Function zTe

main.js:125–125

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`),i},r.prototype.toJSON=function(){var n=nr(this.doc);return n.mathjs="Help",n},r.fromJSON=function(n){var i={};return Object.keys(n).filter(a=>a!=="mathjs").forEach(a=>{i[a]=n[a]}),new r(i)},r.prototype.valueOf=r.prototype.toString,r},{isClass:!0});var Uut="Chain",Hut=["?on","math","typed"],x7=X(Uut,Hut,e=>{var{on:t,math:r,typed:n}=e;function i(u){if(!(this instanceof i))throw new SyntaxError("Constructor must be called with the new operator");WE(u)?this.value=u.value:this.value=u}i.prototype.type="Chain",i.prototype.isChain=!0,i.prototype.done=function(){return this.value},i.prototype.valueOf=function(){return this.value},i.prototype.toString=function(){return Er(this.value)},i.prototype.toJSON=function(){return{mathjs:"Chain",value:this.value}},i.fromJSON=function(u){return new i(u.value)};function a(u,c){typeof c=="function"&&(i.prototype[u]=s(c))}function o(u,c){YE(i.prototype,u,function(){var d=c();if(typeof d=="function")return s(d)})}function s(u){return function(){if(arguments.length===0)return new i(u(this.value));for(var c=[this.value],f=0;f<arguments.length;f++)c[f+1]=arguments[f];if(n.isTypedFunction(u)){var d=n.resolve(u,c);if(d.params.length===1)throw new Error("chain function "+u.name+" cannot match rest parameter between chain value and additional arguments.");return new i(d.implementation.apply(u,c))}return new i(u.apply(u,c))}}i.createProxy=function(u,c){if(typeof u=="string")a(u,c);else{var f=function(h){Pt(u,h)&&l[h]===void 0&&o(h,()=>u[h])};for(var d in u)f(d)}};var l={expression:!0,docs:!0,type:!0,classes:!0,json:!0,error:!0,isChain:!0};return i.createProxy(r),t&&t("import",function(u,c,f){f||o(u,c)}),i},{isClass:!0});var BZ={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"]};var axe={name:"false",category:"Constants",syntax:["false"],description:"Boolean value false",examples:["false"],seealso:["true"]};var oxe={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:[]};var sxe={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:[]};var lxe={name:"LN10",category:"Constants",syntax:["LN10"],description:"Returns the natural logarithm of 10, approximately equal to 2.302",examples:["LN10","log(10)"],seealso:[]};var uxe={name:"LN2",category:"Constants",syntax:["LN2"],description:"Returns the natural logarithm of 2, approximately equal to 0.693",examples:["LN2","log(2)"],seealso:[]};var cxe={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:[]};var fxe={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:[]};var dxe={name:"NaN",category:"Constants",syntax:["NaN"],description:"Not a number",examples:["NaN","0 / 0"],seealso:[]};var pxe={name:"null",category:"Constants",syntax:["null"],description:"Value null",examples:["null"],seealso:["true","false"]};var mxe={name:"phi",category:"Constants",syntax:["phi"],description:"Phi is the golden ratio. Two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities. Phi is defined as `(1 + sqrt(5)) / 2` and is approximately 1.618034...",examples:["phi"],seealso:[]};var LZ={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"]};var hxe={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:[]};var gxe={name:"SQRT2",category:"Constants",syntax:["SQRT2"],description:"Returns the square root of 2, approximately equal to 1.414",examples:["SQRT2","sqrt(2)"],seealso:[]};var Axe={name:"tau",category:"Constants",syntax:["tau"],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"]};var vxe={name:"true",category:"Constants",syntax:["true"],description:"Boolean value true",examples:["true"],seealso:["false"]};var yxe={name:"version",category:"Constants",syntax:["version"],description:"A string with the version number of math.js",examples:["version"],seealso:[]};var bxe={name:"bignumber",category:"Construction",syntax:["bignumber(x)"],description:"Create a big number from a number or string.",examples:["0.1 + 0.2","bignumber(0.1) + bignumber(0.2)",'bignumber("7.2")','bignumber("7.2e500")',"bignumber([0.1, 0.2, 0.3])"],seealso:["boolean","complex","fraction","index","matrix","string","unit"]};var xxe={name:"boolean",category:"Construction",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:["bignumber","complex","index","matrix","number","string","unit"]};var wxe={name:"complex",category:"Construction",syntax:["complex()","complex(re, im)","complex(string)"],description:"Create a complex number.",examples:["complex()","complex(2, 3)",'complex("7 - 2i")'],seealso:["bignumber","boolean","index","matrix","number","string","unit"]};var Sxe={name:"createUnit",category:"Construction",syntax:["createUnit(definitions)","createUnit(name, definition)"],description:"Create a user-defined unit and register it with the Unit type.",examples:['createUnit("foo")','createUnit("knot", {definition: "0.514444444 m/s", aliases: ["knots", "kt", "kts"]})','createUnit("mph", "1 mile/hour")'],seealso:["unit","splitUnit"]};var Exe={name:"fraction",category:"Construction",syntax:["fraction(num)","fraction(matrix)","fraction(num,den)","fraction({n: num, d: den})"],description:"Create a fraction from a number or from integer numerator and denominator.",examples:["fraction(0.125)","fraction(1, 3) + fraction(2, 5)","fraction({n: 333, d: 53})","fraction([sqrt(9), sqrt(10), sqrt(11)])"],seealso:["bignumber","boolean","complex","index","matrix","string","unit"]};var kxe={name:"index",category:"Construction",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:["A = [1, 2, 3; 4, 5, 6]","A[1, :]","A[1, 2] = 50","A[1:2, 1:2] = 1","B = [1, 2, 3]","B[B>1 and B<3]"],seealso:["bignumber","boolean","complex","matrix,","number","range","string","unit"]};var Cxe={name:"matrix",category:"Construction",syntax:["[]","[a1, b1, ...; a2, b2, ...]","matrix()",'matrix("dense")',"matrix([...])"],description:"Create a matrix.",examples:["[]","[1, 2, 3]","[1, 2, 3; 4, 5, 6]","matrix()","matrix([3, 4])",'matrix([3, 4; 5, 6], "sparse")','matrix([3, 4; 5, 6], "sparse", "number")'],seealso:["bignumber","boolean","complex","index","number","string","unit","sparse"]};var Dxe={name:"number",category:"Construction",syntax:["x","number(x)","number(unit, valuelessUnit)"],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])",'number(unit("52cm"), "m")'],seealso:["bignumber","boolean","complex","fraction","index","matrix","string","unit"]};var Txe={name:"sparse",category:"Construction",syntax:["sparse()","sparse([a1, b1, ...; a1, b2, ...])",'sparse([a1, b1, ...; a1, b2, ...], "number")'],description:"Create a sparse matrix.",examples:["sparse()","sparse([3, 4; 5, 6])",'sparse([3, 0; 5, 0], "number")'],seealso:["bignumber","boolean","complex","index","number","string","unit","matrix"]};var Nxe={name:"splitUnit",category:"Construction",syntax:["splitUnit(unit: Unit, parts: Unit[])"],description:"Split a unit in an array of units whose sum is equal to the original unit.",examples:['splitUnit(1 m, ["feet", "inch"])'],seealso:["unit","createUnit"]};var Mxe={name:"string",category:"Construction",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:["bignumber","boolean","complex","index","matrix","number","unit"]};var Oxe={name:"unit",category:"Construction",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:["bignumber","boolean","complex","index","matrix","number","string"]};var Fxe={name:"config",category:"Core",syntax:["config()","config(options)"],description:"Get configuration or change configuration.",examples:["config()","1/3 + 1/4",'config({number: "Fraction"})',"1/3 + 1/4"],seealso:[]};var jxe={name:"import",category:"Core",syntax:["import(functions)","import(functions, options)"],description:"Import functions or constants from an object.",examples:["import({myFn: f(x)=x^2, myConstant: 32 })","myFn(2)","myConstant"],seealso:[]};var Pxe={name:"typed",category:"Core",syntax:["typed(signatures)","typed(name, signatures)"],description:"Create a typed function.",examples:['double = typed({ "number": f(x)=x+x, "string": f(x)=concat(x,x) })',"double(2)",'double("hello")'],seealso:[]};var _xe={name:"derivative",category:"Algebra",syntax:["derivative(expr, variable)","derivative(expr, variable, {simplify: boolean})"],description:"Takes the derivative of an expression expressed in parser Nodes. The derivative will be taken over the supplied variable in the second parameter. If there are multiple variables in the expression, it will return a partial derivative.",examples:['derivative("2x^3", "x")','derivative("2x^3", "x", {simplify: false})','derivative("2x^2 + 3x + 4", "x")','derivative("sin(2x)", "x")','f = parse("x^2 + x")','x = parse("x")',"df = derivative(f, x)","df.evaluate({x: 3})"],seealso:["simplify","parse","evaluate"]};var Ixe={name:"leafCount",category:"Algebra",syntax:["leafCount(expr)"],description:"Computes the number of leaves in the parse tree of the given expression",examples:['leafCount("e^(i*pi)-1")','leafCount(parse("{a: 22/7, b: 10^(1/2)}"))'],seealso:["simplify"]};var Bxe={name:"lsolve",category:"Algebra",syntax:["x=lsolve(L, b)"],description:"Finds one solution of the linear system L * x = b where L is an [n x n] lower triangular matrix and b is a [n] column vector.",examples:["a = [-2, 3; 2, 1]","b = [11, 9]","x = lsolve(a, b)"],seealso:["lsolveAll","lup","lusolve","usolve","matrix","sparse"]};var Lxe={name:"lsolveAll",category:"Algebra",syntax:["x=lsolveAll(L, b)"],description:"Finds all solutions of the linear system L * x = b where L is an [n x n] lower triangular matrix and b is a [n] column vector.",examples:["a = [-2, 3; 2, 1]","b = [11, 9]","x = lsolve(a, b)"],seealso:["lsolve","lup","lusolve","usolve","matrix","sparse"]};var Rxe={name:"lup",category:"Algebra",syntax:["lup(m)"],description:"Calculate the Matrix LU decomposition with partial pivoting. Matrix A is decomposed in three matrices (L, U, P) where P * A = L * U",examples:["lup([[2, 1], [1, 4]])","lup(matrix([[2, 1], [1, 4]]))","lup(sparse([[2, 1], [1, 4]]))"],seealso:["lusolve","lsolve","usolve","matrix","sparse","slu","qr"]};var qxe={name:"lusolve",category:"Algebra",syntax:["x=lusolve(A, b)","x=lusolve(lu, b)"],description:"Solves the linear system A * x = b where A is an [n x n] matrix and b is a [n] column vector.",examples:["a = [-2, 3; 2, 1]","b = [11, 9]","x = lusolve(a, b)"],seealso:["lup","slu","lsolve","usolve","matrix","sparse"]};var $xe={name:"polynomialRoot",category:"Algebra",syntax:["x=polynomialRoot(-6, 3)","x=polynomialRoot(4, -4, 1)","x=polynomialRoot(-8, 12, -6, 1)"],description:"Finds the roots of a univariate polynomial given by its coefficients starting from constant, linear, and so on, increasing in degree.",examples:["a = polynomialRoot(-6, 11, -6, 1)"],seealso:["cbrt","sqrt"]};var zxe={name:"qr",category:"Algebra",syntax:["qr(A)"],description:"Calculates the Matrix QR decomposition. Matrix `A` is decomposed in two matrices (`Q`, `R`) where `Q` is an orthogonal matrix and `R` is an upper triangular matrix.",examples:["qr([[1, -1,  4], [1,  4, -2], [1,  4,  2], [1,  -1, 0]])"],seealso:["lup","slu","matrix"]};var Uxe={name:"rationalize",category:"Algebra",syntax:["rationalize(expr)","rationalize(expr, scope)","rationalize(expr, scope, detailed)"],description:"Transform a rationalizable expression in a rational fraction. If rational fraction is one variable polynomial then converts the numerator and denominator in canonical form, with decreasing