mathjs/dist/math.min.js

/**
 * math.js
 * https://github.com/josdejong/mathjs
 *
 * Math.js is an extensive math library for JavaScript and Node.js,
 * It features real and complex numbers, units, matrices, a large set of
 * mathematical functions, and a flexible expression parser.
 *
 * @version 0.15.0
 * @date    2013-10-26
 *
 * @license
 * Copyright (C) 2013 Jos de Jong <wjosdejong@gmail.com>
 *
 * Licensed under the Apache License, Version 2.0 (the "License"); you may not
 * use this file except in compliance with the License. You may obtain a copy
 * of the License at
 *
 * http://www.apache.org/licenses/LICENSE-2.0
 *
 * Unless required by applicable law or agreed to in writing, software
 * distributed under the License is distributed on an "AS IS" BASIS, WITHOUT
 * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the
 * License for the specific language governing permissions and limitations under
 * the License.
 */
!function(e){if("function"==typeof bootstrap)bootstrap("mathjs",e);else if("object"==typeof exports)module.exports=e();else if("function"==typeof define&&define.amd)define(e);else if("undefined"!=typeof ses){if(!ses.ok())return;ses.makeMathjs=e}else"undefined"!=typeof window?window.mathjs=e():global.mathjs=e()}(function(){return function e(t,n,r){function i(a,s){if(!n[a]){if(!t[a]){var u="function"==typeof require&&require;if(!s&&u)return u(a,!0);if(o)return o(a,!0);throw new Error("Cannot find module '"+a+"'")}var l=n[a]={exports:{}};t[a][0].call(l.exports,function(e){var n=t[a][1][e];return i(n?n:e)},l,l.exports,e,t,n,r)}return n[a].exports}for(var o="function"==typeof require&&require,a=0;a<r.length;a++)i(r[a]);return i}({1:[function(e,t){function n(t){var n={};if(n.options={matrix:{defaultType:"matrix"}},r.deepExtend(n.options,t),Object.defineProperty){var i=function(){throw new Error("Option math.options.precision is deprecated. Use math.format(value, precision) instead.")};Object.defineProperty(n.options,"precision",{get:i,set:i,enumerable:!1,configurable:!1});var o=function(){throw new Error("Option math.options.matrix.default is deprecated. Use math.options.matrix.defaultType instead.")};Object.defineProperty(n.options.matrix,"default",{get:o,set:o,enumerable:!1,configurable:!1})}return n.expression={},n.expression.node=e("./lib/expression/node/index.js"),n.expression.Scope=e("./lib/expression/Scope.js"),n.expression.Parser=e("./lib/expression/Parser.js"),n.expression.docs=e("./lib/expression/docs/index.js"),n.expr={},n.expr.Scope=function(){throw new Error("Moved to math.expression.Scope")},n.expr.Parser=function(){throw new Error("Moved to math.expression.Parser")},n.type={},n.type.Complex=e("./lib/type/Complex.js"),n.type.Range=e("./lib/type/Range.js"),n.type.Index=e("./lib/type/Index.js"),n.type.Matrix=e("./lib/type/Matrix.js"),n.type.Unit=e("./lib/type/Unit.js"),n.type.Help=e("./lib/type/Help.js"),n.collection=e("./lib/type/collection.js"),e("./lib/function/expression/eval.js")(n),e("./lib/function/expression/help.js")(n),e("./lib/function/expression/parse.js")(n),e("./lib/function/arithmetic/abs.js")(n),e("./lib/function/arithmetic/add.js")(n),e("./lib/function/arithmetic/add.js")(n),e("./lib/function/arithmetic/ceil.js")(n),e("./lib/function/arithmetic/cube.js")(n),e("./lib/function/arithmetic/divide.js")(n),e("./lib/function/arithmetic/edivide.js")(n),e("./lib/function/arithmetic/emultiply.js")(n),e("./lib/function/arithmetic/epow.js")(n),e("./lib/function/arithmetic/equal.js")(n),e("./lib/function/arithmetic/exp.js")(n),e("./lib/function/arithmetic/fix.js")(n),e("./lib/function/arithmetic/floor.js")(n),e("./lib/function/arithmetic/gcd.js")(n),e("./lib/function/arithmetic/larger.js")(n),e("./lib/function/arithmetic/largereq.js")(n),e("./lib/function/arithmetic/lcm.js")(n),e("./lib/function/arithmetic/log.js")(n),e("./lib/function/arithmetic/log10.js")(n),e("./lib/function/arithmetic/mod.js")(n),e("./lib/function/arithmetic/multiply.js")(n),e("./lib/function/arithmetic/pow.js")(n),e("./lib/function/arithmetic/round.js")(n),e("./lib/function/arithmetic/sign.js")(n),e("./lib/function/arithmetic/smaller.js")(n),e("./lib/function/arithmetic/smallereq.js")(n),e("./lib/function/arithmetic/sqrt.js")(n),e("./lib/function/arithmetic/square.js")(n),e("./lib/function/arithmetic/subtract.js")(n),e("./lib/function/arithmetic/unary.js")(n),e("./lib/function/arithmetic/unequal.js")(n),e("./lib/function/arithmetic/xgcd.js")(n),e("./lib/function/complex/arg.js")(n),e("./lib/function/complex/conj.js")(n),e("./lib/function/complex/re.js")(n),e("./lib/function/complex/im.js")(n),e("./lib/function/construction/boolean.js")(n),e("./lib/function/construction/complex.js")(n),e("./lib/function/construction/index.js")(n),e("./lib/function/construction/matrix.js")(n),e("./lib/function/construction/number.js")(n),e("./lib/function/construction/parser.js")(n),e("./lib/function/construction/string.js")(n),e("./lib/function/construction/unit.js")(n),e("./lib/function/matrix/concat.js")(n),e("./lib/function/matrix/det.js")(n),e("./lib/function/matrix/diag.js")(n),e("./lib/function/matrix/eye.js")(n),e("./lib/function