# MathParser.org-mXparser

**Repository Path**: afunc233/MathParser.org-mXparser

## Basic Information

- **Project Name**: MathParser.org-mXparser
- **Description**: Math Parser Java Android C# .NET/MONO (.NET Framework, .NET Core, .NET Standard, .NET PCL, Xamarin.Android, Xamarin.iOS) CLS Library - a super easy, rich and flexible mathematical expression parser (expression evaluator, expression provided as plain text / strings) for JAVA and C#. Main features: rich built-in library of operators, constants, math functions, user defined: arguments, functions, recursive functions and general recursion (direct / indirect). Additionally parser provides grammar and internal syntax checking.
- **Primary Language**: Unknown
- **License**: Not specified
- **Default Branch**: master
- **Homepage**: None
- **GVP Project**: No

## Statistics

- **Stars**: 1
- **Forks**: 0
- **Created**: 2020-11-10
- **Last Updated**: 2025-03-05

## Categories & Tags

**Categories**: Uncategorized

**Tags**: None

## README

# Package installation

## Nuget

    PM> Install-Package MathParser.org-mXparser -Version 4.4.2

## Maven

    <groupId>org.mariuszgromada.math</groupId>
    <artifactId>MathParser.org-mXparser</artifactId>
    <version>4.4.2</version>
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# MathParser.org-mXparser

![mXparser icon](http://mathparser.org/wp-content/uploads/2020/01/mxparser-icon.png)

![01-mXparser-calc](http://mathparser.org/wp-content/uploads/2017/05/01-mXparser-calc.gif)

# mXparser - optional donation

[![paypall-donation](http://mathparser.org/wp-content/uploads/2017/07/paypall-donation.png)](https://www.paypal.com/cgi-bin/webscr?cmd=_s-xclick&hosted_button_id=QJYYH86583LEN)

# mXparser - a super easy, rich and highly flexible Mathematical Expression Parser (Math Parser, Expression Evaluator) library for JAVA, Android and C# .NET.
    ### 15.10.2020: first 500000 downloads!
    ### 20.12.2019: first 250000 downloads!
    ### 01.01.2019: first 100000 downloads!
    ### 01.08.2018: first 60000 downloads!
    ### 20.11.2017: first 20000 downloads!
    ### 01.09.2017: first 15000 downloads!
    ### 04.05.2017: first 10000 downloads!
    ### 31.03.2016: first 1000 downloads!
    
![02-mXparser-sin.gif](http://mathparser.org/wp-content/uploads/2017/05/02-mXparser-sin.gif)

**mXparser** is **a highly flexible parser of mathematical expressions provided as text**. Software delivers easy to use API for JAVA and C# .NET. 

# Supported frameworks
![mXparser frameworks](http://mathparser.org/wp-content/uploads/2017/05/supported-frameworks.png)
- JAVA: 6+
- Android - tested with mxparser compiled using jdk 1.7
- .NET Framework (2+) / MONO CLS
- .NET Core: 1+
- .NET Standard: 1+
- .NET PCL
- Xamarin

![03-mXparser-sum.gif](http://mathparser.org/wp-content/uploads/2017/05/03-mXparser-sum.gif)

# JAVA intro
![mXparser demo](http://mathparser.org/wp-content/uploads/2017/05/mxparser-demo-r2.gif)

# C# intro
![mXparser demo - csharp](http://mathparser.org/wp-content/uploads/2017/05/mxparser-demo-vs-r2.gif)
# Tutorial

![mXparser tutorial](http://mathparser.org/wp-content/uploads/2017/05/mXparser-tutorial.png)

# [>>> Click to learn from examples <<<](http://mathparser.org/mxparser-tutorial/)

# Main functionalities:
- **basic operators**, i.e.: +, -, *, ^, !
- **[Boolean logic](http://mathparser.org/api/org/mariuszgromada/math/mxparser/mathcollection/BooleanAlgebra.html)** operators i.e.: or, and, xor
- **[binary relations](http://mathparser.org/api/org/mariuszgromada/math/mxparser/mathcollection/BinaryRelations.html)** i.e.: =, <, >
- **[math functions](http://mathparser.org/api/org/mariuszgromada/math/mxparser/mathcollection/MathFunctions.html)** (large library of 1-arg, 2-arg, 3-arg - functions) i.e.: sin, cos, Stirling numbers, log, inverse functions
- **[constants](http://mathparser.org/api/org/mariuszgromada/math/mxparser/mathcollection/MathConstants.html)** (large library), i.e.: pi, e, golden ratio
- **n-args functions**, i.e.: [greatest common divisor](http://mathparser.org/api/org/mariuszgromada/math/mxparser/mathcollection/MathFunctions.html#gcd-int...-)
- **[iterated summation and product operators](http://mathparser.org/api/org/mariuszgromada/math/mxparser/mathcollection/NumberTheory.html#sigmaSummation-org.mariuszgromada.math.mxparser.Expression-org.mariuszgromada.math.mxparser.Argument-double-double-double-)**
- **[differentiation and integration](http://mathparser.org/api/org/mariuszgromada/math/mxparser/mathcollection/NumericalAnalysis.html)**


# High flexibility functionalities
- **[user defined constants](http://mathparser.org/api/org/mariuszgromada/math/mxparser/Constant.html)** and arguments, both free - and dependent on other arguments + possibility of use in functions
- **[user defined functions](http://mathparser.org/api/org/mariuszgromada/math/mxparser/Function.html)** (both free and depended)
- **[user defined recursive arguments](http://mathparser.org/api/org/mariuszgromada/math/mxparser/RecursiveArgument.html)** + simple (controlled) recursion (1 recursive argument)
- **[user defined recursive functions / expressions (any)](http://mathparser.org/api/org/mariuszgromada/math/mxparser/Function.html#getRecursiveMode--)** - complex, many arguments, no limitation 
- **[internal syntax checking](http://mathparser.org/api/org/mariuszgromada/math/mxparser/Expression.html#checkSyntax--)**
- **[internal help](http://mathparser.org/api/org/mariuszgromada/math/mxparser/Expression.html#getHelp--)**
- other useful functionalities, i.e.: [computing time](http://mathparser.org/api/org/mariuszgromada/math/mxparser/Expression.html#getComputingTime--), expression description.

# Project documentation
### - [mXparser - API (english)](http://mathparser.org/api/)
### - [mXparser - WIKI (english)](https://github.com/mariuszgromada/MathParser.org-mXparser/wiki)
### - [mXparser - Tutorial (english)](http://mathparser.org/mxparser-tutorial/)
### - [MathSpace.pl - site about math with mXparser examples (polish)](http://mathspace.pl/)
### - [MathParser.org - site about mXparser (english)](http://mathparser.org/)

[![paypal](https://www.paypalobjects.com/en_US/i/btn/btn_donateCC_LG.gif)](https://www.paypal.com/cgi-bin/webscr?cmd=_s-xclick&hosted_button_id=QJYYH86583LEN)

# mXparser in nutshell

#### You want simple calculator...
![calc](http://mathparser.org/wp-content/uploads/2017/05/calc.png)

    Expression e = new Expression("2+3");
    e.calculate();
:+1: 

#### A calculator supporting parenthesis...
![parenth](http://mathparser.org/wp-content/uploads/2017/05/parenth.png)

    Expression e = new Expression("2+(3-5)^2");
    e.calculate();
:+1: 

#### You care about predefined constants...
![const](http://mathparser.org/wp-content/uploads/2017/05/const.png)

    Expression e = new Expression("2*pi");
    e.calculate();
:+1: 


#### You need to define your own constants...
![const-user](http://mathparser.org/wp-content/uploads/2017/05/const-user.png)

    Constant tau = new Constant("tau = 2*pi");
    Expression e = new Expression("3*tau", tau);
    e.calculate();
:+1: 

#### You enjoy using many built-in functions...
![sinx](http://mathparser.org/wp-content/uploads/2017/05/sinx.png)

    Expression e = new Expression("sin(2*pi)");
    e.calculate();
:+1: 

#### You do not limit yourself to unary functions...
![fun-variadic](http://mathparser.org/wp-content/uploads/2017/05/fun-variadic.png)

    Expression e = new Expression("gcd(2,5,10,30)");
    e.calculate();
:+1: 

#### What about user defined arguments...
![arg-free](http://mathparser.org/wp-content/uploads/2017/05/arg-free.png)

    Argument x = new Argument("x = 5");
    Expression e = new Expression("sin(x)");
    e.calculate();
:+1: 

