid = function () {
                if (!this.options.grid) {
                    return this;
                }

                var _this = this, gridDrawer = function (opts, rotX, rotY) {
                    var size = 10, grid = new THREE.Object3D(), color = new THREE.Color(opts.color), i, ii;

                    if (opts.type === 'cartesian') {
                        var tickX = 'x' in opts.tick ? opts.tick.x : opts.tick.y, tickY = 'z' in opts.tick ? opts.tick.z : opts.tick.y, lines = new THREE.Shape();

                        for (i = -size; i <= size; i += tickX) {
                            lines.moveTo(-size, i);
                            lines.lineTo(size, i);
                        }

                        for (i = -size; i <= size; i += tickY) {
                            lines.moveTo(i, -size);
                            lines.lineTo(i, size);
                        }

                        grid.add(new THREE.Line(lines.createPointsGeometry(), new THREE.LineBasicMaterial({ color: color }), THREE.LinePieces));

                        grid.rotation.x = rotX;
                        grid.rotation.y = rotY;

                        _this.scene.add(grid);
                    } else if (opts.type === 'polar') {
                        var circles = new THREE.Shape(), rays = new THREE.Shape();

                        for (i = 0; i <= size; i += opts.tick.r) {
                            circles.moveTo(i, 0);
                            circles.absarc(0, 0, i, 0, 2 * Math.PI + 0.001, false);
                        }
                        grid.add(new THREE.Line(circles.createPointsGeometry(), new THREE.LineBasicMaterial({ color: color })));

                        for (i = 0, ii = 2 * Math.PI; i < ii; i += opts.angle) {
                            rays.moveTo(0, 0);
                            rays.lineTo(size * Math.cos(i), size * Math.sin(i));
                        }

                        grid.add(new THREE.Line(rays.createPointsGeometry(), new THREE.LineBasicMaterial({ color: color })));

                        grid.rotation.x = rotX;
                        grid.rotation.y = rotY;

                        _this.scene.add(grid);
                    }
                };

                gridDrawer(this.options.grid.xy, 0, 0);
                gridDrawer(this.options.grid.xz, Math.PI / 2, 0);
                gridDrawer(this.options.grid.yz, 0, Math.PI / 2);

                return this;
            };

            // ### Matrix.parametricPlot3D()
            //
            //
            // *@param {function}* The function which is called on every argument
            // *@return {Screen3D}*
            Screen3D.prototype.parametricPlot3D = function (f, options) {
                var defaults = {
                    closed: false,
                    debug: false,
                    min: 0,
                    max: 1,
                    pointNum: 1000,
                    radius: 0.05,
                    segmentsRadius: 6,
                    material: {
                        type: 'MeshLambert'
                    }
                }, opts = MathLib.extendObject(defaults, options), Curve = THREE.Curve.create(function () {
                }, function (t) {
                    t = (opts.max - opts.min) * t + opts.min;
                    var ft = f(t);
                    return new THREE.Vector3(ft[0], ft[1], ft[2]);
                }), mesh = new THREE.Mesh(new THREE.TubeGeometry(new Curve(), opts.pointNum, opts.radius, opts.segmentsRadius, opts.closed, opts.debug), new THREE[opts.material.type + 'Material'](opts.material));

                this.scene.add(mesh);

                /*
                guiObj = {
                color: [mesh.material.color.r, mesh.material.color.g, mesh.material.color.b]
                };

                var folder = _3D.datGUI.addFolder(options.name);
                folder.add(mesh, 'visible');
                folder.addColor(guiObj, 'color')
                .onChange(function (value) {mesh.material.color.setRGB(value[0] / 255, value[1] / 255, value[2] / 255);});
                */
                return this;
            };

            // ### Screen3D.prototype.plot3D()
            //
            //
            // *@param {function}* The map for the height
            // *@param {object}* Options
            // *@return {Screen3D}*
            Screen3D.prototype.plot3D = function (f, options) {
                return this.surfacePlot3D(function (u, v) {
                    return [u, v, f(u, v)];
                }, options);
            };

            // ### Screen3D.prototype.resize()
            // Adjust the rendering if the screen is resized
            //
            // *@param {number}* The new width
            // *@param {number}* The new height
            // *@return {Screen3D}*
            Screen3D.prototype.resize = function (width, height) {
                this.renderer.setSize(width, height);
                this.camera.aspect = width / height;
                this.camera.updateProjectionMatrix();

                return this;
            };

            // ### screen3D.prototype.surfacePlot()
            //
            //
            // *@param {function}* The map for the surface
            // *@param {object}* Options
            // *@return {Screen3D}*
            Screen3D.prototype.surfacePlot3D = function (f, options) {
                var defaults = {
                    material: {
                        type: 'MeshLambert'
                    },
                    pointNumX: 100,
                    pointNumY: 100,
                    xmin: 0,
                    xmax: 1,
                    ymin: 0,
                    ymax: 1
                }, opts = MathLib.extendObject(defaults, options), map = function (u, v) {
                    u = (opts.xmax - opts.xmin) * u + opts.xmin;
                    v = (opts.ymax - opts.ymin) * v + opts.ymin;
                    var fuv = f(u, v);
                    return new THREE.Vector3(fuv[0], fuv[1], fuv[2]);
                }, material = new THREE[opts.material.type + 'Material'](opts.material), mesh;

                material.side = THREE.DoubleSide;

                mesh = new THREE.Mesh(new THREE.ParametricGeometry(map, opts.pointNumX, opts.pointNumY, false), material);

                this.scene.add(mesh);

                // if (options.datGUI) {
                //   guiObj = {
                //     color: [mesh.material.color.r, mesh.material.color.g, mesh.material.color.b]
                //   };
                //   var folder = _3D.datGUI.addFolder(options.datGUI.name);
                //   if (options.datGUI.visible) {
                //     folder.add(mesh, 'visible');
                //   }
                //   if (options.datGUI.wireframe) {
                //     folder.add(mesh.material, 'wireframe');
                //   }
                //   if (options.datGUI.color) {
                //     color = mesh.material.color.getHex();
                //     var guiObj = {
                //       color: color
                //     };
                //     folder.addColor(guiObj, 'color').name('color')
                //       .onChange(function (value) {mesh.material.color = new THREE.Color(value);});
                //   }
                // }
                return this;
            };
            return Screen3D;
        })(MathLib.Screen);
        MathLib.Screen3D = Screen3D;
    })(MathLib || (MathLib = {}));

    /// <reference path='reference.ts'/>
    var MathLib;
    (function (MathLib) {
        // ## <a id="Vector" href="http://mathlib.de/en/docs/Vector">Vector</a>
        // The vector implementation of MathLib makes calculations with vectors of
        // arbitrary size possible. The entries of the vector can be numbers and complex
        // numbers.
        //
        // It is as easy as
        // `new MathLib.Vector([1, 2, 3])`
        // to create the following vector:
        //    ⎛ 1 ⎞
        //    ⎜ 2 ⎟
        //    ⎝ 3 ⎠
        /// import Functn
        var Vector = (function () {
            function Vector(coords) {
                var _this = this;
                this.type = 'vector';
                coords.forEach(function (x, i) {
                    _this[i] = x;
                });
                this.length = coords.length;
            }
            // ### [Vector.prototype.compare()](http://mathlib.de/en/docs/Vector/compare)
            // Compares two vectors.
            //
            // *@param {Vector}* The vector to compare
            // *@return {number}*
            Vector.prototype.compare = function (v) {
                var i, ii;

                if (this.length !== v.length) {
                    return MathLib.sign(this.length - v.length);
                }

                for (i = 0, ii = this.length; i < ii; i++) {
                    if (v[i] - this[i]) {
                        return MathLib.sign(this[i] - v[i]);
                    }
                }

                return 0;
            };

            // ### [Vector.prototype.every()](http://mathlib.de/en/docs/Vector/every)
            // Works like Array.prototype.every.
            //
            // *@return {boolean}*
            Vector.prototype.every = function (f) {
                return Array.prototype.every.call(this, f);
            };

            // ### [Vector.prototype.forEach()](http://mathlib.de/en/docs/Vector/forEach)
            // Works like Array.prototype.forEach.
            //
            Vector.prototype.forEach = function (f) {
                Array.prototype.forEach.call(this, f);
            };

            // ### [Vector.prototype.isEqual()](http://mathlib.de/en/docs/Vector/isEqual)
            // Determines if two vectors are equal
            //
            // *@param {Vector}* v The vector to compare
            // *@return {boolean}*
            Vector.prototype.isEqual = function (v) {
                if (this.length !== v.length) {
                    return false;
                }

                return this.every(function (x, i) {
                    return MathLib.isEqual(x, v[i]);
                });
            };

            // ### [Vector.prototype.isZero()](http://mathlib.de/en/docs/Vector/isZero)
            // Determines if the vector is the zero vector.
            //
            // *@return {boolean}*
            Vector.prototype.isZero = function () {
                return this.every(MathLib.isZero);
            };

            // ### [Vector.prototype.map()](http://mathlib.de/en/docs/Vector/map)
            // Works like Array.prototype.map.
            //
            // *@param {function}*
            // *@return {Vector}*
            Vector.prototype.map = function (f) {
                return new this['constructor'](Array.prototype.map.call(this, f));
            };

            // ### [Vector.prototype.minus()](http://mathlib.de/en/docs/Vector/minus)
            // Calculates the difference of two vectors.
            //
            // *@param {Vector}* The vector to be subtracted.
            // *@return {Vector}*
            Vector.prototype.minus = function (v) {
                if (this.length === v.length) {
                    return this.plus(v.negative());
                } else {
                    MathLib.error({ message: 'Vector sizes not matching', method: 'Vector#minus' });
                    return;
                }
            };

            // ### [Vector.prototype.negative()](http://mathlib.de/en/docs/Vector/negative)
            // Returns the negative vector.
            //
            // *@return {Vector}*
            Vector.prototype.negative = function () {
                return this.map(MathLib.negative);
            };

            // ### [Vector.prototype.norm()](http://mathlib.de/en/docs/Vector/norm)
            // Calcultes the norm of the vector.
            //
            // *@param {number}* [default=2] The p for the p-norm
            // *@return {number}*
            Vector.prototype.norm = function (p) {
                if (typeof p === "undefined") { p = 2; }
                if (p === 2) {
                    return MathLib.hypot.apply(null, this.toArray());
                } else if (p === Infinity) {
                    return Math.max.apply(null, this.map(Math.abs).toArray());
                } else {
                    return MathLib.root(this.reduce(function (prev, curr) {
                        return prev + Math.pow(Math.abs(curr), p);
                    }, 0), p);
                }
            };

            // ### [Vector.prototype.outerProduct()](http://mathlib.de/en/docs/Vector/outerProduct)
            // Calculates the outer product of two vectors.
            //
            // *@param {Vector}*
            // *@return {Matrix}*
            Vector.prototype.outerProduct = function (v) {
                return new MathLib.Matrix(this.map(function (x) {
                    return v.map(function (y) {
                        return MathLib.times(x, y);
                    });
                }));
            };

            // ### [Vector.prototype.plus()](http://mathlib.de/en/docs/Vector/plus)
            // Calculates the sum of two vectors.
            //
            // *@param {Vector}*
            // *@return {Vector}*
            Vector.prototype.plus = function (v) {
                if (this.length === v.length) {
                    return new MathLib.Vector(this.map(function (x, i) {
                        return MathLib.plus(x, v[i]);
                    }));
                } else {
                    MathLib.error({ message: 'Vector sizes not matching', method: 'Vector#plus' });
                    return;
                }
            };

            // ### [Vector.prototype.reduce()](http://mathlib.de/en/docs/Vector/reduce)
            // Works like Array.prototype.reduce.
            //
            // *@return {any}*
            Vector.prototype.reduce = function () {
                var args = [];
                for (var _i = 0; _i < (arguments.length - 0); _i++) {
                    args[_i] = arguments[_i + 0];
                }
                return Array.prototype.reduce.apply(this, args);
            };

            // ### [Vector.prototype.scalarProduct()](http://mathlib.de/en/docs/Vector/scalarProduct)
            // Calculates the scalar product of two vectors.
            //
            // *@param {Vector}*
            // *@return {number|Complex}*
            Vector.prototype.scalarProduct = function (v) {
                if (this.length === v.length) {
                    return this.reduce(function (old, cur, i, w) {
                        return MathLib.plus(old, MathLib.times(w[i], v[i]));
                    }, 0);
                } else {
                    MathLib.error({ message: 'Vector sizes not matching', method: 'Vector#scalarProduct' });
                    return;
                }
            };

            // ### [Vector.prototype.slice()](http://mathlib.de/en/docs/Vector/slice)
            // Works like the Array.prototype.slice function
            //
            // *@return {array}*
            Vector.prototype.slice = function () {
                var args = [];
                for (var _i = 0; _i < (arguments.length - 0); _i++) {
                    args[_i] = arguments[_i + 0];
                }
                return Array.prototype.slice.apply(this, args);
            };

            // ### [Vector.prototype.times()](http://mathlib.de/en/docs/Vector/times)
            // Multiplies the vector by a (complex) number or a matrix.
            // The vector is multiplied from left to the matrix.
            // If you want to multiply it from the right use
            // matrix.times(vector) instead of vector.times(matrix)
            //
            // *@param {number|Complex|Matrix}*
            // *@return {Vector}*
            Vector.prototype.times = function (n) {
                var i, ii, colVectors, product = [];
                if (n.type === 'rational') {
                    n = n.toNumber();
                }
                if (typeof n === 'number' || n.type === 'complex') {
                    return this.map(function (x) {
                        return MathLib.times(n, x);
                    });
                }
                Eif (n.type === 'matrix') {
                    Eif (this.length === n.rows) {
                        colVectors = n.toColVectors();
                        for (i = 0, ii = colVectors.length; i < ii; i++) {
                            product[i] = this.scalarProduct(colVectors[i]);
                        }
                        return new MathLib.Vector(product);
                    } else {
                        MathLib.error({ message: 'Vector/Matrix sizes not matching', method: 'Vector#times' });
                        return;
                    }
                }
            };

            // ### [Vector.prototype.toArray()](http://mathlib.de/en/docs/Vector/toArray)
            // Converts the vector to an array.
            //
            // *@return {array}*
            Vector.prototype.toArray = function () {
                return Array.prototype.slice.call(this);
            };

            // ### [Vector.prototype.toContentMathML()](http://mathlib.de/en/docs/Vector/toContentMathML)
            // Returns the content MathML representation of the vector.
            //
            // *@return {string}*
            Vector.prototype.toContentMathML = function () {
                return this.reduce(function (old, cur) {
                    return old + MathLib.toContentMathML(cur);
                }, '<vector>') + '</vector>';
            };

            // ### [Vector.prototype.toLaTeX()](http://mathlib.de/en/docs/Vector/toLaTeX)
            // Returns a LaTeX representation of the vector.
            //
            // *@return {string}*
            Vector.prototype.toLaTeX = function () {
                return '\\begin{pmatrix}\n\t' + this.reduce(function (old, cur) {
                    return old + '\\\\\n\t' + MathLib.toLaTeX(cur);
                }) + '\n\\end{pmatrix}';
            };

            // ### [Vector.prototype.toMathML()](http://mathlib.de/en/docs/Vector/toMathML)
            // Returns the (presentation) MathML representation of the vector.
            //
            // *@return {string}*
            Vector.prototype.toMathML = function () {
                return this.reduce(function (old, cur) {
                    return old + '<mtr><mtd>' + MathLib.toMathML(cur) + '</mtd></mtr>';
                }, '<mrow><mo>(</mo><mtable>') + '</mtable><mo>)</mo></mrow>';
            };

            // ### [Vector.prototype.toString()](http://mathlib.de/en/docs/Vector/toString)
            // Returns a string representation of the vector.
            //
            // *@return {string}*
            Vector.prototype.toString = function () {
                return '(' + this.reduce(function (old, cur) {
                    return old + ', ' + MathLib.toString(cur);
                }) + ')';
            };

            // ### [Vector.prototype.vectorProduct()](http://mathlib.de/en/docs/Vector/vectorProduct)
            // Calculates the vector product of two vectors.
            //
            // *@param {Vector}*
            // *@return {Vector}*
            Vector.prototype.vectorProduct = function (v) {
                /* TODO: Implement vectorproduct for non three-dimensional vectors */
                if (this.length === 3 && v.length === 3) {
                    return new MathLib.Vector([
                        MathLib.minus(MathLib.times(this[1], v[2]), MathLib.times(this[2], v[1])),
                        MathLib.minus(MathLib.times(this[2], v[0]), MathLib.times(this[0], v[2])),
                        MathLib.minus(MathLib.times(this[0], v[1]), MathLib.times(this[1], v[0]))
                    ]);
                } else {
                    MathLib.error({ message: 'Vectors are not three-dimensional', method: 'Vector#vectorProduct' });
                    return;
                }
            };
            Vector.areLinearIndependent = function (v) {
                var n = v.length, m = v[0].length;

                if (n > m) {
                    return false;
                }

                if (!v.every(function (x) {
                    return x.length === m;
                })) {
                    return undefined;
                }

                return (new MathLib.Matrix(v)).rank() === n;
            };

            Vector.zero = function (n) {
                var vector = [], i;
                for (i = 0; i < n; i++) {
                    vector.push(0);
                }
                return new MathLib.Vector(vector);
            };
            return Vector;
        })();
        MathLib.Vector = Vector;
    })(MathLib || (MathLib = {}));

    /// <reference path='reference.ts'/>
    var MathLib;
    (function (MathLib) {
        // ## <a id="Circle" href="http://mathlib.de/en/docs/Circle">Circle</a>
        // MathLib.Circle expects two arguments.
        // First the center in the form of an Array or a MathLib.point.
        // The second argument should be the radius of the circle.
        //
        // #### Simple use case:
        // ```
        // // Create a circle with center (1, 2) and radius 3.
        // var c = new MathLib.Circle([1, 2], 3);
        // c.center                   // The center of the circle (point)
        // c.radius                   // returns the radius of the circle
        // ```
        /// import Point
        var Circle = (function () {
            function Circle(center, radius) {
                this.type = 'circle';
                if (center.type === undefined) {
                    center = new MathLib.Point(center.concat(1));
                }

                this.center = center;
                this.radius = radius;
            }
            // ### [Circle.prototype.area()](http://mathlib.de/en/docs/Circle/area)
            // Calculates the area of the circle.
            //
            // *@return {number}* The area of the circle
            Circle.prototype.area = function () {
                return this.radius * this.radius * Math.PI;
            };

            // ### [Circle.prototype.circumference()](http://mathlib.de/en/docs/Circle/circumference)
            // Calculates the circumference of the circle.
            //
            // *@return {number}* The circumference of the circle
            Circle.prototype.circumference = function () {
                return 2 * this.radius * Math.PI;
            };

            // ### [Circle.prototype.compare()](http://mathlib.de/en/docs/Circle/compare)
            // Compares two circles
            //
            // *@param {Circle}* The circle to compare
            // *@return {number}*
            Circle.prototype.compare = function (c) {
                return MathLib.sign(this.center.compare(c.center)) || MathLib.sign(this.radius - c.radius);
            };

            // ### [Circle.prototype.draw()](http://mathlib.de/en/docs/Circle/draw)
            // Draw the circle onto the screen.
            //
            // *@param {Screen}* The screen to draw onto.
            // *@param {object}* Optional drawing options
            // *@return {Circle}* Returns the circle for chaining
            Circle.prototype.draw = function (screen, options) {
                if (Array.isArray(screen)) {
                    var circle = this;
                    screen.forEach(function (x) {
                        x.circle(circle, options);
                    });
                } else {
                    screen.circle(this, options);
                }
                return this;
            };