/matrix/inv.js")(n),e("./lib/function/matrix/ones.js")(n),e("./lib/function/matrix/range.js")(n),e("./lib/function/matrix/size.js")(n),e("./lib/function/matrix/squeeze.js")(n),e("./lib/function/matrix/subset.js")(n),e("./lib/function/matrix/transpose.js")(n),e("./lib/function/matrix/zeros.js")(n),e("./lib/function/probability/factorial.js")(n),e("./lib/function/probability/random.js")(n),e("./lib/function/statistics/min.js")(n),e("./lib/function/statistics/max.js")(n),e("./lib/function/statistics/mean.js")(n),e("./lib/function/trigonometry/acos.js")(n),e("./lib/function/trigonometry/asin.js")(n),e("./lib/function/trigonometry/atan.js")(n),e("./lib/function/trigonometry/atan2.js")(n),e("./lib/function/trigonometry/cos.js")(n),e("./lib/function/trigonometry/cot.js")(n),e("./lib/function/trigonometry/csc.js")(n),e("./lib/function/trigonometry/sec.js")(n),e("./lib/function/trigonometry/sin.js")(n),e("./lib/function/trigonometry/tan.js")(n),e("./lib/function/units/in.js")(n),e("./lib/function/utils/clone.js")(n),e("./lib/function/utils/format.js")(n),e("./lib/function/utils/import.js")(n),e("./lib/function/utils/map.js")(n),e("./lib/function/utils/print.js")(n),e("./lib/function/utils/select.js")(n),e("./lib/function/utils/typeof.js")(n),e("./lib/function/utils/forEach.js")(n),e("./lib/constants.js")(n),n.chaining={},n.chaining.Selector=e("./lib/chaining/Selector.js")(n),n.expr.Selector=function(){throw new Error("Moved to math.expression.Selector")},n}var r=e("./lib/util/object");t.exports=n;var i=function(){throw new Error('Static function calls are deprecated. Create an instance of math.js:\n	"var math = require(\'mathjs\')();" on node.js, \n	"var math = mathjs();" in the browser.')},o=n();for(var a in o)if(o.hasOwnProperty(a)){var s=o[a];"function"==typeof s?n[a]=i:Object.defineProperty&&Object.defineProperty(n,a,{get:i,set:i,enumerable:!0,configurable:!1})}"undefined"!=typeof window&&(window.math=n)},{"./lib/chaining/Selector.js":2,"./lib/constants.js":3,"./lib/expression/Parser.js":4,"./lib/expression/Scope.js":5,"./lib/expression/docs/index.js":101,"./lib/expression/node/index.js":114,"./lib/function/arithmetic/abs.js":115,"./lib/function/arithmetic/add.js":116,"./lib/function/arithmetic/ceil.js":117,"./lib/function/arithmetic/cube.js":118,"./lib/function/arithmetic/divide.js":119,"./lib/function/arithmetic/edivide.js":120,"./lib/function/arithmetic/emultiply.js":121,"./lib/function/arithmetic/epow.js":122,"./lib/function/arithmetic/equal.js":123,"./lib/function/arithmetic/exp.js":124,"./lib/function/arithmetic/fix.js":125,"./lib/function/arithmetic/floor.js":126,"./lib/function/arithmetic/gcd.js":127,"./lib/function/arithmetic/larger.js":128,"./lib/function/arithmetic/largereq.js":129,"./lib/function/arithmetic/lcm.js":130,"./lib/function/arithmetic/log.js":131,"./lib/function/arithmetic/log10.js":132,"./lib/function/arithmetic/mod.js":133,"./lib/function/arithmetic/multiply.js":134,"./lib/function/arithmetic/pow.js":135,"./lib/function/arithmetic/round.js":136,"./lib/function/arithmetic/sign.js":137,"./lib/function/arithmetic/smaller.js":138,"./lib/function/arithmetic/smallereq.js":139,"./lib/function/arithmetic/sqrt.js":140,"./lib/function/arithmetic/square.js":141,"./lib/function/arithmetic/subtract.js":142,"./lib/function/arithmetic/unary.js":143,"./lib/function/arithmetic/unequal.js":144,"./lib/function/arithmetic/xgcd.js":145,"./lib/function/complex/arg.js":146,"./lib/function/complex/conj.js":147,"./lib/function/complex/im.js":148,"./lib/function/complex/re.js":149,"./lib/function/construction/boolean.js":150,"./lib/function/construction/complex.js":151,"./lib/function/construction/index.js":152,"./lib/function/construction/matrix.js":153,"./lib/function/construction/number.js":154,"./lib/function/construction/parser.js":155,"./lib/function/construction/string.js":156,"./lib/function/construction/unit.js":157,"./lib/function/expression/eval.js":158,"./lib/function/expression/help.js":159,"./lib/function/expression/parse.js":160,"./lib/function/matrix/concat.js":161,"./lib/function/matrix/det.js":162,"./lib/function/matrix/diag.js":163,"./lib/function/matrix/eye.js":164,"./lib/function/matrix/inv.js":165,"./lib/function/matrix/ones.js":166,"./lib/function/matrix/range.js":167,"./lib/function/matrix/size.js":168,"./lib/function/matrix/squeeze.js":169,"./lib/function/matrix/subset.js":170,"./lib/function/matrix/transpose.js":171,"./lib/function/matrix/zeros.js":172,"./lib/function/probability/factorial.js":173,"./lib/function/probability/random.js":174,"./lib/function/statistics/max.js":175,"./lib/function/statistics/mean.js":176,"./lib/function/statistics/min.js":177,"./lib/function/trigonometry/acos.js":178,"./lib/function/trigonometry/asin.js":179,"./lib/function/trigonometry/atan.js":180,"./lib/function/trigonometry/atan2.js":181,"./lib/function/trigonometry/cos.js":182,"./lib/function/trigonometry/cot.js":183,"./lib/function/trigonometry/csc.js":184,"./lib/function/trigonometry/sec.js":185,"./lib/function/trigonometry/sin.js":186,"./lib/function/trigonometry/tan.js":187,"./lib/function/units/in.js":188,"./lib/function/utils/clone.js":189,"./lib/function/utils/forEach.js":190,"./lib/function/utils/format.js":191,"./lib/function/utils/import.js":192,"./lib/function/utils/map.js":193,"./lib/function/utils/print.js":194,"./lib/function/utils/select.js":195,"./lib/function/utils/typeof.js":196,"./lib/type/Complex.js":197,"./lib/type/Help.js":198,"./lib/type/Index.js":199,"./lib/type/Matrix.js":200,"./lib/type/Range.js":201,"./lib/type/Unit.js":202,"./lib/type/collection.js":203,"./lib/util/object":209}],2:[function(e,t){t.exports=function(t){function n(e){if(!