#### You are considering dependent arguments...
![arg-dep](http://mathparser.org/wp-content/uploads/2017/05/arg-dep.png)

    Argument x = new Argument("x = 5");
    Argument y = new Argument("y = 2*x", x);
    Expression e = new Expression("sin(y)", y);
    e.calculate();
:+1: 

#### You need to apply some logic...
![if-then](http://mathparser.org/wp-content/uploads/2017/05/if-then.png)

    Argument x = new Argument("x = 5");
    Expression e = new Expression("if(sin(x) > 5, 1, 0)", x);
    e.calculate();
:+1:

#### Yes, you are right, there is a support for Boolean algebra!
![true-false](http://mathparser.org/wp-content/uploads/2017/05/true-false.png)

    Expression e = new Expression("5=6");
    e.calculate();
:+1:

#### And for binary relations as well!

    Expression e = new Expression("5 <= 6");
    e.calculate();
:+1:

## mXparser is cool! But this is only the begging, we are just warming up!

#### You want to play with iterated operators...
![sum](http://mathparser.org/wp-content/uploads/2017/05/sum.png)

    Expression e = new Expression("sum(i, 1, 10, 2*i^2 + pi)");
    e.calculate();
:+1:

#### You want to iterate differently by not necessarily whole numbes...
![prod](http://mathparser.org/wp-content/uploads/2017/05/prod.png)

    Expression e = new Expression("prod(i, 1, 5, i, 0.5)");
    e.calculate();
:+1:

#### You want to have more fun with math...
    Argument x = new Argument("x = pi/2");
    Expression e20 = new Expression("sum(n,0,10,(-1)^n*(x^(2*n+1))/(2*n+1)!)", x);
    e.calculate();
:+1:

#### You still want more fun with calculus operations, i.e. differentiation...
![der](http://mathparser.org/wp-content/uploads/2017/05/der.png)

    Argument x = new Argument("x = pi/2");
    Expression e = new Expression("cos(x)-der(sin(x), x)", x);
    e.calculate();
:+1:

#### And definite integrals as well...
![int](http://mathparser.org/wp-content/uploads/2017/05/int.png)

    Expression e = new Expression("2*int(sqrt(1-x^2), x, -1, 1)");
    e.calculate();
:+1:

##  mXparser is even cooler! It is time to ask about ...

#### user defined functions...
![fun-user](http://mathparser.org/wp-content/uploads/2017/05/fun-user.png)

    Function f = new Function("f(x,y) = sin(x) + cos(y)");
    f.calculate(1,2);
    Expression e = new Expression("f(1,2) - 10", f);
    e.calculate();
:+1:

#### Recursion is your desire...
![recur](http://mathparser.org/wp-content/uploads/2017/05/recur.png)

    Function f = new Function("f(n) = if( n>0, n*f(n-1), 1)");
    f.calculate()
:+1:

#### Any kind of recursion...
    Function Cnk = new Function("Cnk(n,k) = if(k>0, if(k<n, Cnk(n-1,k-1)+Cnk(n-1,k), 1), 1)");
    Cnk.calculate()
:+1:

## If anything above matches you then mXparser is a good choce! mXparser is freely distributed under Simplified BSD licence, but still you can give credits to the author, and even donate if you wish :+1: 

[![paypal](https://www.paypalobjects.com/en_US/i/btn/btn_donateCC_LG.gif)](https://www.paypal.com/cgi-bin/webscr?cmd=_s-xclick&hosted_button_id=QJYYH86583LEN)

#### mXparser can interact with end users as it supports syntax checking.
![syntax](http://mathparser.org/wp-content/uploads/2017/05/syntax.png)

    Expression e = new Expression("2+1/a");
    e.checkSyntax();
    mXparser.consolePrintln(e.getErrorMessage());

# Built-in tokens

## Number format
|Key word|Category|Description|Example|Since|
|---|---|---|---|---|
|Number|Decimal Number|Decimal number|1, 1.5, -2.3|1.0|
|Number|Decimal Number|Decimal number - scientific notation|1.2e10, -2.4e-10, 2.3E+10|4.0|
|Number|Binary Number|Binary number - number literal| b.10101, B.10101, b2.10010|4.1|
|Number|Octal Number|Octal number - number literal| o.1027, O.1027, b8.1027|4.1|
|Number|Hexadecimal Number|Hexadecimal number - number literal| h.12fE, H.12fE, b16.12fE|4.1|
|Number|Unary Number|Unary number - number literal| b1.111 , B1.111|4.1|
|Number|Base 1-36|Base 1-36 number - number literal| bN.xxxx , BN.xxxx|4.1|
|Number|Fraction|Number literal as fraction| 1_2 , 2_3_4, 172_345, 345_172 |4.3|

## Operators
|Key word|Category|Description|Example|Since|
|---|---|---|---|---|
| + | Operator | Addition | a + b | 1.0 |
| - | Operator | Subtraction | a - b | 1.0 |
| * | Operator | Multiplication | a * b | 1.0 |
| / | Operator | Division | a / b | 1.0 |
| ^ | Operator | Exponentiation | a^b | 1.0 |
| ! | Operator | Factorial | n! | 1.0 |
| # | Operator | Modulo function | a # b | 1.0 |
| % | Operator | Percentage | n% | 4.1 |
| ^^ | Operator | Tetration | a^^b | 4.3 |

## Boolean Operators
|Key word|Category|Description|Example|Since|
|---|---|---|---|---|
| & |Boolean Operator|Logical conjunction (AND)|p & q|1.0|
| && |Boolean Operator|Logical conjunction (AND)|p && q|1.0|
| /\\ |Boolean Operator|Logical conjunction (AND)|p /\\ q|1.0|
| ~& |Boolean Operator|NAND - Sheffer stroke|p ~& q|1.0|
| ~&& |Boolean Operator|NAND - Sheffer stroke|p ~&& q|1.0|
| ~/\\ |Boolean Operator|NAND - Sheffer stroke|p ~/\\ q|1.0|
| \| |Boolean Operator|Logical disjunction (OR)|p \| q|1.0|
| \|\| |Boolean Operator|Logical disjunction (OR)|p \|\| q|1.0|
| \\/ |Boolean Operator|Logical disjunction (OR)|p \\/ q|1.0|
| ~\| |Boolean Operator|Logical NOR|p ~\| q|1.0|
| ~\|\| |Boolean Operator|Logical NOR|p ~\|\| q|1.0|
| ~\\/ |Boolean Operator|Logical NOR|p ~\\/ q|1.0|
| (+) |Boolean Operator|Exclusive or (XOR)|p (+) q|1.0|
| --> |Boolean Operator|Implication (IMP)|p --> q|1.0|
| <-- |Boolean Operator|Converse implication (CIMP)|p <-- q|1.0|
| -/> |Boolean Operator|Material nonimplication (NIMP)|p -/> q|1.0|
| </- |Boolean Operator|Converse nonimplication (CNIMP)|p </- q|1.0|
| <-> |Boolean Operator|Logical biconditional (EQV)|p <-> q|1.0|
| ~ |Boolean Operator|Negation|~p|1.0|


## Bitwise Operators
|Key word|Category|Description|Example|Since|
|---|---|---|---|---|
| @~ |Bitwise Operator|Bitwise unary complement|@~10|4.0|
| @& |Bitwise Operator|Bitwise AND|10 @& 2|4.0|
| @^ |Bitwise Operator|Bitwise exclusive OR|10 @^ 2|4.0|
| @\| |Bitwise Operator|Bitwise inclusive OR|10 @\| 2|4.0|
| @<< |Bitwise Operator|Signed left shift|10 @<< 2|4.0|
| @>> |Bitwise Operator|Signed right shift|10 @>> 2|4.0|

## Binary Relations
|Key word|Category|Description|Example|Since|
|---|---|---|---|---|
| = |Binary Relation|Equality|a = b|1.0|
| == |Binary Relation|Equality|a == b|1.0|
| <> |Binary Relation|Inequation|a <> b|1.0|
| ~= |Binary Relation|Inequation|a ~= b|1.0|
| != |Binary Relation|Inequation|a != b|1.0|
| < |Binary Relation|Lower than|a < b|1.0|
| > |Binary Relation|Greater than|a > b|1.0|
| <= |Binary Relation|Lower or equal|a <= b|1.0|
| >= |Binary Relation|Greater or equal|a >= b|1.0|