exponents, returning the coefficients of numerator.",examples:['rationalize("2x/y - y/(x+1)")','rationalize("2x/y - y/(x+1)", true)'],seealso:["simplify"]};var Hxe={name:"resolve",category:"Algebra",syntax:["resolve(node, scope)"],description:"Recursively substitute variables in an expression tree.",examples:['resolve(parse("1 + x"), { x: 7 })','resolve(parse("size(text)"), { text: "Hello World" })','resolve(parse("x + y"), { x: parse("3z") })','resolve(parse("3x"), { x: parse("y+z"), z: parse("w^y") })'],seealso:["simplify","evaluate"],mayThrow:["ReferenceError"]};var Vxe={name:"simplify",category:"Algebra",syntax:["simplify(expr)","simplify(expr, rules)"],description:"Simplify an expression tree.",examples:['simplify("3 + 2 / 4")','simplify("2x + x")','f = parse("x * (x + 2 + x)")',"simplified = simplify(f)","simplified.evaluate({x: 2})"],seealso:["simplifyCore","derivative","evaluate","parse","rationalize","resolve"]};var Gxe={name:"simplifyConstant",category:"Algebra",syntax:["simplifyConstant(expr)","simplifyConstant(expr, options)"],description:"Replace constant subexpressions of node with their values.",examples:['simplifyConstant("(3-3)*x")','simplifyConstant(parse("z-cos(tau/8)"))'],seealso:["simplify","simplifyCore","evaluate"]};var Wxe={name:"simplifyCore",category:"Algebra",syntax:["simplifyCore(node)"],description:"Perform simple one-pass simplifications on an expression tree.",examples:['simplifyCore(parse("0*x"))','simplifyCore(parse("(x+0)*2"))'],seealso:["simplify","simplifyConstant","evaluate"]};var Qxe={name:"slu",category:"Algebra",syntax:["slu(A, order, threshold)"],description:"Calculate the Matrix LU decomposition with full pivoting. Matrix A is decomposed in two matrices (L, U) and two permutation vectors (pinv, q) where P * A * Q = L * U",examples:["slu(sparse([4.5, 0, 3.2, 0; 3.1, 2.9, 0, 0.9; 0, 1.7, 3, 0; 3.5, 0.4, 0, 1]), 1, 0.001)"],seealso:["lusolve","lsolve","usolve","matrix","sparse","lup","qr"]};var Yxe={name:"symbolicEqual",category:"Algebra",syntax:["symbolicEqual(expr1, expr2)","symbolicEqual(expr1, expr2, options)"],description:"Returns true if the difference of the expressions simplifies to 0",examples:['symbolicEqual("x*y","y*x")','symbolicEqual("abs(x^2)", "x^2")','symbolicEqual("abs(x)", "x", {context: {abs: {trivial: true}}})'],seealso:["simplify","evaluate"]};var Xxe={name:"usolve",category:"Algebra",syntax:["x=usolve(U, b)"],description:"Finds one solution of the linear system U * x = b where U is an [n x n] upper triangular matrix and b is a [n] column vector.",examples:["x=usolve(sparse([1, 1, 1, 1; 0, 1, 1, 1; 0, 0, 1, 1; 0, 0, 0, 1]), [1; 2; 3; 4])"],seealso:["usolveAll","lup","lusolve","lsolve","matrix","sparse"]};var Kxe={name:"usolveAll",category:"Algebra",syntax:["x=usolve(U, b)"],description:"Finds all solutions of the linear system U * x = b where U is an [n x n] upper triangular matrix and b is a [n] column vector.",examples:["x=usolve(sparse([1, 1, 1, 1; 0, 1, 1, 1; 0, 0, 1, 1; 0, 0, 0, 1]), [1; 2; 3; 4])"],seealso:["usolve","lup","lusolve","lsolve","matrix","sparse"]};var Jxe={name:"abs",category:"Arithmetic",syntax:["abs(x)"],description:"Compute the absolute value.",examples:["abs(3.5)","abs(-4.2)"],seealso:["sign"]};var Zxe={name:"add",category:"Operators",syntax:["x + y","add(x, y)"],description:"Add two values.",examples:["a = 2.1 + 3.6","a - 3.6","3 + 2i","3 cm + 2 inch",'"2.3" + "4"'],seealso:["subtract"]};var ewe={name:"cbrt",category:"Arithmetic",syntax:["cbrt(x)","cbrt(x, allRoots)"],description:"Compute the cubic root value. If x = y * y * y, then y is the cubic root of x. When `x` is a number or complex number, an optional second argument `allRoots` can be provided to return all three cubic roots. If not provided, the principal root is returned",examples:["cbrt(64)","cube(4)","cbrt(-8)","cbrt(2 + 3i)","cbrt(8i)","cbrt(8i, true)","cbrt(27 m^3)"],seealso:["square","sqrt","cube","multiply"]};var twe={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"]};var rwe={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"]};var nwe={name:"divide",category:"Operators",syntax:["x / y","divide(x, y)"],description:"Divide two values.",examples:["a = 2 / 3","a * 3","4.5 / 2","3 + 4 / 2","(3 + 4) / 2","18 km / 4.5"],seealso:["multiply"]};var iwe={name:"dotDivide",category:"Operators",syntax:["x ./ y","dotDivide(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","dotMultiply","divide"]};var awe={name:"dotMultiply",category:"Operators",syntax:["x .* y","dotMultiply(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","dotDivide"]};var owe={name:"dotPow",category:"Operators",syntax:["x .^ y","dotPow(x, y)"],description:"Calculates the power of x to y element wise.",examples:["a = [1, 2, 3; 4, 5, 6]","a .^ 2"],seealso:["pow"]};var swe={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:["expm","expm1","pow","log"]};var lwe={name:"expm",category:"Arithmetic",syntax:["exp(x)"],description:"Compute the matrix exponential, expm(A) = e^A. The matrix must be square. Not to be confused with exp(a), which performs element-wise exponentiation.",examples:["expm([[0,2],[0,0]])"],seealso:["exp"]};var uwe={name:"expm1",category:"Arithmetic",syntax:["expm1(x)"],description:"Calculate the value of subtracting 1 from the exponential value.",examples:["expm1(2)","pow(e, 2) - 1","log(expm1(2) + 1)"],seealso:["exp","pow","log"]};var cwe={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"]};var fwe={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"]};var dwe={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"]};var pwe={name:"hypot",category:"Arithmetic",syntax:["hypot(a, b, c, ...)","hypot([a, b, c, ...])"],description:"Calculate the hypotenusa of a list with values. ",examples:["hypot(3, 4)","sqrt(3^2 + 4^2)","hypot(-2)","hypot([3, 4, 5])"],seealso:["abs","norm"]};var mwe={name:"invmod",category:"Arithmetic",syntax:["invmod(a, b)"],description:"Calculate the (modular) multiplicative inverse of a modulo b. Solution to the equation ax \u2263 1 (mod b)",examples:["invmod(8, 12)","invmod(7, 13)","invmod(15151, 15122)"],seealso:["gcd","xgcd"]};var hwe={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"]};var gwe={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 ^ 4","log(10000, 10)","log(10000) / log(10)","b = log(1024, 2)","2 ^ b"],seealso:["exp","log1p","log2","log10"]};var Awe={name:"log10",category:"Arithmetic",syntax:["log10(x)"],description:"Compute the 10-base logarithm of a value.",examples:["log10(0.00001)","log10(10000)","10 ^ 4","log(10000) / log(10)","log(10000, 10)"],seealso:["exp","log"]};var vwe={name:"log1p",category:"Arithmetic",syntax:["log1p(x)","log1p(x, base)"],description:"Calculate the logarithm of a `value+1`",examples:["log1p(2.5)","exp(log1p(1.4))","pow(10, 4)","log1p(9999, 10)","log1p(9999) / log(10)"],seealso:["exp","log","log2","log10"]};var ywe={name:"log2",category:"Arithmetic",syntax:["log2(x)"],description:"Calculate the 2-base of a value. This is the same as calculating `log(x, 2)`.",examples:["log2(0.03125)","log2(16)","log2(16) / log2(2)","pow(2, 4)"],seealso:["exp","log1p","log","log10"]};var bwe={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","isOdd(x) = x % 2","isOdd(2)","isOdd(3)"],seealso:["divide"]};var xwe={name:"multiply",category:"Operators",syntax:["x * y","multiply(x, y)"],description:"multiply two values.",examples:["a = 2.1 * 3.4","a / 3.4","2 * 3 + 4","2 * (3 + 4)","3 * 2.1 km"],seealso:["divide"]};var wwe={name:"norm",category:"Arithmetic",syntax:["norm(x)","norm(x, p)"],description:"Calculate the norm of a number, vector or matrix.",examples:["abs(-3.5)","norm(-3.5)","norm(3 - 4i)","norm([1, 2, -3], Infinity)","norm([1, 2, -3], -Infinity)","norm([3, 4], 2)","norm([[1, 2], [3, 4]], 1)",'norm([[1, 2], [3, 4]], "inf")','norm([[1, 2], [3, 4]], "fro")']};var Swe={name:"nthRoot",category:"Arithmetic",syntax:["nthRoot(a)","nthRoot(a, root)"],description:'Calculate the nth root of a value. The principal nth root of a positive real number A, is the positive real solution of the equation "x^root = A".',examples:["4 ^ 3","nthRoot(64, 3)","nthRoot(9, 2)","sqrt(9)"],seealso:["nthRoots","pow","sqrt"]};var Ewe={name:"nthRoots",category:"Arithmetic",syntax:["nthRoots(A)","nthRoots(A, root)"],description:'Calculate the nth roots of a value. An nth root of a positive real number A, is a positive real solution of the equation "x^root = A". This function returns an array of complex values.',examples:["nthRoots(1)","nthRoots(1, 3)"],seealso:["sqrt","pow","nthRoot"]};var kwe={name:"pow",category:"Operators",syntax:["x ^ y","pow(x, y)"],description:"Calculates the power of x to y, x^y.",examples:["2^3","2*2*2","1 + e ^ (pi * i)","pow([[1, 2], [4, 3]], 2)","pow([[1, 2], [4, 3]], -1)"],seealso:["multiply","nthRoot","nthRoots","sqrt"]};var Cwe={name:"round",category:"Arithmetic",syntax:["round(x)","round(x, n)","round(unit, valuelessUnit)","round(unit, n, valuelessUnit)"],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)","round(3.241cm, 2, cm)","round([3.2, 3.8, -4.7])"],seealso:["ceil","floor","fix"]};var Dwe={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"]};var Twe={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","sqrtm","multiply","nthRoot","nthRoots","pow"]};var Nwe={name:"sqrtm",category:"Arithmetic",syntax:["sqrtm(x)"],description:"Calculate the principal square root of a square matrix. The principal square root matrix `X` of another matrix `A` is such that `X * X = A`.",examples:["sqrtm([[33, 24], [48, 57]])"],seealso:["sqrt","abs","square","multiply"]};var Mwe={name:"sylvester",category:"Algebra",syntax:["sylvester(A,B,C)"],description:"Solves the real-valued Sylvester equation AX+XB=C for X",examples:["sylvester([[-1, -2], [1, 1]], [[-2, 1], [-1, 2]], [[-3, 2], [3, 0]])","A = [[-1, -2], [1, 1]]; B = [[2, -1], [1, -2]]; C = [[-3, 2], [3, 0]]","sylvester(A, B, C)"],seealso:["schur","lyap"]};var Owe={name:"schur",category:"Algebra",syntax:["schur(A)"],description:"Performs a real Schur decomposition of the real matrix A = UTU'",examples:["schur([[1, 0], [-4, 3]])","A = [[1, 0], [-4, 3]]","schur(A)"],seealso:["lyap","sylvester"]};var Fwe={name:"lyap",category:"Algebra",syntax:["lyap(A,Q)"],description:"Solves the Continuous-time Lyapunov equation AP+PA'+Q=0 for P",examples:["lyap([[-2, 0], [1, -4]], [[3, 1], [1, 3]])","A = [[-2, 0], [1, -4]]","Q = [[3, 1], [1, 3]]","lyap(A,Q)"],seealso:["schur","sylvester"]};var jwe={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"]};var Pwe={name:"subtract",category:"Operators",syntax:["x - y","subtract(x, y)"],description:"subtract two values.",examples:["a = 5.3 - 2","a + 2","2/3 - 1/6","2 * 3 - 3","2.1 km - 500m"],seealso:["add"]};var _we={name:"unaryMinus",category:"Operators",syntax:["-x","unaryMinus(x)"],description:"Inverse the sign of a value. Converts booleans and strings to numbers.",examples:["-4.5","-(-5.6)",'-"22"'],seealso:["add","subtract","unaryPlus"]};var Iwe={name:"unaryPlus",category:"Operators",syntax:["+x","unaryPlus(x)"],description:"Converts booleans and strings to numbers.",examples:["+true",'+"2"'],seealso:["add","subtract","unaryMinus"]};var Bwe={name:"xgcd",category:"Arithmetic",syntax:["xgcd(a, b)"],description:"Calculate the extended greatest common divisor for two values. The result is an array [d, x, y] with 3 entries, where d is the greatest common divisor, and