(this instanceof n))throw new SyntaxError("Selector constructor must be called with the new operator");this.value=e instanceof n?e.value:e}function r(e,t){var r=Array.prototype.slice;n.prototype[e]="function"==typeof t?function(){var e=[this.value].concat(r.call(arguments,0));return new n(t.apply(this,e))}:new n(t)}var i=e("../util/index"),o=i.string;n.prototype={done:function(){return this.value},get:function(){throw new Error("Selector.get is removed. Use Selector.subset(index) instead.")},set:function(){throw new Error("Selector.set is removed. Use Selector.subset(index, replacement) instead.")},valueOf:function(){return this.value},toString:function(){return o.format(this.value)}},n.createProxy=r;for(var a in t)t.hasOwnProperty(a)&&a&&r(a,t[a]);return i.types.addType("selector",n),n}},{"../util/index":207}],3:[function(e,t){t.exports=function(t){var n=e("./type/Complex");t.pi=Math.PI,t.e=Math.E,t.tau=2*Math.PI,t.i=new n(0,1),t.Infinity=1/0,t.NaN=0/0,t["true"]=!0,t["false"]=!1,t.E=Math.E,t.LN2=Math.LN2,t.LN10=Math.LN10,t.LOG2E=Math.LOG2E,t.LOG10E=Math.LOG10E,t.PI=Math.PI,t.SQRT1_2=Math.SQRT1_2,t.SQRT2=Math.SQRT2}},{"./type/Complex":197}],4:[function(e,t){function n(e){if(!(this instanceof n))throw new SyntaxError("Parser constructor must be called with the new operator");this.math=e,this.scope=new r(e)}var r=e("./Scope");n.prototype.parse=function(e){return this.math.parse(e,this.scope)},n.prototype.eval=function(e){var t=this.math.parse(e,this.scope);return t.eval()},n.prototype.get=function(e){return this.scope.get(e)},n.prototype.set=function(e,t){return this.scope.set(e,t)},n.prototype.remove=function(e){this.scope.remove(e)},n.prototype.clear=function(){this.scope.clear()},t.exports=n},{"./Scope":5}],5:[function(e,t){function n(e,t,r){this.math=e,this.parentScope=null,this.subScopes=null,this.symbols={},this.cache={},t&&(t instanceof n?this.parentScope=t:t instanceof Object&&(this.symbols=t)),r&&r instanceof Object&&(this.symbols=r)}var r=e("../type/Unit");n.prototype={createSubScope:function(){var e=new n(this.math,this);return this.subScopes||(this.subScopes=[]),this.subScopes.push(e),e},get:function(e){var t;if(t=this.symbols[e],void 0!==t)return t;var n=this.cache[e];if(n)return n[e];for(var i=this.parentScope;i;){if(t=i.symbols[e],void 0!==t)return this.cache[e]=i.symbols,t;i=i.parentScope}return t=this.math[e],void 0!==t?(this.cache[e]=this.math,t):r.isPlainUnit(e)?(t=new r(null,e),this.cache[e]={},this.cache[e][e]=t,t):void 0},has:function(e){return void 0!==this.symbols[e]},set:function(e,t){return this.symbols[e]=t},remove:function(e){delete this.symbols[e]},clear:function(){var e=this.symbols;for(var t in e)e.hasOwnProperty(t)&&delete e[t];if(this.subScopes)for(var n=this.subScopes,r=0,i=n.length;i>r;r++)n[r].clear();this.clearCache()},clearCache:function(){this.cache={}}},n.context=[],t.exports=n},{"../type/Unit":202}],6:[function(e,t){t.exports={name:"Infinity",category:"Constants",syntax:["Infinity"],description:"Infinity, a number which is larger than the maximum number that can be handled by a floating point number.",examples:["Infinity","1 / 0"],seealso:[]}},{}],7:[function(e,t){t.exports={name:"LN10",category:"Constants",syntax:["LN10"],description:"Returns the natural logarithm of 10, approximately equal to 2.302",examples:["LN10","log(10)"],seealso:[]}},{}],8:[function(e,t){t.exports={name:"LN2",category:"Constants",syntax:["LN2"],description:"Returns the natural logarithm of 2, approximately equal to 0.693",examples:["LN2","log(2)"],seealso:[]}},{}],9:[function(e,t){t.exports={name:"LOG10E",category:"Constants",syntax:["LOG10E"],description:"Returns the base-10 logarithm of E, approximately equal to 0.434",examples:["LOG10E","log(e, 10)"],seealso:[]}},{}],10:[function(e,t){t.exports={name:"LOG2E",category:"Constants",syntax:["LOG2E"],description:"Returns the base-2 logarithm of E, approximately equal to 1.442",examples:["LOG2E","log(e, 2)"],seealso:[]}},{}],11:[function(e,t){t.exports={name:"NaN",category:"Constants",syntax:["NaN"],description:"Not a number",examples:["NaN","0 / 0"],seealso:[]}},{}],12:[function(e,t){t.exports={name:"SQRT1_2",category:"Constants",syntax:["SQRT1_2"],description:"Returns the square root of 1/2, approximately equal to 0.707",examples:["SQRT1_2","sqrt(1/2)"],seealso:[]}},{}],13:[function(e,t){t.exports={name:"SQRT2",category:"Constants",syntax:["SQRT2"],description:"Returns the square root of 2, approximately equal to 1.414",examples:["SQRT2","sqrt(2)"],seealso:[]}},{}],14:[function(e,t){t.exports={name:"e",category:"Constants",syntax:["e"],description:"Euler's