org.mariuszgromada.math:MathParser.org-mXparser

MathParser.org-mXparser has been downloaded more than 3,000,000 times!

mXparser - a super easy, rich and highly flexible Mathematical Expression Parser (Math Parser, Expression Evaluator) library for JAVA, Android, C# .NET, TypeScript and JavaScript.

v.5.2.1 (2023-02-08): Orion: Improvement and standardization of descriptions and messages. Definition of your own translations. Exporting help in multiple formats. Clones for thread safe. Performance improvement.

• Improvement and standardization of built-in elements description, click to see usage example
• Improvement and standardization of error messages, click to see usage example
• Definition of your own translations, click to see usage example
• Help content in the CSV format, click to see usage example
• Help content in the HTML format, click to see usage example
• Help content in the Markdown format, click to see usage example
• Help content in the JSON format, click to see usage example
• Clones for thread safe, click to see usage example
• Performance improvement for calculations in the loop, click to see usage example
• Bug fixed #291 Euler polynomial function producing wrong results
• Bug fixed #292 Implied Multiplication bug when blank character separates
• Bug fixed #283 Unnecessary newline at the end in getErrorMessage()
• Bug fixed #284 Unnecessary space in function expression string returned by getErrorMessage()
• Bug fixed #297 Claculation Steps Register fix - commas / parenthesis / missing parts related to user arguments

v.5.1 Libris: Implied Multiplication, Unicode Math Symbols, Additional Probability Distributions, Calculation Steps Register, Serialization Support

• Implied Multiplication, click to see usage example
• Unicode Math Symbols, click to see usage example
• Calculation Steps Register, click to see usage example
• Serialization Support, click to see usage example
• An Attempt To Fix Expression String
• Student's t-distribution: Probabilisty Density Function, Cumulative Distribution Function, Quantile Function
• Chi-Squared Distribution: Probabilisty Density Function, Cumulative Distribution Function, Quantile Function
• F-Snedecor Distribution: Probabilisty Density Function, Cumulative Distribution Function, Quantile Function
• Minor Bug fixing: 259, 258, 252, 261, 262, 263, 271, 269, 268, 266, 265
• Regression tests refactoring

Package installation

Nuget - Packgae Manager

Install-Package MathParser.org-mXparser -Version 5.2.1

Nuget – .NET CLI

dotnet add package MathParser.org-mXparser --version 5.2.1

Nuget – Package Reference

<PackageReference Include="MathParser.org-mXparser" Version="5.2.1"/>

Maven - Dependency

<dependency>
    <groupId>org.mariuszgromada.math</groupId>
    <artifactId>MathParser.org-mXparser</artifactId>
    <version>5.2.1</version>
</dependency>

Maven - Gradle

implementation 'org.mariuszgromada.math:MathParser.org-mXparser:5.2.1'

Maven – Gradle (Kotlin)

implementation("org.mariuszgromada.math:MathParser.org-mXparser:5.2.1")

NPM

$ npm i mathparser.org-mxparser

• or consider donation: DONATION

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MathParser.org-mXparser

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

Supported frameworks

• 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
• TypeScript, JavaScript
• Chrome, Firefox, MS Edge, Safari
• nodeJS

Tutorial

The tutorial consists of c.a. 180 live examples from c.a. 40 sections. Each of the examples can be copied and run on your own environment. In addition, mXparser provides an extensive collection of over 500 built-in math functions, expressions and symbols. Familiarize yourself with the scope and the syntax. Live testing is the best way to learn. Good luck!

Using internal help

• Full help content
• In-line help searching

Simple expressions

• Simple calculation
• Changing expression string
• Using operators
• Power function
• Using numbers in scientific notation
• Percent sign
• Leading zeros

Implied multiplication

• Numbers and parenthesis
• Numbers and constants / arguments
• Numbers and constants / arguments and parenthesis
• Numbers and constants / arguments and parenthesis and functions
• Implied multiplication and possible ambiguity
• Implied multiplication and list of tokens
• Enable / disable implied multiplication

Evaluating relations

• Binary relation “=”
• Binary relation “<“
• Boolean operator “OR”
• Boolean operator “AND”

Using built-in functions

• Unary function
• Binary function
• Function with 3 arguments
• Function with n-arguments
• Function with even number of arguments

User defined constants

• Defining constant – various options

User defined arguments

• Dealing with free arguments
• Defining dependent arguments
• Implementing your own Argument Extension
• Getting list of missing user defined arguments
• Possible conflict between Implied Multiplication and getting list of missing user defined arguments + recommended solutions

User defined functions

• Fast function definition (performance of creation)
• Handy function constructor, but slower proces of function creation (performance of creation slower, but calculation the same)
• Function with more parameters
• Function in function
• Implementing your own Function Extension
• Getting list of missing user defined functions
• Possible conflict between Implied Multiplication and getting list of missing user defined functions + recommended solutions

Expression pre-compilation

• What is pre-compilation?
• When is pre-compilation done?
• When is pre-compilation done again?
• An example of bad practice in computing the value of an expression for a changing argument value
• An example of good practice in computing the value of an expression for a changing argument value

Variadic user defined functions

• Function returning number of parameters provided
• Function returning sum of first and last parameter provided
• Function returning parameter at position defined by the first parameter
• Function returning sum of all parameters squared
• Implementing your own Variadic Function Extension

“if” and “iff” functions

• Mechanics of the if function
• “if” function and arguments
• “if” function in user defined function
• Mechanics of the “iff” function
• iff function is not limited in number of cases

Summation & Product iterated operators

• SIGMA summation operator
• PI product operator
• SIGMA summation operator – Approximating sin(x) by Taylor series
• SIGMA summation operator – Approximating pi value by integrating sqrt(1-x^2)

Derivatives & Integrals

• General derivative
• Left / right derivative
• Derivative from more complex function
• Derivative – alternative syntax
• Integrals – calculating pi by integration sqrt(1-x^2)

Solving equation f(x) = 0

• Solve 2x-4 = 0 for x in [0, 10]
• Solve cos(x) = 0 for x in [0, pi]
• Solve cos(x) = 0 for x in [pi, pi] (root not bracketed)
• Solve x-y = 0 for x in [0, 10] and y = 4
• Solve sin'(x) = 0 for x in [0, pi]

Prime Numbers

• Primality test function
• Primes counting function
• Using built-in primes cache to accelerate calculations
• Estimating number of primes using Offset logarithmic integral function
• Prime factorization

Built-in constants

• Using built-in constants
• Estimating Moon gravitational acceleration
• Getting list of constants

Built-in Units

• Units of length / distance
• Units of time
• Units of information
• Units of volume
• Express 4 feet in inches
• Express in square kilometers the area of a rectangle measuring 100 meters by 2 kilometers
• List of supported units

Built-in Metric prefixes

• Example: 10 Millions / Kilo
• List of supported metric prefixes

PDF, CDF and Quantile functions

• Expected value estimation using Probability Distribution Function
• Probability estimation using Cumulative Distribution Function – the law of 3*SIGMA
• Calculating quantiles using Inverse Cumulative Distribution Function – males height example assuming males height distribution N(170, 15)

Random numbers

• Random number from uniform continuous distribution
• Random number from uniform discrete distribution
• Random number from normal distribution
• Random number from a given list
• Estimating mean of Normal distribution
• Estimating standard deviation of Normal distribution
• Estimating variance of Normal distribution

Built-in Random Variables

• Random integer
• Random integer N: -10^k <= N <= 10^k for k = 1, 2, …,9
• Random natural number
• Random natural number N <= 10^k for k = 1, 2, …,9
• Uniform continuous distribution U(0,1)
• Normal distribution N(0,1)

User defined Random Variables

• Dependent argument as user defined random variable
• User defined function as user defined random variable – random walk example

Bitwise Operators

• Bitwise unary complement
• Bitwise AND
• Bitwise exclusive OR
• Bitwise inclusive OR
• Signed left / right shift

Fractions

• Fraction (proper) as Number Literal
• Improper Fraction as Number Literal
• Fraction (Mixed Number) as Number Literal
• Fraction (Mixed Numer) and Improper Fraction in one Number Literal
• Operations on Fractions
• Represent double as Fraction