d = x * a + y * b.",examples:["xgcd(8, 12)","gcd(8, 12)","xgcd(36163, 21199)"],seealso:["gcd","lcm"]};var Lwe={name:"bitAnd",category:"Bitwise",syntax:["x & y","bitAnd(x, y)"],description:"Bitwise AND operation. Performs the logical AND operation on each pair of the corresponding bits of the two given values by multiplying them. If both bits in the compared position are 1, the bit in the resulting binary representation is 1, otherwise, the result is 0",examples:["5 & 3","bitAnd(53, 131)","[1, 12, 31] & 42"],seealso:["bitNot","bitOr","bitXor","leftShift","rightArithShift","rightLogShift"]};var Rwe={name:"bitNot",category:"Bitwise",syntax:["~x","bitNot(x)"],description:"Bitwise NOT operation. Performs a logical negation on each bit of the given value. Bits that are 0 become 1, and those that are 1 become 0.",examples:["~1","~2","bitNot([2, -3, 4])"],seealso:["bitAnd","bitOr","bitXor","leftShift","rightArithShift","rightLogShift"]};var qwe={name:"bitOr",category:"Bitwise",syntax:["x | y","bitOr(x, y)"],description:"Bitwise OR operation. Performs the logical inclusive OR operation on each pair of corresponding bits of the two given values. The result in each position is 1 if the first bit is 1 or the second bit is 1 or both bits are 1, otherwise, the result is 0.",examples:["5 | 3","bitOr([1, 2, 3], 4)"],seealso:["bitAnd","bitNot","bitXor","leftShift","rightArithShift","rightLogShift"]};var $we={name:"bitXor",category:"Bitwise",syntax:["bitXor(x, y)"],description:"Bitwise XOR operation, exclusive OR. Performs the logical exclusive OR operation on each pair of corresponding bits of the two given values. The result in each position is 1 if only the first bit is 1 or only the second bit is 1, but will be 0 if both are 0 or both are 1.",examples:["bitOr(1, 2)","bitXor([2, 3, 4], 4)"],seealso:["bitAnd","bitNot","bitOr","leftShift","rightArithShift","rightLogShift"]};var zwe={name:"leftShift",category:"Bitwise",syntax:["x << y","leftShift(x, y)"],description:"Bitwise left logical shift of a value x by y number of bits.",examples:["4 << 1","8 >> 1"],seealso:["bitAnd","bitNot","bitOr","bitXor","rightArithShift","rightLogShift"]};var Uwe={name:"rightArithShift",category:"Bitwise",syntax:["x >> y","rightArithShift(x, y)"],description:"Bitwise right arithmetic shift of a value x by y number of bits.",examples:["8 >> 1","4 << 1","-12 >> 2"],seealso:["bitAnd","bitNot","bitOr","bitXor","leftShift","rightLogShift"]};var Hwe={name:"rightLogShift",category:"Bitwise",syntax:["x >>> y","rightLogShift(x, y)"],description:"Bitwise right logical shift of a value x by y number of bits.",examples:["8 >>> 1","4 << 1","-12 >>> 2"],seealso:["bitAnd","bitNot","bitOr","bitXor","leftShift","rightArithShift"]};var Vwe={name:"bellNumbers",category:"Combinatorics",syntax:["bellNumbers(n)"],description:"The Bell Numbers count the number of partitions of a set. A partition is a pairwise disjoint subset of S whose union is S. `bellNumbers` only takes integer arguments. The following condition must be enforced: n >= 0.",examples:["bellNumbers(3)","bellNumbers(8)"],seealso:["stirlingS2"]};var Gwe={name:"catalan",category:"Combinatorics",syntax:["catalan(n)"],description:"The Catalan Numbers enumerate combinatorial structures of many different types. catalan only takes integer arguments. The following condition must be enforced: n >= 0.",examples:["catalan(3)","catalan(8)"],seealso:["bellNumbers"]};var Wwe={name:"composition",category:"Combinatorics",syntax:["composition(n, k)"],description:"The composition counts of n into k parts. composition only takes integer arguments. The following condition must be enforced: k <= n.",examples:["composition(5, 3)"],seealso:["combinations"]};var Qwe={name:"stirlingS2",category:"Combinatorics",syntax:["stirlingS2(n, k)"],description:"he Stirling numbers of the second kind, counts the number of ways to partition a set of n labelled objects into k nonempty unlabelled subsets. `stirlingS2` only takes integer arguments. The following condition must be enforced: k <= n. If n = k or k = 1, then s(n,k) = 1.",examples:["stirlingS2(5, 3)"],seealso:["bellNumbers"]};var Ywe={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"]};var Xwe={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"]};var Kwe={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"]};var Jwe={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"]};var Zwe={name:"evaluate",category:"Expression",syntax:["evaluate(expression)","evaluate(expression, scope)","evaluate([expr1, expr2, expr3, ...])","evaluate([expr1, expr2, expr3, ...], scope)"],description:"Evaluate an expression or an array with expressions.",examples:['evaluate("2 + 3")','evaluate("sqrt(16)")','evaluate("2 inch to cm")','evaluate("sin(x * pi)", { "x": 1/2 })','evaluate(["width=2", "height=4","width*height"])'],seealso:[]};var e2e={name:"help",category:"Expression",syntax:["help(object)","help(string)"],description:"Display documentation on a function or data type.",examples:["help(sqrt)",'help("complex")'],seealso:[]};var t2e={name:"distance",category:"Geometry",syntax:["distance([x1, y1], [x2, y2])","distance([[x1, y1], [x2, y2]])"],description:"Calculates the Euclidean distance between two points.",examples:["distance([0,0], [4,4])","distance([[0,0], [4,4]])"],seealso:[]};var r2e={name:"intersect",category:"Geometry",syntax:["intersect(expr1, expr2, expr3, expr4)","intersect(expr1, expr2, expr3)"],description:"Computes the intersection point of lines and/or planes.",examples:["intersect([0, 0], [10, 10], [10, 0], [0, 10])","intersect([1, 0, 1],  [4, -2, 2], [1, 1, 1, 6])"],seealso:[]};var n2e={name:"and",category:"Logical",syntax:["x and y","and(x, y)"],description:"Logical and. Test whether two values are both defined with a nonzero/nonempty value.",examples:["true and false","true and true","2 and 4"],seealso:["not","or","xor"]};var i2e={name:"not",category:"Logical",syntax:["not x","not(x)"],description:"Logical not. Flips the boolean value of given argument.",examples:["not true","not false","not 2","not 0"],seealso:["and","or","xor"]};var a2e={name:"or",category:"Logical",syntax:["x or y","or(x, y)"],description:"Logical or. Test if at least one value is defined with a nonzero/nonempty value.",examples:["true or false","false or false","0 or 4"],seealso:["not","and","xor"]};var o2e={name:"xor",category:"Logical",syntax:["x xor y","xor(x, y)"],description:"Logical exclusive or, xor. Test whether one and only one value is defined with a nonzero/nonempty value.",examples:["true xor false","false xor false","true xor true","0 xor 4"],seealso:["not","and","or"]};var s2e={name:"column",category:"Matrix",syntax:["column(x, index)"],description:"Return a column from a matrix or array.",examples:["A = [[1, 2], [3, 4]]","column(A, 1)","column(A, 2)"],seealso:["row","matrixFromColumns"]};var l2e={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 last 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)","concat(A, B, 1)","concat(A, B, 2)"],seealso:["det","diag","identity","inv","ones","range","size","squeeze","subset","trace","transpose","zeros"]};var u2e={name:"count",category:"Matrix",syntax:["count(x)"],description:"Count the number of elements of a matrix, array or string.",examples:["a = [1, 2; 3, 4; 5, 6]","count(a)","size(a)",'count("hello world")'],seealso:["size"]};var c2e={name:"cross",category:"Matrix",syntax:["cross(A, B)"],description:"Calculate the cross product for two vectors in three dimensional space.",examples:["cross([1, 1, 0],  [0, 1, 1])","cross([3, -3, 1], [4, 9, 2])","cross([2, 3, 4],  [5, 6, 7])"],seealso:["multiply","dot"]};var f2e={name:"ctranspose",category:"Matrix",syntax:["x'","ctranspose(x)"],description:"Complex Conjugate and Transpose a matrix",examples:["a = [1, 2, 3; 4, 5, 6]","a'","ctranspose(a)"],seealso:["concat","det","diag","identity","inv","ones","range","size","squeeze","subset","trace","zeros"]};var d2e={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","identity","inv","ones","range","size","squeeze","subset","trace","transpose","zeros"]};var p2e={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","identity","inv","ones","range","size","squeeze","subset","trace","transpose","zeros"]};var m2e={name:"diff",category:"Matrix",syntax:["diff(arr)","diff(arr, dim)"],description:["Create a new matrix or array with the difference of the passed matrix or array.","Dim parameter is optional and used to indicant the dimension of the array/matrix to apply the difference","If no dimension parameter is passed it is assumed as dimension 0","Dimension is zero-based in javascript and one-based in the parser","Arrays must be 'rectangular' meaning arrays like [1, 2]","If something is passed as a matrix it will be returned as a matrix but other than that all matrices are converted to arrays"],examples:["A = [1, 2, 4, 7, 0]","diff(A)","diff(A, 1)","B = [[1, 2], [3, 4]]","diff(B)","diff(B, 1)","diff(B, 2)","diff(B, bignumber(2))","diff([[1, 2], matrix([3, 4])], 2)"],seealso:["subtract","partitionSelect"]};var h2e={name:"dot",category:"Matrix",syntax:["dot(A, B)","A * B"],description:"Calculate the dot product of two vectors. The dot product of A = [a1, a2, a3, ..., an] and B = [b1, b2, b3, ..., bn] is defined as dot(A, B) = a1 * b1 + a2 * b2 + a3 * b3 + ... + an * bn",examples:["dot([2, 4, 1], [2, 2, 3])","[2, 4, 1] * [2, 2, 3]"],seealso:["multiply","cross"]};var g2e={name:"eigs",category:"Matrix",syntax:["eigs(x)"],description:"Calculate the eigenvalues and optionally eigenvectors of a square matrix",examples:["eigs([[5, 2.3], [2.3, 1]])","eigs([[1, 2, 3], [4, 5, 6], [7, 8, 9]], { precision: 1e-6, eigenvectors: false })"],seealso:["inv"]};var A2e={name:"filter",category:"Matrix",syntax:["filter(x, test)"],description:"Filter items in a matrix.",examples:["isPositive(x) = x > 0","filter([6, -2, -1, 4, 3], isPositive)","filter([6, -2, 0, 1, 0], x != 0)"],seealso:["sort","map","forEach"]};var v2e={name:"flatten",category:"Matrix",syntax:["flatten(x)"],description:"Flatten a multi dimensional matrix into a single dimensional matrix.",examples:["a = [1, 2, 3; 4, 5, 6]","size(a)","b = flatten(a)","size(b)"],seealso:["concat","resize","size","squeeze"]};var y2e={name:"forEach",category:"Matrix",syntax:["forEach(x, callback)"],description:"Iterates over all elements of a matrix/array, and executes the given callback function.",examples:["numberOfPets = {}","addPet(n) = numberOfPets[n] = (numberOfPets[n] ? numberOfPets[n]:0 ) + 1;",'forEach(["Dog","Cat","Cat"], addPet)',"numberOfPets"],seealso:["map","sort","filter"]};var b2e={name:"getMatrixDataType",category:"Matrix",syntax:["getMatrixDataType(x)"],description:'Find the data type of all elements in a matrix or array, for example "number" if all items are a number and "Complex" if all values are complex numbers. If a matrix contains more than one data type, it will return "mixed".',examples:["getMatrixDataType([1, 2, 3])","getMatrixDataType([[5 cm], [2 inch]])",'getMatrixDataType([1, "text"])',"getMatrixDataType([1, bignumber(4)])"],seealso:["matrix","sparse","typeOf"]};var x2e={name:"identity",category:"Matrix",syntax:["identity(n)","identity(m, n)","identity([m, n])"],description:"Returns the identity matrix with size m-by-n. The matrix has ones on the diagonal and zeros elsewhere.",examples:["identity(3)","identity(3, 5)","a = [1, 2, 3; 4, 5, 6]","identity(size(a))"],seealso:["concat","det","diag","inv","ones","range","size","squeeze","subset","trace","transpose","zeros"]};var w2e={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","identity","ones","range","size","squeeze","subset","trace","transpose","zeros"]};var S2e={name:"pinv",category:"Matrix",syntax:["pinv(x)"],description:"Calculate the Moore\u2013Penrose inverse of a matrix",examples:["pinv([1, 2; 3, 4])","pinv([[1, 0], [0, 1], [0, 1]])","pinv(4)"],seealso:["inv"]};var E2e={name:"kron",category:"Matrix",syntax:["kron(x, y)"],description:"Calculates the kronecker product of 2 matrices or vectors.",examples:["kron([[1, 0], [0, 1]], [[1, 2], [3, 4]])","kron([1,1], [2,3,4])"],seealso:["multiply","dot","cross"]};var k2e={name:"map",category:"Matrix",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], square)"],seealso:["filter","forEach"]};var C2e={name:"matrixFromColumns",category:"Matrix",syntax:["matrixFromColumns(...arr)","matrixFromColumns(row1, row2)","matrixFromColumns(row1, row2, row3)"],description:"Create a dense matrix from vectors as individual columns.",examples:["matrixFromColumns([1, 2, 3], [[4],[5],[6]])"],seealso:["matrix","matrixFromRows","matrixFromFunction","zeros"]};var D2e={name:"matrixFromFunction",category:"Matrix",syntax:["matrixFromFunction(size, fn)","matrixFromFunction(size, fn, format)","matrixFromFunction(size, fn, format, datatype)","matrixFromFunction(size, format, fn)","matrixFromFunction(size, format, datatype, fn)"],description:"Create a matrix by evaluating a generating function at each index.",examples:["f(I) = I[1] - I[2]","matrixFromFunction([3,3], f)","g(I) = I[1] - I[2] == 1 ? 