number, the base of the natural logarithm. Approximately equal to 2.71828",examples:["e","e ^ 2","exp(2)","log(e)"],seealso:["exp"]}},{}],15:[function(e,t){t.exports={name:"false",category:"Constants",syntax:["false"],description:"Boolean value false",examples:["false"],seealso:["true"]}},{}],16:[function(e,t){t.exports={name:"i",category:"Constants",syntax:["i"],description:"Imaginary unit, defined as i*i=-1. A complex number is described as a + b*i, where a is the real part, and b is the imaginary part.",examples:["i","i * i","sqrt(-1)"],seealso:[]}},{}],17:[function(e,t){t.exports={name:"pi",category:"Constants",syntax:["pi"],description:"The number pi is a mathematical constant that is the ratio of a circle's circumference to its diameter, and is approximately equal to 3.14159",examples:["pi","sin(pi/2)"],seealso:["tau"]}},{}],18:[function(e,t){t.exports={name:"tau",category:"Constants",syntax:["pi"],description:"Tau is the ratio constant of a circle's circumference to radius, equal to 2 * pi, approximately 6.2832.",examples:["tau","2 * pi"],seealso:["pi"]}},{}],19:[function(e,t){t.exports={name:"true",category:"Constants",syntax:["true"],description:"Boolean value true",examples:["true"],seealso:["false"]}},{}],20:[function(e,t){t.exports={name:"abs",category:"Arithmetic",syntax:["abs(x)"],description:"Compute the absolute value.",examples:["abs(3.5)","abs(-4.2)"],seealso:["sign"]}},{}],21:[function(e,t){t.exports={name:"add",category:"Operators",syntax:["x + y","add(x, y)"],description:"Add two values.",examples:["2.1 + 3.6","ans - 3.6","3 + 2i",'"hello" + " world"',"3 cm + 2 inch"],seealso:["subtract"]}},{}],22:[function(e,t){t.exports={name:"ceil",category:"Arithmetic",syntax:["ceil(x)"],description:"Round a value towards plus infinity.If x is complex, both real and imaginary part are rounded towards plus infinity.",examples:["ceil(3.2)","ceil(3.8)","ceil(-4.2)"],seealso:["floor","fix","round"]}},{}],23:[function(e,t){t.exports={name:"cube",category:"Arithmetic",syntax:["cube(x)"],description:"Compute the cube of a value. The cube of x is x * x * x.",examples:["cube(2)","2^3","2 * 2 * 2"],seealso:["multiply","square","pow"]}},{}],24:[function(e,t){t.exports={name:"divide",category:"Operators",syntax:["x / y","divide(x, y)"],description:"Divide two values.",examples:["2 / 3","ans * 3","4.5 / 2","3 + 4 / 2","(3 + 4) / 2","18 km / 4.5"],seealso:["multiply"]}},{}],25:[function(e,t){t.exports={name:"edivide",category:"Operators",syntax:["x ./ y","edivide(x, y)"],description:"divide two values element wise.",examples:["a = [1, 2, 3; 4, 5, 6]","b = [2, 1, 1; 3, 2, 5]","a ./ b"],seealso:["multiply","emultiply","divide"]}},{}],26:[function(e,t){t.exports={name:"emultiply",category:"Operators",syntax:["x .* y","emultiply(x, y)"],description:"multiply two values element wise.",examples:["a = [1, 2, 3; 4, 5, 6]","b = [2, 1, 1; 3, 2, 5]","a .* b"],seealso:["multiply","divide","edivide"]}},{}],27:[function(e,t){t.exports={name:"epow",category:"Operators",syntax:["x .^ y","epow(x, y)"],description:"Calculates the power of x to y element wise.",examples:["a = [1, 2, 3; 4, 5, 6]","a .^ 2"],seealso:["pow"]}},{}],28:[function(e,t){t.exports={name:"equal",category:"Operators",syntax:["x == y","equal(x, y)"],description:"Check equality of two values. Returns 1 if the values are equal, and 0 if not.",examples:["2+2 == 3","2+2 == 4","a = 3.2","b = 6-2.8","a == b","50cm == 0.5m"],seealso:["unequal","smaller","larger","smallereq","largereq"]}},{}],29:[function(e,t){t.exports={name:"exp",category:"Arithmetic",syntax:["exp(x)"],description:"Calculate the exponent of a value.",examples:["exp(1.3)","e ^ 1.3","log(exp(1.3))","x = 2.4","(exp(i*x) == cos(x) + i*sin(x))   # Euler's formula"],seealso:["square","multiply","log"]}},{}],30:[function(e,t){t.exports={name:"fix",category:"Arithmetic",syntax:["fix(x)"],description:"Round a value towards zero.If x is complex, both real and imaginary part are rounded towards zero.",examples:["fix(3.2)","fix(3.8)","fix(-4.2)","fix(-4.8)"],seealso:["ceil","floor","round"]}},{}],31:[function(e,t){t.exports={name:"floor",category:"Arithmetic",syntax:["floor(x)"],description:"Round a value towards minus infinity.If x is complex, both real and imaginary part are rounded towards minus infinity.",examples:["floor(3.2)","floor(3.8)","floor(-4.2)"],seealso:["ceil","fix","round"]}},{}],32:[function(e,t){t.exports={name:"gcd",category:"Arithmetic",syntax:["gcd(a, b)","gcd(a, b, c, ...)"],description:"Compute the greatest common divisor.",examples:["gcd(8, 12)","gcd(-4, 6)","gcd(25, 15, -10)"],seealso:["lcm","xgcd"]}},{}],33:[function(e,t){t.exports={name:"larger",category:"Operators",syntax:["x > y","larger(x, y)"],description:"Check if value x is larger than y. Returns 1 if x is larger than y, and 0 if not.",examples:["2 > 3","5 > 2*2","a = 3.3","b = 6-2.8","(a > b)","(b < a)","5 cm > 2 inch"],seealso:["equal","unequal","smaller","smallereq","largereq"]}},{}],34:[function(e,t){t.exports={name:"largereq",category:"Operators",syntax:["x >= y","largereq(x, y)"],description:"Check if