Various numeral systems

• Binary number
• Octal number
• Hexadecimal number
• Unary number
• Unary zero
• Base 1 – 36 number literals
• Base N numeral system

Fast (limited) user defined recursion

• Fibonacci numbers using fast recursion

User defined recursion – not limited

• Fibonacci numbers using user defined recursive function
• Number of recursive parameters is not limited – binomial coefficient definition using user defined recursive function
• Mixing function parameters – part causing recursive calls, other part as ‘typical’ parameter. Below example is presenting definition of Chebyshev polynomial using recursive function.
• Indirect recursion – approximating sin(x) and cos(x)

Unicode math

• The square root √
• The square root of the square root √√
• The square root and parenthesis √()
• The roots of various orders ∜ ∛ √
• SIGMA summation operator ∑
• Unicode name of a user defined argument
• Show all Unicode built-in keywords
• Enable / disable Unicode built-in keywords
• List of Unicode symbols that grammar accepts

Working with NaN – Not-a-Number

• NaN in condition
• NaN symbol
• First non-NaN value

Radians Mode / Degrees Mode

• Basic trigonometric function
• Inverse trigonometric function
• Using units of angle being in radians mode

Calculation Steps Register

• Simple Expression
• Dependent User Argument
• User Function
• Expression referencing User Argument and User Function

Inspecting calculation process

• Setting the verbose mode
• Syntax checking
• Lexical syntax checking
• Getting computing time

Playing with expression tokens

• Printing expression tokens
• Using tokens to print expression in a fancy way
• Playing with invalid tokens

Built-in tokens (key words) manipulation

• Removing built-in tokens
• Modifying built-in tokens
• Overriding built-in tokens

Smart rounding settings

• A few words on Floating Point Math
• Why mXparser is based on the double data type?
• Smart rounding options available in mXparser
• Check which rounding settings are currently active
• Example - Only Canonical Rounding option is active
• Example - Only Unit In The Last Place Rounding option is active
• Example - Only Almost Integer Rounding option is active
• Example - None of the rounding options are active

Efficient calculations in the loops

• User expression in the loop + output
• User function in the loop + output
• User argument (dependent) in the loop + output
• User expression in the loop – Performance
• User function in the loop – Performance
• User argument (dependent) in the loop – Performance

Extensive list of settings

• Degrees / Radians Mode
• Attempt To Fix Expression String Mode
• Primes Cache
• Epsilon Comparison / Exact Comparison Mode
• Canonical Rounding Mode
• ULP (Unit In The Last Place) Rounding Mode
• Almost Integers Rounding Mode
• Implied Multiplication Mode
• Unicode Builtin Key Words Mode
• Verbose / Silent Mode
• Override Builtin Tokens Mode
• Modify Builtin Tokens Mode
• Remove Builtin Tokens Mode
• Current Calculation Cancellation
• Setting Console Prefix
• Reaching Console Output String
• Maximum Allowed Recursion Depth
• Double to Fraction Conversion
• Random Generator Selection
• Maximum Threads Number
• Default Settings

Serialization & Deserialization

• SerializationUtils class
• Binary serialization SECURITY WARNING
• Enabling / Disabling binary serialization
• Expression serialization / deserialization from / to byte[]
• Expression serialization / deserialization from / to String
• Expression serialization / deserialization from / to File
• Serialization / Deserialization of complex objects

>>> Click to learn from examples <<<

Math Collection

mXparser provides a rich collection of built-in math functions, math expressions, and math symbols. Familiarize yourself with the scope and the syntax. Math collection internal help is also available directly from the software – see the tutorial and the API documentation for all the details.

- Operators

- Binary Relations

- Boolean Operators

- Bitwise Operators

- Unary Functions

- Binary Functions

- 3-args Functions

- Variadic Functions

- Random Variables

- Iterated Operators

- Calculus Operators

- Mathematical Constants

- Physical Constants

- Astronomical Constants

- Metric prefixes

- Units

- Parser Symbols

- Number formats

API documentation

- API documentation

Did you find the software useful?

• please consider donation
• purchase the commercial license from here or from here

JAVA intro

C# intro

TypeScript intro

Main functionalities:

• basic operators, i.e.: +, -, *, ^, !
• Boolean logic operators i.e.: or, and, xor
• binary relations i.e.: =, <, >
• math functions (large library of 1-arg, 2-arg, 3-arg - functions) i.e.: sin, cos, Stirling numbers, log, inverse functions
• constants (large library), i.e.: pi, e, golden ratio
• n-args functions, i.e.: greatest common divisor
• iterated summation and product operators
• differentiation and integration

High flexibility functionalities

• user defined constants and arguments, both free - and dependent on other arguments + possibility of use in functions
• user defined functions (both free and depended)
• user defined recursive arguments + simple (controlled) recursion (1 recursive argument)
• user defined recursive functions / expressions (any) - complex, many arguments, no limitation
• internal syntax checking
• internal help
• other useful functionalities, i.e.: computing time, expression description.

Project documentation

- mXparser - API (english)

- mXparser - WIKI (english)

- mXparser - Tutorial (english)

- MathSpace.pl - site about math with mXparser examples (polish)

- MathParser.org - site about mXparser (english)

mXparser in nutshell

You want simple calculator...

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

:+1:

A calculator supporting parenthesis...

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

:+1:

You care about predefined constants...

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

:+1:

You need to define your own constants...

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

:+1:

You enjoy using many built-in functions...

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

:+1:

You do not limit yourself to unary functions...

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

:+1:

What about user defined arguments...

Argument x = new Argument("x = 5");
Expression e = new Expression("sin(x)", x);
e.calculate();

:+1:

You are considering dependent arguments...

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...

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!

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 beginning, we are just warming up!

You want to play with iterated operators...

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...

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...

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...

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...

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...

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 choice!

mXparser can interact with end users as it supports syntax checking.

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

Keyword	Type	Syntax	Since	Description
+	Operator	a + b	1.0	Addition - Operator
-	Operator	a - b	1.0	Subtraction - Operator
*	Operator	a * b	1.0	Multiplication - Operator
×	Operator	a × b	5.0	Multiplication - Operator - Unicode math symbol
⨉	Operator	a ⨉ b	5.0	Multiplication - Operator - Unicode math symbol
∙	Operator	a ∙ b	5.0	Multiplication - Operator - Unicode math symbol
/	Operator	a / b	1.0	Division - Operator
÷	Operator	a ÷ b	5.0	Division - Operator - Unicode math symbol
^	Operator	a^b	1.0	Exponentiation - Operator
!	Operator	n!	1.0	Factorial - Operator
#	Operator	a # b	1.0	Modulo - Operator
%	Operator	n%	4.1	Percentage - Operator
^^	Operator	a^^b	4.2	Tetration (hyper-4, power tower, exponential tower) - Operator
√	Operator	√x	5.0	Square root - Operator - Unicode math symbol
∛	Operator	∛x	5.0	Cube root - Operator - Unicode math symbol
∜	Operator	∜x	5.0	Fourth root - Operator - Unicode math symbol