4 : 0",'matrixFromFunction([100, 100], "sparse", g)',"matrixFromFunction([5], random)"],seealso:["matrix","matrixFromRows","matrixFromColumns","zeros"]};var T2e={name:"matrixFromRows",category:"Matrix",syntax:["matrixFromRows(...arr)","matrixFromRows(row1, row2)","matrixFromRows(row1, row2, row3)"],description:"Create a dense matrix from vectors as individual rows.",examples:["matrixFromRows([1, 2, 3], [[4],[5],[6]])"],seealso:["matrix","matrixFromColumns","matrixFromFunction","zeros"]};var N2e={name:"ones",category:"Matrix",syntax:["ones(m)","ones(m, n)","ones(m, n, p, ...)","ones([m])","ones([m, n])","ones([m, n, p, ...])"],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","identity","inv","range","size","squeeze","subset","trace","transpose","zeros"]};var M2e={name:"partitionSelect",category:"Matrix",syntax:["partitionSelect(x, k)","partitionSelect(x, k, compare)"],description:"Partition-based selection of an array or 1D matrix. Will find the kth smallest value, and mutates the input array. Uses Quickselect.",examples:["partitionSelect([5, 10, 1], 2)",'partitionSelect(["C", "B", "A", "D"], 1, compareText)',"arr = [5, 2, 1]","partitionSelect(arr, 0) # returns 1, arr is now: [1, 2, 5]","arr","partitionSelect(arr, 1, 'desc') # returns 2, arr is now: [5, 2, 1]","arr"],seealso:["sort"]};var O2e={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")',"range(1m, 1m, 3m)","a = [1, 2, 3, 4; 5, 6, 7, 8]","a[1:2, 1:2]"],seealso:["concat","det","diag","identity","inv","ones","size","squeeze","subset","trace","transpose","zeros"]};var F2e={name:"reshape",category:"Matrix",syntax:["reshape(x, sizes)"],description:"Reshape a multi dimensional array to fit the specified dimensions.",examples:["reshape([1, 2, 3, 4, 5, 6], [2, 3])","reshape([[1, 2], [3, 4]], [1, 4])","reshape([[1, 2], [3, 4]], [4])","reshape([1, 2, 3, 4], [-1, 2])"],seealso:["size","squeeze","resize"]};var j2e={name:"resize",category:"Matrix",syntax:["resize(x, size)","resize(x, size, defaultValue)"],description:"Resize a matrix.",examples:["resize([1,2,3,4,5], [3])","resize([1,2,3], [5])","resize([1,2,3], [5], -1)","resize(2, [2, 3])",'resize("hello", [8], "!")'],seealso:["size","subset","squeeze","reshape"]};var P2e={name:"rotate",category:"Matrix",syntax:["rotate(w, theta)","rotate(w, theta, v)"],description:"Returns a 2-D rotation matrix (2x2) for a given angle (in radians). Returns a 2-D rotation matrix (3x3) of a given angle (in radians) around given axis.",examples:["rotate([1, 0], pi / 2)",'rotate(matrix([1, 0]), unit("35deg"))','rotate([1, 0, 0], unit("90deg"), [0, 0, 1])','rotate(matrix([1, 0, 0]), unit("90deg"), matrix([0, 0, 1]))'],seealso:["matrix","rotationMatrix"]};var _2e={name:"rotationMatrix",category:"Matrix",syntax:["rotationMatrix(theta)","rotationMatrix(theta, v)","rotationMatrix(theta, v, format)"],description:"Returns a 2-D rotation matrix (2x2) for a given angle (in radians). Returns a 2-D rotation matrix (3x3) of a given angle (in radians) around given axis.",examples:["rotationMatrix(pi / 2)",'rotationMatrix(unit("45deg"), [0, 0, 1])','rotationMatrix(1, matrix([0, 0, 1]), "sparse")'],seealso:["cos","sin"]};var I2e={name:"row",category:"Matrix",syntax:["row(x, index)"],description:"Return a row from a matrix or array.",examples:["A = [[1, 2], [3, 4]]","row(A, 1)","row(A, 2)"],seealso:["column","matrixFromRows"]};var B2e={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","count","det","diag","identity","inv","ones","range","squeeze","subset","trace","transpose","zeros"]};var L2e={name:"sort",category:"Matrix",syntax:["sort(x)","sort(x, compare)"],description:'Sort the items in a matrix. Compare can be a string "asc", "desc", "natural", or a custom sort function.',examples:["sort([5, 10, 1])",'sort(["C", "B", "A", "D"], "natural")',"sortByLength(a, b) = size(a)[1] - size(b)[1]",'sort(["Langdon", "Tom", "Sara"], sortByLength)','sort(["10", "1", "2"], "natural")'],seealso:["map","filter","forEach"]};var R2e={name:"squeeze",category:"Matrix",syntax:["squeeze(x)"],description:"Remove inner and outer singleton dimensions from a matrix.",examples:["a = zeros(3,2,1)","size(squeeze(a))","b = zeros(1,1,3)","size(squeeze(b))"],seealso:["concat","det","diag","identity","inv","ones","range","size","subset","trace","transpose","zeros"]};var q2e={name:"subset",category:"Matrix",syntax:["value(index)","value(index) = replacement","subset(value, [index])","subset(value, [index], replacement)"],description:"Get or set a subset of the entries of a matrix or characters of a string. Indexes are one-based. There should be one index specification for each dimension of the target. Each specification can be a single index, a list of indices, or a range in colon notation `l:u`. In a range, both the lower bound l and upper bound u are included; and if a bound is omitted it defaults to the most extreme valid value. The cartesian product of the indices specified in each dimension determines the target of the operation.",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]","f[[1,2], [1,3]] = [9, 10; 11, 12]","f"],seealso:["concat","det","diag","identity","inv","ones","range","size","squeeze","trace","transpose","zeros"]};var $2e={name:"trace",category:"Matrix",syntax:["trace(A)"],description:"Calculate the trace of a matrix: the sum of the elements on the main diagonal of a square matrix.",examples:["A = [1, 2, 3; -1, 2, 3; 2, 0, 3]","trace(A)"],seealso:["concat","det","diag","identity","inv","ones","range","size","squeeze","subset","transpose","zeros"]};var z2e={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","identity","inv","ones","range","size","squeeze","subset","trace","zeros"]};var U2e={name:"zeros",category:"Matrix",syntax:["zeros(m)","zeros(m, n)","zeros(m, n, p, ...)","zeros([m])","zeros([m, n])","zeros([m, n, p, ...])"],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","identity","inv","ones","range","size","squeeze","subset","trace","transpose"]};var H2e={name:"fft",category:"Matrix",syntax:["fft(x)"],description:"Calculate N-dimensional fourier transform",examples:["fft([[1, 0], [1, 0]])"],seealso:["ifft"]};var V2e={name:"ifft",category:"Matrix",syntax:["ifft(x)"],description:"Calculate N-dimensional inverse fourier transform",examples:["ifft([[2, 2], [0, 0]])"],seealso:["fft"]};var G2e={name:"combinations",category:"Probability",syntax:["combinations(n, k)"],description:"Compute the number of combinations of n items taken k at a time",examples:["combinations(7, 5)"],seealso:["combinationsWithRep","permutations","factorial"]};var W2e={name:"combinationsWithRep",category:"Probability",syntax:["combinationsWithRep(n, k)"],description:"Compute the number of combinations of n items taken k at a time with replacements.",examples:["combinationsWithRep(7, 5)"],seealso:["combinations","permutations","factorial"]};var Q2e={name:"factorial",category:"Probability",syntax:["n!","factorial(n)"],description:"Compute the factorial of a value",examples:["5!","5 * 4 * 3 * 2 * 1","3!"],seealso:["combinations","combinationsWithRep","permutations","gamma"]};var Y2e={name:"gamma",category:"Probability",syntax:["gamma(n)"],description:"Compute the gamma function. For small values, the Lanczos approximation is used, and for large values the extended Stirling approximation.",examples:["gamma(4)","3!","gamma(1/2)","sqrt(pi)"],seealso:["factorial"]};var X2e={name:"lgamma",category:"Probability",syntax:["lgamma(n)"],description:"Logarithm of the gamma function for real, positive numbers and complex numbers, using Lanczos approximation for numbers and Stirling series for complex numbers.",examples:["lgamma(4)","lgamma(1/2)","lgamma(i)","lgamma(complex(1.1, 2))"],seealso:["gamma"]};var K2e={name:"kldivergence",category:"Probability",syntax:["kldivergence(x, y)"],description:"Calculate the Kullback-Leibler (KL) divergence  between two distributions.",examples:["kldivergence([0.7,0.5,0.4], [0.2,0.9,0.5])"],seealso:[]};var J2e={name:"multinomial",category:"Probability",syntax:["multinomial(A)"],description:"Multinomial Coefficients compute the number of ways of picking a1, a2, ..., ai unordered outcomes from `n` possibilities. multinomial takes one array of integers as an argument. The following condition must be enforced: every ai > 0.",examples:["multinomial([1, 2, 1])"],seealso:["combinations","factorial"]};var Z2e={name:"permutations",category:"Probability",syntax:["permutations(n)","permutations(n, k)"],description:"Compute the number of permutations of n items taken k at a time",examples:["permutations(5)","permutations(5, 3)"],seealso:["combinations","combinationsWithRep","factorial"]};var eSe={name:"pickRandom",category:"Probability",syntax:["pickRandom(array)","pickRandom(array, number)","pickRandom(array, weights)","pickRandom(array, number, weights)","pickRandom(array, weights, number)"],description:"Pick a random entry from a given array.",examples:["pickRandom(0:10)","pickRandom([1, 3, 1, 6])","pickRandom([1, 3, 1, 6], 2)","pickRandom([1, 3, 1, 6], [2, 3, 2, 1])","pickRandom([1, 3, 1, 6], 2, [2, 3, 2, 1])","pickRandom([1, 3, 1, 6], [2, 3, 2, 1], 2)"],seealso:["random","randomInt"]};var tSe={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:["pickRandom","randomInt"]};var rSe={name:"randomInt",category:"Probability",syntax:["randomInt(max)","randomInt(min, max)","randomInt(size)","randomInt(size, max)","randomInt(size, min, max)"],description:"Return a random integer number",examples:["randomInt(10, 20)","randomInt([2, 3], 10)"],seealso:["pickRandom","random"]};var nSe={name:"compare",category:"Relational",syntax:["compare(x, y)"],description:"Compare two values. Returns 1 when x > y, -1 when x < y, and 0 when x == y.",examples:["compare(2, 