value x is larger or equal to y. Returns 1 if x is larger or equal to y, and 0 if not.",examples:["2 > 1+1","2 >= 1+1","a = 3.2","b = 6-2.8","(a > b)"],seealso:["equal","unequal","smallereq","smaller","largereq"]}},{}],35:[function(e,t){t.exports={name:"lcm",category:"Arithmetic",syntax:["lcm(x, y)"],description:"Compute the least common multiple.",examples:["lcm(4, 6)","lcm(6, 21)","lcm(6, 21, 5)"],seealso:["gcd"]}},{}],36:[function(e,t){t.exports={name:"log",category:"Arithmetic",syntax:["log(x)","log(x, base)"],description:"Compute the logarithm of a value. If no base is provided, the natural logarithm of x is calculated. If base if provided, the logarithm is calculated for the specified base. log(x, base) is defined as log(x) / log(base).",examples:["log(3.5)","a = log(2.4)","exp(a)","10 ^ 3","log(1000, 10)","log(1000) / log(10)","b = logb(1024, 2)","2 ^ b"],seealso:["exp","log10"]}},{}],37:[function(e,t){t.exports={name:"log10",category:"Arithmetic",syntax:["log10(x)"],description:"Compute the 10-base logarithm of a value.",examples:["log10(1000)","10 ^ 3","log10(0.01)","log(1000) / log(10)","log(1000, 10)"],seealso:["exp","log"]}},{}],38:[function(e,t){t.exports={name:"mod",category:"Operators",syntax:["x % y","x mod y","mod(x, y)"],description:"Calculates the modulus, the remainder of an integer division.",examples:["7 % 3","11 % 2","10 mod 4","function isOdd(x) = x % 2","isOdd(2)","isOdd(3)"],seealso:[]}},{}],39:[function(e,t){t.exports={name:"multiply",category:"Operators",syntax:["x * y","multiply(x, y)"],description:"multiply two values.",examples:["2.1 * 3.6","ans / 3.6","2 * 3 + 4","2 * (3 + 4)","3 * 2.1 km"],seealso:["divide"]}},{}],40:[function(e,t){t.exports={name:"pow",category:"Operators",syntax:["x ^ y","pow(x, y)"],description:"Calculates the power of x to y, x^y.",examples:["2^3 = 8","2*2*2","1 + e ^ (pi * i)"],seealso:["unequal","smaller","larger","smallereq","largereq"]}},{}],41:[function(e,t){t.exports={name:"round",category:"Arithmetic",syntax:["round(x)","round(x, n)"],description:"round a value towards the nearest integer.If x is complex, both real and imaginary part are rounded towards the nearest integer. When n is specified, the value is rounded to n decimals.",examples:["round(3.2)","round(3.8)","round(-4.2)","round(-4.8)","round(pi, 3)","round(123.45678, 2)"],seealso:["ceil","floor","fix"]}},{}],42:[function(e,t){t.exports={name:"sign",category:"Arithmetic",syntax:["sign(x)"],description:"Compute the sign of a value. The sign of a value x is 1 when x>1, -1 when x<0, and 0 when x=0.",examples:["sign(3.5)","sign(-4.2)","sign(0)"],seealso:["abs"]}},{}],43:[function(e,t){t.exports={name:"smaller",category:"Operators",syntax:["x < y","smaller(x, y)"],description:"Check if value x is smaller than value y. Returns 1 if x is smaller than y, and 0 if not.",examples:["2 < 3","5 < 2*2","a = 3.3","b = 6-2.8","(a < b)","5 cm < 2 inch"],seealso:["equal","unequal","larger","smallereq","largereq"]}},{}],44:[function(e,t){t.exports={name:"smallereq",category:"Operators",syntax:["x <= y","smallereq(x, y)"],description:"Check if value x is smaller or equal to value y. Returns 1 if x is smaller than y, and 0 if not.",examples:["2 < 1+1","2 <= 1+1","a = 3.2","b = 6-2.8","(a < b)"],seealso:["equal","unequal","larger","smaller","largereq"]}},{}],45:[function(e,t){t.exports={name:"sqrt",category:"Arithmetic",syntax:["sqrt(x)"],description:"Compute the square root value. If x = y * y, then y is the square root of x.",examples:["sqrt(25)","5 * 5","sqrt(-1)"],seealso:["square","multiply"]}},{}],46:[function(e,t){t.exports={name:"square",category:"Arithmetic",syntax:["square(x)"],description:"Compute the square of a value. The square of x is x * x.",examples:["square(3)","sqrt(9)","3^2","3 * 3"],seealso:["multiply","pow","sqrt","cube"]}},{}],47:[function(e,t){t.exports={name:"subtract",category:"Operators",syntax:["x - y","subtract(x, y)"],description:"subtract two values.",examples:["5.3 - 2","ans + 2","2/3 - 1/6","2 * 3 - 3","2.1 km - 500m"],seealso:["add"]}},{}],48:[function(e,t){t.exports={name:"unary",category:"Operators",syntax:["-x","unary(x)"],description:"Inverse the sign of a value.",examples:["-4.5","-(-5.6)"],seealso:["add","subtract"]}},{}],49:[function(e,t){t.exports={name:"unequal",category:"Operators",syntax:["x != y","unequal(x, y)"],description:"Check unequality of two values. Returns 1 if the values are unequal, and 0 if they are equal.",examples:["2+2 != 3","2+2 != 4","a = 3.2","b = 6-2.8","a != b","50cm != 0.5m","5 cm != 2 inch"],seealso:["equal","smaller","larger","smallereq","largereq"]}},{}],50:[function(e,t){t.exports={name:"xgcd",category:"Arithmetic",syntax:["xgcd(a, b)"],description:"Calculate the extended greatest common divisor for two values",examples:["xgcd(8, 12)","gcd(8, 12)","xgcd(36163, 21199)"],seealso:["gcd","lcm"]}},{}],51:[function(e,t){t.exports={name:"arg",category:"Complex",syntax:["arg(x)"],description:"Compute the argument of a complex value. If x = a+bi, the argument is computed as atan2(b, a).",examples:["arg(2 + 2i)","atan2(3, 2)","arg(2 - 