            // ### [Circle.prototype.isEqual()](http://mathlib.de/en/docs/Circle/isEqual)
            // Checks if two circles are equal
            //
            // *@return {boolean}*
            Circle.prototype.isEqual = function (c) {
                return MathLib.isEqual(this.radius, c.radius) && this.center.isEqual(c.center);
            };

            // ### [Circle.prototype.positionOf()](http://mathlib.de/en/docs/Circle/positionOf)
            // Determine if a point is in, on or outside a circle.
            //
            // *@return {string}*
            Circle.prototype.positionOf = function (p) {
                var diff;
                Eif (p.type === 'point' && p.dimension === 2) {
                    diff = p.distanceTo(this.center) - this.radius;
                    if (MathLib.isZero(diff)) {
                        return 'on';
                    } else if (diff < 0) {
                        return 'in';
                    } else {
                        return 'out';
                    }
                }
            };

            // ### [Circle.prototype.reflectAt()](http://mathlib.de/en/docs/Circle/reflectAt)
            // Reflect the circle at a point or line
            //
            // *@return {Circle}*
            Circle.prototype.reflectAt = function (a) {
                return new MathLib.Circle(this.center.reflectAt(a), this.radius);
            };

            // ### [Circle.prototype.toLaTeX()](http://mathlib.de/en/docs/Circle/toLaTeX)
            // Returns a LaTeX expression of the circle
            //
            // *@return {string}*
            Circle.prototype.toLaTeX = function () {
                return 'B_{' + MathLib.toLaTeX(this.radius) + '}\\left(' + this.center.toLaTeX() + '\\right)';
            };

            // ### [Circle.prototype.toMatrix()](http://mathlib.de/en/docs/Circle/toMatrix)
            // Converts the circle to the corresponding matrix.
            //
            // *@return {Matrix}*
            Circle.prototype.toMatrix = function () {
                var x = this.center[0] / this.center[2], y = this.center[1] / this.center[2], r = this.radius;
                return new MathLib.Matrix([[1, 0, -x], [0, 1, -y], [-x, -y, x * x + y * y - r * r]]);
            };
            return Circle;
        })();
        MathLib.Circle = Circle;
    })(MathLib || (MathLib = {}));

    /// <reference path='reference.ts'/>
    var MathLib;
    (function (MathLib) {
        // ## <a id="Complex"></a>Complex
        // MathLib.Complex is the MathLib implementation of complex numbers.
        //
        // There are two ways of defining complex numbers:
        //
        // * Two numbers representing the real and the complex part.
        // * MathLib.Complex.polar(abs, arg)
        //
        // #### Simple example:
        // ```
        // // Create the complex number 1 + 2i
        // var c = new MathLib.Complex(1, 2);
        // ```
        /// import Functn, Point
        var Complex = (function () {
            function Complex(re, im) {
                if (typeof im === "undefined") { im = 0; }
                this.type = 'complex';
                if (MathLib.isNaN(re) || MathLib.isNaN(im)) {
                    this.re = NaN;
                    this.im = NaN;
                } else if (!MathLib.isFinite(re) || !MathLib.isFinite(im)) {
                    this.re = Infinity;
                    this.im = Infinity;
                } else {
                    this.re = re;
                    this.im = im;
                }
            }
            // ### [Complex.prototype.abs()](http://mathlib.de/en/docs/Complex/abs)
            // Returns the absolute value of the number.
            //
            // *@return {number}*
            Complex.prototype.abs = function () {
                return MathLib.hypot(this.re, this.im);
            };

            // ### [Complex.prototype.arccos()](http://mathlib.de/en/docs/Complex/arccos)
            // Returns the inverse cosine of the number.
            //
            // *@return {Complex}*
            Complex.prototype.arccos = function () {
                return MathLib.minus(Math.PI / 2, this.arcsin());
            };

            // ### [Complex.prototype.arccot()](http://mathlib.de/en/docs/Complex/arccot)
            // Returns the inverse cotangent of the number.
            //
            // *@return {Complex}*
            Complex.prototype.arccot = function () {
                if (this.isZero()) {
                    return new MathLib.Complex(MathLib.sign(1 / this.re) * Math.PI / 2, -this.im);
                }
                return this.inverse().arctan();
                //var c = this.arctan();
                //console.log(c.toString());
                //return new MathLib.Complex(Math.PI / 2 - c.re, c.im);
                //return MathLib.minus(Math.PI / 2, this.arctan());
            };

            // ### [Complex.prototype.arccsc()](http://mathlib.de/en/docs/Complex/arccsc)
            // Returns the inverse cosecant of the number
            //
            // *@return {Complex}*
            Complex.prototype.arccsc = function () {
                // arccsc(0) = ComplexInfinity not ComplexNaN
                if (this.isZero()) {
                    return new MathLib.Complex(Infinity);
                }

                return this.inverse().arcsin();
            };

            // ### [Complex.prototype.arcsec()](http://mathlib.de/en/docs/Complex/arcsec)
            // Returns the inverse secant of the number
            //
            // *@return {Complex}*
            Complex.prototype.arcsec = function () {
                // arcsec(0) = ComplexInfinity not ComplexNaN
                if (this.isZero()) {
                    return new MathLib.Complex(Infinity);
                }

                return this.inverse().arccos();
            };

            // ### [Complex.prototype.arcsin()](http://mathlib.de/en/docs/Complex/arcsin)
            // Returns the inverse sine of the number
            //
            // *@return {Complex}*
            Complex.prototype.arcsin = function () {
                var a = this.re, b = this.im, aa = a * a, bb = b * b, sqrt = Math.sqrt(Math.pow(aa + bb - 1, 2) + 4 * bb), sgn = function (x) {
                    if (x > 0) {
                        return 1;
                    }
                    if (x < 0) {
                        return -1;
                    }
                    if (1 / x === Infinity) {
                        return 1;
                    }
                    if (1 / x === -Infinity) {
                        return -1;
                    }
                };

                if (a === Infinity) {
                    return new MathLib.Complex(Infinity);
                }

                return new MathLib.Complex(sgn(a) / 2 * MathLib.arccos(sqrt - (aa + bb)), sgn(b) / 2 * MathLib.arcosh(sqrt + (aa + bb)));
            };

            // ### [Complex.prototype.arctan()](http://mathlib.de/en/docs/Complex/arctan)
            // Returns the inverse tangent of the number
            //
            // *@return {Complex}*
            Complex.prototype.arctan = function () {
                var res, iz = new MathLib.Complex(-this.im, this.re);

                if (this.isZero()) {
                    return new MathLib.Complex(this.re, this.im);
                }

                res = MathLib.times(new MathLib.Complex(0, -0.5), MathLib.plus(1, iz).divide(MathLib.minus(1, iz)).ln());

                // Correct some values on the axis imaginary axis.
                // TODO: Are this all the wrong values?
                if (MathLib.isNegZero(this.re) && res.re !== Infinity && (this.im < 0 || this.im > 1)) {
                    res.re = -res.re;
                }

                return res;
            };

            // ### [Complex.prototype.arg()](http://mathlib.de/en/docs/Complex/arg)
            // Returns the argument (= the angle) of the complex number
            //
            // *@return {number}*
            Complex.prototype.arg = function () {
                if (this.re === Infinity) {
                    return NaN;
                }
                return Math.atan2(this.im, this.re);
            };

            // ### Complex.prototype.artanh()
            // Returns the inverse hyperbolic tangent of the number
            //
            // *@return {Complex}*
            Complex.prototype.artanh = function () {
                if (this.isZero()) {
                    return new MathLib.Complex(this.re, this.im);
                }

                if (this.re === Infinity) {
                    return new MathLib.Complex(NaN);
                }

                return MathLib.times(0.5, MathLib.minus(MathLib.ln(MathLib.plus(1, this)), MathLib.ln(MathLib.minus(1, this))));
            };

            // ### [Complex.prototype.compare()](http://mathlib.de/en/docs/Complex/compare)
            // Compares two complex numbers
            //
            // *@return {number}*
            Complex.prototype.compare = function (x) {
                var a = MathLib.sign(this.abs() - x.abs());

                if (MathLib.isNaN(this.re)) {
                    if (MathLib.isNaN(x.re)) {
                        return 0;
                    }
                    return -1;
                }

                if (this.re === Infinity) {
                    if (x.re === Infinity) {
                        return 0;
                    }
                    return 1;
                }

                return a ? a : MathLib.sign(this.arg() - x.arg());
            };

            // ### [Complex.prototype.conjugate()](http://mathlib.de/en/docs/Complex/conjugate)
            // Calculates the conjugate of a complex number
            //
            // *@return {Complex}*
            Complex.prototype.conjugate = function () {
                return new MathLib.Complex(this.re, MathLib.negative(this.im));
            };

            // ### [Complex.prototype.copy()](http://mathlib.de/en/docs/Complex/copy)
            // Copies the complex number
            //
            // *@return {Complex}*
            Complex.prototype.copy = function () {
                return new MathLib.Complex(MathLib.copy(this.re), MathLib.copy(this.im));
            };

            // ### [Complex.prototype.cos()](http://mathlib.de/en/docs/Complex/cos)
            // Calculates the cosine of a complex number
            //
            // *@return {Complex}*
            Complex.prototype.cos = function () {
                return new MathLib.Complex(MathLib.cos(this.re) * MathLib.cosh(this.im), -MathLib.sin(this.re) * MathLib.sinh(this.im));
            };

            // ### [Complex.prototype.cosh()](http://mathlib.de/en/docs/Complex/cosh)
            // Calculates the hyperbolic cosine of a complex number
            //
            // *@return {Complex}*
            Complex.prototype.cosh = function () {
                return new MathLib.Complex(MathLib.cos(this.im) * MathLib.cosh(this.re), MathLib.sin(this.im) * MathLib.sinh(this.re));
            };

            // ### [Complex.prototype.cot()](http://mathlib.de/en/docs/Complex/cot)
            // Calculates the cotangent of a complex number
            //
            // *@return {Complex}*
            Complex.prototype.cot = function () {
                var aa = 2 * this.re, bb = 2 * this.im, d = MathLib.cos(aa) - MathLib.cosh(bb);

                if (this.isZero()) {
                    return new MathLib.Complex(Infinity);
                }

                return new MathLib.Complex(-MathLib.sin(aa) / d, MathLib.sinh(bb) / d);
            };

            // ### [Complex.prototype.coth()](http://mathlib.de/en/docs/Complex/coth)
            // Calculates the hyperbolic cotangent of a complex number
            //
            // *@return {Complex}*
            Complex.prototype.coth = function () {
                var aa = 2 * this.re, bb = 2 * this.im, d = MathLib.cosh(aa) - MathLib.cos(bb);

                if (this.isZero()) {
                    return new MathLib.Complex(Infinity);
                }

                return new MathLib.Complex(MathLib.sinh(aa) / d, -MathLib.sin(bb) / d);
            };

            // ### [Complex.prototype.csc()](http://mathlib.de/en/docs/Complex/csc)
            // Calculates the cosecant of a complex number
            //
            // *@return {Complex}*
            Complex.prototype.csc = function () {
                var a = this.re, b = this.im, d = MathLib.cos(2 * a) - MathLib.cosh(2 * b);

                if (this.isZero()) {
                    return new MathLib.Complex(Infinity);
                }

                return new MathLib.Complex(-2 * MathLib.sin(a) * MathLib.cosh(b) / d, 2 * MathLib.cos(a) * MathLib.sinh(b) / d);
            };

            // ### [Complex.prototype.csch()](http://mathlib.de/en/docs/Complex/csch)
            // Calculates the hyperbolic cosecant of a complex number
            //
            // *@return {Complex}*
            Complex.prototype.csch = function () {
                var a = this.re, b = this.im, d = MathLib.cosh(2 * a) - MathLib.cos(2 * b);

                if (this.isZero()) {
                    return new MathLib.Complex(Infinity);
                }

                return new MathLib.Complex(2 * MathLib.sinh(a) * MathLib.cos(b) / d, -2 * MathLib.cosh(a) * MathLib.sin(b) / d);
            };

            // ### [Complex.prototype.divide()](http://mathlib.de/en/docs/Complex/divide)
            // Divides a complex number by an other
            //
            // *@param {number|Complex}* The divisor
            // *@return {Complex}*
            Complex.prototype.divide = function (c) {
                return this.times(MathLib.inverse(c));
            };

            // ### [Complex.prototype.exp()](http://mathlib.de/en/docs/Complex/exp)
            // Evaluates the exponential function with a complex argument
            //
            // *@return {Complex}*
            Complex.prototype.exp = function () {
                return new MathLib.Complex(MathLib.exp(this.re) * MathLib.cos(this.im), MathLib.exp(this.re) * MathLib.sin(this.im));
            };

            // ### [Complex.prototype.inverse()](http://mathlib.de/en/docs/Complex/inverse)
            // Calculates the inverse of a complex number
            //
            // *@return {Complex}*
            Complex.prototype.inverse = function () {
                var d = MathLib.plus(MathLib.pow(this.re, 2), MathLib.pow(this.im, 2));

                if (this.isZero()) {
                    return new MathLib.Complex(Infinity);
                }

                if (this.re === Infinity) {
                    return new MathLib.Complex(0);
                }

                return new MathLib.Complex(MathLib.divide(this.re, d), MathLib.divide(MathLib.negative(this.im), d));
            };

            // ### [Complex.prototype.isEqual()](http://mathlib.de/en/docs/Complex/isEqual)
            // Determines if the complex number is equal to another number.
            //
            // *@param {Complex|number|Rational}* The number to be compared
            // *@return {boolean}*
            Complex.prototype.isEqual = function (n) {
                if (typeof n === 'number') {
                    return MathLib.isEqual(this.re, n) && MathLib.isZero(this.im);
                }
                Eif (n.type === 'complex') {
                    return MathLib.isEqual(this.re, n.re) && MathLib.isEqual(this.im, n.im);
                }
                return false;
            };

            // ### [Complex.prototype.isFinite()](http://mathlib.de/en/docs/Complex/isFinite)
            // Determines if the complex number is finite.
            //
            // *@return {boolean}*
            Complex.prototype.isFinite = function () {
                return MathLib.isFinite(this.re);
            };

            // ### [Complex.prototype.isZero()](http://mathlib.de/en/docs/Complex/isZero)
            // Determines if the complex number is equal to 0.
            //
            // *@return {boolean}*
            Complex.prototype.isZero = function () {
                return MathLib.isZero(this.re) && MathLib.isZero(this.im);
            };

            // ### [Complex.prototype.ln()](http://mathlib.de/en/docs/Complex/ln)
            // Evaluates the natural logarithm with complex arguments
            //
            // *@return {Complex}*
            Complex.prototype.ln = function () {
                if (this.re === Infinity) {
                    return new MathLib.Complex(Infinity);
                }
                return new MathLib.Complex(MathLib.ln(this.abs()), this.arg());
            };

            // ### [Complex.prototype.minus()](http://mathlib.de/en/docs/Complex/minus)
            // Calculates the difference of two complex numbers
            //
            // *@param {number|Complex}* The subtrahend
            // *@return {Complex}*
            Complex.prototype.minus = function (c) {
                return this.plus(MathLib.negative(c));
            };

            // ### [Complex.prototype.negative()](http://mathlib.de/en/docs/Complex/negative)
            // Calculates the negative of the complex number
            //
            // *@return {Complex}*
            Complex.prototype.negative = function () {
                return new MathLib.Complex(MathLib.negative(this.re), MathLib.negative(this.im));
            };

            // ### [Complex.prototype.plus()](http://mathlib.de/en/docs/Complex/plus)
            // Add complex numbers
            //
            // *@param {Complex|number|Rational}* The number to be added
            // *@return {Complex}*
            Complex.prototype.plus = function (c) {
                if (c.type === 'complex') {
                    return new MathLib.Complex(MathLib.plus(this.re, c.re), MathLib.plus(this.im, c.im));
                } else Iif (c.type === 'rational') {
                    c = c.toNumber();
                }
                Eif (typeof c === 'number') {
                    return new MathLib.Complex(MathLib.plus(this.re, c), this.im);
                }
            };

            // ### [Complex.prototype.pow()](http://mathlib.de/en/docs/Complex/pow)
            // Calculates the complex number raised to some power
            //
            // *@param {numeric}* The power to which the complex number should be raised
            // *@return {Complex}*
            Complex.prototype.pow = function (c) {
                var re, im, abs, arg;

                if (MathLib.type(c) === 'complex') {
                    re = c.re;
                    im = c.im;
                    abs = this.abs();
                    arg = this.arg();

                    // Fixes inf^(2+5i) = inf and 0^(2+5i) = 0
                    if ((this.isZero() || this.re === Infinity) && !(c.isZero() || c.re === Infinity || MathLib.isNaN(c.re))) {
                        return new MathLib.Complex(this.re, this.im);
                    }

                    return MathLib.Complex.polar(MathLib.times(MathLib.pow(abs, re), MathLib.exp(MathLib.negative(MathLib.times(im, arg)))), MathLib.plus(MathLib.times(re, arg), MathLib.times(im, MathLib.ln(abs))));
                } else {
                    // The naive pow method has some rounding errrors. For example
                    // (2+5i)^3 = -142.00000000000006-64.99999999999999i
                    // instead of -142-65i which are errors of magnitude around 1e-14.
                    // This error increases quickly for increasing exponents.
                    // (2+5i)^21 has an error of 5.8 in the real part
                    /*
                    return MathLib.Complex.polar(MathLib.pow(abs, c), MathLib.times(arg, c));
                    */
                    // The following algorithm uses a sifferent approach for integer exponents,
                    // where it yields exact results.
                    // Non integer exponents are evaluated using the naive approach.
                    // TODO: Improve the algorithm.
                    var i, int = MathLib.floor(Math.abs(c)), res = new MathLib.Complex(1), power = this, bin = int.toString(2);

                    // If the exponent is not an integer we use the naive approach
                    if (c % 1) {
                        abs = this.abs();
                        arg = this.arg();
                        return MathLib.Complex.polar(MathLib.pow(abs, c), MathLib.times(arg, c));
                    }

                    // The imaginary part of (2+5i)^-0 should be -0 not +0.
                    if (MathLib.isZero(c)) {
                        return new MathLib.Complex(1, c);
                    }

                    for (i = bin.length - 1; i >= 0; i--) {
                        Eif (bin[i] === '1') {
                            res = MathLib.times(res, power);
                        }
                        power = MathLib.times(power, power);
                    }

                    if (c < 0) {
                        res = res.inverse();
                    }

                    return res;
                }
            };

            // ### [Complex.prototype.sec()](http://mathlib.de/en/docs/Complex/sec)
            // Calculates the secant of a complex number
            //
            // *@return {Complex}*
            Complex.prototype.sec = function () {
                var a = this.re, b = this.im, d = MathLib.cos(2 * a) + MathLib.cosh(2 * b);

                return new MathLib.Complex(2 * MathLib.cos(a) * MathLib.cosh(b) / d, 2 * MathLib.sin(a) * MathLib.sinh(b) / d);
            };