3)","compare(3, 2)","compare(2, 2)","compare(5cm, 40mm)","compare(2, [1, 2, 3])"],seealso:["equal","unequal","smaller","smallerEq","largerEq","compareNatural","compareText"]};var iSe={name:"compareNatural",category:"Relational",syntax:["compareNatural(x, y)"],description:"Compare two values of any type in a deterministic, natural way. Returns 1 when x > y, -1 when x < y, and 0 when x == y.",examples:["compareNatural(2, 3)","compareNatural(3, 2)","compareNatural(2, 2)","compareNatural(5cm, 40mm)",'compareNatural("2", "10")',"compareNatural(2 + 3i, 2 + 4i)","compareNatural([1, 2, 4], [1, 2, 3])","compareNatural([1, 5], [1, 2, 3])","compareNatural([1, 2], [1, 2])","compareNatural({a: 2}, {a: 4})"],seealso:["equal","unequal","smaller","smallerEq","largerEq","compare","compareText"]};var aSe={name:"compareText",category:"Relational",syntax:["compareText(x, y)"],description:"Compare two strings lexically. Comparison is case sensitive. Returns 1 when x > y, -1 when x < y, and 0 when x == y.",examples:['compareText("B", "A")','compareText("A", "B")','compareText("A", "A")','compareText("2", "10")','compare("2", "10")',"compare(2, 10)",'compareNatural("2", "10")','compareText("B", ["A", "B", "C"])'],seealso:["compare","compareNatural"]};var oSe={name:"deepEqual",category:"Relational",syntax:["deepEqual(x, y)"],description:"Check equality of two matrices element wise. Returns true if the size of both matrices is equal and when and each of the elements are equal.",examples:["deepEqual([1,3,4], [1,3,4])","deepEqual([1,3,4], [1,3])"],seealso:["equal","unequal","smaller","larger","smallerEq","largerEq","compare"]};var sSe={name:"equal",category:"Relational",syntax:["x == y","equal(x, y)"],description:"Check equality of two values. Returns true if the values are equal, and false 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","compare","deepEqual","equalText"]};var lSe={name:"equalText",category:"Relational",syntax:["equalText(x, y)"],description:"Check equality of two strings. Comparison is case sensitive. Returns true if the values are equal, and false if not.",examples:['equalText("Hello", "Hello")','equalText("a", "A")','equal("2e3", "2000")','equalText("2e3", "2000")','equalText("B", ["A", "B", "C"])'],seealso:["compare","compareNatural","compareText","equal"]};var uSe={name:"larger",category:"Relational",syntax:["x > y","larger(x, y)"],description:"Check if value x is larger than y. Returns true if x is larger than y, and false 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","compare"]};var cSe={name:"largerEq",category:"Relational",syntax:["x >= y","largerEq(x, y)"],description:"Check if value x is larger or equal to y. Returns true if x is larger or equal to y, and false if not.",examples:["2 >= 1+1","2 > 1+1","a = 3.2","b = 6-2.8","(a >= b)"],seealso:["equal","unequal","smallerEq","smaller","compare"]};var fSe={name:"smaller",category:"Relational",syntax:["x < y","smaller(x, y)"],description:"Check if value x is smaller than value y. Returns true if x is smaller than y, and false 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","compare"]};var dSe={name:"smallerEq",category:"Relational",syntax:["x <= y","smallerEq(x, y)"],description:"Check if value x is smaller or equal to value y. Returns true if x is smaller than y, and false if not.",examples:["2 <= 1+1","2 < 1+1","a = 3.2","b = 6-2.8","(a <= b)"],seealso:["equal","unequal","larger","smaller","largerEq","compare"]};var pSe={name:"unequal",category:"Relational",syntax:["x != y","unequal(x, y)"],description:"Check unequality of two values. Returns true if the values are unequal, and false 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","compare","deepEqual"]};var mSe={name:"setCartesian",category:"Set",syntax:["setCartesian(set1, set2)"],description:"Create the cartesian product of two (multi)sets. Multi-dimension arrays will be converted to single-dimension arrays and the values will be sorted in ascending order before the operation.",examples:["setCartesian([1, 2], [3, 4])"],seealso:["setUnion","setIntersect","setDifference","setPowerset"]};var hSe={name:"setDifference",category:"Set",syntax:["setDifference(set1, set2)"],description:"Create the difference of two (multi)sets: every element of set1, that is not the element of set2. Multi-dimension arrays will be converted to single-dimension arrays before the operation.",examples:["setDifference([1, 2, 3, 4], [3, 4, 5, 6])","setDifference([[1, 2], [3, 4]], [[3, 4], [5, 6]])"],seealso:["setUnion","setIntersect","setSymDifference"]};var gSe={name:"setDistinct",category:"Set",syntax:["setDistinct(set)"],description:"Collect the distinct elements of a multiset. A multi-dimension array will be converted to a single-dimension array before the operation.",examples:["setDistinct([1, 1, 1, 2, 2, 3])"],seealso:["setMultiplicity"]};var ASe={name:"setIntersect",category:"Set",syntax:["setIntersect(set1, set2)"],description:"Create the intersection of two (multi)sets. Multi-dimension arrays will be converted to single-dimension arrays before the operation.",examples:["setIntersect([1, 2, 3, 4], [3, 4, 5, 6])","setIntersect([[1, 2], [3, 4]], [[3, 4], [5, 6]])"],seealso:["setUnion","setDifference"]};var vSe={name:"setIsSubset",category:"Set",syntax:["setIsSubset(set1, set2)"],description:"Check whether a (multi)set is a subset of another (multi)set: every element of set1 is the element of set2. Multi-dimension arrays will be converted to single-dimension arrays before the operation.",examples:["setIsSubset([1, 2], [3, 4, 5, 6])","setIsSubset([3, 4], [3, 4, 5, 6])"],seealso:["setUnion","setIntersect","setDifference"]};var ySe={name:"setMultiplicity",category:"Set",syntax:["setMultiplicity(element, set)"],description:"Count the multiplicity of an element in a multiset. A multi-dimension array will be converted to a single-dimension array before the operation.",examples:["setMultiplicity(1, [1, 2, 2, 4])","setMultiplicity(2, [1, 2, 2, 4])"],seealso:["setDistinct","setSize"]};var bSe={name:"setPowerset",category:"Set",syntax:["setPowerset(set)"],description:"Create the powerset of a (multi)set: the powerset contains very possible subsets of a (multi)set. A multi-dimension array will be converted to a single-dimension array before the operation.",examples:["setPowerset([1, 2, 3])"],seealso:["setCartesian"]};var xSe={name:"setSize",category:"Set",syntax:["setSize(set)","setSize(set, unique)"],description:'Count the number of elements of a (multi)set. When the second parameter "unique" is true, count only the unique values. A multi-dimension array will be converted to a single-dimension array before the operation.',examples:["setSize([1, 2, 2, 4])","setSize([1, 2, 2, 4], true)"],seealso:["setUnion","setIntersect","setDifference"]};var wSe={name:"setSymDifference",category:"Set",syntax:["setSymDifference(set1, set2)"],description:"Create the symmetric difference of two (multi)sets. Multi-dimension arrays will be converted to single-dimension arrays before the operation.",examples:["setSymDifference([1, 2, 3, 4], [3, 4, 5, 6])","setSymDifference([[1, 2], [3, 4]], [[3, 4], [5, 6]])"],seealso:["setUnion","setIntersect","setDifference"]};var SSe={name:"setUnion",category:"Set",syntax:["setUnion(set1, set2)"],description:"Create the union of two (multi)sets. Multi-dimension arrays will be converted to single-dimension arrays before the operation.",examples:["setUnion([1, 2, 3, 4], [3, 4, 5, 6])","setUnion([[1, 2], [3, 4]], [[3, 4], [5, 6]])"],seealso:["setIntersect","setDifference"]};var ESe={name:"zpk2tf",category:"Signal",syntax:["zpk2tf(z, p, k)"],description:"Compute the transfer function of a zero-pole-gain model.",examples:["zpk2tf([1, 2], [-1, -2], 1)","zpk2tf([1, 2], [-1, -2])","zpk2tf([1 - 3i, 2 + 2i], [-1, -2])"],seealso:[]};var kSe={name:"freqz",category:"Signal",syntax:["freqz(b, a)","freqz(b, a, w)"],description:"Calculates the frequency response of a filter given its numerator and denominator coefficients.",examples:["freqz([1, 2], [1, 2, 3])","freqz([1, 2], [1, 2, 3], [0, 1])","freqz([1, 2], [1, 2, 3], 512)"],seealso:[]};var CSe={name:"erf",category:"Special",syntax:["erf(x)"],description:"Compute the erf function of a value using a rational Chebyshev approximations for different intervals of x",examples:["erf(0.2)","erf(-0.5)","erf(4)"],seealso:[]};var DSe={name:"zeta",category:"Special",syntax:["zeta(s)"],description:"Compute the Riemann Zeta Function using an infinite series and Riemanns Functional Equation for the entire complex plane",examples:["zeta(0.2)","zeta(-0.5)","zeta(4)"],seealso:[]};var TSe={name:"mad",category:"Statistics",syntax:["mad(a, b, c, ...)","mad(A)"],description:"Compute the median absolute deviation of a matrix or a list with values. The median absolute deviation is defined as the median of the absolute deviations from the median.",examples:["mad(10, 20, 30)","mad([1, 2, 3])"],seealso:["mean","median","std","abs"]};var NSe={name:"max",category:"Statistics",syntax:["max(a, b, c, ...)","max(A)","max(A, dimension)"],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])","max([2, 5; 4, 3], 1)","max([2, 5; 4, 3], 2)","max(2.7, 7.1, -4.5, 2.0, 4.1)","min(2.7, 7.1, -4.5, 2.0, 4.1)"],seealso:["mean","median","min","prod","std","sum","variance"]};var MSe={name:"mean",category:"Statistics",syntax:["mean(a, b, c, ...)","mean(A)","mean(A, dimension)"],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])","mean([2, 5; 4, 3], 1)","mean([2, 5; 4, 3], 2)","mean([1.0, 2.7, 3.2, 4.0])"],seealso:["max","median","min","prod","std","sum","variance"]};var OSe={name:"median",category:"Statistics",syntax:["median(a, b, c, ...)","median(A)"],description:"Compute the median of all values. The values are sorted and the middle value is returned. In case of an even number of values, the average of the two middle values is returned.",examples:["median(5, 2, 7)","median([3, -1, 5, 7])"],seealso:["max","mean","min","prod","std","sum","variance","quantileSeq"]};var FSe={name:"min",category:"Statistics",syntax:["min(a, b, c, ...)","min(A)","min(A, dimension)"],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])","min([2, 5; 4, 3], 1)","min([2, 5; 4, 3], 2)","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","median","prod","std","sum","variance"]};var jSe={name:"mode",category:"Statistics",syntax:["mode(a, b, c, ...)","mode(A)","mode(A, a, b, B, c, ...)"],description:"Computes the mode of all values as an array. In case mode being more than one, multiple values are returned in an array.",examples:["mode(2, 1, 4, 3, 1)","mode([1, 2.7, 3.2, 4, 2.7])","mode(1, 4, 6, 1, 6)"],seealso:["max","mean","min","median","prod","std","sum","variance"]};var PSe={name:"prod",category:"Statistics",syntax:["prod(a, b, c, ...)","prod(A)"],description:"Compute the product of all values.",examples:["prod(2, 3, 4)","prod([2, 3, 4])","prod([2, 5; 4, 3])"],seealso:["max","mean","min","median","min","std","sum","variance"]};var _Se={name:"quantileSeq",category:"Statistics",syntax:["quantileSeq(A, prob[, sorted])","quantileSeq(A, [prob1, prob2, ...][, sorted])","quantileSeq(A, N[, sorted])"],description:`Compute the prob order quantile of a matrix or a list with values. The sequence is sorted and the middle value is returned. Supported types of sequence values are: Number, BigNumber, Unit Supported types of probablity are: Number, BigNumber. 