Boolean Operators

Keyword	Type	Syntax	Since	Description
&	Boolean operator	p & q	1.0	Logical conjunction AND - Boolean operator
∧	Boolean operator	p ∧ q	5.0	Logical conjunction AND - Boolean operator - Unicode math symbol
&&	Boolean operator	p && q	1.0	Logical conjunction AND - Boolean operator
/\	Boolean operator	p /\ q	1.0	Logical conjunction AND - Boolean operator
⊼	Boolean operator	p ⊼ q	5.0	Sheffer stroke NAND - Boolean operator - Unicode math symbol
~&	Boolean operator	p ~& q	1.0	Sheffer stroke NAND - Boolean operator
~∧	Boolean operator	p ~∧ q	5.0	Sheffer stroke NAND - Boolean operator - Unicode math symbol
¬&	Boolean operator	p ¬& q	5.0	Sheffer stroke NAND - Boolean operator - Unicode math symbol
¬∧	Boolean operator	p ¬∧ q	5.0	Sheffer stroke NAND - Boolean operator - Unicode math symbol
~&&	Boolean operator	p ~&& q	1.0	Sheffer stroke NAND - Boolean operator
~/\	Boolean operator	p ~/\ q	1.0	Sheffer stroke NAND - Boolean operator
¬&&	Boolean operator	p ¬&& q	5.0	Sheffer stroke NAND - Boolean operator - Unicode math symbol
¬/\	Boolean operator	p ¬/\ q	5.0	Sheffer stroke NAND - Boolean operator - Unicode math symbol
|	Boolean operator	p | q	1.0	Logical disjunction OR - Boolean operator
∨	Boolean operator	p ∨ q	5.0	Logical disjunction OR - Boolean operator - Unicode math symbol
||	Boolean operator	p || q	1.0	Logical disjunction OR - Boolean operator
\/	Boolean operator	p \/ q	1.0	Logical disjunction OR - Boolean operator
⊽	Boolean operator	p ⊽ q	5.0	Logical not or (joint denial) NOR - Boolean operator - Unicode math symbol
~|	Boolean operator	p ~| q	1.0	Logical not or (joint denial) NOR - Boolean operator
~∨	Boolean operator	p ~∨ q	5.0	Logical not or (joint denial) NOR - Boolean operator - Unicode math symbol
¬|	Boolean operator	p ¬| q	5.0	Logical not or (joint denial) NOR - Boolean operator - Unicode math symbol
¬∨	Boolean operator	p ¬∨ q	5.0	Logical not or (joint denial) NOR - Boolean operator - Unicode math symbol
~||	Boolean operator	p ~|| q	1.0	Logical not or (joint denial) NOR - Boolean operator
~\/	Boolean operator	p ~\/ q	1.0	Logical not or (joint denial) NOR - Boolean operator
¬||	Boolean operator	p ¬|| q	5.0	Logical not or (joint denial) NOR - Boolean operator - Unicode math symbol
¬\/	Boolean operator	p ¬\/ q	5.0	Logical not or (joint denial) NOR - Boolean operator - Unicode math symbol
⊻	Boolean operator	p ⊻ q	5.0	Exclusive or XOR - Boolean operator - Unicode math symbol
(+)	Boolean operator	p (+) q	1.0	Exclusive or XOR - Boolean operator
⇒	Boolean operator	p ⇒ q	5.0	Implication IMP - Boolean operator - Unicode math symbol
-->	Boolean operator	p --> q	1.0	Implication IMP - Boolean operator
⇐	Boolean operator	p ⇐ q	5.0	Converse implication CIMP - Boolean operator - Unicode math symbol
<--	Boolean operator	p <-- q	1.0	Converse implication CIMP - Boolean operator
⇏	Boolean operator	p ⇏ q	5.0	Material nonimplication NIMP - Boolean operator - Unicode math symbol
-/>	Boolean operator	p -/> q	1.0	Material nonimplication NIMP - Boolean operator
⇍	Boolean operator	p ⇍ q	5.0	Converse nonimplication CNIMP - Boolean operator - Unicode math symbol
</-	Boolean operator	p </- q	1.0	Converse nonimplication CNIMP - Boolean operator
⇔	Boolean operator	p ⇔ q	5.0	Logical biconditional EQV - Boolean operator - Unicode math symbol
<->	Boolean operator	p <-> q	1.0	Logical biconditional EQV - Boolean operator
~	Boolean operator	~p	1.0	Negation - Boolean operator
¬	Boolean operator	¬p	5.0	Negation - Boolean operator - Unicode math symbol

Bitwise Operators

Keyword	Type	Syntax	Since	Description
@~	Bitwise operator	@~a	4.0	Bitwise unary complement - Bitwise operator
@&	Bitwise operator	a @& b	4.0	Bitwise and AND - Bitwise operator
@^	Bitwise operator	a @^ b	4.0	Bitwise exclusive or XOR - Bitwise operator
@|	Bitwise operator	a @| b	4.0	Bitwise inclusive or OR - Bitwise operator
@<<	Bitwise operator	a @<< b	4.0	Signed left shift - Bitwise operator
@>>	Bitwise operator	a @>> b	4.0	Signed right shift - Bitwise operator

Binary Relations

Keyword	Type	Syntax	Since	Description
=	Binary relation	a = b	1.0	Equality - Binary relation
==	Binary relation	a == b	1.0	Equality - Binary relation
≠	Binary relation	a ≠ b	5.0	Inequation - Binary relation - Unicode math symbol
<>	Binary relation	a <> b	1.0	Inequation - Binary relation
~=	Binary relation	a ~= b	1.0	Inequation - Binary relation
!=	Binary relation	a != b	1.0	Inequation - Binary relation
<	Binary relation	a < b	1.0	Lower than - Binary relation
>	Binary relation	a > b	1.0	Greater than - Binary relation
≤	Binary relation	a ≤ b	5.0	Lower or equal - Binary relation - Unicode math symbol
⋜	Binary relation	a ⋜ b	5.0	Lower or equal - Binary relation - Unicode math symbol
<=	Binary relation	a <= b	1.0	Lower or equal - Binary relation
≥	Binary relation	a ≥ b	5.0	Greater or equal - Binary relation - Unicode math symbol
⋝	Binary relation	a ⋝ b	5.0	Greater or equal - Binary relation - Unicode math symbol
>=	Binary relation	a >= b	1.0	Greater or equal - Binary relation