3i)"],seealso:["re","im","conj","abs"]}},{}],52:[function(e,t){t.exports={name:"conj",category:"Complex",syntax:["conj(x)"],description:"Compute the complex conjugate of a complex value. If x = a+bi, the complex conjugate is a-bi.",examples:["conj(2 + 3i)","conj(2 - 3i)","conj(-5.2i)"],seealso:["re","im","abs","arg"]}},{}],53:[function(e,t){t.exports={name:"im",category:"Complex",syntax:["im(x)"],description:"Get the imaginary part of a complex number.",examples:["im(2 + 3i)","re(2 + 3i)","im(-5.2i)","im(2.4)"],seealso:["re","conj","abs","arg"]}},{}],54:[function(e,t){t.exports={name:"re",category:"Complex",syntax:["re(x)"],description:"Get the real part of a complex number.",examples:["re(2 + 3i)","im(2 + 3i)","re(-5.2i)","re(2.4)"],seealso:["im","conj","abs","arg"]}},{}],55:[function(e,t){t.exports={name:"boolean",category:"Type",syntax:["x","boolean(x)"],description:"Convert a string or number into a boolean.",examples:["boolean(0)","boolean(1)","boolean(3)",'boolean("true")','boolean("false")',"boolean([1, 0, 1, 1])"],seealso:["complex","index","matrix","number","string","unit"]}},{}],56:[function(e,t){t.exports={name:"complex",category:"Type",syntax:["complex()","complex(re, im)","complex(string)"],description:"Create a complex number.",examples:["complex()","complex(2, 3)",'complex("7 - 2i")'],seealso:["boolean","index","matrix","number","string","unit"]}},{}],57:[function(e,t){t.exports={name:"index",category:"Type",syntax:["[start]","[start:end]","[start:step:end]","[start1, start 2, ...]","[start1:end1, start2:end2, ...]","[start1:step1:end1, start2:step2:end2, ...]"],description:"Create an index to get or replace a subset of a matrix",examples:["[]","[1, 2, 3]","A = [1, 2, 3; 4, 5, 6]","A[1, :]","A[1, 2] = 50","A[0:2, 0:2] = ones(2, 2)"],seealso:["boolean","complex","matrix,","number","range","string","unit"]}},{}],58:[function(e,t){t.exports={name:"matrix",category:"Type",syntax:["[]","[a1, b1, ...; a2, b2, ...]","matrix()","matrix([...])"],description:"Create a matrix.",examples:["[]","[1, 2, 3]","[1, 2, 3; 4, 5, 6]","matrix()","matrix([3, 4])"],seealso:["boolean","complex","index","number","string","unit"]}},{}],59:[function(e,t){t.exports={name:"number",category:"Type",syntax:["x","number(x)"],description:"Create a number or convert a string or boolean into a number.",examples:["2","2e3","4.05","number(2)",'number("7.2")',"number(true)","number([true, false, true, true])"],seealso:["boolean","complex","index","matrix","string","unit"]}},{}],60:[function(e,t){t.exports={name:"string",category:"Type",syntax:['"text"',"string(x)"],description:"Create a string or convert a value to a string",examples:['"Hello World!"',"string(4.2)","string(3 + 2i)"],seealso:["boolean","complex","index","matrix","number","unit"]}},{}],61:[function(e,t){t.exports={name:"unit",category:"Type",syntax:["value unit","unit(value, unit)","unit(string)"],description:"Create a unit.",examples:["5.5 mm","3 inch",'unit(7.1, "kilogram")','unit("23 deg")'],seealso:["boolean","complex","index","matrix","number","string"]}},{}],62:[function(e,t){t.exports={name:"eval",category:"Expression",syntax:["eval(expression)","eval([expr1, expr2, expr3, ...])"],description:"Evaluate an expression or an array with expressions.",examples:['eval("2 + 3")','eval("sqrt(" + 4 + ")")'],seealso:[]}},{}],63:[function(e,t){t.exports={name:"help",category:"Expression",syntax:["help(object)","help(string)"],description:"Display documentation on a function or data type.",examples:["help(sqrt)",'help("complex")'],seealso:[]}},{}],64:[function(e,t){t.exports={name:"concat",category:"Matrix",syntax:["concat(a, b, c, ...)","concat(a, b, c, ..., dim)"],description:"Concatenate matrices. By default, the matrices are concatenated by the first dimension. The dimension on which to concatenate can be provided as last argument.",examples:["a = [1, 2; 5, 6]","b = [3, 4; 7, 8]","concat(a, b)","[a, b]","concat(a, b, 2)","[a; b]"],seealso:["det","diag","eye","inv","ones","range","size","squeeze","subset","transpose","zeros"]}},{}],65:[function(e,t){t.exports={name:"det",category:"Matrix",syntax:["det(x)"],description:"Calculate the determinant of a matrix",examples:["det([1, 2; 3, 4])","det([-2, 2, 3; -1, 1, 3; 2, 0, -1])"],seealso:["concat","diag","eye","inv","ones","range","size","squeeze","subset","transpose","zeros"]}},{}],66:[function(e,t){t.exports={name:"diag",category:"Matrix",syntax:["diag(x)","diag(x, k)"],description:"Create a diagonal matrix or retrieve the diagonal of a matrix. When x is a vector, a matrix with the vector values on the diagonal will be returned. When x is a matrix, a vector with the diagonal values of the matrix is returned.When k is provided, the k-th diagonal will be filled in or retrieved, if k is positive, the values are placed on the super diagonal. When k is negative, the values are placed on the sub diagonal.",examples:["diag(1:3)","diag(1:3, 1)","a = [1, 2, 3; 4, 5, 6; 7, 8, 9]","diag(a)"],seealso:["concat","det","eye","inv","ones","range","size","squeeze","subset","transpose","zeros"]}},{}],67:[function(e,t){t.exports={name:"eye",category:"Matrix",syntax:["eye(n)","eye(m, n)","eye([m, n])","eye"],description:"Returns