In case of a (multi dimensional) array or matrix, the prob order quantile of all elements will be calculated.`,examples:["quantileSeq([3, -1, 5, 7], 0.5)","quantileSeq([3, -1, 5, 7], [1/3, 2/3])","quantileSeq([3, -1, 5, 7], 2)","quantileSeq([-1, 3, 5, 7], 0.5, true)"],seealso:["mean","median","min","max","prod","std","sum","variance"]};var ISe={name:"std",category:"Statistics",syntax:["std(a, b, c, ...)","std(A)","std(A, dimension)","std(A, normalization)","std(A, dimension, normalization)"],description:'Compute the standard deviation of all values, defined as std(A) = sqrt(variance(A)). Optional parameter normalization can be "unbiased" (default), "uncorrected", or "biased".',examples:["std(2, 4, 6)","std([2, 4, 6, 8])",'std([2, 4, 6, 8], "uncorrected")','std([2, 4, 6, 8], "biased")',"std([1, 2, 3; 4, 5, 6])"],seealso:["max","mean","min","median","prod","sum","variance"]};var BSe={name:"cumsum",category:"Statistics",syntax:["cumsum(a, b, c, ...)","cumsum(A)"],description:"Compute the cumulative sum of all values.",examples:["cumsum(2, 3, 4, 1)","cumsum([2, 3, 4, 1])","cumsum([1, 2; 3, 4])","cumsum([1, 2; 3, 4], 1)","cumsum([1, 2; 3, 4], 2)"],seealso:["max","mean","median","min","prod","std","sum","variance"]};var LSe={name:"sum",category:"Statistics",syntax:["sum(a, b, c, ...)","sum(A)","sum(A, dimension)"],description:"Compute the sum of all values.",examples:["sum(2, 3, 4, 1)","sum([2, 3, 4, 1])","sum([2, 5; 4, 3])"],seealso:["max","mean","median","min","prod","std","sum","variance"]};var RSe={name:"variance",category:"Statistics",syntax:["variance(a, b, c, ...)","variance(A)","variance(A, dimension)","variance(A, normalization)","variance(A, dimension, normalization)"],description:'Compute the variance of all values. 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Y=0;Y<ae;Y++)for(var Z=0;Z<ae;Z++)pe[Y][Z]=h(pe[Y][Z]);return"BigNumber"}if(ue){for(var re=0;re<ae;re++)for(var he=0;he<ae;he++)pe[re][he]=w(pe[re][he]);return"number"}else throw TypeError("Matrix contains unsupported types only.")}});var LEe="expm",Jut=["typed","abs","add","identity","inv","multiply"],T7=X(LEe,Jut,e=>{var{typed:t,abs:r,add:n,identity:i,inv:a,multiply:o}=e;return t(LEe,{Matrix:function(f){var d=f.size();if(d.length!==2||d[0]!==d[1])throw new RangeError("Matrix must be square (size: "+Er(d)+")");for(var p=d[0],h=1e-15,m=s(f),v=l(m,h),A=v.q,x=v.j,g=o(f,Math.pow(2,-x)),w=i(p),b=i(p),y=1,S=g,T=-1,D=1;D<=A;D++)D>1&&(S=o(S,g),T=-T),y=y*(A-D+1)/((2*A-D+1)*D),w=n(w,o(y,S)),b=n(b,o(y*T,S));for(var k=o(a(b),w),M=0;M<x;M++)k=o(k,k);return _d(f)?f.createSparseMatrix(k):k}});function s(c){for(var f=c.size()[0],d=0,p=0;p<f;p++){for(var h=0,m=0;m<f;m++)h+=r(c.get([p,m]));d=Math.max(h,d)}return d}function l(c,f){for(var d=30,p=0;p<d;p++)for(var h=0;h<=p;h++){var m=p-h;if(u(c,h,m)<f)return{q:h,j:m}}throw new Error("Could not find acceptable parameters to compute the matrix exponential (try increasing maxSearchSize in expm.js)")}function u(c,f,d){for(var p=1,h=2;h<=f;h++)p*=h;for(var m=p,v=f+1;v<=2*f;v++)m*=v;var A=m*(2*f+1);return 8*Math.pow(c/Math.pow(2,d),2*f)*p*p/(m*A)}});var REe="sqrtm",Zut=["typed","abs","add","multiply","map","sqrt","subtract","inv","size","max","identity"],N7=X(REe,Zut,e=>{var{typed:t,abs:r,add:n,multiply:i,map:a,sqrt:o,subtract:s,inv:l,size:u,max:c,identity:f}=e,d=1e3,p=1e-6;function h(m){var v,A=0,x=m,g=f(u(m));do{var w=x;if(x=i(.5,n(w,l(g))),g=i(.5,n(g,l(w))),v=c(r(s(x,w))),v>p&&++A>d)throw new Error("computing square root of matrix: iterative method could not converge")}while(v>p);return x}return t(REe,{"Array | Matrix":function(v){var A=jt(v)?v.size():gr(v);switch(A.length){case 1:if(A[0]===1)return a(v,o);throw new RangeError("Matrix must be square (size: "+Er(A)+")");case 2:{var x=A[0],g=A[1];if(x===g)return 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v(A,x,g){for(var w=x.size()[0],b=A.size()[0],y=r(A),S=y.T,T=y.U,D=r(a(-1,x)),k=D.T,M=D.U,E=a(a(l(T),g),M),O=o(0,b),P=[],_=(H,ye)=>s(H,ye,1),B=(H,ye)=>s(H,ye,0),F=0;F<w;F++)if(F<w-1&&m(c(k,u(F+1,F)))>1e-5){for(var L=B(c(E,u(O,F)),c(E,u(O,F+1))),I=0;I<F;I++)L=f(L,B(a(P[I],c(k,u(I,F))),a(P[I],c(k,u(I,F+1)))));var R=a(p(b),a(-1,c(k,u(F,F)))),J=a(p(b),a(-1,c(k,u(F+1,F)))),Q=a(p(b),a(-1,c(k,u(F,F+1)))),q=a(p(b),a(-1,c(k,u(F+1,F+1)))),ie=B(_(f(S,R),J),_(Q,f(S,q))),Ae=h(ie,L);P[F]=Ae.subset(u(o(0,b),0)),P[F+1]=Ae.subset(u(o(b,2*b),0)),F++}else{for(var le=c(E,u(O,F)),pe=0;pe<F;pe++)le=f(le,a(P[pe],c(k,u(pe,F))));var ae=c(k,u(F,F)),oe=d(S,a(ae,p(b)));P[F]=h(oe,le)}var ue=i(n(...P)),Se=a(T,a(ue,l(M)));return Se}});var $Ee="schur",tct=["typed","matrix","identity","multiply","qr","norm","subtract"],O7=X($Ee,tct,e=>{var{typed:t,matrix:r,identity:n,multiply:i,qr:a,norm:o,subtract:s}=e;return t($Ee,{Array:function(c){var f=l(r(c));return{U:f.U.valueOf(),T:f.T.valueOf()}},Matrix:function(c){return 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c("*","multiply",[w,new u("tanh",[y.clone()])]);break;case"csch":D=!0,k=new c("*","multiply",[w,new u("coth",[y.clone()])]);break;case"coth":D=!0,k=new c("^","pow",[new u("csch",[y.clone()]),x(2)]);break;case"asinh":T=!0,k=new u("sqrt",[new c("+","add",[new c("^","pow",[y.clone(),x(2)]),x(1)])]);break;case"acosh":T=!0,k=new u("sqrt",[new c("-","subtract",[new c("^","pow",[y.clone(),x(2)]),x(1)])]);break;case"atanh":T=!0,k=new c("-","subtract",[x(1),new c("^","pow",[y.clone(),x(2)])]);break;case"asech":T=!0,D=!0,k=new c("*","multiply",[y.clone(),new u("sqrt",[new c("-","subtract",[x(1),new c("^","pow",[y.clone(),x(2)])])])]);break;case"acsch":T=!0,D=!0,k=new c("*","multiply",[new u("abs",[y.clone()]),new u("sqrt",[new c("+","add",[new c("^","pow",[y.clone(),x(2)]),x(1)])])]);break;case"acoth":T=!0,D=!0,k=new c("-","subtract",[x(1),new c("^","pow",[y.clone(),x(2)])]);break;case"abs":k=new c("/","divide",[new u(new d("abs"),[y.clone()]),y.clone()]);break;case"gamma":default:throw new Error('Cannot process function "'+w.name+'" in derivative: the function is not supported, undefined, or the number of arguments passed to it are not supported')}var M,E;T?(M="/",E="divide"):(M="*",E="multiply");var O=A(y,b);return D&&(O=new c("-","unaryMinus",[O])),new c(M,E,[O,k])},"OperatorNode, Object":function(w,b){if(b[w]!==void 0)return x(0);if(w.op==="+")return new c(w.op,w.fn,w.args.map(function(_){return A(_,b)}));if(w.op==="-"){if(w.isUnary())return new c(w.op,w.fn,[A(w.args[0],b)]);if(w.isBinary())return new c(w.op,w.fn,[A(w.args[0],b),A(w.args[1],b)])}if(w.op==="*"){var y=w.args.filter(function(_){return b[_]!==void 0});if(y.length>0){var S=w.args.filter(function(_){return b[_]===void 0}),T=S.length===1?S[0]:new c("*","multiply",S),D=y.concat(A(T,b));return new c("*","multiply",D)}return new c("+","add",w.args.map(function(_){return new c("*","multiply",w.args.map(function(B){return B===_?A(B,b):B.clone()}))}))}if(w.op==="/"&&w.isBinary()){var k=w.args[0],M=w.args[1];return b[M]!==void 0?new c("/","divide",[A(k,b),M]):b[k]!==void 0?new c("*","multiply",[new c("-","unaryMinus",[k]),new c("/","divide",[A(M,b),new c("^","pow",[M.clone(),x(2)])])]):new c("/","divide",[new c("-","subtract",[new c("*","multiply",[A(k,b),M.clone()]),new c("*","multiply",[k.clone(),A(M,b)])]),new c("^","pow",[M.clone(),x(2)])])}if(w.op==="^"&&w.isBinary()){var E=w.args[0],O=w.args[1];if(b[E]!==void 0)return Hr(E)&&(o(E.value)||a(E.value,1))?x(0):new c("*","multiply",[w,new c("*","multiply",[new u("log",[E.clone()]),A(O.clone(),b)])]);if(b[O]!==void 0){if(Hr(O)){if(o(O.value))return x(0);if(a(O.value,1))return A(E,b)}var P=new c("^","pow",[E.clone(),new c("-","subtract",[O,x(1)])]);return new c("*","multiply",[O.clone(),new c("*","multiply",[A(E,b),P])])}return new c("*","multiply",[new c("^","pow",[E.clone(),O.clone()]),new c("+","add",[new c("*","multiply",[A(E,b),new c("/","divide",[O.clone(),E.clone()])]),new c("*","multiply",[A(O,b),new u("log",[E.clone()])])])])}throw new Error('Cannot process operator "'+w.op+'" in derivative: the operator is not supported, undefined, or the number of arguments passed to it are not supported')}});function x(g,w){return new l(s(g,w||r.number))}return h});var Bke="rationalize",Kct=["config","typed","equal","isZero","add","subtract","multiply","divide","pow","parse","simplifyConstant","simplifyCore","simplify","?bignumber","?fraction","mathWithTransform","matrix","AccessorNode","ArrayNode","ConstantNode","FunctionNode","IndexNode","ObjectNode","OperatorNode","SymbolNode","ParenthesisNode"],uL=X(Bke,Kct,e=>{var{config:t,typed:r,equal:n,isZero:i,add:a,subtract:o,multiply:s,divide:l,pow:u,parse:c,simplifyConstant:f,simplifyCore:d,simplify:p,fraction:h,bignumber:m,mathWithTransform:v,matrix:A,AccessorNode:x,ArrayNode:g,ConstantNode:w,FunctionNode:b,IndexNode:y,ObjectNode:S,OperatorNode:T,SymbolNode:D,ParenthesisNode:k}=e;function M(B){var F=arguments.length>1&&arguments[1]!==void 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le=Ae.type;if(le==="FunctionNode")throw new Error("There is an unsolved function call");if(le==="OperatorNode")if(Ae.op==="^"){if(Ae.args[1].type!=="ConstantNode"||!Ot(parseFloat(Ae.args[1].value)))throw new Error("There is a non-integer exponent");ie(Ae.args[0])}else{if(!Q.includes(Ae.op))throw new Error("Operator "+Ae.op+" invalid in polynomial expression");for(var pe=0;pe<Ae.args.length;pe++)ie(Ae.args[pe])}else if(le==="SymbolNode"){var ae=Ae.name,oe=R.indexOf(ae);oe===-1&&R.push(ae)}else if(le==="ParenthesisNode")ie(Ae.content);else if(le!