            // ### [Complex.prototype.sech()](http://mathlib.de/en/docs/Complex/sech)
            // Calculates the hyperbolic secant of a complex number
            //
            // *@return {Complex}*
            Complex.prototype.sech = function () {
                var a = this.re, b = this.im, d = MathLib.cosh(2 * a) + MathLib.cos(2 * b);

                return new MathLib.Complex(2 * MathLib.cosh(a) * MathLib.cos(b) / d, -2 * MathLib.sinh(a) * MathLib.sin(b) / d);
            };

            // ### [Complex.prototype.sign()](http://mathlib.de/en/docs/Complex/sign)
            // Calculates the signum of a complex number
            //
            // *@return {Complex}*
            Complex.prototype.sign = function () {
                if (this.isZero() || MathLib.isNaN(this.re)) {
                    return this;
                } else if (this.re === Infinity) {
                    return new MathLib.Complex(NaN);
                }
                return MathLib.Complex.polar(1, this.arg());
            };

            // ### [Complex.prototype.sin()](http://mathlib.de/en/docs/Complex/sin)
            // Calculates the sine of a complex number
            //
            // *@return {Complex}*
            Complex.prototype.sin = function () {
                return new MathLib.Complex(MathLib.sin(this.re) * MathLib.cosh(this.im), MathLib.cos(this.re) * MathLib.sinh(this.im));
            };

            // ### [Complex.prototype.sinh()](http://mathlib.de/en/docs/Complex/sinh)
            // Calculates the hyperbolic sine of a complex number
            //
            // *@return {Complex}*
            Complex.prototype.sinh = function () {
                return new MathLib.Complex(MathLib.cos(this.im) * MathLib.sinh(this.re), MathLib.sin(this.im) * MathLib.cosh(this.re));
            };

            // ### [Complex.prototype.sqrt()](http://mathlib.de/en/docs/Complex/sqrt)
            // Takes the square root of a complex number
            //
            // *@return {Complex}*
            Complex.prototype.sqrt = function () {
                return MathLib.Complex.polar(Math.sqrt(this.abs()), this.arg() / 2);
            };

            // ### [Complex.prototype.tan()](http://mathlib.de/en/docs/Complex/tan)
            // Calculates the tangent of a complex number
            //
            // *@return {Complex}*
            Complex.prototype.tan = function () {
                var aa = 2 * this.re, bb = 2 * this.im, d = MathLib.cos(aa) + MathLib.cosh(bb);

                return new MathLib.Complex(MathLib.sin(aa) / d, MathLib.sinh(bb) / d);
            };

            // ### [Complex.prototype.tanh()](http://mathlib.de/en/docs/Complex/tanh)
            // Calculates the hyperbolic tangent of a complex number
            //
            // *@return {Complex}*
            Complex.prototype.tanh = function () {
                var aa = 2 * this.re, bb = 2 * this.im, d = MathLib.cosh(aa) + MathLib.cos(bb);

                return new MathLib.Complex(MathLib.sinh(aa) / d, MathLib.sin(bb) / d);
            };

            // ### [Complex.prototype.times()](http://mathlib.de/en/docs/Complex/times)
            // Multiplies complex numbers
            //
            // *@param {Complex|number|Rational}* The number to be multiplied
            // *@return {Complex}*
            Complex.prototype.times = function (c) {
                if (c.type === 'complex') {
                    if (this.re === Infinity) {
                        if (c.isZero() || MathLib.isNaN(c.re)) {
                            return new MathLib.Complex(NaN);
                        } else {
                            return new MathLib.Complex(Infinity);
                        }
                    }

                    if (c.re === Infinity) {
                        if (this.isZero() || MathLib.isNaN(this.re)) {
                            return new MathLib.Complex(NaN);
                        } else {
                            return new MathLib.Complex(Infinity);
                        }
                    }

                    return new MathLib.Complex(MathLib.minus(MathLib.times(this.re, c.re), MathLib.times(this.im, c.im)), MathLib.plus(MathLib.times(this.re, c.im), MathLib.times(this.im, c.re)));
                } else if (c.type === 'rational') {
                    c = c.toNumber();
                }
                Eif (typeof c === 'number') {
                    return new MathLib.Complex(MathLib.times(this.re, c), MathLib.times(this.im, c));
                }
            };

            // ### [Complex.prototype.toContentMathML()](http://mathlib.de/en/docs/Complex/toContentMathML)
            // Returns the content MathML representation of the number
            //
            // *@return {string}*
            Complex.prototype.toContentMathML = function () {
                if (!this.isFinite()) {
                    return '<csymbol cd="nums1">' + (this.re === Infinity ? 'infinity' : 'NaN') + '</csymbol>';
                }

                return '<apply><plus />' + MathLib.toContentMathML(this.re) + '<apply><times />' + MathLib.toContentMathML(this.im) + '<imaginaryi /></apply></apply>';
            };

            // ### [Complex.prototype.toLaTeX()](http://mathlib.de/en/docs/Complex/toLaTeX)
            // Returns the LaTeX representation of the complex number
            //
            // *@return {string}*
            Complex.prototype.toLaTeX = function () {
                var str = '', reFlag = false;

                if (!this.isFinite()) {
                    return '\\text{Complex' + this.re + '}';
                }

                if (!MathLib.isZero(this.re)) {
                    str = MathLib.toLaTeX(this.re);
                    reFlag = true;
                }
                if (!MathLib.isZero(this.im)) {
                    str += MathLib.toLaTeX(this.im, reFlag) + 'i';
                }
                if (str.length === 0) {
                    str = '0';
                }
                return str;
            };

            // ### [Complex.prototype.toMathML()](http://mathlib.de/en/docs/Complex/toMathML)
            // Returns the (presentation) MathML representation of the number
            //
            // *@return {string}*
            Complex.prototype.toMathML = function () {
                var str = '', reFlag = false;

                if (!this.isFinite()) {
                    return '<mi>Complex' + this.re + '</mi>';
                }

                if (!MathLib.isZero(this.re)) {
                    str = MathLib.toMathML(this.re);
                    reFlag = true;
                }
                if (!MathLib.isZero(this.im)) {
                    str += MathLib.toMathML(this.im, reFlag) + '<mo>&#x2062;</mo><mi>i</mi>';
                }
                if (str.length === 0) {
                    str = '<mn>0</mn>';
                }
                return str;
            };

            // ### [Complex.prototype.toPoint()](http://mathlib.de/en/docs/Complex/toPoint)
            // Interprets the complex number as point in the two dimensional plane
            //
            // *@return {Point}*
            Complex.prototype.toPoint = function () {
                if (this.re == Infinity || MathLib.isNaN(this.re)) {
                    return new MathLib.Point([0, 0, 0]);
                }

                return new MathLib.Point([this.re, this.im, 1]);
            };

            // ### [Complex.prototype.toString()](http://mathlib.de/en/docs/Complex/toString)
            // Custom toString function
            //
            // *@return {string}*
            Complex.prototype.toString = function () {
                var str = '';

                if (!this.isFinite()) {
                    return 'Complex' + this.re;
                }

                if (!MathLib.isZero(this.re)) {
                    str = MathLib.toString(this.re);
                }
                if (!MathLib.isZero(this.im)) {
                    str += (this.im > 0 ? (str.length ? '+' : '') : '-') + MathLib.toString(Math.abs(this.im)) + 'i';
                }
                if (str.length === 0) {
                    str = '0';
                }
                return str;
            };
            Complex.polar = function (abs, arg) {
                if (abs === Infinity) {
                    return new MathLib.Complex(Infinity);
                }
                return new MathLib.Complex(abs * Math.cos(arg), abs * Math.sin(arg));
            };
            return Complex;
        })();
        MathLib.Complex = Complex;
    })(MathLib || (MathLib = {}));

    var __extends = this.__extends || function (d, b) {
        for (var p in b) {
          if (b.hasOwnProperty(p)) {
            d[p] = b[p];
          }
        }
        function __() {
          this.constructor = d;
        }
        __.prototype = b.prototype;
        d.prototype = new __();
    };
    /// <reference path='reference.ts'/>
    var MathLib;
    (function (MathLib) {
        // ## <a id="Line"></a>Line
        // The line implementation of MathLib makes calculations with lines in the
        // real plane possible. (Higher dimensions will be supported later)
        /// import Functn, Vector
        var Line = (function (_super) {
            __extends(Line, _super);
            function Line(coords) {
                _super.call(this, coords);
                this.type = 'line';
                this.dimension = 2;
            }
            // ### Line.prototype.draw()
            // Draws the line on one or more screens
            //
            // *@param {Screen}* The screen to draw onto.
            // *@param {object}* [options] Drawing options
            // *@return {boolean}*
            Line.prototype.draw = function (screen, options) {
                if (Array.isArray(screen)) {
                    var line = this;
                    screen.forEach(function (x) {
                        x.line(line, options);
                    });
                } else {
                    screen.line(this, options);
                }
                return this;
            };

            // ### Line.prototype.isEqual()
            // Determines if two lines are equal.
            //
            // *@param {Line}*
            // *@return {boolean}*
            Line.prototype.isEqual = function (q) {
                var p = this.normalize();
                q = q.normalize();

                if (this.length !== q.length) {
                    return false;
                }

                return p.every(function (x, i) {
                    return MathLib.isEqual(x, q[i]);
                });
            };

            // ### Line.prototype.isFinite()
            // Determines if the line is finite
            //
            // *@return {boolean}*
            Line.prototype.isFinite = function () {
                return !MathLib.isZero(this[0]) || !MathLib.isZero(this[1]);
            };

            // ### Line.prototype.isParallelTo()
            // Determines if two lines are parallel.
            //
            // *@param {Line}*
            // *@return {boolean}*
            Line.prototype.isParallelTo = function (l) {
                return MathLib.isZero(this[0] * l[1] - this[1] * l[0]);
            };

            // ### Line.prototype.meet()
            // Calculates the meeting point of two lines
            //
            // *@param {Line}*
            // *@return {Point}*
            Line.prototype.meet = function (l) {
                var point, k = this;

                Eif (this.dimension === 2 && l.dimension === 2) {
                    point = new MathLib.Point(this.vectorProduct(l).toArray());

                    Object.defineProperties(point, {
                        '0': {
                            get: function () {
                                return k[1] * l[2] - k[2] * l[1];
                            },
                            set: function () {
                                MathLib.warning({ message: 'Trying to change the coordinates of a completely dependent point.', method: 'Line#meet' });
                            },
                            enumerable: true
                        },
                        '1': {
                            get: function () {
                                return k[2] * l[0] - k[0] * l[2];
                            },
                            set: function () {
                                MathLib.warning({ message: 'Trying to change the coordinates of a completely dependent point.', method: 'Line#meet' });
                            },
                            enumerable: true
                        },
                        '2': {
                            get: function () {
                                return k[0] * l[1] - k[1] * l[0];
                            },
                            set: function () {
                                MathLib.warning({ message: 'Trying to change the coordinates of a completely dependent point.', method: 'Line#meet' });
                            },
                            enumerable: true
                        }
                    });

                    return point;
                }
            };

            // ### Line.prototype.normalize()
            // Normalizes the line.
            //
            // *@return {Line}*
            Line.prototype.normalize = function () {
                var h = MathLib.hypot(this[0], this[1]);

                if (h !== 0) {
                    return this.map(function (x) {
                        return x / h;
                    });
                } else {
                    return new MathLib.Line([0, 0, 1]);
                }
            };

            // ### Line.prototype.parallelThrough()
            // Determines an parallel line through a given point.
            //
            // *@param {Point}*
            // *@return {Line}*
            Line.prototype.parallelThrough = function (p) {
                var l = this, parallel = new MathLib.Line([0, 0, 0]);

                Object.defineProperties(parallel, {
                    '0': {
                        get: function () {
                            return -l[0] * p[2];
                        },
                        set: function () {
                            MathLib.warning({ message: 'Trying to change the coordinates of a completely dependent line.', method: 'Line#parallelThrough' });
                        },
                        enumerable: true
                    },
                    '1': {
                        get: function () {
                            return -l[1] * p[2];
                        },
                        set: function () {
                            MathLib.warning({ message: 'Trying to change the coordinates of a completely dependent line.', method: 'Line#parallelThrough' });
                        },
                        enumerable: true
                    },
                    '2': {
                        get: function () {
                            return l[1] * p[1] + l[0] * p[0];
                        },
                        set: function () {
                            MathLib.warning({ message: 'Trying to change the coordinates of a completely dependent line.', method: 'Line#parallelThrough' });
                        },
                        enumerable: true
                    }
                });

                return parallel;
            };
            return Line;
        })(MathLib.Vector);
        MathLib.Line = Line;
    })(MathLib || (MathLib = {}));

    /// <reference path='reference.ts'/>
    var MathLib;
    (function (MathLib) {
        // ## <a id="Matrix"></a>Matrix
        // The matrix implementation of MathLib makes calculations with matrices of
        // arbitrary size possible. The entries of a matrix can be numbers and complex
        // numbers.
        //
        // It is as easy as
        // ```
        // new MathLib.Matrix([[1, 2, 3], [4, 5, 6], [7, 8, 9]])
        // ```
        // to create the following matrix:
        //    ⎛ 1 2 3 ⎞
        //    ⎜ 4 5 6 ⎟
        //    ⎝ 7 8 9 ⎠
        /// import Functn, Permutation
        var Matrix = (function () {
            function Matrix(matrix) {
                var _this = this;
                this.type = 'matrix';
                Iif (typeof matrix === 'string') {
                    // If there is a < in the string we assume it's MathML
                    if (matrix.indexOf('<') > -1) {
                        return MathLib.Expression.parseContentMathML(matrix).evaluate();
                    } else {
                        matrix = matrix.trim().replace(/;?\n/g, '],[');
                        matrix = JSON.parse('[[' + matrix + ']]');
                    }
                }
                matrix.forEach(function (x, i) {
                    _this[i] = x;
                });
                this.length = matrix.length;
                this.cols = matrix[0].length;
                this.rows = matrix.length;
            }
            // ### Matrix.prototype.LU()
            // Calculates the LU decomposition of a matrix
            // The result is cached.
            //
            // *@return {Matrix}*
            Matrix.prototype.LU = function () {
                var i, j, k, t, p, LU = this.toArray(), m = this.rows, n = this.cols, permutation = [];

                for (k = 0; k < n; k++) {
                    // Find the pivot
                    p = k;
                    for (i = k + 1; i < m; i++) {
                        if (Math.abs(LU[i][k]) > Math.abs(LU[p][k])) {
                            p = i;
                        }
                    }

                    // Exchange if necessary
                    if (p !== k) {
                        permutation.unshift([p, k]);
                        t = LU[p];
                        LU[p] = LU[k];
                        LU[k] = t;
                    }

                    // The elimination
                    if (LU[k][k] !== 0) {
                        for (i = k + 1; i < m; i++) {
                            LU[i][k] = MathLib.divide(LU[i][k], LU[k][k]);
                            for (j = k + 1; j < n; j++) {
                                LU[i][j] = MathLib.minus(LU[i][j], MathLib.times(LU[i][k], LU[k][j]));
                            }
                        }
                    }
                }
                LU = new MathLib.Matrix(LU);
                this.LU = function () {
                    return LU;
                };
                this.LUpermutation = new MathLib.Permutation(permutation);
                return LU;
            };

            // ### Matrix.prototype.adjoint()
            // Calculates the adjoint matrix
            //
            // *@return {Matrix}*
            Matrix.prototype.adjoint = function () {
                return this.map(MathLib.conjugate).transpose();
            };

            // ### Matrix.prototype.adjugate()
            // Calculates the adjugate matrix
            //
            // *@return {Matrix}*
            Matrix.prototype.adjugate = function () {
                return this.map(function (x, r, c, m) {
                    return MathLib.times(m.remove(c, r).determinant(), 1 - ((r + c) % 2) * 2);
                });
            };

            // ### Matrix.prototype.cholesky()
            // The cholesky decomposition of a matrix
            // using the Cholesky–Banachiewicz algorithm.
            // Does not change the current matrix, but returns a new one.
            // The result is cached.
            //
            // *@return {Matrix}*
            Matrix.prototype.cholesky = function () {
                var i, ii, j, jj, k, kk, sum, choleskyMatrix, cholesky = [];

                for (i = 0, ii = this.rows; i < ii; i++) {
                    cholesky.push([]);
                }

                for (i = 0, ii = this.rows; i < ii; i++) {
                    for (j = 0; j < i; j++) {
                        sum = 0;
                        for (k = 0, kk = j; k < kk; k++) {
                            sum = MathLib.plus(sum, MathLib.times(cholesky[i][k], cholesky[j][k]));
                        }
                        cholesky[i][j] = (this[i][j] - sum) / cholesky[j][j];
                    }

                    sum = 0;
                    for (k = 0, kk = j; k < kk; k++) {
                        sum = MathLib.plus(sum, MathLib.times(cholesky[i][k], cholesky[i][k]));
                    }
                    cholesky[i][j] = Math.sqrt(this[j][j] - sum);

                    for (j++, jj = this.cols; j < jj; j++) {
                        cholesky[i][j] = 0;
                    }
                }
                choleskyMatrix = new MathLib.Matrix(cholesky);

                this.cholesky = function () {
                    return choleskyMatrix;
                };
                return choleskyMatrix;
            };

            // ### Matrix.prototype.compare()
            // Compares the matrix to an other matrix.
            //
            // *@param {Matrix}* The matrix to compare.
            // *@return {number}*
            Matrix.prototype.compare = function (m) {
                var i, ii, j, jj;

                Iif (this.rows !== m.rows) {
                    return MathLib.sign(this.rows - m.rows);
                }

                if (this.cols !== m.cols) {
                    return MathLib.sign(this.cols - m.cols);
                }

                for (i = 0, ii = this.rows; i < ii; i++) {
                    for (j = 0, jj = this.cols; j < jj; j++) {
                        if (this[i][j] - m[i][j]) {
                            return MathLib.sign(this[i][j] - m[i][j]);
                        }
                    }
                }

                return 0;
            };

            // ### Matrix.prototype.copy()
            // Copies the matrix
            //
            // *@return {Matrix}*
            Matrix.prototype.copy = function () {
                return this.map(MathLib.copy);
            };

            // ### Matrix.prototype.determinant()
            // Calculates the determinant of the matrix via the LU decomposition.
            // The result is cached.
            //
            // *@return {number|Complex}*
            Matrix.prototype.determinant = function () {
                var LU, determinant;

                if (!this.isSquare()) {
                    MathLib.error({ message: 'Determinant of non square matrix', method: 'Matrix#determinant' });
                    return;
                }

                if (this.rank() < this.rows) {
                    determinant = 0;
                } else {
                    LU = this.LU();
                    determinant = MathLib.times(this.LUpermutation.sgn(), MathLib.times.apply(null, LU.diag()));
                }

                this.determinant = function () {
                    return determinant;
                };
                return determinant;
            };

            // ### Matrix.prototype.diag()
            // Returns the entries on the diagonal in an array
            //
            // *@return {array}*
            Matrix.prototype.diag = function () {
                var diagonal = [], i, ii;
                for (i = 0, ii = Math.min(this.rows, this.cols); i < ii; i++) {
                    diagonal.push(this[i][i]);
                }
                return diagonal;
            };

            // ### Matrix.prototype.divide()
            // Multiplies the matrix by the inverse of a number or a matrix
            //
            // *@return {Matrix}*
            Matrix.prototype.divide = function (n) {
                return this.times(MathLib.inverse(n));
            };