Unary Functions

Keyword	Type	Syntax	Since	Description
sin	Unary function	sin(x)	1.0	Trigonometric sine - Unary function
cos	Unary function	cos(x)	1.0	Trigonometric cosine - Unary function
tg	Unary function	tg(x)	1.0	Trigonometric tangent - Unary function
tan	Unary function	tan(x)	1.0	Trigonometric tangent - Unary function
ctg	Unary function	ctg(x)	1.0	Trigonometric cotangent - Unary function
cot	Unary function	cot(x)	1.0	Trigonometric cotangent - Unary function
ctan	Unary function	ctan(x)	1.0	Trigonometric cotangent - Unary function
sec	Unary function	sec(x)	1.0	Trigonometric secant - Unary function
csc	Unary function	csc(x)	1.0	Trigonometric cosecant - Unary function
cosec	Unary function	cosec(x)	1.0	Trigonometric cosecant - Unary function
asin	Unary function	asin(x)	1.0	Inverse trigonometric sine - Unary function
arsin	Unary function	arsin(x)	1.0	Inverse trigonometric sine - Unary function
arcsin	Unary function	arcsin(x)	1.0	Inverse trigonometric sine - Unary function
acos	Unary function	acos(x)	1.0	Inverse trigonometric cosine - Unary function
arcos	Unary function	arcos(x)	1.0	Inverse trigonometric cosine - Unary function
arccos	Unary function	arccos(x)	1.0	Inverse trigonometric cosine - Unary function
atg	Unary function	atg(x)	1.0	Inverse trigonometric tangent - Unary function
atan	Unary function	atan(x)	1.0	Inverse trigonometric tangent - Unary function
arctg	Unary function	arctg(x)	1.0	Inverse trigonometric tangent - Unary function
arctan	Unary function	arctan(x)	1.0	Inverse trigonometric tangent - Unary function
actg	Unary function	actg(x)	1.0	Inverse trigonometric cotangent - Unary function
acot	Unary function	acot(x)	1.0	Inverse trigonometric cotangent - Unary function
actan	Unary function	actan(x)	1.0	Inverse trigonometric cotangent - Unary function
arcctg	Unary function	arcctg(x)	1.0	Inverse trigonometric cotangent - Unary function
arccot	Unary function	arccot(x)	1.0	Inverse trigonometric cotangent - Unary function
arcctan	Unary function	arcctan(x)	1.0	Inverse trigonometric cotangent - Unary function
ln	Unary function	ln(x)	1.0	Natural logarithm (base e) - Unary function
log2	Unary function	log2(x)	1.0	Binary logarithm (base 2) - Unary function
lg	Unary function	lg(x)	5.0	Common logarithm (base 10) - Unary function
log10	Unary function	log10(x)	1.0	Common logarithm (base 10) - Unary function
rad	Unary function	rad(x)	1.0	Degrees to radians - Unary function
exp	Unary function	exp(x)	1.0	Exponential - Unary function
sqrt	Unary function	sqrt(x)	1.0	Squre root - Unary function
sinh	Unary function	sinh(x)	1.0	Hyperbolic sine - Unary function
cosh	Unary function	cosh(x)	1.0	Hyperbolic cosine - Unary function
tgh	Unary function	tgh(x)	1.0	Hyperbolic tangent - Unary function
tanh	Unary function	tanh(x)	1.0	Hyperbolic tangent - Unary function
coth	Unary function	coth(x)	1.0	Hyperbolic cotangent - Unary function
ctgh	Unary function	ctgh(x)	1.0	Hyperbolic cotangent - Unary function
ctanh	Unary function	ctanh(x)	1.0	Hyperbolic cotangent - Unary function
sech	Unary function	sech(x)	1.0	Hyperbolic secant - Unary function
csch	Unary function	csch(x)	1.0	Hyperbolic cosecant - Unary function
cosech	Unary function	cosech(x)	1.0	Hyperbolic cosecant - Unary function
deg	Unary function	deg(x)	1.0	Radians to degrees - Unary function
abs	Unary function	abs(x)	1.0	Absolut value - Unary function
sgn	Unary function	sgn(x)	1.0	Signum - Unary function
floor	Unary function	floor(x)	1.0	Floor - Unary function
ceil	Unary function	ceil(x)	1.0	Ceiling - Unary function
not	Unary function	not(x)	1.0	Negation - Unary function
asinh	Unary function	asinh(x)	1.0	Inverse hyperbolic sine - Unary function
arsinh	Unary function	arsinh(x)	1.0	Inverse hyperbolic sine - Unary function
arcsinh	Unary function	arcsinh(x)	1.0	Inverse hyperbolic sine - Unary function
acosh	Unary function	acosh(x)	1.0	Inverse hyperbolic cosine - Unary function
arcosh	Unary function	arcosh(x)	1.0	Inverse hyperbolic cosine - Unary function
arccosh	Unary function	arccosh(x)	1.0	Inverse hyperbolic cosine - Unary function
atgh	Unary function	atgh(x)	1.0	Inverse hyperbolic tangent - Unary function
atanh	Unary function	atanh(x)	1.0	Inverse hyperbolic tangent - Unary function
arctgh	Unary function	arctgh(x)	1.0	Inverse hyperbolic tangent - Unary function
arctanh	Unary function	arctanh(x)	1.0	Inverse hyperbolic tangent - Unary function
acoth	Unary function	acoth(x)	1.0	Inverse hyperbolic cotangent - Unary function
actgh	Unary function	actgh(x)	1.0	Inverse hyperbolic cotangent - Unary function
actanh	Unary function	actanh(x)	1.0	Inverse hyperbolic cotangent - Unary function
arcoth	Unary function	arcoth(x)	1.0	Inverse hyperbolic cotangent - Unary function
arccoth	Unary function	arccoth(x)	1.0	Inverse hyperbolic cotangent - Unary function
arcctgh	Unary function	arcctgh(x)	1.0	Inverse hyperbolic cotangent - Unary function
arcctanh	Unary function	arcctanh(x)	1.0	Inverse hyperbolic cotangent - Unary function
asech	Unary function	asech(x)	1.0	Inverse hyperbolic secant - Unary function
arsech	Unary function	arsech(x)	1.0	Inverse hyperbolic secant - Unary function
arcsech	Unary function	arcsech(x)	1.0	Inverse hyperbolic secant - Unary function
acsch	Unary function	acsch(x)	1.0	Inverse hyperbolic cosecant - Unary function
arcsch	Unary function	arcsch(x)	1.0	Inverse hyperbolic cosecant - Unary function
arccsch	Unary function	arccsch(x)	1.0	Inverse hyperbolic cosecant - Unary function
acosech	Unary function	acosech(x)	1.0	Inverse hyperbolic cosecant - Unary function
arcosech	Unary function	arcosech(x)	1.0	Inverse hyperbolic cosecant - Unary function
arccosech	Unary function	arccosech(x)	1.0	Inverse hyperbolic cosecant - Unary function
Sa	Unary function	Sa(x)	1.0	Sinc (normalized) - Unary function
sinc	Unary function	sinc(x)	1.0	Sinc (normalized) - Unary function
Sinc	Unary function	Sinc(x)	1.0	Sinc (unnormalized) - Unary function
Bell	Unary function	Bell(n)	1.0	Bell number - Unary function
Luc	Unary function	Luc(n)	1.0	Lucas number - Unary function
Fib	Unary function	Fib(n)	1.0	Fibonacci number - Unary function
harm	Unary function	harm(n)	1.0	Harmonic number - Unary function
ispr	Unary function	ispr(n)	2.3	Prime number test (is number a prime?) - Unary function
Pi	Unary function	Pi(n)	2.3	Prime-counting π(n) - Unary function
Ei	Unary function	Ei(x)	2.3	Exponential integral - Special function Ei(x) - Unary function
li	Unary function	li(x)	2.3	Logarithmic integral - Special function li(x) - Unary function
Li	Unary function	Li(x)	2.3	Offset logarithmic integral - Special function Li(x) - Unary function
erf	Unary function	erf(x)	3.0	Gauss error - Special function erf(x) - Unary function
erfc	Unary function	erfc(x)	3.0	Gauss complementary error - Special function erfc(x) - Unary function
erfInv	Unary function	erfInv(x)	3.0	Inverse Gauss error - Special function erf⁻¹(y) - Unary function
erfcInv	Unary function	erfcInv(x)	3.0	Inverse Gauss complementary error - Special function erfc⁻¹(x) - Unary function
ulp	Unary function	ulp(x)	3.0	Unit in The Last Place - Unary function
isNaN	Unary function	isNaN(x)	4.1	Returns true if value is a Not-a-Number (NaN), false otherwise (true=1, false=1) - Unary function
ndig10	Unary function	ndig10(x)	4.1	Number of digits in numeral system with base 10 - Unary function
nfact	Unary function	nfact(x)	4.1	Prime decomposition - number of distinct prime factors - Unary function
arcsec	Unary function	arcsec(x)	4.1	Inverse trigonometric secant - Unary function
arccsc	Unary function	arccsc(x)	4.1	Inverse trigonometric cosecant - Unary function
Gamma	Unary function	Gamma(x)	4.2	Gamma - Special function Γ(s) - Unary function
LambW0	Unary function	LambW0(x)	4.2	Lambert-W, principal branch 0, also called the omega or product logarithm - Special function W₀(x) - Unary function
LambW1	Unary function	LambW1(x)	4.2	Lambert-W, branch -1, also called the omega or product logarithm - Special function W₋₁(x) - Unary function
sgnGamma	Unary function	sgnGamma(x)	4.2	Signum of Gamma - Special function Γ(s) - Unary function
logGamma	Unary function	logGamma(x)	4.2	Log Gamma - Special function lnΓ(s) - Unary function
diGamma	Unary function	diGamma(x)	4.2	Digamma as the logarithmic derivative of the Gamma - Special function ψ(x) - Unary function
rStud	Unary function	rStud(v)	5.0	Random variable - Student's t-distribution - Unary function
rChi2	Unary function	rChi2(k)	5.0	Random variable - Chi-squared distribution - Unary function