=="ConstantNode")throw new Error("type "+le+" is not allowed in polynomial expression")}}function O(){var B=[d,{l:"n+n",r:"2*n"},{l:"n+-n",r:"0"},f,{l:"n*(n1^-1)",r:"n/n1"},{l:"n*n1^-n2",r:"n/n1^n2"},{l:"n1^-1",r:"1/n1"},{l:"n*(n1/n2)",r:"(n*n1)/n2"},{l:"1*n",r:"n"}],F=[{l:"(-n1)/(-n2)",r:"n1/n2"},{l:"(-n1)*(-n2)",r:"n1*n2"},{l:"n1--n2",r:"n1+n2"},{l:"n1-n2",r:"n1+(-n2)"},{l:"(n1+n2)*n3",r:"(n1*n3 + 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n.state[e.id][t][a]}catch{}}return n}var B3=(e,t)=>e.hiddenExtensions.some(r=>t.endsWith(r))||t.endsWith("/"+e.spaceSubFolder)||t==e.spaceSubFolder||t.split("/").pop()==e.spaceSubFolder||t.startsWith(e.spacesFolder+"/#")||e.hiddenFiles.some(r=>t.startsWith(r)),Yee=(e,t)=>e.skipFolderNames.some(r=>t.endsWith(r))||t.endsWith("/"+e.spaceSubFolder)||t==e.spaceSubFolder||t.split("/").pop()==e.spaceSubFolder||t.startsWith(e.spacesFolder+"/#")||t.startsWith(e.spacesFolder+"/$")||e.hiddenFiles.some(r=>t.startsWith(r));var L3="templates",R3="kits",q3="actions",$3="waypoints.json",z3=class{constructor(t,r){this.fileSystem=t;this.dataPath=r;this.schemes=["spaces","vault"];this.onFocusesUpdated=()=>{this.spaceManager.onFocusesUpdated()};this.onSpaceUpdated=t=>{t.type=="views.mdb"?this.spaceManager.onSpaceUpdated(t.path,"frame"):t.type=="context.mdb"?this.spaceManager.onSpaceUpdated(t.path,"context"):t.type=="commands.mdb"&&this.spaceManager.onSpaceUpdated(t.path,"action")};this.loadPath=async t=>this.fileSystem.loadPath(t);this.onCreate=async t=>{t.file.isFolder?this.spaceManager.onSpaceCreated(t.file.path):this.spaceManager.onPathCreated(t.file.path)};this.onDelete=t=>{!t.file||(!t.file.isFolder&&t.file.extension!="mdb"?this.spaceManager.onPathDeleted(t.file.path):t.file.isFolder&&this.spaceManager.onSpaceDeleted(t.file.path))};this.onRename=t=>{!t.file||(!t.file.isFolder&&t.file.extension!="mdb"?this.spaceManager.onPathChanged(t.file.path,t.oldPath):t.file.isFolder&&this.spaceManager.onSpaceRenamed(t.file.path,t.oldPath))};this.authorities=["vault"];t.eventDispatch.addListener("onCreate",this.onCreate,0,this),t.eventDispatch.addListener("onRename",this.onRename,0,this),t.eventDispatch.addListener("onDelete",this.onDelete,0,this),t.eventDispatch.addListener("onFocusesUpdated",this.onFocusesUpdated,0,this),t.eventDispatch.addListener("onSpaceUpdated",this.onSpaceUpdated,0,this),t.eventDispatch.addListener("onCacheUpdated",this.onMetadataChange,0,this)}initiateAdapter(t){this.spaceManager=t}async readTemplates(t){return(await this.childrenForPath(`${t}/${this.spaceManager.superstate.settings.spaceSubFolder}/templates`)).filter(r=>!r.startsWith(".")).map(r=>r.split("/").pop())}async saveTemplate(t,r){return this.copyPath(t,`${r}/${this.spaceManager.superstate.settings.spaceSubFolder}/templates`)}deleteTemplate(t,r){return this.deletePath(`${r}/${this.spaceManager.superstate.settings.spaceSubFolder}/templates/${t}`)}async readFocuses(){return await this.fileSystem.fileExists(this.dataPath)||await this.fileSystem.createFolder(this.dataPath),await this.fileSystem.fileExists(`${this.dataPath}/${$3}`)?this.fileSystem.readTextFromFile(`${this.dataPath}/${$3}`).then(t=>Ks(or(t))):[]}async saveFocuses(t){return await this.fileSystem.fileExists(this.dataPath)||await this.fileSystem.createFolder(this.dataPath),this.fileSystem.writeTextToFile(`${this.dataPath}/${$3}`,JSON.stringify(t))}async readTemplate(t){let r=`${this.dataPath}/${L3}/${t}`;if(await this.fileSystem.fileExists(r))return this.fileSystem.readFileFragments({path:`${r}/${this.spaceManager.superstate.settings.spaceSubFolder}/views.mdb`,name:"views",filename:"views.mdb",parent:r,isFolder:!1,extension:"mdb"},"mdbTables")}async readAllKits(){let t=(await this.childrenForPath(`${this.dataPath}/${R3}`)).map(n=>n.split("/").pop());return Promise.all(t.map(async n=>{let i=await this.readKitFrames(n);return{id:n,name:n,colors:{},frames:Object.values(i??{})}}))}async readAllTemplates(){let t=(await this.childrenForPath(`${this.dataPath}/${L3}`)).map(n=>n.split("/").pop()),r={};for(let n of t){let i=await this.readTemplate(n);i&&(r[n]=i)}return r}async readKitFrames(t){return this.fileSystem.readFileFragments({path:`${this.dataPath}/${R3}/${t}/kit.mdb`,name:"kit",filename:"kit.mdb",parent:`${this.dataPath}/${R3}/${t}`,isFolder:!1,extension:"mdb"},"mdbTables")}async saveFrameKit(t,r){let n={path:`${this.dataPath}/${R3}/${r}/kit.mdb`,name:"kit",filename:"kit.mdb",parent:`${this.dataPath}/${R3}/${r}`,isFolder:!1,extension:"mdb"};await this.fileSystem.saveFileFragment(n,"schema",t.schema.id,()=>t.schema),this.fileSystem.saveFileFragment(n,"mdbFrame",t.schema.id,()=>t)}async saveSpaceTemplate(t,r){let n=r;if(await this.fileSystem.fileExists(`${this.dataPath}/${L3}`)){let i=await this.childrenForPath(`${this.dataPath}/${L3}/${r}`);n=qi(n,i)}await this.fileSystem.newFile(`${this.dataPath}/${L3}/${n}/${this.spaceManager.superstate.settings.spaceSubFolder}`,"view","mdb",t)}async onMetadataChange(t){if(!t.path)return;if(t.path.endsWith(".json")){let n=t.path.split("/").slice(0,-2).join("/");this.spaceManager.onPathPropertyChanged(n);return}let r=this.spaceManager.superstate.pathsIndex.get(t.path);if(r?.metadata.spacePath?.length>0){this.spaceManager.onPathPropertyChanged(r?.metadata.spacePath);return}this.spaceManager.onPathPropertyChanged(t.path)}uriByPath(t){return 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this.fileSystem.getFileCacheTypeByRefString(a,n.refStr);return await this.fileSystem.saveFileFragment(a,o,n.refStr,()=>i.refStr),r}return await this.fileSystem.renameFile(t,r)}async deletePath(t){let r=this.uriByPath(t);if(r.refStr){let n=await this.fileSystem.getFile(r.path),i=await this.fileSystem.getFileCacheTypeByRefString(n,r.refStr);return this.fileSystem.deleteFileFragment(n,i,r.refStr)}return this.fileSystem.deleteFile(t)}async getPathInfo(t){let r=this.uriByPath(t),n=await this.fileSystem.getFile(r.path);if(r.refStr){let i=this.fileSystem.getFileCacheTypeByRefString(n,r.refStr)}return n}keysForCacheType(t){return this.fileSystem.keysForCacheType(t)}async readPathCache(t){let r=this.uriByPath(t);if(r.scheme=="spaces"){if(r.authority.charAt(0)=="$"){let n=Object.keys(Um).find(i=>i==r.authority.slice(1));if(n)return{file:null,metadata:null,label:{name:Um[n].name,sticker:Um[n].icon,color:""},readOnly:!1,type:"space",parent:"",tags:[]}}if(r.authority.charAt(0)=="#")return{file:null,metadata:null,label:{name:r.authority,sticker:"",color:""},type:"space",parent:"",tags:[],readOnly:!1}}return t=="/"?{file:{name:this.spaceManager.superstate.settings.systemName,path:"/",isFolder:!0},metadata:{},label:{name:this.spaceManager.superstate.settings.systemName,sticker:"",color:""},type:"space",subtype:"folder",parent:"",tags:[],readOnly:!1}:this.fileSystem.getFileCache(t)}async readPath(t){let r=this.uriByPath(t),n=await this.fileSystem.getFile(r.path);if(r.refStr){let i=this.fileSystem.getFileCacheTypeByRefString(n,r.refStr);this.fileSystem.getFileContent(n,i,r.refStr)}return this.fileSystem.readTextFromFile(t)}async copyPath(t,r,n){let i=this.uriByPath(t),a=await this.fileSystem.getFile(i.path);return this.fileSystem.copyFile(a.path,r,n)}async writeToPath(t,r,n){let i=this.uriByPath(t),a=await this.fileSystem.getFile(i.path);if(i.refStr){let o=this.fileSystem.getFileCacheTypeByRefString(a,i.refStr);this.fileSystem.saveFileFragment(a,o,i.refStr,()=>r)}return n?this.fileSystem.writeBinaryToFile(t,r):this.fileSystem.writeTextToFile(t,r)}async childrenForPath(t,r){return await this.fileSystem.fileExists(t)?this.fileSystem.childrenForFolder(t,r):[]}parentPathForPath(t){return this.fileSystem.parentPathForPath(t)}async readFrame(t,r){let n=await this.fileSystem.getFile(this.spaceInfoForPath(t).framePath);if(!n){let i=this.defaultFrame(t);if(Object.keys(i).some(a=>a==r))return i[r]}return this.fileSystem.readFileFragments(n,"mdbTable",r)}async readAllFrames(t){let r=await this.fileSystem.getFile(this.spaceInfoForPath(t).framePath);return r?this.fileSystem.readFileFragments(r,"mdbTables"):this.defaultFrame(t)}async readTable(t,r){let n=this.spaceInfoForPath(t),i=await this.fileSystem.getFile(n.dbPath),a;!i&&r==yd.id?a=XS(this.spaceManager.superstate,n):(a=await this.fileSystem.readFileFragments(i,"mdbTable",r),!a&&r==yd.id&&(a=XS(this.spaceManager.superstate,n)));let o=ew(a.cols),s=this.spaceManager.superstate.pathsIndex,l=this.spaceManager.superstate.contextsIndex,u=s.get(t),c=a.rows;return r==yd.id&&(c=dNe(this.spaceManager.superstate.getSpaceItems(t).map(f=>f.path),a.rows,s,this.spaceManager.superstate.spacesMap,u).map(f=>Z1(s,f,a.cols,u))),c=c.map(f=>Gf(this.spaceManager.superstate.formulaContext,s,l,this.spaceManager.superstate.spacesMap,f,a.cols,u,this.spaceManager.superstate.settings,o)),{...a,rows:c}}async spaceInitiated(t){return!0}async contextInitiated(t){let r=this.spaceInfoForPath(t);return await this.fileSystem.fileExists(r.dbPath)}async tablesForSpace(t){let r=this.spaceInfoForPath(t),n=await this.fileSystem.getFile(r.dbPath);if(!n)return ZA.rows;let i=await this.fileSystem.readFileFragments(n,"schemas",null);return i.length==0?ZA.rows:i}defaultDBTablesForContext(t){let r=XS(this.spaceManager.superstate,t),n=PQ(t);return{...Dfe(t),m_fields:{uniques:n.uniques,cols:n.cols,rows:[...n.rows??[],...r.cols]},[r.schema.id]:{uniques:r.cols.filter(a=>a.unique=="true").map(a=>a.name),cols:r.cols.map(a=>a.name),rows:r.rows}}}defaultFrame(t){return t.startsWith(Wv)&&t==Wv+"overview"?Fpe:this.spaceManager.superstate.settings.defaultSpaceTemplate.length>0&&this.spaceManager.superstate.templateCache.has(this.spaceManager.superstate.settings.defaultSpaceTemplate)?this.spaceManager.superstate.templateCache.get(this.spaceManager.superstate.settings.defaultSpaceTemplate):this.spaceManager.superstate.settings.enableFolderNote?sE:lE}async createDefaultTable(t){let r=this.spaceInfoForPath(t),n=this.spaceInfoForPath(t).dbPath,i=n.split(".").pop(),a=n.split("/").slice(0,-1).join("/"),o=n.split("/").pop().split(".")[0];return this.fileSystem.newFile(a,o,i,this.defaultDBTablesForContext(r))}async createDefaultFrames(t){let r=this.defaultFrame(t),n={...YT(r),m_schema:Efe},i=this.spaceInfoForPath(t).framePath,a=i.split(".").pop(),o=i.split("/").slice(0,-1).join("/"),s=i.split("/").pop().split(".")