            // ### Matrix.prototype.every()
            // This function works like the Array.prototype.every function.
            // The matrix is processed row by row.
            // The function is called with the following arguments:
            // the entry at the current position, the number of the row,
            // the number of the column and the complete matrix
            //
            // *@param {function}* The function which is called on every argument
            // *@return {boolean}*
            Matrix.prototype.every = function (f) {
                return Array.prototype.every.call(this, function (x, i) {
                    return Array.prototype.every.call(x, function (y, j) {
                        return f(y, i, j, this);
                    });
                });
            };

            // ### Matrix.prototype.forEach()
            // This function works like the Array.prototype.forEach function.
            // The matrix is processed row by row.
            // The function is called with the following arguments:
            // the entry at the current position, the number of the row,
            // the number of the column and the complete matrix
            //
            // *@param {function}* The function which is called on every argument
            Matrix.prototype.forEach = function (f) {
                Array.prototype.forEach.call(this, function (x, i) {
                    return Array.prototype.forEach.call(x, function (y, j) {
                        return f(y, i, j, this);
                    });
                });
            };

            // ### Matrix.prototype.gershgorin()
            // Returns the Gershgorin circles of the matrix.
            //
            // *@return {array}* Returns an array of circles
            Matrix.prototype.gershgorin = function () {
                var c = [], rc = [], rr = [], circles = [], i, ii;

                for (i = 0, ii = this.rows; i < ii; i++) {
                    rc.push(0);
                    rr.push(0);
                }

                this.forEach(function (x, i, j) {
                    if (i === j) {
                        if (MathLib.is(x, 'complex')) {
                            c.push(x.toPoint());
                        } else {
                            c.push(new MathLib.Point([x, 0, 1]));
                        }
                    } else {
                        rc[j] += MathLib.abs(x);
                        rr[i] += MathLib.abs(x);
                    }
                });

                for (i = 0, ii = this.rows; i < ii; i++) {
                    circles.push(new MathLib.Circle(c[i], Math.min(rc[i], rr[i])));
                }

                return circles;
            };

            // ### Matrix.prototype.givens()
            // QR decomposition with the givens method.
            //
            // *@return {[Matrix, Matrix]}*
            Matrix.prototype.givens = function () {
                var rows = this.rows, cols = this.cols, R = this.copy(), Q = MathLib.Matrix.identity(rows), c, s, rho, i, j, k, ri, rj, qi, qj;

                for (i = 0; i < cols; i++) {
                    for (j = i + 1; j < rows; j++) {
                        if (!MathLib.isZero(R[j][i])) {
                            // We can't use the sign function here, because we want the factor
                            // to be 1 if A[i][i] is zero.
                            rho = (R[i][i] < 0 ? -1 : 1) * MathLib.hypot(R[i][i], R[j][i]);
                            c = R[i][i] / rho;
                            s = R[j][i] / rho;

                            // Apply the rotation
                            ri = [];
                            rj = [];
                            qi = [];
                            qj = [];

                            for (k = 0; k < cols; k++) {
                                ri.push(R[i][k]);
                                rj.push(R[j][k]);
                            }
                            for (k = 0; k < cols; k++) {
                                R[i][k] = rj[k] * s + ri[k] * c;
                                R[j][k] = rj[k] * c - ri[k] * s;
                            }

                            for (k = 0; k < rows; k++) {
                                qi.push(Q[k][i]);
                                qj.push(Q[k][j]);
                            }
                            for (k = 0; k < rows; k++) {
                                Q[k][i] = qi[k] * c + qj[k] * s;
                                Q[k][j] = -qi[k] * s + qj[k] * c;
                            }
                        }
                    }
                }

                return [Q, R];
            };

            // ### Matrix.prototype.inverse()
            // Calculates the inverse matrix.
            //
            // *@return {Matrix}*
            Matrix.prototype.inverse = function () {
                var i, ii, res, inverse, col = [], matrix = [], n = this.rows;

                Iif (!this.isSquare()) {
                    MathLib.error({ message: 'Inverse of non square matrix', method: 'Matrix#inverse' });
                    return;
                }

                for (i = 0, ii = n - 1; i < ii; i++) {
                    matrix.push([]);
                    col.push(0);
                }

                matrix.push([]);

                col.push(1);
                col = col.concat(col).slice(0, -1);

                for (i = 0, ii = n; i < ii; i++) {
                    res = this.solve(col.slice(n - i - 1, 2 * n - i - 1));

                    if (res === undefined) {
                        return;
                    }

                    res.forEach(function (x, i) {
                        matrix[i].push(x);
                    });
                }

                inverse = new MathLib.Matrix(matrix);
                this.inverse = function () {
                    return inverse;
                };
                return inverse;
            };

            // ### Matrix.prototype.isBandMatrix()
            // Determines if the matrix is a band matrix.
            //
            // *@param {number}*
            // *@param {number}*
            // *@return {boolean}*
            Matrix.prototype.isBandMatrix = function (l, u) {
                // var i, j, ii, jj;
                Iif (arguments.length === 1) {
                    u = l;
                }

                return this.every(function (x, i, j) {
                    return (i - l <= j && i + u >= j) || MathLib.isZero(x);
                });
                // for (i = 0, ii = this.rows; i < ii; i++) {
                //   for (j = 0, jj = this.cols; j < jj; j++) {
                //     if (i - j < l && this[i][j] !== 0) {
                //       return false;
                //     }
                //   }
                // }
                // return true;
            };

            // ### Matrix.prototype.isDiag()
            // Determines if the matrix is a diagonal matrix.
            //
            // *@return {boolean}*
            Matrix.prototype.isDiag = function () {
                var i, j, ii, jj;
                Iif (Number(this.hasOwnProperty('isUpper') && this.isUpper()) + Number(this.hasOwnProperty('isLower') && this.isLower()) + Number(this.hasOwnProperty('isSymmetric') && this.isSymmetric()) > 1) {
                    return true;
                }
                for (i = 0, ii = this.rows; i < ii; i++) {
                    for (j = 0, jj = this.cols; j < jj; j++) {
                        if (i !== j && !MathLib.isZero(this[i][j])) {
                            return false;
                        }
                    }
                }
                return true;
            };

            // ### Matrix.prototype.isEqual()
            // Determines if the matrix is equal to an other matrix.
            //
            // *@param {Matrix}* the matrix to compare with
            // *@return {boolean}*
            Matrix.prototype.isEqual = function (x) {
                var i, j, ii, jj;
                Iif (this === x) {
                    return true;
                }
                Eif (this.rows === x.rows && this.cols === x.cols) {
                    for (i = 0, ii = this.rows; i < ii; i++) {
                        for (j = 0, jj = this.cols; j < jj; j++) {
                            Iif (!MathLib.isEqual(this[i][j], x[i][j])) {
                                return false;
                            }
                        }
                    }
                    return true;
                }
                return false;
            };

            // ### Matrix.prototype.isIdentity()
            // Determines if the matrix is a identity matrix.
            //
            // *@return {boolean}*
            Matrix.prototype.isIdentity = function () {
                Iif (!this.isSquare()) {
                    return false;
                }

                var isIdentity = this.every(function (x, r, c) {
                    return r === c ? MathLib.isOne(x) : MathLib.isZero(x);
                });

                this.isIdentity = function () {
                    return isIdentity;
                };
                return isIdentity;
            };

            // ### Matrix.prototype.isInvertible()
            // Determines if the matrix is invertible.
            //
            // *@return {boolean}*
            Matrix.prototype.isInvertible = function () {
                return this.isSquare() && this.rank() === this.rows;
            };

            // ### Matrix.prototype.isLower()
            // Determines if the matrix is a lower triangular matrix.
            //
            // *@return {boolean}*
            Matrix.prototype.isLower = function () {
                return this.slice(0, -1).every(function (x, i) {
                    return x.slice(i + 1).every(MathLib.isZero);
                });
            };

            // ### Matrix.prototype.isNegDefinite()
            // Determines if the matrix is negative definite
            //
            // *@return {boolean}*
            Matrix.prototype.isNegDefinite = function () {
                if (!this.isSquare()) {
                    return;
                }
                if (this.rows === 1) {
                    return this[0][0] < 0;
                }

                // Sylvester's criterion
                if (this.rows % 2 === 0) {
                    return this.determinant() > 0 && this.remove(this.rows - 1, this.cols - 1).isNegDefinite();
                } else {
                    return this.determinant() < 0 && this.remove(this.rows - 1, this.cols - 1).isNegDefinite();
                }
            };

            // ### Matrix.prototype.isOrthogonal()
            // Determines if the matrix is a orthogonal.
            //
            // *@return {boolean}*
            Matrix.prototype.isOrthogonal = function () {
                return this.transpose().times(this).isIdentity();
            };

            // ### Matrix.prototype.isPermutation()
            // Determines if the matrix is a permutation matrix
            //
            // *@return {boolean}*
            Matrix.prototype.isPermutation = function () {
                var rows = [], cols = [];

                return this.every(function (x, r, c) {
                    if (MathLib.isOne(x)) {
                        Iif (rows[r] || cols[c]) {
                            return false;
                        } else {
                            rows[r] = true;
                            cols[c] = true;
                            return true;
                        }
                    } else if (MathLib.isZero(x)) {
                        return true;
                    }
                    return false;
                }) && rows.length === this.rows && cols.length === this.cols;
            };

            // ### Matrix.prototype.isPosDefinite()
            // Determines if the matrix is positive definite
            //
            // *@return {boolean}*
            Matrix.prototype.isPosDefinite = function () {
                Iif (!this.isSquare()) {
                    return;
                }
                if (this.rows === 1) {
                    return this[0][0] > 0;
                }

                // Sylvester's criterion
                return this.determinant() > 0 && this.remove(this.rows - 1, this.cols - 1).isPosDefinite();
            };

            // ### Matrix.prototype.isReal()
            // Determines if the matrix has only real entries
            //
            // *@return {boolean}*
            Matrix.prototype.isReal = function () {
                return this.every(MathLib.isReal);
            };

            // ### Matrix.prototype.isScalar()
            // Determines if the matrix is a scalar matrix
            // (that is a multiple of the identity matrix)
            //
            // *@return {boolean}*
            Matrix.prototype.isScalar = function () {
                var i, ii, diag = this.diag;
                if (this.hasOwnProperty('isIdentity') && this.hasOwnProperty('isZero')) {
                    if (this.isIdentity() || this.isZero()) {
                        return true;
                    } else {
                        return false;
                    }
                }
                if (this.isDiag()) {
                    for (i = 1, ii = this.rows; i < ii; i++) {
                        if (!MathLib.isEqual(diag[0], diag[i])) {
                            return false;
                        }
                    }
                    return true;
                }
                return false;
            };

            // ### Matrix.prototype.isSquare()
            // Determines if the matrix is a square matrix
            //
            // *@return {boolean}*
            Matrix.prototype.isSquare = function () {
                return this.cols === this.rows;
            };

            // ### Matrix.prototype.isSymmetric()
            // Determines if the matrix is symmetric
            //
            // *@return {boolean}*
            Matrix.prototype.isSymmetric = function () {
                var i, ii, j, jj, isSymmetric = true;

                Iif (!this.isSquare()) {
                    isSymmetric = false;
                } else {
                    lp:
                    for (i = 0, ii = this.rows; i < ii; i++) {
                        for (j = i + 1, jj = this.cols; j < jj; j++) {
                            if (!MathLib.isEqual(this[i][j], this[j][i])) {
                                isSymmetric = false;
                                break lp;
                            }
                        }
                    }
                }

                this.isSymmetric = function () {
                    return isSymmetric;
                };
                return isSymmetric;
            };

            // ### Matrix.prototype.isUpper()
            // Determines if the matrix is a upper triangular matrix
            //
            // *@return {boolean}*
            Matrix.prototype.isUpper = function () {
                return this.slice(1).every(function (x, i) {
                    return x.slice(0, i + 1).every(MathLib.isZero);
                });
            };

            // ### Matrix.prototype.isVector()
            // Determines if the matrix is a vector
            // (only one row or one column)
            //
            // *@return {boolean}*
            Matrix.prototype.isVector = function () {
                return (this.rows === 1) || (this.cols === 1);
            };

            // ### Matrix.prototype.isZero()
            // Determines if the matrix the zero matrix
            // The result is cached.
            //
            // *@return {boolean}*
            Matrix.prototype.isZero = function () {
                var isZero = this.every(MathLib.isZero);

                this.isZero = function () {
                    return isZero;
                };
                return isZero;
            };

            // ### Matrix.prototype.map()
            // This function works like the Array.prototype.map function.
            // The matrix is processed row by row.
            // The function is called with the following arguments:
            // the entry at the current position, the number of the row,
            // the number of the column and the complete matrix
            //
            // *@param {function}* The function which is called on every argument
            // *@return {Matrix}*
            Matrix.prototype.map = function (f) {
                var m = this;
                return new MathLib.Matrix(Array.prototype.map.call(this, function (x, i) {
                    return Array.prototype.map.call(x, function (y, j) {
                        return f(y, i, j, m);
                    });
                }));
            };

            // ### Matrix.prototype.minor()
            // Calculates a minor
            //
            // *@param {number}* The row to be removed.
            // *@param {number}* The column to be removed.
            // *@return {Matrix}*
            Matrix.prototype.minor = function (r, c) {
                return this.remove(r, c).determinant();
            };

            // ### Matrix.prototype.minus()
            // Calculates the difference of two matrices
            //
            // *@param {Matrix}* The matrix to be subtracted.
            // *@return {Matrix}*
            Matrix.prototype.minus = function (m) {
                Eif (this.rows === m.rows && this.cols === m.cols) {
                    return this.plus(m.negative());
                } else {
                    MathLib.error({ message: 'Matrix sizes not matching', method: 'Matrix#minus' });
                    return;
                }
            };

            // ### Matrix.prototype.negative()
            // Returns the negative matrix
            //
            // *@return {Matrix}*
            Matrix.prototype.negative = function () {
                var i, ii, negative = [];

                for (i = 0, ii = this.rows; i < ii; i++) {
                    negative.push(this[i].map(MathLib.negative));
                }
                return new MathLib.Matrix(negative);
            };

            // ### Matrix.prototype.plus()
            // This function adds a matrix to the current matrix
            // and returns the result as a new matrix.
            //
            // *@param {Matrix}* The matrix to be added.
            // *@return {Matrix}*
            Matrix.prototype.plus = function (m) {
                var i, ii, j, jj, sum = [];

                Eif (this.rows === m.rows && this.cols === m.cols) {
                    for (i = 0, ii = this.rows; i < ii; i++) {
                        sum[i] = [];
                        for (j = 0, jj = this.cols; j < jj; j++) {
                            sum[i][j] = MathLib.plus(this[i][j], m[i][j]);
                        }
                    }
                    return new MathLib.Matrix(sum);
                } else {
                    MathLib.error({ message: 'Matrix sizes not matching', method: 'Matrix#plus' });
                    return;
                }
            };

            // ### Matrix.prototype.rank()
            // Determines the rank of the matrix
            //
            // *@return {number}*
            Matrix.prototype.rank = function () {
                var i, j, rank = 0, mat = this.rref();

                rankloop:
                for (i = Math.min(this.rows, this.cols) - 1; i >= 0; i--) {
                    for (j = this.cols - 1; j >= i; j--) {
                        if (!MathLib.isZero(mat[i][j])) {
                            rank = i + 1;
                            break rankloop;
                        }
                    }
                }

                this.rank = function () {
                    return rank;
                };
                return rank;
            };

            // ### Matrix.prototype.reduce()
            // This function works like the Array.prototype.reduce function.
            //
            // *@return {any}*
            Matrix.prototype.reduce = function () {
                var args = [];
                for (var _i = 0; _i < (arguments.length - 0); _i++) {
                    args[_i] = arguments[_i + 0];
                }
                return Array.prototype.reduce.apply(this, args);
            };

            // ### Matrix.prototype.remove()
            // This function removes the specified rows and/or columns for the matrix.
            //
            // *@param {number|array}* The row(s) to be removed.
            // *@param {number|array}* The column(s) to be removed.
            // *@return {Matrix}*
            Matrix.prototype.remove = function (row, col) {
                var rest = this.toArray();

                if (row || row === 0) {
                    if (typeof row === 'number') {
                        row = [row];
                    }
                    rest = rest.filter(function (x, i) {
                        return row.indexOf(i) === -1;
                    });
                }

                if (col || col === 0) {
                    if (typeof col === 'number') {
                        col = [col];
                    }
                    col = col.sort().reverse();
                    col.forEach(function (n) {
                        rest = rest.map(function (x) {
                            x.splice(n, 1);
                            return x;
                        });
                    });
                }

                return new MathLib.Matrix(rest);
            };

            // ### Matrix.prototype.rref()
            // Calculate the reduced row echelon form (rref) of a matrix.
            //
            // *@return {Matrix}*
            Matrix.prototype.rref = function () {
                var i, ii, j, jj, k, kk, pivot, factor, swap, lead = 0, rref = this.toArray();

                for (i = 0, ii = this.rows; i < ii; i++) {
                    if (this.cols <= lead) {
                        return new MathLib.Matrix(rref);
                    }

                    // Find the row with the biggest pivot element
                    j = i;
                    while (rref[j][lead] === 0) {
                        j++;
                        if (this.rows === j) {
                            j = i;
                            lead++;
                            if (this.cols === lead) {
                                return new MathLib.Matrix(rref);
                            }
                        }
                    }

                    // Swap the pivot row to the top
                    if (i !== j) {
                        swap = rref[j];
                        rref[j] = rref[i];
                        rref[i] = swap;
                    }

                    pivot = rref[i][lead];

                    for (j = lead, jj = this.cols; j < jj; j++) {
                        rref[i][j] /= pivot;
                    }

                    for (j = 0, jj = this.rows; j < jj; j++) {
                        if (j === i) {
                            continue;
                        }
                        factor = rref[j][lead];
                        for (k = 0, kk = this.cols; k < kk; k++) {
                            rref[j][k] = MathLib.minus(rref[j][k], MathLib.times(factor, rref[i][k]));
                        }
                    }
                    lead++;
                }
                return new MathLib.Matrix(rref);
            };

            // ### Matrix.prototype.slice()
            // This function works like the Array.prototype.slice function.
            //
            // *@return {array}*
            Matrix.prototype.slice = function () {
                var args = [];
                for (var _i = 0; _i < (arguments.length - 0); _i++) {
                    args[_i] = arguments[_i + 0];
                }
                return Array.prototype.slice.apply(this, args);
            };

            // ### Matrix.prototype.solve()
            // Solves the system of linear equations Ax = b
            // given by the matrix A and a vector or point b.
            //
            // *@param {Vector|Point}* The b in Ax = b
            // *@return {Vector|Point}*
            Matrix.prototype.solve = function (b) {
                // Ax = b -> LUx = b. Then y is defined to be Ux
                var LU = this.LU(), i, j, n = b.length, x = [], y = [];

                // Permutate b according to the LU decomposition
                b = this.LUpermutation.applyTo(b);

                for (i = 0; i < n; i++) {
                    y[i] = b[i];
                    for (j = 0; j < i; j++) {
                        y[i] = MathLib.minus(y[i], MathLib.times(LU[i][j], y[j]));
                    }
                }

                for (i = n - 1; i >= 0; i--) {
                    x[i] = y[i];
                    for (j = i + 1; j < n; j++) {
                        x[i] = MathLib.minus(x[i], MathLib.times(LU[i][j], x[j]));
                    }

                    if (LU[i][i] === 0) {
                        if (x[i] !== 0) {
                            return undefined;
                        } else {
                            x[i] = x[i];
                        }
                    } else {
                        x[i] = MathLib.divide(x[i], LU[i][i]);
                    }
                }

                if (MathLib.type(b) === 'array') {
                    return x;
                } else {
                    return new b.constructor(x);
                }
            };