Binary Functions

Keyword	Type	Syntax	Since	Description
log	Binary function	log(a, b)	1.0	Logarithm - Binary function
mod	Binary function	mod(a, b)	1.0	Modulo - Binary function
C	Binary function	C(n, k)	1.0	Binomial coefficient, number of k-combinations that can be drawn from n-elements set - Binary function
nCk	Binary function	nCk(n, k)	4.2	Binomial coefficient, number of k-combinations that can be drawn from n-elements set - Binary function
Bern	Binary function	Bern(m, n)	1.0	Bernoulli numbers - Binary function
Stirl1	Binary function	Stirl1(n, k)	1.0	Stirling numbers of the first kind - Binary function
Stirl2	Binary function	Stirl2(n, k)	1.0	Stirling numbers of the second kind - Binary function
Worp	Binary function	Worp(n, k)	1.0	Worpitzky number - Binary function
Euler	Binary function	Euler(n, k)	1.0	Euler number - Binary function
KDelta	Binary function	KDelta(i, j)	1.0	Kronecker delta - Binary function
EulerPol	Binary function	EulerPol(m, x)	1.0	Euler polynomial - Binary function
Harm	Binary function	Harm(x, n)	1.0	Harmonic number - Binary function
rUni	Binary function	rUni(a, b)	3.0	Random variable - Uniform continuous distribution U(a,b) - Binary function
rUnid	Binary function	rUnid(a, b)	3.0	Random variable - Uniform discrete distribution U{a,b} - Binary function
round	Binary function	round(x, n)	3.0	Half-up rounding - Binary function
rNor	Binary function	rNor(mean, stdv)	3.0	Random variable - Normal distribution N(μ,σ) - Binary function
ndig	Binary function	ndig(number, base)	4.1	Number of digits representing the number in numeral system with given base - Binary function
dig10	Binary function	dig10(num, pos)	4.1	Digit at position 1 ... n (left -> right) or 0 ... -(n-1) (right -> left) - base 10 numeral system - Binary function
factval	Binary function	factval(number, factorid)	4.1	Prime decomposition - factor value at position between 1 ... nfact(n) - ascending order by factor value - Binary function
factexp	Binary function	factexp(number, factorid)	4.1	Prime decomposition - factor exponent / multiplicity at position between 1 ... nfact(n) - ascending order by factor value - Binary function
root	Binary function	root(rootorder, number)	4.1	N-th order root of a number - Binary function
GammaL	Binary function	GammaL(s, x)	4.2	Lower incomplete gamma - Special function γ(s,x) - Binary function
GammaU	Binary function	GammaU(s, x)	4.2	Upper incomplete Gamma - Special function Γ(s,x) - Binary function
GammaP	Binary function	GammaP(s, x)	4.2	Lower regularized P gamma - Special function P(s,x) - Binary function
GammaRegL	Binary function	GammaRegL(s, x)	4.2	Lower regularized P gamma - Special function P(s,x) - Binary function
GammaQ	Binary function	GammaQ(s, x)	4.2	Upper regularized Q Gamma - Special function Q(s,x) - Binary function
GammaRegU	Binary function	GammaRegU(s, x)	4.2	Upper regularized Q Gamma - Special function Q(s,x) - Binary function
nPk	Binary function	nPk(n, k)	4.2	Number of k-permutations that can be drawn from n-elements set - Binary function
Beta	Binary function	Beta(x, y)	4.2	The Beta, also called the Euler integral of the first kind - Special function B(x,y) - Binary function
logBeta	Binary function	logBeta(x, y)	4.2	The Log Beta, also called the Log Euler integral of the first kind - Special function lnB(x,y) - Binary function
pStud	Binary function	pStud(x, v)	5.0	Student's t-distribution - Probability distribution function - Binary function
cStud	Binary function	cStud(x, v)	5.0	Student's t-distribution - Cumulative distribution function - Binary function
qStud	Binary function	qStud(p, v)	5.0	Student's t-distribution - Quantile function (inverse cumulative distribution function) - Binary function
pChi2	Binary function	pChi2(x, k)	5.0	Chi-squared distribution - Probability distribution function - Binary function
cChi2	Binary function	cChi2(x, k)	5.0	Chi-squared distribution - Cumulative distribution function - Binary function
qChi2	Binary function	qChi2(p, k)	5.0	Chi-squared distribution - Quantile function (inverse cumulative distribution function) - Binary function
rFSned	Binary function	rFSned(d1, d2)	5.1	Random variable - Snedecor's F distribution (F-distribution or F-ratio, also known as Fisher–Snedecor distribution) - Binary function

3-args Functions

Keyword	Type	Syntax	Since	Description
if	Ternary function	if(cond, expr-if-true, expr-if-false)	1.0	If - Ternary function
chi	Ternary function	chi(x, a, b)	1.0	Characteristic function for x in (a,b) - Ternary function
CHi	Ternary function	CHi(x, a, b)	1.0	Characteristic function for x in [a,b] - Ternary function
Chi	Ternary function	Chi(x, a, b)	1.0	Characteristic function for x in [a,b) - Ternary function
cHi	Ternary function	cHi(x, a, b)	1.0	Characteristic function for x in (a,b] - Ternary function
pUni	Ternary function	pUni(x, a, b)	3.0	Uniform continuous distribution - Probability distribution function U(a,b) - Ternary function
cUni	Ternary function	cUni(a, a, b)	3.0	Uniform continuous distribution - Cumulative distribution function U(a,b) - Ternary function
qUni	Ternary function	qUni(q, a, b)	3.0	Uniform continuous distribution - Quantile function (inverse cumulative distribution function) U(a,b) - Ternary function
pNor	Ternary function	pNor(x, mean, stdv)	3.0	Normal distribution - Probability distribution function N(μ,σ) - Ternary function
cNor	Ternary function	cNor(x, mean, stdv)	3.0	Normal distribution - Cumulative distribution function N(μ,σ) - Ternary function
qNor	Ternary function	qNor(q, mean, stdv)	3.0	Normal distribution - Quantile function (inverse cumulative distribution function) N(μ,σ) - Ternary function
dig	Ternary function	dig(num, pos, base)	4.1	Digit at position 1 ... n (left -> right) or 0 ... -(n-1) (right -> left) - numeral system with given base - Ternary function
BetaInc	Ternary function	BetaInc(x, a, b)	4.2	The incomplete Beta, also called the incomplete Euler integral of the first kind - Special function B(x,a,b) - Ternary function
BetaI	Ternary function	BetaI(x, a, b)	4.2	The regularized incomplete Beta (or regularized beta), also called the regularized incomplete Euler integral of the first kind - Special function I(x,a,b) - Ternary function
BetaReg	Ternary function	BetaReg(x, a, b)	4.2	The regularized incomplete Beta (or regularized beta), also called the regularized incomplete Euler integral of the first kind - Special function I(x,a,b) - Ternary function
pFSned	Ternary function	pFSned(x, d1, d2)	5.1	Snedecor's F distribution (F-distribution or F-ratio, also known as Fisher–Snedecor distribution) - Probability distribution function - Ternary function
cFSned	Ternary function	cFSned(x, d1, d2)	5.1	Snedecor's F distribution (F-distribution or F-ratio, also known as Fisher–Snedecor distribution) - Cumulative distribution function - Ternary function
qFSned	Ternary function	qFSned(p, d1, d2)	5.1	Snedecor's F distribution (F-distribution or F-ratio, also known as Fisher–Snedecor distribution) - Quantile function (inverse cumulative distribution function) - Ternary function

Variadic Functions

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

Calculus Operators / Iterated Operators

Keyword	Type	Syntax	Since	Description
∑	Calculus operator	∑(i, from, to, expr, )	5.0	Summation SIGMA - Iterated operator Σ - Calculus operator - Unicode math symbol
Σ	Calculus operator	Σ(i, from, to, expr, )	5.0	Summation SIGMA - Iterated operator Σ - Calculus operator - Unicode math symbol
sum	Calculus operator	sum(i, from, to, expr, )	1.0	Summation SIGMA - Iterated operator Σ - Calculus operator
∏	Calculus operator	∏(i, from, to, expr, )	5.0	Product PI - Iterated operator ∏ - Calculus operator - Unicode math symbol
ℿ	Calculus operator	ℿ(i, from, to, expr, )	5.0	Product PI - Iterated operator ∏ - Calculus operator - Unicode math symbol
Π	Calculus operator	Π(i, from, to, expr, )	5.0	Product PI - Iterated operator ∏ - Calculus operator - Unicode math symbol
prod	Calculus operator	prod(i, from, to, expr, )	1.0	Product PI - Iterated operator ∏ - Calculus operator
∫	Calculus operator	∫(expr, arg, from, to)	5.0	Definite integral ∫ - Calculus operator - Unicode math symbol
int	Calculus operator	int(expr, arg, from, to)	1.0	Definite integral ∫ - Calculus operator
∂	Calculus operator	∂(expr, arg, )	5.0	Derivative ∂ - Calculus operator - Unicode math symbol
der	Calculus operator	der(expr, arg, )	1.0	Derivative ∂ - Calculus operator
∂-	Calculus operator	∂-(expr, arg, )	5.0	Left derivative ∂- - Calculus operator - Unicode math symbol
der-	Calculus operator	der-(expr, arg, )	1.0	Left derivative ∂- - Calculus operator
∂+	Calculus operator	∂+(expr, arg, )	5.0	Right derivative ∂+ - Calculus operator - Unicode math symbol
der+	Calculus operator	der+(expr, arg, )	1.0	Right derivative ∂+ - Calculus operator
dern	Calculus operator	dern(expr, n, arg)	1.0	n-th derivative ∂ⁿ - Calculus operator
∆	Calculus operator	∆(expr, arg, )	5.0	Forward difference ∆ - Calculus operator - Unicode math symbol
Δ	Calculus operator	Δ(expr, arg, )	5.0	Forward difference ∆ - Calculus operator - Unicode math symbol
diff	Calculus operator	diff(expr, arg, )	1.0	Forward difference ∆ - Calculus operator
∇	Calculus operator	∇(expr, arg, )	5.0	Backward difference ∇ - Calculus operator - Unicode math symbol
difb	Calculus operator	difb(expr, arg, )	1.0	Backward difference ∇ - Calculus operator
avg	Calculus operator	avg(i, from, to, expr, )	2.4	Average - Iterated operator - Calculus operator
vari	Calculus operator	vari(i, from, to, expr, )	2.4	Bias-corrected sample variance - Iterated operator - Calculus operator
stdi	Calculus operator	stdi(i, from, to, expr, )	2.4	Bias-corrected sample standard deviation - Iterated operator - Calculus operator
mini	Calculus operator	mini(i, from, to, expr, )	2.4	Minimum value - Iterated operator - Calculus operator
maxi	Calculus operator	maxi(i, from, to, expr, )	2.4	Maximum value - Iterated operator - Calculus operator
solve	Calculus operator	solve(expr, arg, from, to)	4.0	Equation solving (root finding) f(x)=0 - Calculus operator