## Unary Functions
|Key word|Category|Description|Example|Since|
|---|---|---|---|---|
| sin | Unary Function | Trigonometric sine function | sin(x) | 1.0 |
| cos | Unary Function | Trigonometric cosine function | cos(x) | 1.0 |
| tg | Unary Function | Trigonometric tangent function | tg(x) | 1.0 |
| tan | Unary Function | Trigonometric tangent function | tan(x) | 1.0 |
| ctg | Unary Function | Trigonometric cotangent function | ctg(x) | 1.0 |
| cot | Unary Function | Trigonometric cotangent function | cot(x) | 1.0 |
| ctan | Unary Function | Trigonometric cotangent function | ctan(x) | 1.0 |
| sec | Unary Function | Trigonometric secant function | sec(x) | 1.0 |
| csc | Unary Function | Trigonometric cosecant function | csc(x) | 1.0 |
| cosec | Unary Function | Trigonometric cosecant function | cosec(x) | 1.0 |
| asin | Unary Function | Inverse trigonometric sine function | asin(x) | 1.0 |
| arsin | Unary Function | Inverse trigonometric sine function | arsin(x) | 1.0 |
| arcsin | Unary Function | Inverse trigonometric sine function | arcsin(x) | 1.0 |
| acos | Unary Function | Inverse trigonometric cosine function | acos(x) | 1.0 |
| arcos | Unary Function | Inverse trigonometric cosine function | arcos(x) | 1.0 |
| arccos | Unary Function | Inverse trigonometric cosine function | arccos(x) | 1.0 |
| atg | Unary Function | Inverse trigonometric tangent function | atg(x) | 1.0 |
| atan | Unary Function | Inverse trigonometric tangent function | atan(x) | 1.0 |
| arctg | Unary Function | Inverse trigonometric tangent function | arctg(x) | 1.0 |
| arctan | Unary Function | Inverse trigonometric tangent function | arctan(x) | 1.0 |
| actg | Unary Function | Inverse trigonometric cotangent function | actg(x) | 1.0 |
| acot | Unary Function | Inverse trigonometric cotangent function | acot(x) | 1.0 |
| actan | Unary Function | Inverse trigonometric cotangent function | actan(x) | 1.0 |
| arcctg | Unary Function | Inverse trigonometric cotangent function | arcctg(x) | 1.0 |
| arccot | Unary Function | Inverse trigonometric cotangent function | arccot(x) | 1.0 |
| arcctan | Unary Function | Inverse trigonometric cotangent function | arcctan(x) | 1.0 |
| ln | Unary Function | Natural logarithm function (base e) | ln(x) | 1.0 |
| log2 | Unary Function | Binary logarithm function (base 2) | log2(x) | 1.0 |
| log10 | Unary Function | Common logarithm function (base 10) | log10(x) | 1.0 |
| rad | Unary Function | Degrees to radians function | rad(x) | 1.0 |
| exp | Unary Function | Exponential function | exp(x) | 1.0 |
| sqrt | Unary Function | Squre root function | sqrt(x) | 1.0 |
| sinh | Unary Function | Hyperbolic sine function | sinh(x) | 1.0 |
| cosh | Unary Function | Hyperbolic cosine function | cosh(x) | 1.0 |
| tgh | Unary Function | Hyperbolic tangent function | tgh(x) | 1.0 |
| tanh | Unary Function | Hyperbolic tangent function | tanh(x) | 1.0 |
| coth | Unary Function | Hyperbolic cotangent function | coth(x) | 1.0 |
| ctgh | Unary Function | Hyperbolic cotangent function | ctgh(x) | 1.0 |
| ctanh | Unary Function | Hyperbolic cotangent function | ctanh(x) | 1.0 |
| sech | Unary Function | Hyperbolic secant function | sech(x) | 1.0 |
| csch | Unary Function | Hyperbolic cosecant function | csch(x) | 1.0 |
| cosech | Unary Function | Hyperbolic cosecant function | cosech(x) | 1.0 |
| deg | Unary Function | Radians to degrees function | deg(x) | 1.0 |
| abs | Unary Function | Absolut value function | abs(x) | 1.0 |
| sgn | Unary Function | Signum function | sgn(x) | 1.0 |
| floor | Unary Function | Floor function | floor(x) | 1.0 |
| ceil | Unary Function | Ceiling function | ceil(x) | 1.0 |
| not | Unary Function | Negation function | not(x) | 1.0 |
| asinh | Unary Function | Inverse hyperbolic sine function | asinh(x) | 1.0 |
| arsinh | Unary Function | Inverse hyperbolic sine function | arsinh(x) | 1.0 |
| arcsinh | Unary Function | Inverse hyperbolic sine function | arcsinh(x) | 1.0 |
| acosh | Unary Function | Inverse hyperbolic cosine function | acosh(x) | 1.0 |
| arcosh | Unary Function | Inverse hyperbolic cosine function | arcosh(x) | 1.0 |
| arccosh | Unary Function | Inverse hyperbolic cosine function | arccosh(x) | 1.0 |
| atgh | Unary Function | Inverse hyperbolic tangent function | atgh(x) | 1.0 |
| atanh | Unary Function | Inverse hyperbolic tangent function | atanh(x) | 1.0 |
| arctgh | Unary Function | Inverse hyperbolic tangent function | arctgh(x) | 1.0 |
| arctanh | Unary Function | Inverse hyperbolic tangent function | arctanh(x) | 1.0 |
| acoth | Unary Function | Inverse hyperbolic cotangent function | acoth(x) | 1.0 |
| actgh | Unary Function | Inverse hyperbolic cotangent function | actgh(x) | 1.0 |
| actanh | Unary Function | Inverse hyperbolic cotangent function | actanh(x) | 1.0 |
| arcoth | Unary Function | Inverse hyperbolic cotangent function | arcoth(x) | 1.0 |
| arccoth | Unary Function | Inverse hyperbolic cotangent function | arccoth(x) | 1.0 |
| arcctgh | Unary Function | Inverse hyperbolic cotangent function | arcctgh(x) | 1.0 |
| arcctanh | Unary Function | Inverse hyperbolic cotangent function | arcctanh(x) | 1.0 |
| asech | Unary Function | Inverse hyperbolic secant function | asech(x) | 1.0 |
| arsech | Unary Function | Inverse hyperbolic secant function | arsech(x) | 1.0 |
| arcsech | Unary Function | Inverse hyperbolic secant function | arcsech(x) | 1.0 |
| acsch | Unary Function | Inverse hyperbolic cosecant function | acsch(x) | 1.0 |
| arcsch | Unary Function | Inverse hyperbolic cosecant function | arcsch(x) | 1.0 |
| arccsch | Unary Function | Inverse hyperbolic cosecant function | arccsch(x) | 1.0 |
| acosech | Unary Function | Inverse hyperbolic cosecant function | acosech(x) | 1.0 |
| arcosech | Unary Function | Inverse hyperbolic cosecant function | arcosech(x) | 1.0 |
| Sa | Unary Function | Sinc function (normalized) | Sa(x) | 1.0 |
| sinc | Unary Function | Sinc function (normalized) | sinc(x) | 1.0 |
| Sinc | Unary Function | Sinc function (unnormalized) | Sinc(x) | 1.0 |
| Bell | Unary Function | Bell number | Bell(n) | 1.0 |
| Luc | Unary Function | Lucas number | Luc(n) | 1.0 |
| Fib | Unary Function | Fibonacci number | Fib(n) | 1.0 |
| harm | Unary Function | Harmonic number | harm(n) | 1.0 |
| ispr | Unary Function | Prime number test (is number a prime?) | ispr(n) | 2.3 |
| Pi | Unary Function | Prime-counting function - Pi(x) | Pi(n) | 2.3 |
| Ei | Unary Function | Exponential integral function (non-elementary special function) - usage example: Ei(x) | Ei(x) | 2.3 |
| li | Unary Function | Logarithmic integral function (non-elementary special function) - usage example: li(x) | li(x) | 2.3 |
| Li | Unary Function | Offset logarithmic integral function (non-elementary special function) - usage example: Li(x) | Li(x) | 2.3 |
| erf | Unary Function | Gauss error function (non-elementary special function) - usage example: 2 + erf(x) | erf(x) | 3.0 |
| erfc | Unary Function | Gauss complementary error function (non-elementary special function) - usage example: 1 - erfc(x) | erfc(x) | 3.0 |
| erfInv | Unary Function | Inverse Gauss error function (non-elementary special function) - usage example: erfInv(x) | erfInv(x) | 3.0 |
| erfcInv | Unary Function | Inverse Gauss complementary error function (non-elementary special function) - usage example: erfcInv(x) | erfcInv(x) | 3.0 |
| ulp | Unary Function | Unit in The Last Place - ulp(0.1) | ulp(x) | 3.0 |
| isNaN | Unary Function | Returns true = 1 if value is a Not-a-Number (NaN), false = 0 otherwise - usage example: isNaN(x) | isNaN(x) | 4.1 |
| ndig10 | Unary Function | Number of digits in numeral system with base 10 | ndig10(x) | 4.1 |
| nfact | Unary Function | Prime decomposition - number of distinct prime factors | nfact(x) | 4.1 |
| arcsec | Unary Function | Inverse trigonometric secant | arcsec(x) | 4.1 |
| Gamma | Unary Function |  Gamma special function Γ(s) | Gamma(x) | 4.3 |
| LambW0(x) | Unary Function | Lambert-W special function, principal branch 0, also called the omega function or product logarithm | LambW0(x) | 4.3 |
| LambW1(x) | Unary Function | Lambert-W special function, branch -1, also called the omega function or product logarithm | LambW1(x) | 4.3 |
| sgnGamma | Unary Function | Signum of Gamma special function, Γ(x) | sgnGamma(x) | 4.3 |
| logGamma | Unary Function | Log Gamma special function, lnΓ(x) | logGamma(x) | 4.3 |
| diGamma | Unary Function | Digamma function as the logarithmic derivative of the Gamma special function, ψ(x) | diGamma(x) | 4.3 |