            // ### Matrix.prototype.some()
            // This function works like the Array.prototype.some function.
            // The matrix is processed row by row.
            // The function is called with the following arguments:
            // the entry at the current position, the number of the row,
            // the number of the column and the complete matrix
            //
            // *@param {function}* The function which is called on every argument
            // *@return {boolean}*
            Matrix.prototype.some = function (f) {
                return Array.prototype.some.call(this, function (x, i) {
                    return Array.prototype.some.call(x, function (y, j) {
                        return f(y, i, j, this);
                    });
                });
            };

            // ### Matrix.prototype.times()
            // Multiplies the current matrix with a number, a matrix, a point or a vector.
            //
            // *@param {number|Matrix|Point|Rational|Vector}*
            // *@return {Matrix|Point|Vector}*
            Matrix.prototype.times = function (a) {
                var i, ii, j, jj, k, kk, product = [], entry;

                if (a.type === 'rational') {
                    a = a.toNumber();
                }
                if (typeof a === 'number' || a.type === 'complex') {
                    return this.map(function (x) {
                        return MathLib.times(x, a);
                    });
                } else if (a.type === 'matrix') {
                    Eif (this.cols === a.rows) {
                        for (i = 0, ii = this.rows; i < ii; i++) {
                            product[i] = [];
                            for (j = 0, jj = a.cols; j < jj; j++) {
                                entry = 0;

                                for (k = 0, kk = this.cols; k < kk; k++) {
                                    entry = MathLib.plus(entry, MathLib.times(this[i][k], a[k][j]));
                                }
                                product[i][j] = entry;
                            }
                        }
                        return new MathLib.Matrix(product);
                    } else {
                        MathLib.error({ message: 'Matrix sizes not matching', method: 'Matrix#times' });
                        return;
                    }
                } else Eif (a.type === 'point' || a.type === 'vector') {
                    Eif (this.cols === a.length) {
                        for (i = 0, ii = this.rows; i < ii; i++) {
                            entry = 0;
                            for (j = 0, jj = this.cols; j < jj; j++) {
                                entry = MathLib.plus(entry, MathLib.times(this[i][j], a[j]));
                            }
                            product.push(entry);
                        }
                        return new a.constructor(product);
                    }
                }
            };

            // ### Matrix.prototype.toArray()
            // Converts the matrix to a two-dimensional array
            //
            // *@return {array}*
            Matrix.prototype.toArray = function () {
                return Array.prototype.map.call(this, function (x) {
                    return Array.prototype.map.call(x, function (y) {
                        return MathLib.copy(y);
                    });
                });
            };

            // ### Matrix.prototype.toColVectors()
            // Converts the columns of the matrix to vectors
            //
            // *@return {array}*
            Matrix.prototype.toColVectors = function () {
                return this.transpose().toRowVectors();
            };

            // ### Matrix.prototype.toContentMathML()
            // converting the matrix to content MathML
            //
            // *@return {string}*
            Matrix.prototype.toContentMathML = function () {
                return this.reduce(function (str, x) {
                    return str + x.reduce(function (prev, cur) {
                        return prev + MathLib.toContentMathML(cur);
                    }, '<matrixrow>') + '</matrixrow>';
                }, '<matrix>') + '</matrix>';
            };

            // ### Matrix.prototype.toLaTeX()
            // Converting the matrix to LaTeX
            //
            // *@return {string}*
            Matrix.prototype.toLaTeX = function () {
                return '\\begin{pmatrix}\n' + this.reduce(function (str, x) {
                    return str + x.reduce(function (prev, cur) {
                        return prev + ' & ' + MathLib.toLaTeX(cur);
                    }) + '\\\n';
                }, '').slice(0, -2) + '\n\\end{pmatrix}';
            };

            // ### Matrix.prototype.toMathML()
            // converting the matrix to (presentation) MathML
            //
            // *@return {string}*
            Matrix.prototype.toMathML = function () {
                return this.reduce(function (str, x) {
                    return str + x.reduce(function (prev, cur) {
                        return prev + '<mtd>' + MathLib.toMathML(cur) + '</mtd>';
                    }, '<mtr>') + '</mtr>';
                }, '<mrow><mo> ( </mo><mtable>') + '</mtable><mo> ) </mo></mrow>';
            };

            // ### Matrix.prototype.toRowVectors()
            // Converts the rows of the matrix to vectors
            //
            // *@return {array}*
            Matrix.prototype.toRowVectors = function () {
                return this.toArray().map(function (v) {
                    return new MathLib.Vector(v);
                });
            };

            // ### Matrix.prototype.toString()
            // Creating a custom .toString() function
            //
            // *@return {string}*
            Matrix.prototype.toString = function () {
                return this.reduce(function (str, x) {
                    return str + x.reduce(function (prev, cur) {
                        return prev + '\t' + MathLib.toString(cur);
                    }) + '\n';
                }, '').slice(0, -1);
            };

            // ### Matrix.prototype.trace()
            // Calculating the trace of the matrix
            //
            // *@return {number|Complex}*
            Matrix.prototype.trace = function () {
                var trace = MathLib.plus.apply(null, this.diag());

                this.trace = function () {
                    return trace;
                };
                return trace;
            };

            // ### Matrix.prototype.transpose()
            // Calculating the transpose of the matrix
            // The result is cached.
            //
            // *@return {Matrix}*
            Matrix.prototype.transpose = function () {
                var transposedMatrix, row, i, j, ii, jj, transpose = [];

                for (i = 0, ii = this.cols; i < ii; i++) {
                    row = [];
                    for (j = 0, jj = this.rows; j < jj; j++) {
                        row.push(this[j][i]);
                    }
                    transpose.push(row);
                }

                transposedMatrix = new MathLib.Matrix(transpose);
                this.transpose = function () {
                    return transposedMatrix;
                };
                return transposedMatrix;
            };
            Matrix.givensMatrix = function (n, i, k, phi) {
                var givens = MathLib.Matrix.identity(n);
                givens[k][k] = givens[i][i] = Math.cos(phi);
                givens[i][k] = Math.sin(phi);
                givens[k][i] = -givens[i][k];
                return givens;
            };

            Matrix.identity = function (n) {
                var row = [], matrix = [], i, ii;
                n = n || 1;

                for (i = 0, ii = n - 1; i < ii; i++) {
                    row.push(0);
                }
                row.push(1);
                row = row.concat(row);
                row = row.slice(0, -1);

                for (i = 0, ii = n; i < ii; i++) {
                    matrix.push(row.slice(n - i - 1, 2 * n - i - 1));
                }

                return new MathLib.Matrix(matrix);
            };

            Matrix.numbers = function (n, r, c) {
                var i, ii, row = [], matrix = [];

                for (i = 0, ii = c || r || 1; i < ii; i++) {
                    row.push(n);
                }
                for (i = 0, ii = r || 1; i < ii; i++) {
                    matrix.push(row.slice(0));
                }
                return new MathLib.Matrix(matrix);
            };

            Matrix.one = function (r, c) {
                r = r || 1;
                c = c || 1;
                return MathLib.Matrix.numbers(1, r, c);
            };

            Matrix.random = function (r, c) {
                var row, matrix = [], i, j, ii, jj;
                for (i = 0, ii = r || 1; i < ii; i++) {
                    row = [];
                    for (j = 0, jj = c || r || 1; j < jj; j++) {
                        row.push(Math.random());
                    }
                    matrix.push(row);
                }
                return new MathLib.Matrix(matrix);
            };

            Matrix.zero = function (r, c) {
                r = r || 1;
                c = c || 1;
                return MathLib.Matrix.numbers(0, r, c);
            };
            return Matrix;
        })();
        MathLib.Matrix = Matrix;
    })(MathLib || (MathLib = {}));

    /// <reference path='reference.ts'/>
    var MathLib;
    (function (MathLib) {
        // ## <a id="Permutation"></a>Permutation
        /// import Functn, Matrix
        var Permutation = (function () {
            function Permutation(p) {
                var _this = this;
                this.type = 'permutation';
                var cycle, permutation;

                if (Array.isArray(p[0])) {
                    cycle = p;
                    permutation = Permutation.cycleToList(cycle);
                } else {
                    permutation = p;
                    cycle = Permutation.listToCycle(permutation);
                }

                permutation.forEach(function (x, i) {
                    _this[i] = x;
                });
                this.length = permutation.length;
                this.cycle = cycle;
            }
            // ### Permutation.prototype.applyTo()
            // Applies the permutation to a number or a array/matrix/point/vector
            //
            // *@param {number|array|Matrix|Point|Vector}*
            // *@return {number|array|Matrix|Point|Vector}*
            Permutation.prototype.applyTo = function (n) {
                var p, permutatedObj;
                if (typeof n === 'number') {
                    if (n >= this.length) {
                        return n;
                    }
                    return this[n];
                } else {
                    p = this;
                    permutatedObj = n.map(function (x, i) {
                        return n[p.applyTo(i)];
                    });

                    return (n.type === undefined ? permutatedObj : new n.constructor(permutatedObj));
                }
            };

            // ### Permutation.prototype.compare()
            // Compares two permutations.
            //
            // *@param {Permutation}* The permutation to compare
            // *@return {number}*
            Permutation.prototype.compare = function (p) {
                var i, ii;

                if (this.length !== p.length) {
                    return MathLib.sign(this.length - p.length);
                }

                for (i = 0, ii = this.length; i < ii; i++) {
                    if (p[i] - this[i]) {
                        return MathLib.sign(this[i] - p[i]);
                    }
                }

                return 0;
            };

            // ### Permutation.cycleToList()
            // Converts a cycle representation to a list representation
            //
            // *@param {array}* cycle The cycle to be converted
            // *@return {array}*
            Permutation.cycleToList = function (cycle) {
                var index, list = [], cur, i, ii, j, jj, max;

                max = cycle.map(function (b) {
                    return Math.max.apply(null, b);
                });
                max = Math.max.apply(null, max);

                for (i = 0, ii = max; i <= ii; i++) {
                    cur = i;
                    for (j = 0, jj = cycle.length; j < jj; j++) {
                        index = cycle[j].indexOf(cur);
                        if (++index) {
                            cur = cycle[j][index % cycle[j].length];
                        }
                    }
                    list.push(cur);
                }
                return list;
            };

            // ### Permutation.prototype.inverse()
            // Calculates the inverse of the permutation
            //
            // *@return {Permutation}*
            Permutation.prototype.inverse = function () {
                var cycle = this.cycle.slice(0);
                cycle.reverse().forEach(function (e) {
                    e.reverse();
                });
                return new MathLib.Permutation(cycle);
            };

            // ### Permutation.listToCycle()
            // Converts a list representation to a cycle representation
            //
            // *@param {array}* list The list to be converted
            // *@return {array}*
            Permutation.listToCycle = function (list) {
                var finished = [], cur, i, ii, cycle, cycles = [];

                for (i = 0, ii = list.length; i < ii; i++) {
                    cur = i;
                    cycle = [];
                    while (!finished[cur]) {
                        finished[cur] = true;
                        cycle.push(cur);
                        cur = list[cur];
                    }
                    if (cycle.length) {
                        cycles.push(cycle);
                    }
                }
                return cycles;
            };

            // ### Permutation.prototype.map()
            // Works like Array.prototype.map.
            //
            // *@return {Permutation}*
            Permutation.prototype.map = function () {
                var args = [];
                for (var _i = 0; _i < (arguments.length - 0); _i++) {
                    args[_i] = arguments[_i + 0];
                }
                return new MathLib.Permutation(Array.prototype.map.apply(this, args));
            };

            // ### Permutation.prototype.sgn()
            // Calculates the signum of the permutation
            //
            // *@return {number}*
            Permutation.prototype.sgn = function () {
                var i, ii, count = 0;

                for (i = 0, ii = this.cycle.length; i < ii; i++) {
                    count += this.cycle[i].length;
                }
                count += this.cycle.length;
                return -2 * (count % 2) + 1;
            };

            // ### Permutation.prototype.times()
            // Multiplies two permutations
            //
            // *@return {Permutation}*
            Permutation.prototype.times = function (p) {
                var a = this;
                return p.map(function (x) {
                    return a[x];
                });
            };

            // ### Permutation.prototype.toMatrix()
            // Converts the permuatation to a matrix.
            //
            // *@param {number}* [size] The size of the matrix
            // *@return {Matrix}*
            Permutation.prototype.toMatrix = function (n) {
                var row = [], matrix = [], index, i, ii;
                n = n || this.length;

                for (i = 0, ii = n - 1; i < ii; i++) {
                    row.push(0);
                }
                row = row.concat([1]).concat(row);
                for (i = 0, ii = n; i < ii; i++) {
                    index = n - this.applyTo(i) - 1;
                    matrix.push(row.slice(index, index + n));
                }
                return new MathLib.Matrix(matrix);
            };

            // ### Permutation.prototype.toString()
            // String representation of the permutation.
            //
            // *@return {string}*
            Permutation.prototype.toString = function () {
                var str = '';
                this.cycle.forEach(function (elem) {
                    str += '(' + elem.toString() + ')';
                });
                return str;
            };
            Permutation.id = new Permutation([[]]);
            return Permutation;
        })();
        MathLib.Permutation = Permutation;
    })(MathLib || (MathLib = {}));

    /// <reference path='reference.ts'/>
    var MathLib;
    (function (MathLib) {
        // ## <a id="Conic" href="http://mathlib.de/en/docs/Conic">Conic</a>
        // The conic implementation of MathLib makes calculations with conics possible.
        /// import Functn, Matrix
        var Conic = (function () {
            function Conic(primal, dual) {
                this.type = 'conic';
                if (primal.type !== 'matrix') {
                    primal = new MathLib.Matrix(primal);
                }
                this.primal = primal;

                //		if (!dual) {
                //			dual = primal.adjugate();
                //		}
                //		else if (!primal.times(dual).isScalar()) {
                //			// Throw error
                //		}
                if (primal.rank() > 1) {
                    Object.defineProperties(this, {
                        'dual': {
                            get: function () {
                                return this.primal.adjugate();
                            },
                            set: function () {
                            },
                            enumerable: true,
                            configurable: true
                        }
                    });
                } else {
                    this.dual = dual;
                }
            }
            // ### [Conic.prototype.draw()](http://mathlib.de/en/docs/Conic/draw)
            // Draws the conic on one or more screens
            //
            // *@param {Screen}* The screen to draw onto.
            // *@param {object}* [options] Drawing options
            // *@return {boolean}*
            Conic.prototype.draw = function (screen, options, redraw) {
                if (typeof redraw === "undefined") { redraw = false; }
                if (Array.isArray(screen)) {
                    var conic = this;
                    screen.forEach(function (x) {
                        conic.draw(x, options);
                    });
                } else {
                    options.from = 0;
                    options.to = 2 * Math.PI;
                    options.conic = this;

                    var lines, alpha, cos, sin, sgn, a = this.primal[0][0], b = this.primal[0][1] * 2, c = this.primal[1][1], d = this.primal[0][2] * 2, e = this.primal[1][2] * 2, disc = 4 * a * c - b * b, rank = this.primal.rank(), cx = (b * e - 2 * c * d) / (4 * a * c - b * b), cy = (b * d - 2 * a * e) / (4 * a * c - b * b), normalForm = this.normalize(), A = Math.sqrt(Math.abs(normalForm.primal[2][2] / normalForm.primal[0][0])), C = Math.sqrt(Math.abs(normalForm.primal[2][2] / normalForm.primal[1][1]));

                    if (rank === 3) {
                        alpha = Math.atan2(b, a - c) / 2;
                        cos = Math.cos(alpha);
                        sin = Math.sin(alpha);

                        // Parabola
                        if (disc === 0) {
                            options.from = -10;
                            options.to = 10;

                            var param = -this.primal[1][2] / (2 * this.primal[0][0]);
                            cx = 0;
                            cy = this.primal[2][2] / this.primal[0][0];

                            screen.path([
                                function (t) {
                                    return cx + cos * param * t * t - sin * 2 * param * t;
                                },
                                function (t) {
                                    return cy + sin * param * t * t + cos * 2 * param * t;
                                }
                            ], options, redraw);
                        } else if (disc > 0) {
                            options.from = 0;
                            options.to = 2 * Math.PI;

                            screen.path([
                                function (t) {
                                    return cx + cos * Math.cos(t) * A - sin * Math.sin(t) * C;
                                },
                                function (t) {
                                    return cy + sin * Math.cos(t) * A + cos * Math.sin(t) * C;
                                }
                            ], options, redraw);
                        } else if (disc < 0) {
                            options.from = 0;
                            options.to = 2 * Math.PI;

                            // This function changes the direction of the path for the second branch.
                            // Otherwise we get some lines which shouldn't be there.
                            sgn = function (t) {
                                return +((t + Math.PI / 2) % (2 * Math.PI) < Math.PI) * 2 - 1;
                            };

                            if (normalForm.primal[2][2] * normalForm.primal[0][0] > 0) {
                                var swap = A;
                                A = C;
                                C = swap;

                                cos = Math.cos(alpha + Math.PI / 2);
                                sin = Math.sin(alpha + Math.PI / 2);
                            } else {
                                cos = Math.cos(alpha);
                                sin = Math.sin(alpha);
                            }

                            screen.path([
                                function (t) {
                                    return cx + cos * MathLib.sec(t) * A - sin * MathLib.tan(t) * C * sgn(t);
                                },
                                function (t) {
                                    return cy + sin * MathLib.sec(t) * A + cos * MathLib.tan(t) * C * sgn(t);
                                }
                            ], options, redraw);
                        }
                    } else if (rank === 2) {
                        lines = this.splitDegenerated();

                        screen.line(lines[0], options);
                        screen.line(lines[1], options);
                    } else if (rank === 1) {
                        lines = this.splitDegenerated();

                        screen.line(lines[0], options);
                    }
                }
                return this;
            };

            // ### [Conic.prototype.eccentricity()](http://mathlib.de/en/docs/Conic/eccentricity)
            // Calculates the eccentricity of a conic.
            //
            // *@return {number}*
            Conic.prototype.eccentricity = function () {
                var normalform = this.normalize(), a = normalform.primal[0][0], c = normalform.primal[1][1];

                if (!this.isDegenerated()) {
                    // parabola
                    if (c === 0) {
                        return 1;
                    }
                    if (c > 0) {
                        return Math.sqrt(1 - c / a);
                    }
                    return Math.sqrt(1 - a / c);
                }
            };

            // ### [Conic.prototype.isDegenerated()](http://mathlib.de/en/docs/Conic/isDegenerated)
            // Determines if a conic is degenerated.
            //
            // *@return {boolean}*
            Conic.prototype.isDegenerated = function () {
                return this.primal.rank() !== 3;
            };

            // ### [Conic.prototype.isEqual()](http://mathlib.de/en/docs/Conic/isEqual)
            // Determines if two conics are equal.
            //
            // *@param {Conic}*
            // *@return {boolean}*
            Conic.prototype.isEqual = function (c) {
                if (this === c) {
                    return true;
                }

                var compare = function (M, N) {
                    var i, j, m, n;

                    Iif (M === N) {
                        return true;
                    }

                    nonZeroSearch:
                    for (i = 0; i < 3; i++) {
                        for (j = 0; j < 3; j++) {
                            Eif (M[i][j] !== 0) {
                                break nonZeroSearch;
                            }
                        }
                    }