Random Variables

Keyword	Type	Syntax	Since	Description
[Uni]	Random variable	[Uni]	3.0	Uniform continuous distribution U(0,1) - Random variable
[Int]	Random variable	[Int]	3.0	Random integer - Random variable
[Int1]	Random variable	[Int1]	3.0	Uniform discrete distribution - Random integer U{-10¹,10¹} - Random variable
[Int2]	Random variable	[Int2]	3.0	Uniform discrete distribution - Random integer U{-10²,10²} - Random variable
[Int3]	Random variable	[Int3]	3.0	Uniform discrete distribution - Random integer U{-10³,10³} - Random variable
[Int4]	Random variable	[Int4]	3.0	Uniform discrete distribution - Random integer U{-10⁴,10⁴} - Random variable
[Int5]	Random variable	[Int5]	3.0	Uniform discrete distribution - Random integer U{-10⁵,10⁵} - Random variable
[Int6]	Random variable	[Int6]	3.0	Uniform discrete distribution - Random integer U{-10⁶,10⁶} - Random variable
[Int7]	Random variable	[Int7]	3.0	Uniform discrete distribution - Random integer U{-10⁷,10⁷} - Random variable
[Int8]	Random variable	[Int8]	3.0	Uniform discrete distribution - Random integer U{-10⁸,10⁸} - Random variable
[Int9]	Random variable	[Int9]	3.0	Uniform discrete distribution - Random integer U{-10⁹,10⁹} - Random variable
[nat]	Random variable	[nat]	3.0	Random natural number including 0 - Random variable
[nat1]	Random variable	[nat1]	3.0	Uniform discrete distribution - Random natural number including 0 U{0,10¹} - Random variable
[nat2]	Random variable	[nat2]	3.0	Uniform discrete distribution - Random natural number including 0 U{0,10²} - Random variable
[nat3]	Random variable	[nat3]	3.0	Uniform discrete distribution - Random natural number including 0 U{0,10³} - Random variable
[nat4]	Random variable	[nat4]	3.0	Uniform discrete distribution - Random natural number including 0 U{0,10⁴} - Random variable
[nat5]	Random variable	[nat5]	3.0	Uniform discrete distribution - Random natural number including 0 U{0,10⁵} - Random variable
[nat6]	Random variable	[nat6]	3.0	Uniform discrete distribution - Random natural number including 0 U{0,10⁶} - Random variable
[nat7]	Random variable	[nat7]	3.0	Uniform discrete distribution - Random natural number including 0 U{0,10⁷} - Random variable
[nat8]	Random variable	[nat8]	3.0	Uniform discrete distribution - Random natural number including 0 U{0,10⁸} - Random variable
[nat9]	Random variable	[nat9]	3.0	Uniform discrete distribution - Random natural number including 0 U{0,10⁹} - Random variable
[Nat]	Random variable	[Nat]	3.0	Random natural number - Random variable
[Nat1]	Random variable	[Nat1]	3.0	Uniform discrete distribution - Random natural number U{1,10¹} - Random variable
[Nat2]	Random variable	[Nat2]	3.0	Uniform discrete distribution - Random natural number U{1,10²} - Random variable
[Nat3]	Random variable	[Nat3]	3.0	Uniform discrete distribution - Random natural number U{1,10³} - Random variable
[Nat4]	Random variable	[Nat4]	3.0	Uniform discrete distribution - Random natural number U{1,10⁴} - Random variable
[Nat5]	Random variable	[Nat5]	3.0	Uniform discrete distribution - Random natural number U{1,10⁵} - Random variable
[Nat6]	Random variable	[Nat6]	3.0	Uniform discrete distribution - Random natural number U{1,10⁶} - Random variable
[Nat7]	Random variable	[Nat7]	3.0	Uniform discrete distribution - Random natural number U{1,10⁷} - Random variable
[Nat8]	Random variable	[Nat8]	3.0	Uniform discrete distribution - Random natural number U{1,10⁸} - Random variable
[Nat9]	Random variable	[Nat9]	3.0	Uniform discrete distribution - Random natural number U{1,10⁹} - Random variable
[Nor]	Random variable	[Nor]	3.0	Normal distribution N(0,1) - Random variable