## Binary Functions
|Key word|Category|Description|Example|Since|
|---|---|---|---|---|
| log | Binary Function | Logarithm function | log(a, b) | 1.0 |
| mod | Binary Function | Modulo function | mod(a, b) | 1.0 |
| C | Binary Function | Binomial coefficient function | C(n, k) | 1.0 |
| Bern | Binary Function | Bernoulli numbers | Bern(m, n) | 1.0 |
| Stirl1 | Binary Function | Stirling numbers of the first kind | Stirl1(n, k) | 1.0 |
| Stirl2 | Binary Function | Stirling numbers of the second kind | Stirl2(n, k) | 1.0 |
| Worp | Binary Function | Worpitzky number | Worp(n, k) | 1.0 |
| Euler | Binary Function | Euler number | Euler(n, k) | 1.0 |
| KDelta | Binary Function | Kronecker delta | KDelta(i, j) | 1.0 |
| EulerPol | Binary Function | EulerPol | EulerPol | 1.0 |
| Harm | Binary Function | Harmonic number | Harm(x, n) | 1.0 |
| rUni | Binary Function | Random variable - Uniform continuous distribution U(a,b), usage example: 2*rUni(2,10) | rUni(a, b) | 3.0 |
| rUnid | Binary Function | Random variable - Uniform discrete distribution U{a,b}, usage example: 2*rUnid(2,100) | rUnid(a, b) | 3.0 |
| round | Binary Function | Half-up rounding, usage examples: round(2.2, 0) = 2, round(2.6, 0) = 3, round(2.66,1) = 2.7 | round(x, n) | 3.0 |
| rNor | Binary Function | Random variable - Normal distribution N(m,s) m - mean, s - stddev, usage example: 3*rNor(0,1) | rNor(mean, stdv) | 3.0 |
| ndig | Binary Function | Number of digits representing the number in numeral system with given base | ndig(number, base) | 4.1 |
| dig10 | Binary Function | Digit at position 1 ... n (left -> right) or 0 ... -(n-1) (right -> left) - base 10 numeral system | dig10(num, pos) | 4.1 |
| factval | Binary Function | Prime decomposition - factor value at position between 1 ... nfact(n) - ascending order by factor value | factval(number, factorid) | 4.1 |
| factexp | Binary Function | Prime decomposition - factor exponent / multiplicity at position between 1 ... nfact(n) - ascending order by factor value | factexp(number, factorid) | 4.1 |
| root | Binary Function | N-th order root of a number | root(rootorder, number) | 4.1 |
| GammaL | Binary Function | Lower incomplete gamma special function, γ(s,x) | GammaL(s,x) | 4.3 |
| GammaU | Binary Function | Upper incomplete Gamma special function, Γ(s,x) | GammaU(s,x) | 4.3 |
| GammaP | Binary Function | Lower regularized P gamma special function, P(s,x) | GammaP(s,x) | 4.3 |
| GammaRegL | Binary Function | Lower regularized P gamma special function, P(s,x) | GammaRegL(s,x) | 4.3 |
| GammaQ | Binary Function | Upper regularized Q Gamma special function, Q(s,x) | GammaQ(s,x) | 4.3 |
| GammaRegU | Binary Function | Upper regularized Q Gamma special function, Q(s,x) | GammaRegU(s,x) | 4.3 |
| Beta | Binary Function | The Beta special function B(x,y), also called the Euler integral of the first kind | Beta(x,y) | 4.3 |
| logBeta | Binary Function | The Log Beta special function ln B(x,y), also called the Log Euler integral of the first kind, ln B(x,y) | logBeta(x,y) | 4.3 |

## 3-args Functions
|Key word|Category|Description|Example|Since|
|---|---|---|---|---|
| if | 3-args Function | If function | if( cond, expr-if-true, expr-if-false ) | 1.0 |
| chi | 3-args Function | Characteristic function for x in (a,b) | chi(x, a, b) | 1.0 |
| CHi | 3-args Function | Characteristic function for x in [a,b] | CHi(x, a, b) | 1.0 |
| Chi | 3-args Function | Characteristic function for x in [a,b) | Chi(x, a, b) | 1.0 |
| cHi | 3-args Function | Characteristic function for x in (a,b] | cHi(x, a, b) | 1.0 |
| pUni | 3-args Function | Probability distribution function - Uniform continuous distribution U(a,b) | pUni(x, a, b) | 3.0 |
| cUni | 3-args Function | Cumulative distribution function - Uniform continuous distribution U(a,b) | cUni(x, a, b) | 3.0 |
| qUni | 3-args Function | Quantile function (inverse cumulative distribution function) - Uniform continuous distribution U(a,b) | qUni(q, a, b) | 3.0 |
| pNor | 3-args Function | Probability distribution function - Normal distribution N(m,s) | pNor(x, mean, stdv) | 3.0 |
| cNor | 3-args Function | Cumulative distribution function - Normal distribution N(m,s) | cNor(x, mean, stdv) | 3.0 |
| qNor | 3-args Function | Quantile function (inverse cumulative distribution function) | qNor(q, mean, stdv) | 3.0 |
| dig | 3-args Function | Digit at position 1 ... n (left -> right) or 0 ... -(n-1) (right -> left) - numeral system with given base | dig(num, pos, base) | 4.1 |
| BetaInc | 3-args Function | The incomplete beta special function B(x; a, b), also called the incomplete Euler integral of the first kind | BetaInc(x,a,b) | 4.3 |
| BetaI | 3-args Function | The regularized incomplete beta (or regularized beta) special function I(x; a, b), also called the regularized incomplete Euler integral of the first kind | BetaI(x,a,b) | 4.3 |
| BetaReg | 3-args Function | The regularized incomplete beta (or regularized beta) special function I(x; a, b), also called the regularized incomplete Euler integral of the first kind | BetaReg(x,a,b) | 4.3 |