                    Iif (N[i][j] === 0) {
                        return false;
                    }

                    m = M[i][j];
                    n = N[i][j];

                    for (i = 0; i < 3; i++) {
                        for (j = 0; j < 3; j++) {
                            if (n / m * M[i][j] !== N[i][j]) {
                                return false;
                            }
                        }
                    }

                    return true;
                };

                return compare(this.primal, c.primal) && compare(this.dual, c.dual);
            };

            // ### [Conic.prototype.latusRectum()](http://mathlib.de/en/docs/Conic/latusRectum)
            // Calculates the latusRectum of a conic.
            //
            // *@return {number}*
            Conic.prototype.latusRectum = function () {
                var normalForm = this.normalize(), a = normalForm.primal[0][0], c = normalForm.primal[1][1], min = Math.min(Math.abs(a), Math.abs(c)), max = Math.max(Math.abs(a), Math.abs(c));

                if (!this.isDegenerated()) {
                    // Parabola
                    if (c === 0) {
                        return -2 * normalForm.primal[1][2] / a;
                    }

                    return 2 * Math.sqrt(max) / min;
                }
            };

            // ### [Conic.prototype.linearEccentricity()](http://mathlib.de/en/docs/Conic/linearEccentricity)
            // Calculates the linear eccentricity of a conic.
            //
            // *@return {number}*
            Conic.prototype.linearEccentricity = function () {
                var normalForm = this.normalize(), a = normalForm.primal[0][0], c = normalForm.primal[1][1], max = Math.max(Math.abs(a), Math.abs(c)), min = Math.min(Math.abs(a), Math.abs(c));

                if (!this.isDegenerated()) {
                    // parabola
                    if (c === 0) {
                        return normalForm.primal[1][2] / (-2 * a);
                    }

                    if (c > 0) {
                        return Math.sqrt(1 / min - 1 / max);
                    }
                    return Math.sqrt(1 / max + 1 / min);
                }
            };

            // ### [Conic.prototype.meet()](http://mathlib.de/en/docs/Conic/meet)
            // Calculates the meet of the conic with a line or a conic.
            //
            // *@return {Point[]}*
            Conic.prototype.meet = function (x) {
                var B, C, alpha, i, j, p1, p2, Ml, a, b, c, d, Delta0, Delta1, lambda, degenerated, lines, A = this.primal;

                Eif (x.type === 'line') {
                    var setter = function () {
                        MathLib.warning({ message: 'Trying to change the coordinates of a completely dependent point.', method: 'Conic#meet' });
                    }, recalculate = function () {
                        Ml = new MathLib.Matrix([[0, x[2], -x[1]], [-x[2], 0, x[0]], [x[1], -x[0], 0]]);
                        B = Ml.transpose().times(A).times(Ml);

                        Eif (!MathLib.isZero(x[0])) {
                            alpha = Math.sqrt(B[2][1] * B[1][2] - B[1][1] * B[2][2]) / x[0];
                        } else if (!MathLib.isZero(x[1])) {
                            alpha = Math.sqrt(B[0][2] * B[2][0] - B[2][2] * B[0][0]) / x[1];
                        } else {
                            alpha = Math.sqrt(B[1][0] * B[0][1] - B[0][0] * B[1][1]) / x[2];
                        }

                        C = Ml.times(alpha).plus(B);

                        nonZeroSearch:
                        for (i = 0; i < 3; i++) {
                            for (j = 0; j < 3; j++) {
                                if (C[i][j] !== 0) {
                                    break nonZeroSearch;
                                }
                            }
                        }
                    };

                    recalculate();

                    p1 = new MathLib.Point(C[i]);
                    Object.defineProperties(p1, {
                        '0': {
                            get: function () {
                                recalculate();
                                return C[i][0];
                            },
                            set: setter,
                            enumerable: true
                        },
                        '1': {
                            get: function () {
                                recalculate();
                                return C[i][1];
                            },
                            set: setter,
                            enumerable: true
                        },
                        '2': {
                            get: function () {
                                recalculate();
                                return C[i][2];
                            },
                            set: setter,
                            enumerable: true
                        }
                    });

                    p2 = new MathLib.Point([C[0][j], C[1][j], C[2][j]]);
                    Object.defineProperties(p2, {
                        '0': {
                            get: function () {
                                recalculate();
                                return C[0][j];
                            },
                            set: setter,
                            enumerable: true
                        },
                        '1': {
                            get: function () {
                                recalculate();
                                return C[1][j];
                            },
                            set: setter,
                            enumerable: true
                        },
                        '2': {
                            get: function () {
                                recalculate();
                                return C[2][j];
                            },
                            set: setter,
                            enumerable: true
                        }
                    });

                    return [p1, p2];
                } else if (x.type === 'conic') {
                    B = x.primal;
                    a = A.determinant();
                    b = (new MathLib.Matrix([A[0], A[1], B[2]])).plus(new MathLib.Matrix([A[0], B[1], A[2]])).plus(new MathLib.Matrix([B[0], A[1], A[2]])).determinant();
                    c = (new MathLib.Matrix([A[0], B[1], B[2]])).plus(new MathLib.Matrix([B[0], A[1], B[2]])).plus(new MathLib.Matrix([B[0], B[1], A[2]])).determinant();
                    d = B.determinant();
                    Delta0 = b * b - 3 * a * c;
                    Delta1 = 2 * b * b - 9 * a * b * c + 27 * a * a * d;
                    C = MathLib.cbrt((Delta1 + Math.sqrt(Math.pow(Delta1, 2) - 4 * Math.pow(Delta0, 3))) / 2);
                    lambda = -(b + C + Delta0 / C) / (3 * a);
                    degenerated = new MathLib.Conic(B.times(lambda).plus(A));
                    lines = degenerated.splitDegenerated();

                    return this.meet(lines[0]).concat(this.meet(lines[1]));
                }
            };

            // ### [Conic.prototype.normalize()](http://mathlib.de/en/docs/Conic/normalize)
            // Calculates the normal form of a conic.
            //
            // *@return {Conic}*
            Conic.prototype.normalize = function () {
                var A = this.primal[0][0], B = this.primal[0][1] * 2, C = this.primal[1][1], D = this.primal[0][2] * 2, E = this.primal[1][2] * 2, F = this.primal[2][2], r = Math.atan2(B, A - C) / 2, cos = Math.cos(r), sin = Math.sin(r), a = A * cos * cos + B * sin * cos + C * sin * sin, c = A * sin * sin - B * sin * cos + C * cos * cos, d = D * cos + E * sin, e = E * cos - D * sin, f = F;

                if (a !== 0) {
                    f += -d * d / (4 * a);
                    d = 0;
                }

                if (c !== 0) {
                    f += -e * e / (4 * c);
                    e = 0;
                }

                if (f !== 0) {
                    a = -a / f;
                    c = -c / f;
                    d = -d / f;
                    e = -e / f;
                    f = -1;
                }

                return new MathLib.Conic(new MathLib.Matrix([[a, 0, d / 2], [0, c, e / 2], [d / 2, e / 2, f]]));
            };

            // ### [Conic.prototype.polarity()](http://mathlib.de/en/docs/Conic/polarity)
            // Calculates the four polarity of a conic.
            //
            // *@return {Point[]}*
            Conic.prototype.polarity = function (x) {
                var object, m, c = this;

                if (x.type === 'line') {
                    object = new MathLib.Point([0, 0, 0]);
                    m = 'dual';
                } else Eif (x.type === 'point') {
                    object = new MathLib.Line([0, 0, 0]);
                    m = 'primal';
                }

                Object.defineProperties(object, {
                    '0': {
                        get: function () {
                            return c[m][0][0] * x[0] + c[m][0][1] * x[1] + c[m][0][2] * x[2];
                        },
                        set: function () {
                            MathLib.warning({ message: 'Trying to change the coordinates of a completely dependent ' + object.type + '.', method: 'Conic#polarity' });
                        },
                        enumerable: true
                    },
                    '1': {
                        get: function () {
                            return c[m][1][0] * x[0] + c[m][1][1] * x[1] + c[m][1][2] * x[2];
                        },
                        set: function () {
                            MathLib.warning({ message: 'Trying to change the coordinates of a completely dependent ' + object.type + '.', method: 'Conic#polarity' });
                        },
                        enumerable: true
                    },
                    '2': {
                        get: function () {
                            return c[m][2][0] * x[0] + c[m][2][1] * x[1] + c[m][2][2] * x[2];
                        },
                        set: function () {
                            MathLib.warning({ message: 'Trying to change the coordinates of a completely dependent ' + object.type + '.', method: 'Conic#polarity' });
                        },
                        enumerable: true
                    }
                });

                return object;
            };

            // ### [Conic.prototype.splitDegenerated()](http://mathlib.de/en/docs/Conic/splitDegenerated)
            // Splits a conic into one or two lines if the conic is degenerated.
            //
            // *@return {boolean}*
            Conic.prototype.splitDegenerated = function () {
                var n, i, j, B, C, p0, p1, p2, rank = this.primal.rank(), nonZeroSearch = function (C) {
                    for (i = 0; i < 3; i++) {
                        for (j = 0; j < 3; j++) {
                            Eif (C[i][j] !== 0) {
                                return;
                            }
                        }
                    }
                };

                if (rank === 2) {
                    Iif (this.dual[0][0] !== 0) {
                        n = 0;
                    } else Iif (this.dual[1][1] !== 0) {
                        n = 1;
                    } else {
                        n = 2;
                    }

                    Iif (this.dual[n][n] < 0) {
                        B = this.dual.negative();
                    } else {
                        B = this.dual;
                    }

                    p0 = B[0][n] / Math.sqrt(B[n][n]);
                    p1 = B[1][n] / Math.sqrt(B[n][n]);
                    p2 = B[2][n] / Math.sqrt(B[n][n]);
                    C = this.primal.plus(new MathLib.Matrix([[0, p2, -p1], [-p2, 0, p0], [p1, -p0, 0]]));

                    nonZeroSearch(C);

                    return [new MathLib.Line(C[i]), new MathLib.Line([C[0][j], C[1][j], C[2][j]])];
                } else if (rank === 1) {
                    nonZeroSearch(this.primal);
                    return [new MathLib.Line(this.primal[i]), new MathLib.Line(this.primal[i])];
                }
            };

            // ### [Conic.prototype.throughFivePoints()](http://mathlib.de/en/docs/Conic/throughFivePoints)
            // Calculates the conic through five points.
            //
            // *@return {Conic}*
            Conic.throughFivePoints = function (p, q, r, s, t) {
                var conic = new MathLib.Conic(new MathLib.Matrix([[1, 0, 0], [0, 1, 0], [0, 0, 1]]));

                Object.defineProperties(conic, {
                    'primal': {
                        get: function () {
                            var G = p.vectorProduct(r).outerProduct(q.vectorProduct(s)), H = p.vectorProduct(s).outerProduct(q.vectorProduct(r)), M = G.times(t.times(H).scalarProduct(t)).minus(H.times(t.times(G).scalarProduct(t)));
                            return M.transpose().plus(M);
                        },
                        set: function () {
                        },
                        enumerable: true,
                        configurable: true
                    }
                });

                return conic;
            };
            return Conic;
        })();
        MathLib.Conic = Conic;
    })(MathLib || (MathLib = {}));

    var __extends = this.__extends || function (d, b) {
        for (var p in b) {
          if (b.hasOwnProperty(p)) {
            d[p] = b[p];
          }
        }
        function __() {
          this.constructor = d;
        }
        __.prototype = b.prototype;
        d.prototype = new __();
    };
    /// <reference path='reference.ts'/>
    var MathLib;
    (function (MathLib) {
        // ## <a id="Point"></a>Point
        // The point implementation of MathLib makes calculations with point in
        // arbitrary dimensions possible.
        //
        // MathLib uses the homogeneous form of a point for calculations and storage.
        //
        // To create the point (4, 2) on the two dimensional plane use
        // `new MathLib.Point([4, 2, 1])`
        // Alternatively you can use
        // `new MathLib.Point(4, 2)`
        // The 1 will be added for you.
        /// import Complex, Vector
        var Point = (function (_super) {
            __extends(Point, _super);
            function Point(coords) {
                _super.call(this, arguments.length > 1 ? Array.prototype.slice.call(arguments).concat(1) : coords);
                this.type = 'point';

                this.dimension = 2;
            }
            // ### Point.prototype.crossRatio()
            // Calculates the distance crossratio (A,B,C,D) of four points
            // as seen from the current point.
            //
            // *@param {Point}* a The point A
            // *@param {Point}* b The point B
            // *@param {Point}* c The point C
            // *@param {Point}* d The point D
            // *@return {number}*
            Point.prototype.crossRatio = function (a, b, c, d) {
                var xa = this.vectorProduct(a), xb = this.vectorProduct(b);

                return xa.scalarProduct(c) * xb.scalarProduct(d) / (xa.scalarProduct(d) * xb.scalarProduct(c));
            };

            // ### Point.prototype.distanceTo()
            // Calculates the distance to an other point.
            // If no other point is provided, it calculates the distance to the origin.
            //
            // *@param {Point}* [point] The point to calculate the distance to
            // *@return {number}*
            Point.prototype.distanceTo = function (p /*, geom = MathLib.Geometry.active*/ ) {
                if (arguments.length === 0) {
                    return MathLib.hypot.apply(null, this.slice(0, -1)) / Math.abs(this[this.dimension]);
                }

                Eif (p.type === 'point' && this.dimension === p.dimension) {
                    return MathLib.hypot.apply(null, this.normalize().minus(p.normalize()).slice(0, -1));
                }
                //	if (p.type === 'point' && this.dimension === p.dimension) {
                //		var Otp = this.times(geom.fundamentalConic.primal).times(p),
                //				Ott = this.times(geom.fundamentalConic.primal).times(this),
                //				Opp = p.times(geom.fundamentalConic.primal).times(p),
                //				Dtp = Math.sqrt(Otp * Otp - Ott * Opp);
                //
                //		return MathLib.Geometry.active.cDist * Math.log((Otp + Dtp) / (Otp - Dtp));
                //	}
            };

            // ### Point.prototype.draw()
            // Draws the point on a canvas or svg element.
            //
            // *@param {Screen}* screen The screen to draw onto
            // *@param {object}* [options] Drawing options
            // *@return {Point}* The current point
            Point.prototype.draw = function (screen, options) {
                if (Array.isArray(screen)) {
                    var point = this;
                    screen.forEach(function (x) {
                        x.point(point, options);
                    });
                } else {
                    screen.point(this, options);
                }

                return this;
            };

            // ### Point.prototype.isEqual()
            // Determines if the point has the same coordinates as an other point
            //
            // *@param {Point}* The point to compare
            // *@return {boolean}*
            Point.prototype.isEqual = function (q) {
                var p = this.normalize();
                q = q.normalize();

                if (this.length !== q.length) {
                    return false;
                }

                return p.every(function (x, i) {
                    return MathLib.isEqual(x, q[i]);
                });
            };

            // ### Point.prototype.isFinite()
            // Determines if the point is finite
            //
            // *@return {boolean}*
            Point.prototype.isFinite = function () {
                return !MathLib.isZero(this[this.length - 1]);
            };

            // ### Point.prototype.isInside()
            // Determines wether a point is inside a circle
            //
            // *@param {Circle}*
            // *@return {boolean}*
            Point.prototype.isInside = function (a) {
                Eif (a.type === 'circle') {
                    return this.distanceTo(a.center) < a.radius;
                }
            };

            // ### Point.prototype.isOn()
            // Determines wether a point is on a line or circle
            //
            // *@param {Line|Point}*
            // *@return {boolean}*
            Point.prototype.isOn = function (a) {
                Iif (a.type === 'line') {
                    return this.distanceTo(a.center) === a.radius;
                } else Eif (a.type === 'circle') {
                    return this.distanceTo(a.center) === a.radius;
                }
            };

            // ### Point.prototype.isOutside()
            // Determines wether a point is outside a circle
            //
            // *@param {Circle}*
            // *@return {boolean}*
            Point.prototype.isOutside = function (a) {
                Eif (a.type === 'circle') {
                    return this.distanceTo(a.center) > a.radius;
                }
            };

            // ### Point.prototype.join()
            // Calculates a line connecting two points
            //
            // *@param {Point}* The point to calculate the line to
            // *@return {Line}*
            Point.prototype.join = function (q) {
                var line, p = this;

                Eif (this.dimension === 2 && q.dimension === 2) {
                    line = new MathLib.Line(this.vectorProduct(q).toArray());

                    Object.defineProperties(line, {
                        '0': {
                            get: function () {
                                return p[1] * q[2] - p[2] * q[1];
                            },
                            set: function () {
                                MathLib.warning({ message: 'Trying to change the coordinates of a completely dependent line.', method: 'Point#join' });
                            },
                            enumerable: true
                        },
                        '1': {
                            get: function () {
                                return p[2] * q[0] - p[0] * q[2];
                            },
                            set: function () {
                                MathLib.warning({ message: 'Trying to change the coordinates of a completely dependent line.', method: 'Point#join' });
                            },
                            enumerable: true
                        },
                        '2': {
                            get: function () {
                                return p[0] * q[1] - p[1] * q[0];
                            },
                            set: function () {
                                MathLib.warning({ message: 'Trying to change the coordinates of a completely dependent line.', method: 'Point#join' });
                            },
                            enumerable: true
                        }
                    });

                    return line;
                }
            };

            // ### Point.prototype.normalize()
            // Normalizes the point.
            //
            // *@return {Point}*
            Point.prototype.normalize = function () {
                var last = this[this.dimension] || 1;
                return this.map(function (x) {
                    return x / last;
                });
            };

            // ### Point.prototype.reflectAt()
            // Reflects the point at an other point
            //
            // *@return {Point}*
            Point.prototype.reflectAt = function (a) {
                var i, ii, reflectedPoint = [], p = this.normalize();

                Eif (a.type === 'point') {
                    Eif (this.dimension === a.dimension) {
                        a = a.normalize();
                        for (i = 0, ii = this.dimension; i < ii; i++) {
                            reflectedPoint.push(2 * a[i] - p[i]);
                        }
                        reflectedPoint.push(1);
                        return new MathLib.Point(reflectedPoint);
                    }
                }
            };

            // ### Point.prototype.restrictTo()
            // Restricts the point to a line.
            //
            // *@param {Line}*
            Point.prototype.restrictTo = function (l) {
                var p = this.slice();

                Object.defineProperties(this, {
                    '0': {
                        get: function () {
                            return l[1] * l[1] * p[0] - l[0] * (l[1] * p[1] + l[2] * p[2]);
                        },
                        set: function (point) {
                            p[0] = point;
                        },
                        enumerable: true,
                        configurable: true
                    },
                    '1': {
                        get: function () {
                            return -l[1] * l[2] * p[2] + l[0] * (l[0] * p[1] - l[1] * p[0]);
                        },
                        set: function (point) {
                            p[1] = point;
                        },
                        enumerable: true,
                        configurable: true
                    },
                    '2': {
                        get: function () {
                            return l[1] * l[1] * p[2] + l[0] * l[0] * p[2];
                        },
                        set: function (point) {
                            p[2] = point;
                        },
                        enumerable: true,
                        configurable: true
                    }
                });
            };

            // ### Point.prototype.toComplex()
            // Converts a two dimensional point to the corresponding complex number.
            //
            // *@return {Complex}*
            Point.prototype.toComplex = function () {
                Eif (this.dimension === 2) {
                    if (MathLib.isZero(this[2])) {
                        return new MathLib.Complex(Infinity);
                    }
                    return new MathLib.Complex(this[0] / this[2], this[1] / this[2]);
                }
            };