Mathematical Constants

Keyword	Type	Syntax	Since	Description
π	Constant value	π	5.0	Pi, Archimedes' or Ludolph's number - Mathematical constant π - Constant value - Unicode math symbol
ℼ	Constant value	ℼ	5.0	Pi, Archimedes' or Ludolph's number - Mathematical constant π - Constant value - Unicode math symbol
pi	Constant value	pi	1.0	Pi, Archimedes' or Ludolph's number - Mathematical constant π - Constant value
e	Constant value	e	1.0	Napier's or Euler's number (base of Natural logarithm) - Mathematical constant e - Constant value
ℯ	Constant value	ℯ	5.0	Napier's or Euler's number (base of Natural logarithm) - Mathematical constant e - Constant value - Unicode math symbol
ⅇ	Constant value	ⅇ	5.0	Napier's or Euler's number (base of Natural logarithm) - Mathematical constant e - Constant value - Unicode math symbol
[gam]	Constant value	[gam]	1.0	Euler-Mascheroni constant - Mathematical constant γ - Constant value
[phi]	Constant value	[phi]	1.0	Golden ratio - Mathematical constant φ - Constant value
[PN]	Constant value	[PN]	1.0	Plastic constant - Mathematical constant ρ - Constant value
[B*]	Constant value	[B*]	1.0	Embree-Trefethen constant - Mathematical constant β* - Constant value
[F'd]	Constant value	[F'd]	1.0	Feigenbaum delta constant - Mathematical constant δ - Constant value
[F'a]	Constant value	[F'a]	1.0	Feigenbaum alpha constant - Mathematical constant α - Constant value
[C2]	Constant value	[C2]	1.0	Twin prime constant - Mathematical constant ∏₂ - Constant value
[M1]	Constant value	[M1]	1.0	Meissel-Mertens constant - Mathematical constant M₁, B₁ - Constant value
[B2]	Constant value	[B2]	1.0	Brun's constant for twin primes - Mathematical constant B₂ - Constant value
[B4]	Constant value	[B4]	1.0	Brun's constant for prime quadruplets - Mathematical constant B₄ - Constant value
[BN'L]	Constant value	[BN'L]	1.0	de Bruijn-Newman constant - Mathematical constant Λ - Constant value
[Kat]	Constant value	[Kat]	1.0	Catalan's constant - Mathematical constant G - Constant value
[K*]	Constant value	[K*]	1.0	Landau-Ramanujan constant - Mathematical constant b - Constant value
[K.]	Constant value	[K.]	1.0	Viswanath's constant - Mathematical constant V - Constant value
[B'L]	Constant value	[B'L]	1.0	Legendre's constant - Mathematical constant B - Constant value
[RS'm]	Constant value	[RS'm]	1.0	Ramanujan-Soldner constant - Mathematical constant μ - Constant value
[EB'e]	Constant value	[EB'e]	1.0	Erdos-Borwein constant - Mathematical constant E - Constant value
[Bern]	Constant value	[Bern]	1.0	Bernstein's constant - Mathematical constant β - Constant value
[GKW'l]	Constant value	[GKW'l]	1.0	Gauss-Kuzmin-Wirsing constant - Mathematical constant λ - Constant value
[HSM's]	Constant value	[HSM's]	1.0	Hafner-Sarnak-McCurley constant - Mathematical constant σ - Constant value
[lm]	Constant value	[lm]	1.0	Golomb-Dickman constant - Mathematical constant λ - Constant value
[Cah]	Constant value	[Cah]	1.0	Cahen's constant - Mathematical constant C - Constant value
[Ll]	Constant value	[Ll]	1.0	Laplace limit constant - Mathematical constant - Constant value
[AG]	Constant value	[AG]	1.0	Alladi-Grinstead constant - Mathematical constant - Constant value
[L*]	Constant value	[L*]	1.0	Lengyel's constant - Mathematical constant Λ - Constant value
[L.]	Constant value	[L.]	1.0	Levy's constant - Mathematical constant - Constant value
[Dz3]	Constant value	[Dz3]	1.0	Apery's constant - Mathematical constant ζ(3) - Constant value
[A3n]	Constant value	[A3n]	1.0	Mills' constant - Mathematical constant A - Constant value
[Bh]	Constant value	[Bh]	1.0	Backhouse's constant - Mathematical constant B - Constant value
[Pt]	Constant value	[Pt]	1.0	Porter's constant - Mathematical constant C - Constant value
[L2]	Constant value	[L2]	1.0	Lieb's square ice constant - Mathematical constant - Constant value
[Nv]	Constant value	[Nv]	1.0	Niven's constant - Mathematical constant C - Constant value
[Ks]	Constant value	[Ks]	1.0	Sierpinski's constant - Mathematical constant K - Constant value
[Kh]	Constant value	[Kh]	1.0	Khinchin's constant - Mathematical constant K₀ - Constant value
[FR]	Constant value	[FR]	1.0	Fransen-Robinson constant - Mathematical constant F - Constant value
[La]	Constant value	[La]	1.0	Landau's constant - Mathematical constant L - Constant value
[P2]	Constant value	[P2]	1.0	Parabolic constant - Mathematical constant P - Constant value
[Om]	Constant value	[Om]	1.0	Omega constant - Mathematical constant Ω - Constant value
[MRB]	Constant value	[MRB]	1.0	MRB constant - Mathematical constant S - Constant value
[li2]	Constant value	[li2]	2.3	Logarithmic integral at point 2 - Mathematical constant li(2) - Constant value
[EG]	Constant value	[EG]	2.3	Gompertz constant - Mathematical constant δ - Constant value

Physical Constant

Keyword	Type	Syntax	Since	Description
[c]	Constant value	[c]	4.0	Light speed in vacuum - Physical constant c [m/s] (m=1, s=1) - Constant value
[G.]	Constant value	[G.]	4.0	Gravitational constant - Physical constant G (m=1, kg=1, s=1) - Constant value
[g]	Constant value	[g]	4.0	Gravitational acceleration on Earth - Physical constant g [m/s²] (m=1, s=1) - Constant value
[hP]	Constant value	[hP]	4.0	Planck constant - Physical constant h (m=1, kg=1, s=1) - Constant value
[h-]	Constant value	[h-]	4.0	Reduced Planck constant (Dirac constant) - Physical constant ħ (m=1, kg=1, s=1) - Constant value
[lP]	Constant value	[lP]	4.0	Planck length - Physical constant lᵖ [m] (m=1) - Constant value
[mP]	Constant value	[mP]	4.0	Planck mass - Physical constant mᵖ [kg] (kg=1) - Constant value
[tP]	Constant value	[tP]	4.0	Planck time - Physical constant tᵖ [s] (s=1) - Constant value

Astronomical Constant

Keyword	Type	Syntax	Since	Description
[ly]	Constant value	[ly]	4.0	Light year - Astronomical constant ly [m] (m=1) - Constant value
[au]	Constant value	[au]	4.0	Astronomical unit - Astronomical constant au, AU [m] (m=1) - Constant value
[pc]	Constant value	[pc]	4.0	Parsec - Astronomical constant pc [m] (m=1) - Constant value
[kpc]	Constant value	[kpc]	4.0	Kiloparsec - Astronomical constant kpc [m] (m=1) - Constant value
[Earth-R-eq]	Constant value	[Earth-R-eq]	4.0	Earth equatorial radius - Astronomical constant Rª⊕ [m] (m=1) - Constant value
[Earth-R-po]	Constant value	[Earth-R-po]	4.0	Earth polar radius - Astronomical constant Rᵇ⊕ [m] (m=1) - Constant value
[Earth-R]	Constant value	[Earth-R]	4.0	Earth mean radius - Astronomical constant R⊕ (m=1) - Constant value
[Earth-M]	Constant value	[Earth-M]	4.0	Earth mass - Astronomical constant M⊕ [kg] (kg=1) - Constant value
[Earth-D]	Constant value	[Earth-D]	4.0	Earth-Sun distance - Astronomical constant - Semi major axis [m] (m=1) - Constant value
[Moon-R]	Constant value	[Moon-R]	4.0	Moon mean radius - Astronomical constant [m] (m=1) - Constant value
[Moon-M]	Constant value	[Moon-M]	4.0	Moon mass - Astronomical constant [kg] (kg=1) - Constant value
[Moon-D]	Constant value	[Moon-D]	4.0	Moon-Earth distance - Astronomical constant - Semi major axis [m] (m=1) - Constant value
[Solar-R]	Constant value	[Solar-R]	4.0	Solar mean radius - Astronomical constant R☉ [m] (m=1) - Constant value
[Solar-M]	Constant value	[Solar-M]	4.0	Solar mass - Astronomical constant M☉ [kg] (kg=1) - Constant value
[Mercury-R]	Constant value	[Mercury-R]	4.0	Mercury mean radius - Astronomical constant [m] (m=1) - Constant value
[Mercury-M]	Constant value	[Mercury-M]	4.0	Mercury mass - Astronomical constant [kg] (kg=1) - Constant value
[Mercury-D]	Constant value	[Mercury-D]	4.0	Mercury-Sun distance - Astronomical constant - Semi major axis [m] (m=1) - Constant value
[Venus-R]	Constant value	[Venus-R]	4.0	Venus mean radius - Astronomical constant [m] (m=1) - Constant value
[Venus-M]	Constant value	[Venus-M]	4.0	Venus mass - Astronomical constant [kg] (kg=1) - Constant value
[Venus-D]	Constant value	[Venus-D]	4.0	Venus-Sun distance - Astronomical constant - Semi major axis [m] (m=1) - Constant value
[Mars-R]	Constant value	[Mars-R]	4.0	Mars mean radius - Astronomical constant [m] (m=1) - Constant value
[Mars-M]	Constant value	[Mars-M]	4.0	Mars mass - Astronomical constant [kg] (kg=1) - Constant value
[Mars-D]	Constant value	[Mars-D]	4.0	Mars-Sun distance - Astronomical constant - Semi major axis [m] (m=1) - Constant value
[Jupiter-R]	Constant value	[Jupiter-R]	4.0	Jupiter mean radius - Astronomical constant [m] (m=1) - Constant value
[Jupiter-M]	Constant value	[Jupiter-M]	4.0	Jupiter mass - Astronomical constant [kg] (kg=1) - Constant value
[Jupiter-D]	Constant value	[Jupiter-D]	4.0	Jupiter-Sun distance - Astronomical constant - Semi major axis [m] (m=1) - Constant value
[Saturn-R]	Constant value	[Saturn-R]	4.0	Saturn mean radius - Astronomical constant [m] (m=1) - Constant value
[Saturn-M]	Constant value	[Saturn-M]	4.0	Saturn mass - Astronomical constant [kg] (kg=1) - Constant value
[Saturn-D]	Constant value	[Saturn-D]	4.0	Saturn-Sun distance - Astronomical constant - Semi major axis [m] (m=1) - Constant value
[Uranus-R]	Constant value	[Uranus-R]	4.0	Uranus mean radius - Astronomical constant [m] (m=1) - Constant value
[Uranus-M]	Constant value	[Uranus-M]	4.0	Uranus mass - Astronomical constant [kg] (kg=1) - Constant value
[Uranus-D]	Constant value	[Uranus-D]	4.0	Uranus-Sun distance - Astronomical constant - Semi major axis [m] (m=1) - Constant value
[Neptune-R]	Constant value	[Neptune-R]	4.0	Neptune mean radius - Astronomical constant [m] (m=1) - Constant value
[Neptune-M]	Constant value	[Neptune-M]	4.0	Neptune mass - Astronomical constant [kg] (kg=1) - Constant value
[Neptune-D]	Constant value	[Neptune-D]	4.0	Neptune-Sun distance - Astronomical constant - Semi major axis [m] (m=1) - Constant value