## Variadic Functions
|Key word|Category|Description|Example|Since|
|---|---|---|---|---|
| iff | Variadic Function | If function | iff( cond-1, expr-1; ... ; cond-n, expr-n ) | 1.0 |
| min | Variadic Function | Minimum function | min(a1, ..., an) | 1.0 |
| max | Variadic Function | Maximum function | max(a1, ..., an) | 1.0 |
| ConFrac | Variadic Function | Continued fraction | ConFrac(a1, ..., an) | 1.0 |
| ConPol | Variadic Function | Continued polynomial | ConPol(a1, ..., an) | 1.0 |
| gcd | Variadic Function | Greatest common divisor | gcd(a1, ..., an) | 1.0 |
| lcm | Variadic Function | Least common multiple | lcm(a1, ..., an) | 1.0 |
| add | Variadic Function | Summation operator | add(a1, ..., an) | 2.4 |
| multi | Variadic Function | Multiplication | multi(a1, ..., an) | 2.4 |
| mean | Variadic Function | Mean / average value | mean(a1, ..., an) | 2.4 |
| var | Variadic Function | Bias-corrected sample variance | var(a1, ..., an) | 2.4 |
| std | Variadic Function | Bias-corrected sample standard deviation | std(a1, ..., an) | 2.4 |
| rList | Variadic Function | Random number from given list of numbers | rList(a1, ..., an) | 3.0 |
| coalesce | Variadic Function | Returns the first non-NaN value | coalesce(a1, ..., an) | 4.1 |
| or | Variadic Function | Logical disjunction (OR) - variadic | or(a1, ..., an) | 4.1 |
| and | Variadic Function | Logical conjunction (AND) - variadic | and(a1, ..., an) | 4.1 |
| xor | Variadic Function | Exclusive or (XOR) - variadic | xor(a1, ..., an) | 4.1 |
| argmin | Variadic Function | Arguments / indices of the minima | argmin(a1, ..., an) | 4.1 |
| argmax | Variadic Function | Arguments / indices of the maxima | argmax(a1, ..., an) | 4.1 |
| med | Variadic Function | The sample median | med(a1, ..., an) | 4.1 |
| mode | Variadic Function | Mode - the value that appears most often | mode(a1, ..., an) | 4.1 |
| base | Variadic Function | Returns number in given numeral system base represented by list of digits | base(b, d1, ..., dn) | 4.1 |
| ndist | Variadic Function | Number of distinct values | ndist(v1, ..., vn) | 4.1 |

## Calculus Operators / Iterated Operators
|Key word|Category|Description|Example|Since|
|---|---|---|---|---|
| sum | Calculus Operator | Summation operator - SIGMA | sum( i, from, to, expr , <by> ) | 1.0 |
| prod | Calculus Operator | Product operator - PI | prod( i, from, to, expr , <by> ) | 1.0 |
| int | Calculus Operator | Definite integral operator | int( expr, arg, from, to ) | 1.0 |
| der | Calculus Operator | Derivative operator | der( expr, arg, <point> ) | 1.0 |
| der- | Calculus Operator | Left derivative operator | der-( expr, arg, <point> ) | 1.0 |
| der+ | Calculus Operator | Right derivative operator | der+( expr, arg, <point> ) | 1.0 |
| dern | Calculus Operator | n-th derivative operator | dern( expr, n, arg ) | 1.0 |
| diff | Calculus Operator | Forward difference operator | diff( expr, arg, <delta> ) | 1.0 |
| difb | Calculus Operator | Backward difference operator | difb( expr, arg, <delta> ) | 1.0 |
| avg | Calculus Operator | Average operator | avg( i, from, to, expr , <by> ) | 2.4 |
| vari | Calculus Operator | Bias-corrected sample variance operator | vari( i, from, to, expr , <by> ) | 2.4 |
| stdi | Calculus Operator | Bias-corrected sample standard deviation operator | stdi( i, from, to, expr , <by> ) | 2.4 |
| mini | Calculus Operator | Minimum value | mini( i, from, to, expr , <by> ) | 2.4 |
| maxi | Calculus Operator | Maximum value | maxi( i, from, to, expr , <by> ) | 2.4 |
| solve | Calculus Operator | f(x) = 0 equation solving, function root finding | solve( expr, a, b ) | 4.0 |

## Random Variables
|Key word|Category|Description|Example|Since|
|---|---|---|---|---|
| [Uni] |Random Variable|Random variable - Uniform continuous distribution U(0,1), usage example: 2*[Uni]|2*[Uni]|3.0|
| [Int] |Random Variable|Random variable - random integer - usage example sin( 3*[Int] )|[Int]*3|3.0|
| [Int1] |Random Variable|Random variable - random integer - Uniform discrete distribution U{-10^1, 10^1} - usage example sin( 3*[Int1] )|2*[Int1]|3.0|
| [Int2] |Random Variable|Random variable - random integer - Uniform discrete distribution U{-10^2, 10^2} - usage example sin( 3*[Int2] )|[Int2]*3|3.0|
| [Int3] |Random Variable|Random variable - random integer - Uniform discrete distribution U{-10^3, 10^3} - usage example sin( 3*[Int3] )|2*[Int3]|3.0|
| [Int4] |Random Variable|Random variable - random integer - Uniform discrete distribution U{-10^4, 10^4} - usage example sin( 3*[Int4] )|[Int4]*3|3.0|
| [Int5] |Random Variable|Random variable - random integer - Uniform discrete distribution U{-10^5, 10^5} - usage example sin( 3*[Int5] )|2*[Int5]|3.0|
| [Int6] |Random Variable|Random variable - random integer - Uniform discrete distribution U{-10^6, 10^6} - usage example sin( 3*[Int6] )|[Int6]*3|3.0|
| [Int7] |Random Variable|Random variable - random integer - Uniform discrete distribution U{-10^7, 10^7} - usage example sin( 3*[Int7] )|2*[Int7]|3.0|
| [Int8] |Random Variable|Random variable - random integer - Uniform discrete distribution U{-10^8, 10^8} - usage example sin( 3*[Int8] )|[Int8]*3|3.0|
| [Int9] |Random Variable|Random variable - random integer - Uniform discrete distribution U{-10^9, 10^9} - usage example sin( 3*[Int9] )|2*[Int9]|3.0|
| [nat] |Random Variable|Random variable - random natural number including 0 - usage example sin( 3*[nat] )|[nat]*3|3.0|
| [nat1] |Random Variable|Random variable - random natural number including 0 - Uniform discrete distribution U{0, 10^1} - usage example sin( 3*[nat1] )|2*[nat1]|3.0|
| [nat2] |Random Variable|Random variable - random natural number including 0 - Uniform discrete distribution U{0, 10^2} - usage example sin( 3*[nat2] )|[nat2]*3|3.0|
| [nat3] |Random Variable|Random variable - random natural number including 0 - Uniform discrete distribution U{0, 10^3} - usage example sin( 3*[nat3] )|2*[nat3]|3.0|
| [nat4] |Random Variable|Random variable - random natural number including 0 - Uniform discrete distribution U{0, 10^4} - usage example sin( 3*[nat4] )|[nat4]*3|3.0|
| [nat5] |Random Variable|Random variable - random natural number including 0 - Uniform discrete distribution U{0, 10^5} - usage example sin( 3*[nat5] )|2*[nat5]|3.0|
| [nat6] |Random Variable|Random variable - random natural number including 0 - Uniform discrete distribution U{0, 10^6} - usage example sin( 3*[nat6] )|[nat6]*3|3.0|
| [nat7] |Random Variable|Random variable - random natural number including 0 - Uniform discrete distribution U{0, 10^7} - usage example sin( 3*[nat7] )|2*[nat7]|3.0|
| [nat8] |Random Variable|Random variable - random natural number including 0 - Uniform discrete distribution U{0, 10^8} - usage example sin( 3*[nat8] )|[nat8]*3|3.0|
| [nat9] |Random Variable|Random variable - random natural number including 0 - Uniform discrete distribution U{0, 10^9} - usage example sin( 3*[nat9] )|2*[nat9]|3.0|
| [Nat] |Random Variable|Random variable - random natural number - usage example sin( 3*[Nat] )|[Nat]*3|3.0|
| [Nat1] |Random Variable|Random variable - random natural number - Uniform discrete distribution U{1, 10^1} - usage example sin( 3*[Nat1] )|2*[Nat1]|3.0|
| [Nat2] |Random Variable|Random variable - random natural number - Uniform discrete distribution U{1, 10^2} - usage example sin( 3*[Nat2] )|[Nat2]*3|3.0|
| [Nat3] |Random Variable|Random variable - random natural number - Uniform discrete distribution U{1, 10^3} - usage example sin( 3*[Nat3] )|2*[Nat3]|3.0|
| [Nat4] |Random Variable|Random variable - random natural number - Uniform discrete distribution U{1, 10^4} - usage example sin( 3*[Nat4] )|[Nat4]*3|3.0|
| [Nat5] |Random Variable|Random variable - random natural number - Uniform discrete distribution U{1, 10^5} - usage example sin( 3*[Nat5] )|2*[Nat5]|3.0|
| [Nat6] |Random Variable|Random variable - random natural number - Uniform discrete distribution U{1, 10^6} - usage example sin( 3*[Nat6] )|[Nat6]*3|3.0|
| [Nat7] |Random Variable|Random variable - random natural number - Uniform discrete distribution U{1, 10^7} - usage example sin( 3*[Nat7] )|2*[Nat7]|3.0|
| [Nat8] |Random Variable|Random variable - random natural number - Uniform discrete distribution U{1, 10^8} - usage example sin( 3*[Nat8] )|[Nat8]*3|3.0|
| [Nat9] |Random Variable|Random variable - random natural number - Uniform discrete distribution U{1, 10^9} - usage example sin( 3*[Nat9] )|2*[Nat9]|3.0|
| [Nor] |Random Variable|Random variable - Normal distribution N(0,1) - usage example cos( 3*[Nor]+1 )|[Nor]*3|3.0|