            // ### Point.prototype.toContentMathML()
            // Returns content MathML representation of the point
            //
            // *@return {string}*
            /* toContentMathML(opt) { */
            /* } */
            // ### Point.prototype.toLaTeX()
            // Returns LaTeX representation of the point
            //
            // *@param {boolean}* Optional parameter to indicate if the output should be projective.
            // *@return {string}*
            Point.prototype.toLaTeX = function (opt) {
                if (typeof opt === "undefined") { opt = false; }
                var p = opt ? this.toArray() : this.normalize().slice(0, -1);

                return '\\begin{pmatrix}' + p.reduce(function (old, cur) {
                    return old + '\\\\' + MathLib.toLaTeX(cur);
                }) + '\\end{pmatrix}';
            };

            // ### Point.prototype.toMathML()
            // Returns (presentation) MathML representation of the point
            //
            // *@param {boolean}* Optional parameter to indicate if the output should be projective.
            // *@return {string}*
            Point.prototype.toMathML = function (opt) {
                if (typeof opt === "undefined") { opt = false; }
                var p = opt ? this.toArray() : this.normalize().slice(0, -1);

                return p.reduce(function (old, cur) {
                    return old + '<mtr><mtd>' + MathLib.toMathML(cur) + '</mtd></mtr>';
                }, '<mrow><mo>(</mo><mtable>') + '</mtable><mo>)</mo></mrow>';
            };

            // ### Point.prototype.toString()
            // Returns string representation of the point
            //
            // *@param {boolean}* Optional parameter to indicate if the output should be projective.
            // *@return {string}*
            Point.prototype.toString = function (opt) {
                if (typeof opt === "undefined") { opt = false; }
                var p = opt ? this.toArray() : this.normalize().slice(0, -1);

                return '(' + p.reduce(function (old, cur) {
                    return old + ', ' + MathLib.toString(cur);
                }) + ')';
            };
            Point.I = new Point([new MathLib.Complex(0, -1), 0, 1]);

            Point.J = new Point([new MathLib.Complex(0, 1), 0, 1]);
            return Point;
        })(MathLib.Vector);
        MathLib.Point = Point;
    })(MathLib || (MathLib = {}));

    /// <reference path='reference.ts'/>
    var MathLib;
    (function (MathLib) {
        // ## <a id="Polynomial"></a>Polynomial
        // The polynomial implementation of MathLib makes calculations with polynomials.
        // Both the coefficients and the arguments of a polynomial can be numbers,
        // complex numbers and matrices.
        //
        // It is as easy as
        // ```
        // new MathLib.Polynomial([1, 2, 3])
        // ```
        // to create the polynomial 1 + 2x + 3x²
        // The polynomial x¹⁰⁰ can be created with the following statement:
        // ```
        // new MathLib.Polynomial(100)
        // ```
        /// import Functn
        var Polynomial = (function () {
            function Polynomial(polynomial) {
                var _this = this;
                this.type = 'polynomial';
                var coefficients = [];

                if (polynomial === undefined || polynomial.length === 0) {
                    polynomial = [0];
                } else if (typeof polynomial === 'number') {
                    while (polynomial--) {
                        coefficients.push(0);
                    }
                    coefficients.push(1);
                    polynomial = coefficients;
                }

                polynomial.forEach(function (x, i) {
                    _this[i] = x;
                });
                this.length = polynomial.length;
                this.deg = polynomial.length - 1;
                this.subdeg = (function (a) {
                    var i = 0;
                    if (a.length > 1 || a[0]) {
                        while (i < a.length && MathLib.isZero(a[i])) {
                            i++;
                        }
                        return i;
                    }
                    return Infinity;
                }(polynomial));
            }
            // ### Polynomial.prototype.compare()
            // Compares two polynomials.
            //
            // *@param {Polynomial}* The polynomial to compare
            // *@return {number}*
            Polynomial.prototype.compare = function (p) {
                var i, ii;

                if (this.length !== p.length) {
                    return MathLib.sign(this.length - p.length);
                }

                for (i = 0, ii = this.length; i < ii; i++) {
                    if (p[i] - this[i]) {
                        return MathLib.sign(this[i] - p[i]);
                    }
                }

                return 0;
            };

            // ### Polynomial.prototype.differentiate()
            // Differentiates the polynomial
            //
            // *@param {number}* [n] the number of times to differentiate the polynomial.
            // *@return {Polynomial}*
            Polynomial.prototype.differentiate = function (n) {
                if (typeof n === "undefined") { n = 1; }
                var i, ii, derivative = [];

                Iif (n === 0) {
                    return this;
                }

                for (i = 0, ii = this.deg - n; i <= ii; i++) {
                    derivative[i] = MathLib.times(this[i + n], MathLib.fallingFactorial(i + n, n));
                }
                return new MathLib.Polynomial(derivative);
            };

            // ### Polynomial.prototype.draw()
            // Draws the polynomial on the screen
            //
            // *@param {Screen}* The screen to draw the polynomial onto.
            // *@param {object}* [options] Optional drawing options.
            // *@return {Polynomial}*
            Polynomial.prototype.draw = function (screen, options) {
                var path = [], i, line = this;

                if (this.deg < 2) {
                    if (Array.isArray(screen)) {
                        screen.forEach(function (x) {
                            x.line([[-50, line.valueAt(-50)], [50, line.valueAt(50)]], options);
                        });
                    } else {
                        screen.line([[-50, this.valueAt(-50)], [50, this.valueAt(50)]], options);
                    }
                } else {
                    for (i = -50; i <= 50; i = Math.round((i + 0.01) * 100) / 100) {
                        path.push([i, this.valueAt(i)]);
                    }
                    if (Array.isArray(screen)) {
                        screen.forEach(function (x) {
                            x.path(path, options);
                        });
                    } else {
                        screen.path(path, options);
                    }
                }

                return this;
            };

            // ### Polynomial.prototype.every()
            // Works like Array.prototype.every.
            //
            // *@return {boolean}*
            Polynomial.prototype.every = function (f) {
                return Array.prototype.every.call(this, f);
            };

            // ### Polynomial.prototype.forEach()
            // Works like the Array.prototype.forEach function
            //
            Polynomial.prototype.forEach = function () {
                var args = [];
                for (var _i = 0; _i < (arguments.length - 0); _i++) {
                    args[_i] = arguments[_i + 0];
                }
                Array.prototype.forEach.apply(this, args);
            };

            // ### Polynomial.prototype.integrate()
            // Integrates the polynomial
            //
            // *@param {number}* [n] the number of times to integrate the polynomial.
            // *@return {Polynomial}*
            Polynomial.prototype.integrate = function (n) {
                if (typeof n === "undefined") { n = 1; }
                var i, ii, antiderivative = [];

                Iif (MathLib.isZero(n)) {
                    return this;
                }

                for (i = 0; i < n; i++) {
                    antiderivative.push(0);
                }

                for (i = 0, ii = this.deg; i <= ii; i++) {
                    antiderivative[i + n] = this[i] / MathLib.fallingFactorial(i + n, n);
                }
                return new MathLib.Polynomial(antiderivative);
            };

            // ### Polynomial.interpolation
            // Interpolates points.
            //
            // *@return {Polynomial}*
            Polynomial.interpolation = function (a, b) {
                var basisPolynomial, interpolant = new MathLib.Polynomial([0]), n = a.length, i, j;

                if (arguments.length === 2) {
                    a = a.map(function (x, i) {
                        return [x, b[i]];
                    });
                }

                for (i = 0; i < n; i++) {
                    basisPolynomial = new MathLib.Polynomial([1]);
                    for (j = 0; j < n; j++) {
                        if (i !== j) {
                            basisPolynomial = basisPolynomial.times(new MathLib.Polynomial([-a[j][0] / (a[i][0] - a[j][0]), 1 / (a[i][0] - a[j][0])]));
                        }
                    }
                    interpolant = interpolant.plus(basisPolynomial.times(a[i][1]));
                }
                return interpolant;
            };

            // ### Polynomial.prototype.isEqual()
            // Decides if two polynomials are equal.
            //
            // *@param {Polynomial}*
            // *@return {boolean}*
            Polynomial.prototype.isEqual = function (p) {
                var i, ii;
                Iif (this.deg !== p.deg || this.subdeg !== p.subdeg) {
                    return false;
                }
                for (i = 0, ii = this.deg; i <= ii; i++) {
                    Iif (!MathLib.isEqual(this[i], p[i])) {
                        return false;
                    }
                }
                return true;
            };

            // ### Polynomial.prototype.map()
            // Works like the Array.prototype.map function
            //
            // *@return {Polynomial}*
            Polynomial.prototype.map = function (f) {
                return new MathLib.Polynomial(Array.prototype.map.call(this, f));
            };

            // ### Polynomial.prototype.negative()
            // Returns the negative polynomial
            //
            // *@return {Polynomial}*
            Polynomial.prototype.negative = function () {
                return new MathLib.Polynomial(this.map(MathLib.negative));
            };

            // ### Polynomial.prototype.plus()
            // Adds a number or a polynomial
            //
            // *@return {Polynomial}*
            Polynomial.prototype.plus = function (a) {
                var plus = [], i;
                if (typeof a === 'number') {
                    plus = this.slice();
                    plus[0] = MathLib.plus(plus[0], a);
                } else Eif (a.type === 'polynomial') {
                    for (i = 0; i <= Math.min(this.deg, a.deg); i++) {
                        plus[i] = MathLib.plus(this[i], a[i]);
                    }
                    plus = plus.concat((this.deg > a.deg ? this : a).slice(i));
                }
                return new MathLib.Polynomial(plus);
            };

            // ### Polynomial.regression
            // Calculates the regression line for some points
            //
            // *@return {Polynomial}*
            Polynomial.regression = function (x, y) {
                var length = x.length, xy = 0, xi = 0, yi = 0, x2 = 0, m, c, i;

                if (arguments.length === 2) {
                    for (i = 0; i < length; i++) {
                        xy += x[i] * y[i];
                        xi += x[i];
                        yi += y[i];
                        x2 += x[i] * x[i];
                    }
                } else {
                    for (i = 0; i < length; i++) {
                        xy += x[i][0] * x[i][1];
                        xi += x[i][0];
                        yi += x[i][1];
                        x2 += x[i][0] * x[i][0];
                    }
                }

                m = (length * xy - xi * yi) / (length * x2 - xi * xi);
                c = (yi * x2 - xy * xi) / (length * x2 - xi * xi);
                return new MathLib.Polynomial([c, m]);
            };

            // ### Polynomial.roots
            // Returns a polynomial with the specified roots
            //
            // *@return {Polynomial}*
            Polynomial.roots = function (zeros) {
                var elemSymPoly, i, ii, coef = [];

                if (MathLib.type(zeros) === 'array') {
                    zeros = new MathLib.Set(zeros);
                }

                elemSymPoly = zeros.powerset();
                for (i = 0, ii = zeros.card; i < ii; i++) {
                    coef[i] = 0;
                }

                // Vieta's theorem
                elemSymPoly.slice(1).forEach(function (x) {
                    coef[ii - x.card] = MathLib.plus(coef[ii - x.card], x.times());
                });

                coef = coef.map(function (x, i) {
                    if ((ii - i) % 2) {
                        return MathLib.negative(x);
                    }
                    return x;
                });

                coef.push(1);
                return new MathLib.Polynomial(coef);
            };

            // ### Polynomial.prototype.slice()
            // Works like the Array.prototype.slice function
            //
            // *@return {array}*
            Polynomial.prototype.slice = function () {
                var args = [];
                for (var _i = 0; _i < (arguments.length - 0); _i++) {
                    args[_i] = arguments[_i + 0];
                }
                return Array.prototype.slice.apply(this, args);
            };

            // ### Polynomial.prototype.times()
            // Multiplies the polynomial by a number or an other polynomial
            //
            // *@param {number|Polynomial}* The multiplicator
            // *@return {Polynomial}*
            Polynomial.prototype.times = function (a) {
                var i, ii, j, jj, product = [];

                if (a.type === 'polynomial') {
                    for (i = 0, ii = this.deg; i <= ii; i++) {
                        for (j = 0, jj = a.deg; j <= jj; j++) {
                            product[i + j] = MathLib.plus((product[i + j] ? product[i + j] : 0), MathLib.times(this[i], a[j]));
                        }
                    }
                    return new MathLib.Polynomial(product);
                } else if (a.type === 'rational') {
                    a = a.toNumber();
                }

                // we we multiply it to every coefficient
                return this.map(function (b) {
                    return MathLib.times(a, b);
                });
            };

            // ### Polynomial.prototype.toContentMathML()
            // Returns a content MathML representation of the polynomial
            //
            // *@return {string}*
            Polynomial.prototype.toContentMathML = function (math) {
                var str = '<apply><csymbol cd="arith1">plus</csymbol>', i;
                for (i = this.deg; i >= 0; i--) {
                    if (!MathLib.isZero(this[i])) {
                        if (i === 0) {
                            str += MathLib.toContentMathML(this[i]);
                        } else {
                            str += '<apply><csymbol cd="arith1">times</csymbol>' + MathLib.toContentMathML(this[i], true);
                        }

                        if (i > 1) {
                            str += '<apply><csymbol cd="arith1">power</csymbol><ci>x</ci>' + MathLib.toContentMathML(i) + '</apply></apply>';
                        } else if (i === 1) {
                            str += '<ci>x</ci></apply>';
                        }
                    }
                }

                str += '</apply>';

                Iif (math) {
                    str = '<math xmlns="http://www.w3.org/1998/Math/MathML"><lambda><bvar><ci>x</ci></bvar><domainofapplication><complexes/></domainofapplication>' + str + '</lambda></math>';
                }

                return str;
            };

            // ### Polynomial.prototype.toExpression()
            // Custom toExpression function
            //
            // *@return {Expression}*
            Polynomial.prototype.toExpression = function () {
                var content = [], sum, i;

                for (i = this.deg; i >= 0; i--) {
                    Eif (!MathLib.isZero(this[i])) {
                        if (i > 1) {
                            content.push(new MathLib.Expression({
                                subtype: 'naryOperator',
                                value: '^',
                                name: 'pow',
                                content: [
                                    new MathLib.Expression({
                                        subtype: 'naryOperator',
                                        content: [
                                            new MathLib.Expression({
                                                subtype: 'number',
                                                value: this[i].toString()
                                            }),
                                            new MathLib.Expression({
                                                subtype: 'variable',
                                                value: 'x'
                                            })
                                        ],
                                        value: '*',
                                        name: 'times'
                                    }),
                                    new MathLib.Expression({
                                        subtype: 'number',
                                        value: i.toString()
                                    })
                                ]
                            }));
                        } else if (i === 1) {
                            content.push(new MathLib.Expression({
                                subtype: 'naryOperator',
                                content: [
                                    new MathLib.Expression({
                                        subtype: 'number',
                                        value: this[i].toString()
                                    }),
                                    new MathLib.Expression({
                                        subtype: 'variable',
                                        value: 'x'
                                    })
                                ],
                                value: '*',
                                name: 'times'
                            }));
                        } else Eif (i === 0) {
                            content.push(new MathLib.Expression({
                                subtype: 'number',
                                value: this[i].toString()
                            }));
                        }
                    }
                }

                sum = new MathLib.Expression({
                    content: content,
                    subtype: 'naryOperator',
                    value: '+',
                    name: 'plus'
                });

                return new MathLib.Expression({
                    subtype: 'functionDefinition',
                    arguments: ['x'],
                    content: [sum]
                });
            };

            // ### Polynomial.prototype.toFunctn()
            // Converts the polynomial to a functn
            //
            // *@return {Functn}*
            Polynomial.prototype.toFunctn = function () {
                var str = '', i, ii;
                for (i = 0, ii = this.deg; i <= ii; i++) {
                    Eif (!MathLib.isZero(this[i])) {
                        if (i === 0) {
                            str += MathLib.toString(this[i]);
                        } else {
                            str += MathLib.toString(this[i], true);
                        }

                        if (i > 1) {
                            str += ' * Math.pow(x, ' + MathLib.toString(i) + ')';
                        } else if (i === 1) {
                            str += ' * x';
                        }
                    }
                }

                return MathLib.Functn(new Function('x', 'return ' + str), {
                    expression: this.toExpression()
                });
            };

            // ### Polynomial.prototype.toLaTeX()
            // Returns a LaTeX representation of the polynomial
            //
            // *@return {string}*
            Polynomial.prototype.toLaTeX = function () {
                var str = MathLib.toString(this[this.deg]) + 'x^{' + this.deg + '}', i;

                for (i = this.deg - 1; i >= 0; i--) {
                    if (!MathLib.isZero(this[i])) {
                        // if (i === 0) {
                        //   str += MathLib.toLaTeX(this[i]);
                        // }
                        // else {
                        str += MathLib.toLaTeX(this[i], true);

                        // }
                        Iif (i > 1) {
                            str += 'x^{' + MathLib.toLaTeX(i) + '}';
                        } else if (i === 1) {
                            str += 'x';
                        }
                    }
                }
                return str;
            };

            // ### Polynomial.prototype.toMathML()
            // Returns a MathML representation of the polynomial
            //
            // *@return {string}*
            Polynomial.prototype.toMathML = function () {
                var str = '<mrow>' + MathLib.toMathML(this[this.deg]) + '<mo>&#x2062;</mo><msup><mi>x</mi>' + MathLib.toMathML(this.deg) + '</msup>', i;
                for (i = this.deg - 1; i >= 0; i--) {
                    if (!MathLib.isZero(this[i])) {
                        // if (i === 0) {
                        //   str += MathLib.toMathML(this[i]);
                        // }
                        // else {
                        str += MathLib.toMathML(this[i], true);

                        // }
                        Iif (i > 1) {
                            str += '<mo>&#x2062;</mo><msup><mi>x</mi>' + MathLib.toMathML(i) + '</msup>';
                        } else if (i === 1) {
                            str += '<mo>&#x2062;</mo><mi>x</mi>';
                        }
                    }
                }

                str += '</mrow>';

                return str;
            };

            // ### Polynomial.prototype.toString()
            // Custom toString function
            //
            // *@return {string}*
            Polynomial.prototype.toString = function () {
                var str = MathLib.toString(this[this.deg]) + '*x^' + this.deg, i;
                for (i = this.deg - 1; i >= 0; i--) {
                    if (!MathLib.isZero(this[i])) {
                        str += MathLib.toString(this[i], true);

                        Iif (i > 1) {
                            str += '*x^' + MathLib.toString(i);
                        } else if (i === 1) {
                            str += '*x';
                        }
                    }
                }
                return str;
            };

            // ### Polynomial.prototype.valueAt()
            // Evaluates the polynomial at a given point
            //
            // *@param {number|Complex|Matrix}*
            // *@return {number|Complex|Matrix}*
            Polynomial.prototype.valueAt = function (x) {
                // TODO: warn if x is non square matrix
                var pot = MathLib.is(x, 'matrix') ? MathLib.Matrix.identity(x.rows) : 1, value = MathLib.is(x, 'matrix') ? MathLib.Matrix.zero(x.rows, x.cols) : 0, i, ii;

                for (i = 0, ii = this.deg; i <= ii; i++) {
                    value = MathLib.plus(value, MathLib.times(this[i], pot));
                    pot = MathLib.times(pot, x);
                }
                return value;
            };
            Polynomial.one = new Polynomial([1]);