[0];return this.fileSystem.newFile(o,s,a,n)}async createTable(t,r){let n=await this.fileSystem.getFile(this.spaceInfoForPath(t).dbPath);return n||(n=await this.createDefaultTable(t)),this.fileSystem.newFileFragment(n,"schema",r.id,r)}async saveTableSchema(t,r,n){let i=await this.fileSystem.getFile(this.spaceInfoForPath(t).dbPath);return i||(i=await this.createDefaultTable(t)),this.fileSystem.saveFileFragment(i,"schema",r,n)}async saveTable(t,r,n){let i=await this.fileSystem.getFile(this.spaceInfoForPath(t).dbPath);if(!i)if(n)i=await this.createDefaultTable(t);else return!1;return this.fileSystem.saveFileFragment(i,"mdbTable",r.schema.id,()=>r)}async deleteTable(t,r){let n=await this.fileSystem.getFile(this.spaceInfoForPath(t).dbPath);return this.fileSystem.deleteFileFragment(n,"schema",r)}async readAllTables(t){let r=this.spaceInfoForPath(t),n=await this.fileSystem.getFile(r.dbPath);if(!n){let i=XS(this.spaceManager.superstate,r);return{[i.schema.id]:i}}return this.fileSystem.readFileFragments(n,"mdbTables",null)}async framesForSpace(t){let r=await this.fileSystem.getFile(this.spaceInfoForPath(t).framePath);if(!r){let n=this.defaultFrame(t);return Object.values(n).map(i=>i.schema)}return this.fileSystem.readFileFragments(r,"schemas",null)}async createFrame(t,r){let n=await this.fileSystem.getFile(this.spaceInfoForPath(t).framePath);return n||(n=await this.createDefaultFrames(t)),this.fileSystem.newFileFragment(n,"schema",r.id,r)}async deleteFrame(t,r){let n=await this.fileSystem.getFile(this.spaceInfoForPath(t).framePath);return this.fileSystem.deleteFileFragment(n,"schema",r)}async saveFrameSchema(t,r,n){let i=await this.fileSystem.getFile(this.spaceInfoForPath(t).framePath);return i||(i=await this.createDefaultFrames(t)),this.fileSystem.saveFileFragment(i,"schema",r,n)}async saveFrame(t,r){let n=await this.fileSystem.getFile(this.spaceInfoForPath(t).framePath);return n||(n=await this.createDefaultFrames(t)),this.fileSystem.saveFileFragment(n,"mdbFrame",r.schema.id,()=>r)}async createDefaultCommands(t){let r={m_fields:{uniques:Va.uniques,cols:Va.cols,rows:[]},m_schema:{uniques:[],cols:["id","name","type","def","predicate","primary"],rows:[]}},n=this.spaceInfoForPath(t).commandsPath,i=n.split(".").pop(),a=n.split("/").slice(0,-1).join("/"),o=n.split("/").pop().split(".")[0];return this.fileSystem.newFile(a,o,i,r)}async commandsForSpace(t){let r=await this.fileSystem.getFile(this.spaceInfoForPath(t).commandsPath);return r?this.fileSystem.readFileFragments(r,"mdbCommands",null):[]}async runCommand(t,r,n){let i=await this.fileSystem.getFile(this.spaceInfoForPath(t).commandsPath);if(!i)return{result:null,error:"No commands file found"};let a=await this.fileSystem.readFileFragments(i,"mdbCommand",r);if(!a)return{result:null,error:"No command found"};let o,s;try{a.schema.type=="script"&&(o=rC(a.code,n)),a.schema.type=="formula"&&(o=zd(this.spaceManager.superstate.formulaContext,this.spaceManager.superstate.pathsIndex,this.spaceManager.superstate.spacesMap,a.code,a.fields.reduce((l,u)=>({...l,[u.name]:u}),{}),n,this.spaceManager.superstate.pathsIndex.get(t)))}catch(l){s=l}return{result:o,error:s}}async createCommand(t,r){let n=await this.fileSystem.getFile(this.spaceInfoForPath(t).commandsPath);return n||(n=await this.createDefaultCommands(t)),this.fileSystem.newFileFragment(n,"schema",r.id,r)}async readSystemCommands(){let t=(await this.childrenForPath(`${this.dataPath}/${q3}`,"folder")).map(n=>n.split("/").pop());return Promise.all(t.map(async n=>{let i=await this.readLibraryCommands(n);return{name:n,commands:Object.values(i??{})}}))}async readLibraryCommands(t){return this.fileSystem.readFileFragments({path:`${this.dataPath}/${q3}/${t}/commands.mdb`,name:"commands",filename:"commands.mdb",parent:`${this.dataPath}/${q3}/${t}`,isFolder:!1,extension:"mdb"},"mdbCommands")}async saveSystemCommand(t,r){let n={path:`${this.dataPath}/${q3}/${t}/commands.mdb`,name:"commands",filename:"commands.mdb",parent:`${this.dataPath}/${q3}/${t}`,isFolder:!1,extension:"mdb"};if(r)await this.fileSystem.saveFileFragment(n,"schema",r.schema.id,()=>r.schema),await this.fileSystem.saveFileFragment(n,"mdbCommand",r.schema.id,()=>r);else{let i={m_fields:{uniques:Va.uniques,cols:Va.cols,rows:[]},m_schema:{uniques:[],cols:["id","name","type","def","predicate","primary"],rows:[]}},a=n.path,o=a.split(".").pop(),s=a.split("/").slice(0,-1).join("/"),l=a.split("/").pop().split(".")[0];await this.fileSystem.newFile(s,l,o,i)}}async deleteCommand(t,r){let n=await this.fileSystem.getFile(this.spaceInfoForPath(t).commandsPath);return this.fileSystem.deleteFileFragment(n,"mdbCommand",r)}async saveCommand(t,r,n){let i=await this.fileSystem.getFile(this.spaceInfoForPath(t).commandsPath);return i||(i=await this.createDefaultCommands(t)),this.fileSystem.saveFileFragment(i,"mdbCommand",r,n)}async contextForSpace(t){let r=await this.fileSystem.getFile(this.spaceInfoForPath(t).dbPath);return r?this.fileSystem.readFileFragments(r,"mdbTable",lr):XS(this.spaceManager.superstate,this.spaceInfoForPath(t))}async addSpaceProperty(t,r){let n=await this.fileSystem.getFile(this.spaceInfoForPath(t)?.dbPath);return n||await this.createDefaultTable(t),this.fileSystem.newFileFragment(n,"field",r.name,r)}async deleteSpaceProperty(t,r){let n=await this.fileSystem.getFile(this.spaceInfoForPath(t).dbPath);return this.fileSystem.deleteFileFragment(n,"field",r)}async saveSpaceProperty(t,r,n){let i=await this.fileSystem.getFile(this.spaceInfoForPath(t).dbPath);return i||await this.createDefaultTable(t),this.fileSystem.saveFileFragment(i,"field",n,a=>({...a,...r}))}async addProperty(t,r){let n=await this.fileSystem.getFile(t);this.fileSystem.newFileFragment(n,"property",r.name,r)}async saveProperties(t,r){let n=await this.fileSystem.getFile(t);return this.fileSystem.saveFileFragment(n,"property",null,i=>({...i,...r}))}async readLabel(t){let r=this.fileSystem.getFileCache(t)?.label;if(!r){let n=await this.fileSystem.getFile(t);return n?this.fileSystem.readFileFragments(n,"label",null):{}}return r}async saveLabel(t,r,n){if(this.spaceManager.superstate.spacesIndex.has(t)){let a=this.spaceInfoForPath(t),o=await this.fileSystem.getFile(a.defPath),s=await this.fileSystem.getFile(a.notePath);if(this.spaceManager.superstate.settings.enableFolderNote)s||(s=await this.fileSystem.newFile(a.folderPath,a.name,"md"));else{if(!o){let l=this.spaceInfoForPath(t).defPath,u=l.split(".").pop(),c=l.split("/").slice(0,-1).join("/"),f=l.split("/").pop().split(".")[0];o=await this.fileSystem.newFile(c,f,u)}s=o}await this.fileSystem.saveFileLabel(s,r,n);return}let i=await this.fileSystem.getFile(t);this.fileSystem.saveFileLabel(i,r,n)}async renameProperty(t,r,n){let i=await this.fileSystem.getFile(t);this.fileSystem.saveFileFragment(i,"property",null,a=>{let{[r]:o,...s}=a;return o?{...s,[n]:o}:a})}async readProperties(t){let r=await this.fileSystem.getFile(t);return this.fileSystem.readFileFragments(r,"property",null)}async deleteProperty(t,r){let n=await this.fileSystem.getFile(t);this.fileSystem.deleteFileFragment(n,"property",r)}allSpaces(t){let n=(()=>this.allPaths(["folder"],t).filter(a=>!Yee(this.spaceManager.superstate.settings,a)&&!t).map(a=>nN(this.spaceManager,a)))();if(this.spaceManager.superstate.settings.enableDefaultSpaces){let i=Object.keys(Um).map(s=>this.spaceManager.spaceInfoForPath(`spaces://$${s}`)),o=(()=>this.readTags().map(s=>t1(this.spaceManager,dP(s)))??[])();return[...i,...o,...n]}return n}readTags(){return this.fileSystem.allTags()}spaceInfoForPath(t){return Ppe(this.spaceManager,t)}allCaches(){return this.fileSystem.allCaches()}async spaceDefForSpace(t){let r=this.spaceInfoForPath(t);if(!r)return null;let n=r.defPath?await this.fileSystem.readTextFromFile(r.defPath):null;if(!n){let a=await this.fileSystem.getFile(r.notePath),s=(a?this.fileSystem.getFileCache(a.path)?.frontmatter:null)??{};return bq(s,this.spaceManager.superstate.settings)}let i=or(n)??{};return bq(i,this.spaceManager.superstate.settings)}async createSpace(t,r,n){let i=this.spaceInfoForPath(r),a=i.folderPath=="/"?t:i.folderPath+"/"+t;if(await this.fileSystem.createFolder(a),Object.keys(n??{}).length>0)return this.saveSpace(a,()=>n)}async saveSpace(t,r,n){let i=r(await this.spaceDefForSpace(t))??{},a=this.spaceInfoForPath(t),o=await this.fileSystem.getFile(a.defPath);if(!o){let l=this.spaceInfoForPath(t).defPath,u=l.split(".").pop(),c=l.split("/").slice(0,-1).join("/"),f=l.split("/").pop().split(".")[0];o=await this.fileSystem.newFile(c,f,u)}let s=await this.fileSystem.getFile(a.notePath);this.spaceManager.superstate.settings.enableFolderNote?s||(s=await this.fileSystem.newFile(a.folderPath,wd(a.notePath),"md")):s=o,n&&await this.fileSystem.saveFileFragment(s,"property",null,l=>({...l,...n??{}})),await this.fileSystem.saveFileFragment(o,"definition",null,l=>({[eN]:i.joins,[KT]:i.contexts,[tN]:i.links,[rN]:i.sort,[JT]:i.template,[ZT]:i.templateName,defaultSticker:i.defaultSticker,defaultColor:i.defaultColor,readMode:i.readMode,fullWidth:i.fullWidth}))}renameSpace(t,r){let n=this.spaceInfoForPath(t),i=this.spaceInfoForPath(r);return this.fileSystem.renameFile(n.folderPath,i.folderPath).then(a=>(this.spaceManager.superstate.settings.enableFolderNote&&this.fileSystem.renameFile(Jh(n.notePath,i.path),i.notePath),a))}deleteSpace(t){let r=this.spaceInfoForPath(t),n=t1(this.spaceManager,r.name);this.fileSystem.deleteFile(n.folderPath)}childrenForSpace(t){return this.fileSystem.allFiles().filter(r=>r.parent==t).map(r=>r.path)}async addTag(t,r){let n=this.fileSystem.getFileCache(t);if(n.subtype=="md"||n.subtype=="folder"){this.fileSystem.addTagToFile(t,r);return}let i=ii(r),a=await this.spaceDefForSpace(fP(r)),o=Ks(a.links)??[];o.find(u=>u==t)||o.push(t);let l={...a,links:o};await this.saveSpace(i,u=>({...u,...l})),await this.spaceManager.superstate.updateSpaceMetadata(i,l),this.spaceManager.superstate.reloadPath(t,!0).then(u=>this.spaceManager.superstate.dispatchEvent("pathStateUpdated",{path:t}))}renameTag(t,r,n){this.fileSystem.renameTagForFile(t,r,n)}deleteTag(t,r){this.fileSystem.removeTagFromFile(t,r)}pathsForTag(t){return this.fileSystem.filesForTag(t)}resolvePath(t,r){return this.fileSystem.resolvePath(t,r)}};var mNe={"image-select":`<svg width="100" height="100" viewBox="0 0 100 100" fill="none" xmlns="http://www.w3.org/2000/svg">
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