## Mathematical Constants
|Key word|Category|Description|Example|Since|
|---|---|---|---|---|
| pi |Constant Value|Pi, Archimedes' constant or Ludolph's number|2*pi|1.0|
| e |Constant Value|Napier's constant, or Euler's number, base of Natural logarithm|e*3|1.0|
| [gam] |Constant Value|Euler-Mascheroni constant|2*[gam]|1.0|
| [phi] |Constant Value|Golden ratio|[phi]*3|1.0|
| [PN] |Constant Value|Plastic constant|2*[PN]|1.0|
| [B*] |Constant Value|Embree-Trefethen constant|[B*]*3|1.0|
| [F'd] |Constant Value|Feigenbaum constant alfa|2*[F'd]|1.0|
| [F'a] |Constant Value|Feigenbaum constant delta|[F'a]*3|1.0|
| [C2] |Constant Value|Twin prime constant|2*[C2]|1.0|
| [M1] |Constant Value|Meissel-Mertens constant|[M1]*3|1.0|
| [B2] |Constant Value|Brun's constant for twin primes|2*[B2]|1.0|
| [B4] |Constant Value|Brun's constant for prime quadruplets|[B4]*3|1.0|
| [BN'L] |Constant Value|De Bruijn-Newman constant|2*[BN'L]|1.0|
| [Kat] |Constant Value|Catalan's constant|[Kat]*3|1.0|
| [K*] |Constant Value|Landau-Ramanujan constant|2*[K*]|1.0|
| [K.] |Constant Value|Viswanath's constant|[K.]*3|1.0|
| [B'L] |Constant Value|Legendre's constant|2*[B'L]|1.0|
| [RS'm] |Constant Value|Ramanujan-Soldner constant|[RS'm]*3|1.0|
| [EB'e] |Constant Value|Erdos-Borwein constant|2*[EB'e]|1.0|
| [Bern] |Constant Value|Bernstein's constant|[Bern]*3|1.0|
| [GKW'l] |Constant Value|Gauss-Kuzmin-Wirsing constant|2*[GKW'l]|1.0|
| [HSM's] |Constant Value|Hafner-Sarnak-McCurley constant|[HSM's]*3|1.0|
| [lm] |Constant Value|Golomb-Dickman constant|2*[lm]|1.0|
| [Cah] |Constant Value|Cahen's constant|[Cah]*3|1.0|
| [Ll] |Constant Value|Laplace limit|2*[Ll]|1.0|
| [AG] |Constant Value|Alladi-Grinstead constant|[AG]*3|1.0|
| [L*] |Constant Value|Lengyel's constant|2*[L*]|1.0|
| [L.] |Constant Value|Levy's constant|[L.]*3|1.0|
| [Dz3] |Constant Value|Apery's constant|2*[Dz3]|1.0|
| [A3n] |Constant Value|Mills' constant|[A3n]*3|1.0|
| [Bh] |Constant Value|Backhouse's constant|2*[Bh]|1.0|
| [Pt] |Constant Value|Porter's constant|[Pt]*3|1.0|
| [L2] |Constant Value|Lieb's square ice constant|2*[L2]|1.0|
| [Nv] |Constant Value|Niven's constant|[Nv]*3|1.0|
| [Ks] |Constant Value|Sierpinski's constant|2*[Ks]|1.0|
| [Kh] |Constant Value|Khinchin's constant|[Kh]*3|1.0|
| [FR] |Constant Value|Fransen-Robinson constant|2*[FR]|1.0|
| [La] |Constant Value|Landau's constant|[La]*3|1.0|
| [P2] |Constant Value|Parabolic constant|2*[P2]|1.0|
| [Om] |Constant Value|Omega constant|[Om]*3|1.0|
| [MRB] |Constant Value|MRB constant|2*[MRB]|1.0|
| [li2] |Constant Value|li(2) - logarithmic integral function at x=2|[li2]*3|2.3|
| [EG] |Constant Value|Gompertz constant|2*[EG]|2.3|
| [true] | Constant Value | Boolean True represented as double, [true] = 1 | [true] | 4.1 |
| [false] | Constant Value | Boolean False represented as double, [false] = 0 | [false] | 4.1 |
| [NaN] | Constant Value | Not-a-Number | [NaN] | 4.1 |


## Physical Constant
|Key word|Category|Description|Example|Since|
|---|---|---|---|---|
| [c] |Constant Value|\<Physical Constant\> Light speed in vacuum [m/s] (m=1, s=1)|[c]*3|4.0|
| [G.] |Constant Value|\<Physical Constant\> Gravitational constant (m=1, kg=1, s=1)]|2*[G.]|4.0|
| [g] |Constant Value|\<Physical Constant\> Gravitational acceleration on Earth [m/s^2] (m=1, s=1)|[g]*3|4.0|
| [hP] |Constant Value|\<Physical Constant\> Planck constant (m=1, kg=1, s=1)|2*[hP]|4.0|
| [h-] |Constant Value|\<Physical Constant\> Reduced Planck constant / Dirac constant (m=1, kg=1, s=1)]|[h-]*3|4.0|
| [lP] |Constant Value|\<Physical Constant\> Planck length [m] (m=1)|2*[lP]|4.0|
| [mP] |Constant Value|\<Physical Constant\> Planck mass [kg] (kg=1)|[mP]*3|4.0|
| [tP] |Constant Value|\<Physical Constant\> Planck time [s] (s=1)|2*[tP]|4.0|