            Polynomial.zero = new Polynomial([0]);
            return Polynomial;
        })();
        MathLib.Polynomial = Polynomial;
    })(MathLib || (MathLib = {}));

    /// <reference path='reference.ts'/>
    var MathLib;
    (function (MathLib) {
        // ## <a id="Rational" href="http://mathlib.de/en/docs/Rational">Rational</a>
        // MathLib.Rational is the MathLib implementation of rational numbers.
        //
        //
        // #### Simple use case:
        // ```
        // // Create the rational number 2/3
        // var r = new MathLib.Rational(2, 3);
        // ```
        /// import Functn
        var Rational = (function () {
            function Rational(numerator, denominator) {
                if (typeof denominator === "undefined") { denominator = 1; }
                this.type = 'rational';
                if (MathLib.isZero(denominator)) {
                    MathLib.error({ message: 'The denominator cannot be zero.', method: 'Rational.constructor' });
                    throw 'The denominator cannot be zero.';
                }
                this.numerator = numerator;
                this.denominator = denominator;
            }
            // ### [Rational.prototype.compare()](http://mathlib.de/en/docs/Rational/compare)
            // Compares two rational numbers
            //
            // *@param {Rational}* The number to compare
            // *@return {number}*
            Rational.prototype.compare = function (r) {
                return MathLib.sign(this.numerator * r.denominator - this.denominator * r.numerator);
            };

            // ### [Rational.prototype.divide()](http://mathlib.de/en/docs/Rational/divide)
            // Divides rational numbers
            //
            // *@param {Rational|number}* The divisor
            // *@return {Rational}*
            Rational.prototype.divide = function (r) {
                if (r.type === 'rational') {
                    return new MathLib.Rational(MathLib.times(this.numerator, r.denominator), MathLib.times(this.denominator, r.numerator));
                } else Eif (typeof r === 'number') {
                    return new MathLib.Rational(this.numerator, MathLib.times(this.denominator, r));
                } else {
                    return r.inverse().times(this);
                }
            };

            // ### [Rational.prototype.inverse()](http://mathlib.de/en/docs/Rational/inverse)
            // Calculates the inverse of a rational number
            //
            // *@return {Rational}*
            Rational.prototype.inverse = function () {
                if (!MathLib.isZero(this.numerator)) {
                    return new MathLib.Rational(this.denominator, this.numerator);
                }
            };

            // ### [Rational.prototype.isEqual()](http://mathlib.de/en/docs/Rational/isEqual)
            // Checks if the rational number is equal to an other number
            //
            // *@return {boolean}*
            Rational.prototype.isEqual = function (r) {
                return MathLib.isEqual(MathLib.times(this.numerator, r.denominator), MathLib.times(this.denominator, r.numerator));
            };

            // ### [Rational.prototype.isZero()](http://mathlib.de/en/docs/Rational/isZero)
            // Checks if the rational number is zero
            //
            // *@return {boolean}*
            Rational.prototype.isZero = function () {
                return MathLib.isZero(this.numerator);
            };

            // ### [Rational.prototype.minus()](http://mathlib.de/en/docs/Rational/minus)
            // Subtracts rational numbers
            //
            // *@param {Rational|number}* The number to be subtracted
            // *@return {Rational}*
            Rational.prototype.minus = function (r) {
                var n = this.numerator, d = this.denominator;

                if (r.type === 'rational') {
                    return new MathLib.Rational(MathLib.minus(MathLib.times(n, r.denominator), MathLib.times(d, r.numerator)), MathLib.times(d, r.denominator));
                } else Eif (typeof r === 'number') {
                    return new MathLib.Rational(MathLib.minus(n, MathLib.times(r, d)), d);
                } else {
                    return r.minus(this).negative();
                }
            };

            // ### [Rational.prototype.negative()](http://mathlib.de/en/docs/Rational/negative)
            // Calculates the negative of a rational number
            //
            // *@return {Rational}*
            Rational.prototype.negative = function () {
                return new MathLib.Rational(-this.numerator, this.denominator);
            };

            // ### [Rational.prototype.plus()](http://mathlib.de/en/docs/Rational/plus)
            // Adds rational numbers
            //
            // *@param {Rational|number}* The number to be added
            // *@return {Rational}*
            Rational.prototype.plus = function (r) {
                var n = this.numerator, d = this.denominator;

                if (r.type === 'rational') {
                    return new MathLib.Rational(MathLib.plus(MathLib.times(d, r.numerator), MathLib.times(n, r.denominator)), MathLib.times(d, r.denominator));
                } else Eif (typeof r === 'number') {
                    return new MathLib.Rational(MathLib.plus(n, MathLib.times(r, d)), d);
                } else {
                    return r.plus(this);
                }
            };

            // ### [Rational.prototype.reduce()](http://mathlib.de/en/docs/Rational/reduce)
            // Reduces the rational number
            //
            // *@return {Rational}*
            Rational.prototype.reduce = function () {
                var gcd = MathLib.sign(this.denominator) * MathLib.gcd([this.numerator, this.denominator]);
                return new MathLib.Rational(this.numerator / gcd, this.denominator / gcd);
            };

            // ### [Rational.prototype.times()](http://mathlib.de/en/docs/Rational/times)
            // Multiplies rational numbers
            //
            // *@param {Rational|number}* The number to be multiplied
            // *@return {Rational}*
            Rational.prototype.times = function (r) {
                if (r.type === 'rational') {
                    return new MathLib.Rational(MathLib.times(this.numerator, r.numerator), MathLib.times(this.denominator, r.denominator));
                } else Eif (typeof r === 'number') {
                    return new MathLib.Rational(MathLib.times(this.numerator, r), this.denominator);
                } else {
                    return r.times(this);
                }
            };

            // ### [Rational.prototype.toContentMathML()](http://mathlib.de/en/docs/Rational/toContentMathML)
            // Returns the Content MathML representation of the rational number
            //
            // *@return {string}*
            Rational.prototype.toContentMathML = function () {
                return '<cn type="rational">' + this.numerator + '<sep/>' + this.denominator + '</cn>';
            };

            // ### [Rational.prototype.toLaTeX()](http://mathlib.de/en/docs/Rational/toLaTeX)
            // Returns the LaTeX representation of the rational number
            //
            // *@return {string}*
            Rational.prototype.toLaTeX = function () {
                return '\\frac{' + MathLib.toLaTeX(this.numerator) + '}{' + MathLib.toLaTeX(this.denominator) + '}';
            };

            // ### [Rational.prototype.toMathML()](http://mathlib.de/en/docs/Rational/toMathML)
            // Returns the MathML representation of the rational number
            //
            // *@return {string}*
            Rational.prototype.toMathML = function () {
                return '<mfrac>' + MathLib.toMathML(this.numerator) + MathLib.toMathML(this.denominator) + '</mfrac>';
            };

            // ### [Rational.prototype.toNumber()](http://mathlib.de/en/docs/Rational/toNumber)
            // Returns the number represented by the rational number
            //
            // *@return {number}*
            Rational.prototype.toNumber = function () {
                return this.numerator / this.denominator;
            };

            // ### [Rational.prototype.toString()](http://mathlib.de/en/docs/Rational/toString)
            // Custom toString function
            //
            // *@return {string}*
            Rational.prototype.toString = function () {
                return MathLib.toString(this.numerator) + '/' + MathLib.toString(this.denominator);
            };
            return Rational;
        })();
        MathLib.Rational = Rational;
    })(MathLib || (MathLib = {}));

    /// <reference path='reference.ts'/>
    var MathLib;
    (function (MathLib) {
        // ## <a id="Set"></a>Set
        //
        // To generate the set {1, 2, 3, 4, 5} you simply need to type
        // ```
        // new MathLib.Set([1, 2, 3, 4, 5])
        // ```
        /// no import
        var Set = (function () {
            function Set(elements) {
                var _this = this;
                this.type = 'set';
                // ### Set.prototype.intersect()
                // Returns the intersection of two sets.
                //
                // *@param {Set}*
                // *@return {Set}*
                this.intersect = Set.createSetOperation(false, true, false);
                // ### Set.prototype.union()
                // Returns the union of two sets.
                //
                // *@param {Set}*
                // *@return {Set}*
                this.union = Set.createSetOperation(true, true, true);
                // ### Set.prototype.without()
                // Returns all elements, which are in the first set, but not in the second.
                //
                // *@param {Set}*
                // *@return {Set}*
                this.without = Set.createSetOperation(true, false, false);
                // ### Set.prototype.xor()
                // Returns all elements which are in either the first or the second set.
                //
                // *@param {Set}*
                // *@return {Set}*
                this.xor = Set.createSetOperation(true, false, true);
                if (!elements) {
                    elements = [];
                }

                elements = elements.sort(MathLib.compare).filter(function (x, i, a) {
                    return (a.length === i + 1) || !MathLib.isEqual(x, a[i + 1]) || (typeof x.isEqual !== 'undefined' && !x.isEqual(a[i + 1]));
                });

                elements.forEach(function (x, i) {
                    _this[i] = x;
                });
                this.length = elements.length;
                this.card = elements.length;
            }
            // ### Set.prototype.compare()
            // Compare function for sets
            //
            // *@return {number}*
            Set.prototype.compare = function (x) {
                var a, i, ii;

                if (this.card !== x.card) {
                    return MathLib.sign(this.card - x.card);
                } else {
                    for (i = 0, ii = this.card; i < ii; i++) {
                        a = MathLib.compare(this[i], x[i]);
                        if (a !== 0) {
                            return a;
                        }
                    }
                    return 0;
                }
            };

            // ### Set.prototype.every()
            // Works like the Array.prototype.every function
            //
            // *@return {boolean}*
            Set.prototype.every = function () {
                var args = [];
                for (var _i = 0; _i < (arguments.length - 0); _i++) {
                    args[_i] = arguments[_i + 0];
                }
                return Array.prototype.every.apply(this, args);
            };

            // ### Set.prototype.filter()
            // Works like the Array.prototype.filter function
            //
            // *@return {Set}*
            Set.prototype.filter = function () {
                var args = [];
                for (var _i = 0; _i < (arguments.length - 0); _i++) {
                    args[_i] = arguments[_i + 0];
                }
                return new MathLib.Set(Array.prototype.filter.apply(this, args));
            };

            // ### Set.prototype.forEach()
            // Works like the Array.prototype.forEach function
            //
            //
            Set.prototype.forEach = function () {
                var args = [];
                for (var _i = 0; _i < (arguments.length - 0); _i++) {
                    args[_i] = arguments[_i + 0];
                }
                Array.prototype.forEach.apply(this, args);
            };

            // ### Set.prototype.indexOf()
            // Works like the Array.prototype.indexOf function
            //
            // *@return {number}*
            Set.prototype.indexOf = function () {
                var args = [];
                for (var _i = 0; _i < (arguments.length - 0); _i++) {
                    args[_i] = arguments[_i + 0];
                }
                return Array.prototype.indexOf.apply(this, args);
            };

            // ### Set.prototype.insert()
            // Inserts an element into the set.
            //
            // *@return {Set}* Returns the current set
            Set.prototype.insert = function (x) {
                var i = this.locate(x);
                if (this[i] !== x) {
                    this.splice(i, 0, x);
                    this.card++;
                }
                return this;
            };

            // ### Set.prototype.isEmpty()
            // Determines if the set is empty.
            //
            // *@return {boolean}*
            Set.prototype.isEmpty = function () {
                return this.card === 0;
            };

            // ### Set.prototype.isEqual()
            // Determines if the set is equal to an other set.
            //
            // *@param {Set}* The set to compare
            // *@return {boolean}*
            Set.prototype.isEqual = function (x) {
                if (this.card !== x.card) {
                    return false;
                } else {
                    return this.every(function (y, i) {
                        return MathLib.isEqual(y, x[i]);
                    });
                }
            };

            // ### Set.prototype.isSubsetOf()
            // Determines if the set is a subset of an other set.
            //
            // *@param {Set}* The potential superset
            // *@return {boolean}*
            Set.prototype.isSubsetOf = function (a) {
                return this.every(function (x) {
                    return a.indexOf(x) !== -1;
                });
            };

            // ### Set.prototype.locate()
            // Array.prototype.indexOf() returns only the position of an element in the
            // array and not the position where one should be inserted.
            //
            // *@param {Set}* The element to locate
            // *@return {number}*
            Set.prototype.locate = function (x) {
                var left = 0, right = this.card - 1, middle, i = this.indexOf(x);

                if (i !== -1) {
                    return i;
                }

                while (left <= right) {
                    middle = left + Math.floor((right - left) / 2);
                    if (this[middle] < x) {
                        left = middle + 1;
                    } else Eif (this[middle] > x) {
                        right = middle - 1;
                    } else {
                        return middle;
                    }
                }
                return left;
            };

            // ### Set.prototype.map()
            // Works like the Array.prototype.map function
            //
            // *@param {function}* The mapping function
            // *@return {Set}*
            Set.prototype.map = function () {
                var args = [];
                for (var _i = 0; _i < (arguments.length - 0); _i++) {
                    args[_i] = arguments[_i + 0];
                }
                return new MathLib.Set(Array.prototype.map.apply(this, args));
            };

            // ### Set.prototype.plus()
            // Adds the argument to all elements in the set,
            // or if no argument is provided adds up all the elements in the set.
            //
            // *@param {number|MathLib object}*
            // *@return {Set|any}*
            Set.prototype.plus = function (n) {
                var sum = [];
                if (!arguments.length) {
                    return MathLib.plus.apply(null, this.toArray());
                } else if (n.type === 'set') {
                    this.forEach(function (x) {
                        n.forEach(function (y) {
                            sum.push(MathLib.plus(x, y));
                        });
                    });

                    return new MathLib.Set(sum);
                } else {
                    return this.map(function (x) {
                        return MathLib.plus(x, n);
                    });
                }
            };

            // ### Set.prototype.powerset()
            // Returns the powerset
            //
            // *@return {Set}*
            Set.prototype.powerset = function () {
                var flag, subset, i, ii, j, jj, powerset = [];

                for (i = 0, ii = Math.pow(2, this.card); i < ii; i++) {
                    flag = i.toString(2).split('').reverse();
                    subset = [];
                    for (j = 0, jj = this.card; j < jj; j++) {
                        if (flag[j] === '1') {
                            subset.push(this[j]);
                        }
                    }
                    powerset.push(new MathLib.Set(subset));
                }

                return new MathLib.Set(powerset);
            };

            // ### Set.prototype.reduce()
            // Works like the Array.prototype.reduce function
            //
            // *@return {any}*
            Set.prototype.reduce = function () {
                var args = [];
                for (var _i = 0; _i < (arguments.length - 0); _i++) {
                    args[_i] = arguments[_i + 0];
                }
                return Array.prototype.reduce.apply(this, arguments);
            };

            // ### Set.prototype.remove()
            // Removes a element from a set
            //
            // *@return {Set}*
            Set.prototype.remove = function (a) {
                var i = this.indexOf(a);
                Eif (i !== -1) {
                    this.splice(i, 1);
                    this.card--;
                }
                return this;
            };

            // ### Set.prototype.slice()
            // Works like the Array.prototype.slice function
            //
            // *@return {array}*
            Set.prototype.slice = function () {
                var args = [];
                for (var _i = 0; _i < (arguments.length - 0); _i++) {
                    args[_i] = arguments[_i + 0];
                }
                return Array.prototype.slice.apply(this, args);
            };

            // ### Set.prototype.some()
            // Works like the Array.prototype.some function
            //
            // *@return {boolean}*
            Set.prototype.some = function () {
                var args = [];
                for (var _i = 0; _i < (arguments.length - 0); _i++) {
                    args[_i] = arguments[_i + 0];
                }
                return Array.prototype.some.apply(this, args);
            };

            // ### Set.prototype.splice()
            // Works like the Array.prototype.splice function
            //
            // *@return {Set}*
            Set.prototype.splice = function () {
                var args = [];
                for (var _i = 0; _i < (arguments.length - 0); _i++) {
                    args[_i] = arguments[_i + 0];
                }
                return Array.prototype.splice.apply(this, args);
            };

            // ### Set.prototype.times()
            // Multiplies all elements in the set if no argument is passed.
            // Multiplies all elements by a argument if one is passed.
            //
            // *@param {number|MathLib object}*
            // *@return {Set}*
            Set.prototype.times = function (n) {
                if (!arguments.length) {
                    return MathLib.times.apply(null, this.toArray());
                } else {
                    return this.map(function (x) {
                        return MathLib.times(x, n);
                    });
                }
            };

            // ### Set.prototype.toArray()
            // Converts the set to an array
            //
            // *@return {array}*
            Set.prototype.toArray = function () {
                return Array.prototype.slice.call(this);
            };

            // ### Set.prototype.toContentMathML()
            // Returns the content MathML representation of the set
            //
            // *@return {string}*
            Set.prototype.toContentMathML = function () {
                if (this.isEmpty()) {
                    return '<emptyset/>';
                } else {
                    return this.reduce(function (old, cur) {
                        return old + MathLib.toContentMathML(cur);
                    }, '<set>') + '</set>';
                }
            };

            // ### Set.prototype.toLaTeX()
            // Returns the LaTeX representation of the set
            //
            // *@return {string}*
            Set.prototype.toLaTeX = function () {
                if (this.isEmpty()) {
                    return '\\emptyset';
                } else {
                    return this.reduce(function (old, cur) {
                        return old + MathLib.toLaTeX(cur) + ', ';
                    }, '\\{').slice(0, -2) + '\\}';
                }
            };

            // ### Set.prototype.toMathML()
            // Returns the (presentation) MathML representation of the set
            //
            // *@return {string}*
            Set.prototype.toMathML = function () {
                if (this.isEmpty()) {
                    return '<mi>&#x2205;</mi>';
                } else {
                    return this.reduce(function (old, cur) {
                        return old + MathLib.toMathML(cur) + '<mo>,</mo>';
                    }, '<mrow><mo>{</mo>').slice(0, -10) + '<mo>}</mo></mrow>';
                }
            };

            // ### Set.prototype.toString()
            // Returns a string representation of the set
            //
            // *@return {string}*
            Set.prototype.toString = function () {
                if (this.isEmpty()) {
                    return '∅';
                }
                return '{' + Array.prototype.join.call(this, ', ') + '}';
            };
            Set.fromTo = function (f, t, s) {
                if (typeof s === "undefined") { s = 1; }
                var i, set = [];
                Eif (f <= t) {
                    for (i = f; i <= t; i += s) {
                        set.push(i);
                    }
                    return new MathLib.Set(set);
                }
            };

            Set.createSetOperation = function (left, both, right) {
                return function (a) {
                    var set = [], i = 0, j = 0, tl = this.card, al = a.card;

                    while (i < tl && j < al) {
                        if (MathLib.compare(this[i], a[j]) < 0) {
                            if (left) {
                                set.push(this[i]);
                            }
                            i++;
                            continue;
                        }
                        if (MathLib.compare(this[i], a[j]) > 0) {
                            if (right) {
                                set.push(a[j]);
                            }
                            j++;
                            continue;
                        }
                        Eif (MathLib.isEqual(this[i], a[j])) {
                            if (both) {
                                set.push(this[i]);
                            }
                            i++;
                            j++;
                            continue;
                        }
                    }
                    if (left && j === al) {
                        set = set.concat(this.slice(i));
                    } else if (right && i === tl) {
                        set = set.concat(a.slice(j));
                    }
                    return new MathLib.Set(set);
                };
            };
            return Set;
        })();
        MathLib.Set = Set;
    })(MathLib || (MathLib = {}));