the identity matrix with size m-by-n. The matrix has ones on the diagonal and zeros elsewhere.",examples:["eye(3)","eye(3, 5)","a = [1, 2, 3; 4, 5, 6]","eye(size(a))"],seealso:["concat","det","diag","inv","ones","range","size","squeeze","subset","transpose","zeros"]}},{}],68:[function(e,t){t.exports={name:"inv",category:"Matrix",syntax:["inv(x)"],description:"Calculate the inverse of a matrix",examples:["inv([1, 2; 3, 4])","inv(4)","1 / 4"],seealso:["concat","det","diag","eye","ones","range","size","squeeze","subset","transpose","zeros"]}},{}],69:[function(e,t){t.exports={name:"ones",category:"Matrix",syntax:["ones(n)","ones(m, n)","ones(m, n, p, ...)","ones([m, n])","ones([m, n, p, ...])","ones"],description:"Create a matrix containing ones.",examples:["ones(3)","ones(3, 5)","ones([2,3]) * 4.5","a = [1, 2, 3; 4, 5, 6]","ones(size(a))"],seealso:["concat","det","diag","eye","inv","range","size","squeeze","subset","transpose","zeros"]}},{}],70:[function(e,t){t.exports={name:"range",category:"Type",syntax:["start:end","start:step:end","range(start, end)","range(start, end, step)","range(string)"],description:"Create a range. Lower bound of the range is included, upper bound is excluded.",examples:["1:5","3:-1:-3","range(3, 7)","range(0, 12, 2)",'range("4:10")',"a = [1, 2, 3, 4; 5, 6, 7, 8]","a(1:2, 1:2)"],seealso:["concat","det","diag","eye","inv","ones","size","squeeze","subset","transpose","zeros"]}},{}],71:[function(e,t){t.exports={name:"size",category:"Matrix",syntax:["size(x)"],description:"Calculate the size of a matrix.",examples:["size(2.3)",'size("hello world")',"a = [1, 2; 3, 4; 5, 6]","size(a)","size(1:6)"],seealso:["concat","det","diag","eye","inv","ones","range","squeeze","subset","transpose","zeros"]}},{}],72:[function(e,t){t.exports={name:"squeeze",category:"Matrix",syntax:["squeeze(x)"],description:"Remove singleton dimensions from a matrix.",examples:["a = zeros(1,3,2)","size(squeeze(a))","b = zeros(3,1,1)","size(squeeze(b))"],seealso:["concat","det","diag","eye","inv","ones","range","size","subset","transpose","zeros"]}},{}],73:[function(e,t){t.exports={name:"subset",category:"Matrix",syntax:["value(index)","value(index) = replacement","subset(value, [index])","subset(value, [index], replacement)"],description:"Get or set a subset of a matrix or string. Indexes are one-based. Both the ranges lower-bound and upper-bound are included.",examples:["d = [1, 2; 3, 4]","e = []","e(1, 1:2) = [5, 6]","e(2, :) = [7, 8]","f = d * e","f(2, 1)","f(:, 1)"],seealso:["concat","det","diag","eye","inv","ones","range","size","squeeze","transpose","zeros"]}
},{}],74:[function(e,t){t.exports={name:"transpose",category:"Matrix",syntax:["x'","transpose(x)"],description:"Transpose a matrix",examples:["a = [1, 2, 3; 4, 5, 6]","a'","transpose(a)"],seealso:["concat","det","diag","eye","inv","ones","range","size","squeeze","subset","zeros"]}},{}],75:[function(e,t){t.exports={name:"zeros",category:"Matrix",syntax:["zeros(n)","zeros(m, n)","zeros(m, n, p, ...)","zeros([m, n])","zeros([m, n, p, ...])","zeros"],description:"Create a matrix containing zeros.",examples:["zeros(3)","zeros(3, 5)","a = [1, 2, 3; 4, 5, 6]","zeros(size(a))"],seealso:["concat","det","diag","eye","inv","ones","range","size","squeeze","subset","transpose"]}},{}],76:[function(e,t){t.exports={name:"distribution",category:"Probability",syntax:["distribution(name)","distribution(name, arg1, arg2, ...)"],description:'Create a distribution object of a specific type. A distribution object contains functions `random([size,] [min,] [max])`, `randomInt([size,] [min,] [max])`, and `pickRandom(array)`. Available types of distributions: "uniform", "normal". Note that the function distribution is currently not available via the expression parser.',examples:[],seealso:["random","randomInt"]}},{}],77:[function(e,t){t.exports={name:"factorial",category:"Probability",syntax:["x!","factorial(x)"],description:"Compute the factorial of a value",examples:["5!","5*4*3*2*1","3!"],seealso:[]}},{}],78:[function(e,t){t.exports={name:"pickRandom",category:"Probability",syntax:["pickRandom(array)"],description:"Pick a random entry from a given array.",examples:["pickRandom(0:10)","pickRandom([1, 3, 1, 6])"],seealso:["distribution","random","randomInt"]}},{}],79:[function(e,t){t.exports={name:"random",category:"Probability",syntax:["random()","random(max)","random(min, max)","random(size)","random(size, max)","random(size, min, max)"],description:"Return a random number.",examples:["random()","random(10, 20)","random([2, 3])"],seealso:["distribution","pickRandom","randomInt"]}},{}],80:[function(e,t){t.exports={name:"randInt",category:"Probability",syntax:["randInt()","randInt(max)","randInt(min, max)","randInt(size)","randInt(size, max)","randInt(size, min, max)"],description:"Return a random integer number",examples:["randInt()","randInt(10, 20)","randInt([2, 3], 10)"],seealso:["distribution","pickRandom","random"]}},{}],81:[function(e,t){t.exports={name:"max",category:"Statistics",syntax:["max(a, b, c, ...)","max(A)","max(A, dim)"],description:"Compute