## Astronomical Constant
|Key word|Category|Description|Example|Since|
|---|---|---|---|---|
| [ly] |Constant Value|\<Astronomical Constant\> Light year [m] (m=1)|[ly]*3|4.0|
| [au] |Constant Value|\<Astronomical Constant\> Astronomical unit [m] (m=1)|2*[au]|4.0|
| [pc] |Constant Value|\<Astronomical Constant\> Parsec [m] (m=1)|[pc]*3|4.0|
| [kpc] |Constant Value|\<Astronomical Constant\> Kiloparsec [m] (m=1)|2*[kpc]|4.0|
| [Earth-R-eq] |Constant Value|\<Astronomical Constant\> Earth equatorial radius [m] (m=1)|[Earth-R-eq]*3|4.0|
| [Earth-R-po] |Constant Value|\<Astronomical Constant\> Earth polar radius [m] (m=1)|2*[Earth-R-po]|4.0|
| [Earth-R] |Constant Value|\<Astronomical Constant\> Earth mean radius (m=1)|[Earth-R]*3|4.0|
| [Earth-M] |Constant Value|\<Astronomical Constant\> Earth mass [kg] (kg=1)|2*[Earth-M]|4.0|
| [Earth-D] |Constant Value|\<Astronomical Constant\> Earth-Sun distance - semi major axis [m] (m=1)|[Earth-D]*3|4.0|
| [Moon-R] |Constant Value|\<Astronomical Constant\> Moon mean radius [m] (m=1)|2*[Moon-R]|4.0|
| [Moon-M] |Constant Value|\<Astronomical Constant\> Moon mass [kg] (kg=1)|[Moon-M]*3|4.0|
| [Moon-D] |Constant Value|\<Astronomical Constant\> Moon-Earth distance - semi major axis [m] (m=1)|2*[Moon-D]|4.0|
| [Solar-R] |Constant Value|\<Astronomical Constant\> Solar mean radius [m] (m=1)|[Solar-R]*3|4.0|
| [Solar-M] |Constant Value|\<Astronomical Constant\> Solar mass [kg] (kg=1)|2*[Solar-M]|4.0|
| [Mercury-R] |Constant Value|\<Astronomical Constant\> Mercury mean radius [m] (m=1)|[Mercury-R]*3|4.0|
| [Mercury-M] |Constant Value|\<Astronomical Constant\> Mercury mass [kg] (kg=1)|2*[Mercury-M]|4.0|
| [Mercury-D] |Constant Value|\<Astronomical Constant\> Mercury-Sun distance - semi major axis [m] (m=1)|[Mercury-D]*3|4.0|
| [Venus-R] |Constant Value|\<Astronomical Constant\> Venus mean radius [m] (m=1)|2*[Venus-R]|4.0|
| [Venus-M] |Constant Value|\<Astronomical Constant\> Venus mass [kg] (kg=1)|[Venus-M]*3|4.0|
| [Venus-D] |Constant Value|\<Astronomical Constant\> Venus-Sun distance - semi major axis [m] (m=1)|2*[Venus-D]|4.0|
| [Mars-R] |Constant Value|\<Astronomical Constant\> Mars mean radius [m] (m=1)|[Mars-R]*3|4.0|
| [Mars-M] |Constant Value|\<Astronomical Constant\> Mars mass [kg] (kg=1)|2*[Mars-M]|4.0|
| [Mars-D] |Constant Value|\<Astronomical Constant\> Mars-Sun distance - semi major axis [m] (m=1)|[Mars-D]*3|4.0|
| [Jupiter-R] |Constant Value|\<Astronomical Constant\> Jupiter mean radius [m] (m=1)|2*[Jupiter-R]|4.0|
| [Jupiter-M] |Constant Value|\<Astronomical Constant\> Jupiter mass [kg] (kg=1)|[Jupiter-M]*3|4.0|
| [Jupiter-D] |Constant Value|\<Astronomical Constant\> Jupiter-Sun distance - semi major axis [m] (m=1)|2*[Jupiter-D]|4.0|
| [Saturn-R] |Constant Value|\<Astronomical Constant\> Saturn mean radius [m] (m=1)|[Saturn-R]*3|4.0|
| [Saturn-M] |Constant Value|\<Astronomical Constant\> Saturn mass [kg] (kg=1)|2*[Saturn-M]|4.0|
| [Saturn-D] |Constant Value|\<Astronomical Constant\> Saturn-Sun distance - semi major axis [m] (m=1)|[Saturn-D]*3|4.0|
| [Uranus-R] |Constant Value|\<Astronomical Constant\> Uranus mean radius [m] (m=1)|2*[Uranus-R]|4.0|
| [Uranus-M] |Constant Value|\<Astronomical Constant\> Uranus mass [kg] (kg=1)|[Uranus-M]*3|4.0|
| [Uranus-D] |Constant Value|\<Astronomical Constant\> Uranus-Sun distance - semi major axis [m] (m=1)|2*[Uranus-D]|4.0|
| [Neptune-R] |Constant Value|\<Astronomical Constant\> Neptune mean radius [m] (m=1)|[Neptune-R]*3|4.0|
| [Neptune-M] |Constant Value|\<Astronomical Constant\> Neptune mass [kg] (kg=1)|2*[Neptune-M]|4.0|
| [Neptune-D] |Constant Value|\<Astronomical Constant\> Neptune-Sun distance - semi major axis [m] (m=1)|[Neptune-D]*3|4.0|

## Metric prefixes
|Key word|Category|Description|Example|Since|
|---|---|---|---|---|
| [%] |Unit|\<Ratio, Fraction\> Percentage = 0.01|2*[%]|4.0|
| [%%] |Unit|\<Ratio, Fraction\> Promil, Per mille = 0.001|[%%]*3|4.0|
| [Y] |Unit|\<Metric prefix\> Septillion / Yotta = 10^24|2*[Y]|4.0|
| [sept] |Unit|\<Metric prefix\> Septillion / Yotta = 10^24|[sept]*3|4.0|
| [Z] |Unit|\<Metric prefix\> Sextillion / Zetta = 10^21|2*[Z]|4.0|
| [sext] |Unit|\<Metric prefix\> Sextillion / Zetta = 10^21|[sext]*3|4.0|
| [E] |Unit|\<Metric prefix\> Quintillion / Exa = 10^18|2*[E]|4.0|
| [quint] |Unit|\<Metric prefix\> Quintillion / Exa = 10^18|[quint]*3|4.0|
| [P] |Unit|\<Metric prefix\> Quadrillion / Peta = 10^15|2*[P]|4.0|
| [quad] |Unit|\<Metric prefix\> Quadrillion / Peta = 10^15|[quad]*3|4.0|
| [T] |Unit|\<Metric prefix\> Trillion / Tera = 10^12|2*[T]|4.0|
| [tril] |Unit|\<Metric prefix\> Trillion / Tera = 10^12|[tril]*3|4.0|
| [G] |Unit|\<Metric prefix\> Billion / Giga = 10^9|2*[G]|4.0|
| [bil] |Unit|\<Metric prefix\> Billion / Giga = 10^9|[bil]*3|4.0|
| [M] |Unit|\<Metric prefix\> Million / Mega = 10^6|2*[M]|4.0|
| [mil] |Unit|\<Metric prefix\> Million / Mega = 10^6|[mil]*3|4.0|
| [k] |Unit|\<Metric prefix\> Thousand / Kilo = 10^3|2*[k]|4.0|
| [th] |Unit|\<Metric prefix\> Thousand / Kilo = 10^3|[th]*3|4.0|
| [hecto] |Unit|\<Metric prefix\> Hundred / Hecto = 10^2|2*[hecto]|4.0|
| [hund] |Unit|\<Metric prefix\> Hundred / Hecto = 10^2|[hund]*3|4.0|
| [deca] |Unit|\<Metric prefix\> Ten / Deca = 10|2*[deca]|4.0|
| [ten] |Unit|\<Metric prefix\> Ten / Deca = 10|[ten]*3|4.0|
| [deci] |Unit|\<Metric prefix\> Tenth / Deci = 0.1|2*[deci]|4.0|
| [centi] |Unit|\<Metric prefix\> Hundredth / Centi = 0.01|[centi]*3|4.0|
| [milli] |Unit|\<Metric prefix\> Thousandth / Milli = 0.001|2*[milli]|4.0|
| [mic] |Unit|\<Metric prefix\> Millionth / Micro = 10^-6|[mic]*3|4.0|
| [n] |Unit|\<Metric prefix\> Billionth / Nano = 10^-9|2*[n]|4.0|
| [p] |Unit|\<Metric prefix\> Trillionth / Pico = 10^-12|[p]*3|4.0|
| [f] |Unit|\<Metric prefix\> Quadrillionth / Femto = 10^-15|2*[f]|4.0|
| [a] |Unit|\<Metric prefix\> Quintillionth / Atoo = 10^-18|[a]*3|4.0|
| [z] |Unit|\<Metric prefix\> Sextillionth / Zepto = 10^-21|2*[z]|4.0|
| [y] |Unit|\<Metric prefix\> Septillionth / Yocto = 10^-24|[y]*3|4.0|

## Units of length
|Key word|Category|Description|Example|Since|
|---|---|---|---|---|
| [m] |Unit|\<Unit of length\> Metre / Meter (m=1)|2*[m]|4.0|
| [km] |Unit|\<Unit of length\> Kilometre / Kilometer (m=1)|[km]*3|4.0|
| [cm] |Unit|\<Unit of length\> Centimetre / Centimeter (m=1)|2*[cm]|4.0|
| [mm] |Unit|\<Unit of length\> Millimetre / Millimeter (m=1)|[mm]*3|4.0|
| [inch] |Unit|\<Unit of length\> Inch (m=1)|2*[inch]|4.0|
| [yd] |Unit|\<Unit of length\> Yard (m=1)|[yd]*3|4.0|
| [ft] |Unit|\<Unit of length\> Feet (m=1)|2*[ft]|4.0|
| [mile] |Unit|\<Unit of length\> Mile (m=1)|[mile]*3|4.0|
| [nmi] |Unit|\<Unit of length\> Nautical mile (m=1)|2*[nmi]|4.0|

## Units of area
|Key word|Category|Description|Example|Since|
|---|---|---|---|---|
| [m2] |Unit|\<Unit of area\> Square metre / Square meter (m=1)|[m2]*3|4.0|
| [cm2] |Unit|\<Unit of area\> Square centimetre / Square centimeter (m=1)|2*[cm2]|4.0|
| [mm2] |Unit|\<Unit of area\> Square millimetre / Square millimeter (m=1)|[mm2]*3|4.0|
| [are] |Unit|\<Unit of area\> Are (m=1)|2*[are]|4.0|
| [ha] |Unit|\<Unit of area\> Hectare (m=1)|[ha]*3|4.0|
| [acre] |Unit|\<Unit of area\> Acre (m=1)|2*[acre]|4.0|
| [km2] |Unit|\<Unit of area\> Square kilometre / Square kilometer (m=1)|[km2]*3|4.0|

## Units of volume
|Key word|Category|Description|Example|Since|
|---|---|---|---|---|
| [mm3] |Unit|\<Unit of volume\> Cubic millimetre / Cubic millimeter (m=1)|2*[mm3]|4.0|
| [cm3] |Unit|\<Unit of volume\> Cubic centimetre / Cubic centimeter (m=1)|[cm3]*3|4.0|
| [m3] |Unit|\<Unit of volume\> Cubic metre / Cubic meter (m=1)|2*[m3]|4.0|
| [km3] |Unit|\<Unit of volume\> Cubic kilometre / Cubic kilometer (m=1)|[km3]*3|4.0|
| [ml] |Unit|\<Unit of volume\> Millilitre / Milliliter (m=1)|2*[ml]|4.0|
| [l] |Unit|\<Unit of volume\> Litre / Liter (m=1)|[l]*3|4.0|
| [gall] |Unit|\<Unit of volume\> Gallon (m=1)|2*[gall]|4.0|
| [pint] |Unit|\<Unit of volume\> Pint (m=1)|[pint]*3|4.0|

## Units of time
|Key word|Category|Description|Example|Since|
|---|---|---|---|---|
| [s] |Unit|\<Unit of time\> Second (s=1)|2*[s]|4.0|
| [ms] |Unit|\<Unit of time\> Millisecond (s=1)|[ms]*3|4.0|
| [min] |Unit|\<Unit of time\> Minute (s=1)|2*[min]|4.0|
| [h] |Unit|\<Unit of time\> Hour (s=1)|[h]*3|4.0|
| [day] |Unit|\<Unit of time\> Day (s=1)|2*[day]|4.0|
| [week] |Unit|\<Unit of time\> Week (s=1)|[week]*3|4.0|
| [yearj] |Unit|\<Unit of time\> Julian year = 365.25 days (s=1)|2*[yearj]|4.0|

## Units of mass
|Key word|Category|Description|Example|Since|
|---|---|---|---|---|
| [kg] |Unit|\<Unit of mass\> Kilogram (kg=1)|[kg]*3|4.0|
| [gr] |Unit|\<Unit of mass\> Gram (kg=1)|2*[gr]|4.0|
| [mg] |Unit|\<Unit of mass\> Milligram (kg=1)|[mg]*3|4.0|
| [dag] |Unit|\<Unit of mass\> Decagram (kg=1)|2*[dag]|4.0|
| [t] |Unit|\<Unit of mass\> Tonne (kg=1)|[t]*3|4.0|
| [oz] |Unit|\<Unit of mass\> Ounce (kg=1)|2*[oz]|4.0|
| [lb] |Unit|\<Unit of mass\> Pound (kg=1)|[lb]*3|4.0|

## Units of information
|Key word|Category|Description|Example|Since|
|---|---|---|---|---|
| [b] |Unit|\<Unit of information\> Bit (bit=1)|2*[b]|4.0|
| [kb] |Unit|\<Unit of information\> Kilobit (bit=1)|[kb]*3|4.0|
| [Mb] |Unit|\<Unit of information\> Megabit (bit=1)|2*[Mb]|4.0|
| [Gb] |Unit|\<Unit of information\> Gigabit (bit=1)|[Gb]*3|4.0|
| [Tb] |Unit|\<Unit of information\> Terabit (bit=1)|2*[Tb]|4.0|
| [Pb] |Unit|\<Unit of information\> Petabit (bit=1)|[Pb]*3|4.0|
| [Eb] |Unit|\<Unit of information\> Exabit (bit=1)|2*[Eb]|4.0|
| [Zb] |Unit|\<Unit of information\> Zettabit (bit=1)|[Zb]*3|4.0|
| [Yb] |Unit|\<Unit of information\> Yottabit (bit=1)|2*[Yb]|4.0|
| [B] |Unit|\<Unit of information\> Byte (bit=1)|[B]*3|4.0|
| [kB] |Unit|\<Unit of information\> Kilobyte (bit=1)|2*[kB]|4.0|
| [MB] |Unit|\<Unit of information\> Megabyte (bit=1)|[MB]*3|4.0|
| [GB] |Unit|\<Unit of information\> Gigabyte (bit=1)|2*[GB]|4.0|
| [TB] |Unit|\<Unit of information\> Terabyte (bit=1)|[TB]*3|4.0|
| [PB] |Unit|\<Unit of information\> Petabyte (bit=1)|2*[PB]|4.0|
| [EB] |Unit|\<Unit of information\> Exabyte (bit=1)|[EB]*3|4.0|
| [ZB] |Unit|\<Unit of information\> Zettabyte (bit=1)|2*[ZB]|4.0|
| [YB] |Unit|\<Unit of information\> Yottabyte (bit=1)|[YB]*3|4.0|

## Units of energy
|Key word|Category|Description|Example|Since|
|---|---|---|---|---|
| [J] |Unit|\<Unit of energy\> Joule (m=1, kg=1, s=1)|2*[J]|4.0|
| [eV] |Unit|\<Unit of energy\> Electronovolt (m=1, kg=1, s=1)|[eV]*3|4.0|
| [keV] |Unit|\<Unit of energy\> Kiloelectronovolt (m=1, kg=1, s=1)|2*[keV]|4.0|
| [MeV] |Unit|\<Unit of energy\> Megaelectronovolt (m=1, kg=1, s=1)|[MeV]*3|4.0|
| [GeV] |Unit|\<Unit of energy\> Gigaelectronovolt (m=1, kg=1, s=1)|2*[GeV]|4.0|
| [TeV] |Unit|\<Unit of energy\> Teraelectronovolt (m=1, kg=1, s=1)|[TeV]*3|4.0|

## Units of speed
|Key word|Category|Description|Example|Since|
|---|---|---|---|---|
| [m/s] |Unit|\<Unit of speed\> Metre / Meter per second (m=1, s=1)|2*[m/s]|4.0|
| [km/h] |Unit|\<Unit of speed\> Kilometre / Kilometer per hour (m=1, s=1)|[km/h]*3|4.0|
| [mi/h] |Unit|\<Unit of speed\> Mile per hour (m=1, s=1)|2*[mi/h]|4.0|
| [knot] |Unit|\<Unit of speed\> Knot (m=1, s=1)|[knot]*3|4.0|

## Units of acceleration
|Key word|Category|Description|Example|Since|
|---|---|---|---|---|
| [m/s2] |Unit|\<Unit of acceleration\> Metre / Meter per square second (m=1, s=1)|2*[m/s2]|4.0|
| [km/h2] |Unit|\<Unit of acceleration\> Kilometre / Kilometer per square hour (m=1, s=1)|[km/h2]*3|4.0|
| [mi/h2] |Unit|\<Unit of acceleration\> Mile per square hour (m=1, s=1)|2*[mi/h2]|4.0|

## Units of angle
|Key word|Category|Description|Example|Since|
|---|---|---|---|---|
| [rad] |Unit|\<Unit of angle\> Radian (rad=1)|[rad]*pi|4.0|
| [deg] |Unit|\<Unit of angle\> Degree of arc (rad=1)|180*[deg]|4.0|
| ['] |Unit|\<Unit of angle\> Minute of arc (rad=1)|[']*3|4.0|
| [''] |Unit|\<Unit of angle\> Second of arc (rad=1)|2*['']|4.0|

## Other parser symbols
|Key word|Category|Description|Example|Since|
|---|---|---|---|---|
| ( |Parser Symbol|Left parentheses|(3+2)/4|1.0|
| ) |Parser Symbol|Right parentheses|(3+2)/4|1.0|
| , |Parser Symbol|Comma (function parameters)|min(2,3,1)|1.0|
| ; |Parser Symbol|Semicolon (function parameters)|min(2;3;1)|1.0|

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