the maximum value of a list of values.",examples:["max(2, 3, 4, 1)","max([2, 3, 4, 1])","max([2, 5; 4, 3], 0)","max([2, 5; 4, 3], 1)","max(2.7, 7.1, -4.5, 2.0, 4.1)","min(2.7, 7.1, -4.5, 2.0, 4.1)"],seealso:["mean","min"]}},{}],82:[function(e,t){t.exports={name:"mean",category:"Statistics",syntax:["mean(a, b, c, ...)","mean(A)","mean(A, dim)"],description:"Compute the arithmetic mean of a list of values.",examples:["mean(2, 3, 4, 1)","mean([2, 3, 4, 1])","mean([2, 5; 4, 3], 0)","mean([2, 5; 4, 3], 1)","mean([1.0, 2.7, 3.2, 4.0])"],seealso:["max","min"]}},{}],83:[function(e,t){t.exports={name:"min",category:"Statistics",syntax:["min(a, b, c, ...)","min(A)","min(A, dim)"],description:"Compute the minimum value of a list of values.",examples:["min(2, 3, 4, 1)","min([2, 3, 4, 1])","min([2, 5; 4, 3], 0)","min([2, 5; 4, 3], 1)","min(2.7, 7.1, -4.5, 2.0, 4.1)","max(2.7, 7.1, -4.5, 2.0, 4.1)"],seealso:["max","mean","min"]}},{}],84:[function(e,t){t.exports={name:"acos",category:"Trigonometry",syntax:["acos(x)"],description:"Compute the inverse cosine of a value in radians.",examples:["acos(0.5)","acos(cos(2.3))"],seealso:["cos","acos","asin"]}},{}],85:[function(e,t){t.exports={name:"asin",category:"Trigonometry",syntax:["asin(x)"],description:"Compute the inverse sine of a value in radians.",examples:["asin(0.5)","asin(sin(2.3))"],seealso:["sin","acos","asin"]}},{}],86:[function(e,t){t.exports={name:"atan",category:"Trigonometry",syntax:["atan(x)"],description:"Compute the inverse tangent of a value in radians.",examples:["atan(0.5)","atan(tan(2.3))"],seealso:["tan","acos","asin"]}},{}],87:[function(e,t){t.exports={name:"atan2",category:"Trigonometry",syntax:["atan2(y, x)"],description:"Computes the principal value of the arc tangent of y/x in radians.",examples:["atan2(2, 2) / pi","angle = 60 deg in rad","x = cos(angle)","y = sin(angle)","atan2(y, x)"],seealso:["sin","cos","tan"]}},{}],88:[function(e,t){t.exports={name:"cos",category:"Trigonometry",syntax:["cos(x)"],description:"Compute the cosine of x in radians.",examples:["cos(2)","cos(pi / 4) ^ 2","cos(180 deg)","cos(60 deg)","sin(0.2)^2 + cos(0.2)^2"],seealso:["acos","sin","tan"]}},{}],89:[function(e,t){t.exports={name:"cot",category:"Trigonometry",syntax:["cot(x)"],description:"Compute the cotangent of x in radians. Defined as 1/tan(x)",examples:["cot(2)","1 / tan(2)"],seealso:["sec","csc","tan"]}},{}],90:[function(e,t){t.exports={name:"csc",category:"Trigonometry",syntax:["csc(x)"],description:"Compute the cosecant of x in radians. Defined as 1/sin(x)",examples:["csc(2)","1 / sin(2)"],seealso:["sec","cot","sin"]}},{}],91:[function(e,t){t.exports={name:"sec",category:"Trigonometry",syntax:["sec(x)"],description:"Compute the secant of x in radians. Defined as 1/cos(x)",examples:["sec(2)","1 / cos(2)"],seealso:["cot","csc","cos"]}},{}],92:[function(e,t){t.exports={name:"sin",category:"Trigonometry",syntax:["sin(x)"],description:"Compute the sine of x in radians.",examples:["sin(2)","sin(pi / 4) ^ 2","sin(90 deg)","sin(30 deg)","sin(0.2)^2 + cos(0.2)^2"],seealso:["asin","cos","tan"]}},{}],93:[function(e,t){t.exports={name:"tan",category:"Trigonometry",syntax:["tan(x)"],description:"Compute the tangent of x in radians.",examples:["tan(0.5)","sin(0.5) / cos(0.5)","tan(pi / 4)","tan(45 deg)"],seealso:["atan","sin","cos"]}},{}],94:[function(e,t){t.exports={name:"in",category:"Units",syntax:["x in unit","in(x, unit)"],description:"Change the unit of a value.",examples:["5 inch in cm","3.2kg in g","16 bytes in bits"],seealso:[]}},{}],95:[function(e,t){t.exports={name:"clone",category:"Utils",syntax:["clone(x)"],description:"Clone a variable. Creates a copy of primitive variables,and a deep copy of matrices",examples:["clone(3.5)","clone(2 - 4i)","clone(45 deg)","clone([1, 2; 3, 4])",'clone("hello world")'],seealso:[]}},{}],96:[function(e,t){t.exports={name:"forEach",category:"Utils",syntax:["forEach(x, callback)"],description:"Iterates over all elements of a matrix/array, and executes the given callback.",examples:["forEach([1, 2, 3], function(val) { console.log(val) })"],seealso:[]}},{}],97:[function(e,t){t.exports={name:"format",category:"Utils",syntax:["format(value)","format(value, precision)"],description:"Format a value of any type as string.",examples:["format(2.3)","format(3 - 4i)","format([])","format(pi, 3)"],seealso:["print"]}},{}],98:[function(e,t){t.exports={name:"import",category:"Utils",syntax:["import(string)"],description:"Import functions from a file.",examples:['import("numbers")','import("./mylib.js")'],seealso:[]}},{}],99:[function(e,t){t.exports={name:"map",category:"Utils",syntax:["map(x, callback)"],description:"Create a new matrix or array with the results of the callback function executed on each entry of the matrix/array.",examples:["map([1, 2, 3], function(val) { return math.max(val, 1.5) })"],seealso:[]}},{}],100:[function(e,t){t.exports={name:"typeof",category:"Utils",syntax:["typeof(x)"],description:"Get the type of a variable.",examples:["typeof(3.5)","typeof(2 - 4i)","typeof(45 deg)",'typeof("hello 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