Metric prefixes

Keyword	Type	Syntax	Since	Description
[Y]	Unit	[Y]	4.0	Septillion / Yotta - Metric prefix = 10²⁴ - Dimensionless unit
[sept]	Unit	[sept]	4.0	Septillion / Yotta - Metric prefix = 10²⁴ - Dimensionless unit
[Z]	Unit	[Z]	4.0	Sextillion / Zetta - Metric prefix = 10²¹ - Dimensionless unit
[sext]	Unit	[sext]	4.0	Sextillion / Zetta - Metric prefix = 10²¹ - Dimensionless unit
[E]	Unit	[E]	4.0	Quintillion / Exa - Metric prefix = 10¹⁸ - Dimensionless unit
[quint]	Unit	[quint]	4.0	Quintillion / Exa - Metric prefix = 10¹⁸ - Dimensionless unit
[P]	Unit	[P]	4.0	Quadrillion / Peta - Metric prefix = 10¹⁵ - Dimensionless unit
[quad]	Unit	[quad]	4.0	Quadrillion / Peta - Metric prefix = 10¹⁵ - Dimensionless unit
[T]	Unit	[T]	4.0	Trillion / Tera - Metric prefix = 10¹² - Dimensionless unit
[tril]	Unit	[tril]	4.0	Trillion / Tera - Metric prefix = 10¹² - Dimensionless unit
[G]	Unit	[G]	4.0	Billion / Giga - Metric prefix = 10⁹ - Dimensionless unit
[bil]	Unit	[bil]	4.0	Billion / Giga - Metric prefix = 10⁹ - Dimensionless unit
[M]	Unit	[M]	4.0	Million / Mega - Metric prefix = 10⁶ - Dimensionless unit
[mil]	Unit	[mil]	4.0	Million / Mega - Metric prefix = 10⁶ - Dimensionless unit
[k]	Unit	[k]	4.0	Thousand / Kilo - Metric prefix = 10³ - Dimensionless unit
[th]	Unit	[th]	4.0	Thousand / Kilo - Metric prefix = 10³ - Dimensionless unit
[hund]	Unit	[hund]	4.0	Hundred / Hecto - Metric prefix = 10² - Dimensionless unit
[hecto]	Unit	[hecto]	4.0	Hundred / Hecto - Metric prefix = 10² - Dimensionless unit
[ten]	Unit	[ten]	4.0	Ten / Deca - Metric prefix = 10 - Dimensionless unit
[deca]	Unit	[deca]	4.0	Ten / Deca - Metric prefix = 10 - Dimensionless unit
[deci]	Unit	[deci]	4.0	Tenth / Deci - Metric prefix = 10⁻¹ - Dimensionless unit
[centi]	Unit	[centi]	4.0	Hundredth / Centi - Metric prefix = 10⁻² - Dimensionless unit
[milli]	Unit	[milli]	4.0	Thousandth / Milli - Metric prefix = 10⁻³ - Dimensionless unit
[mic]	Unit	[mic]	4.0	Millionth / Micro - Metric prefix = 10⁻⁶ - Dimensionless unit
[n]	Unit	[n]	4.0	Billionth / Nano - Metric prefix = 10⁻⁹ - Dimensionless unit
[p]	Unit	[p]	4.0	Trillionth / Pico - Metric prefix = 10⁻¹² - Dimensionless unit
[f]	Unit	[f]	4.0	Quadrillionth / Femto - Metric prefix = 10⁻¹⁵ - Dimensionless unit
[a]	Unit	[a]	4.0	Quintillionth / Atoo - Metric prefix = 10⁻¹⁸ - Dimensionless unit
[z]	Unit	[z]	4.0	Sextillionth / Zepto - Metric prefix = 10⁻²¹ - Dimensionless unit
[y]	Unit	[y]	4.0	Septillionth / Yocto - Metric prefix = 10⁻²⁴ - Dimensionless unit

Units of length

Keyword	Type	Syntax	Since	Description
[m]	Unit	[m]	4.0	Meter - Unit of length [m] (m=1) - Unit
[km]	Unit	[km]	4.0	Kilometer - Unit of length [m] (m=1) - Unit
[cm]	Unit	[cm]	4.0	Centimeter - Unit of length [m] (m=1) - Unit
[mm]	Unit	[mm]	4.0	Millimeter - Unit of length [m] (m=1) - Unit
[inch]	Unit	[inch]	4.0	Inch - Unit of length [m] (m=1) - Unit
[yd]	Unit	[yd]	4.0	Yard - Unit of length [m] (m=1) - Unit
[ft]	Unit	[ft]	4.0	Feet - Unit of length [m] (m=1) - Unit
[mile]	Unit	[mile]	4.0	Mile - Unit of length [m] (m=1) - Unit
[nmi]	Unit	[nmi]	4.0	Nautical mile - Unit of length [m] (m=1) - Unit

Units of area

Keyword	Type	Syntax	Since	Description
[m2]	Unit	[m2]	4.0	Square meter - Unit of area [m²] (m=1) - Unit
[cm2]	Unit	[cm2]	4.0	Square centimeter - Unit of area [m²] (m=1) - Unit
[mm2]	Unit	[mm2]	4.0	Square millimeter - Unit of area [m²] (m=1) - Unit
[are]	Unit	[are]	4.0	Are - Unit of area [m²] (m=1) - Unit
[ha]	Unit	[ha]	4.0	Hectare - Unit of area [m²] (m=1) - Unit
[acre]	Unit	[acre]	4.0	Acre - Unit of area [m²] (m=1) - Unit
[km2]	Unit	[km2]	4.0	Square kilometer - Unit of area [m²] (m=1) - Unit

Units of volume

Keyword	Type	Syntax	Since	Description
[mm3]	Unit	[mm3]	4.0	Cubic millimeter - Unit of volume [m³] (m=1) - Unit
[cm3]	Unit	[cm3]	4.0	Cubic centimeter - Unit of volume [m³] (m=1) - Unit
[m3]	Unit	[m3]	4.0	Cubic meter - Unit of volume [m³] (m=1) - Unit
[km3]	Unit	[km3]	4.0	Cubic kilometer - Unit of volume [m³] (m=1) - Unit
[ml]	Unit	[ml]	4.0	Milliliter - Unit of volume [m³] (m=1) - Unit
[l]	Unit	[l]	4.0	Liter - Unit of volume [m³] (m=1) - Unit
[gall]	Unit	[gall]	4.0	Gallon - Unit of volume [m³] (m=1) - Unit
[pint]	Unit	[pint]	4.0	Pint - Unit of volume [m³] (m=1) - Unit

Units of time

Keyword	Type	Syntax	Since	Description
[s]	Unit	[s]	4.0	Second - Unit of time [s] (s=1) - Unit
[ms]	Unit	[ms]	4.0	Millisecond - Unit of time [s] (s=1) - Unit
[min]	Unit	[min]	4.0	Minute - Unit of time [s] (s=1) - Unit
[h]	Unit	[h]	4.0	Hour - Unit of time [s] (s=1) - Unit
[day]	Unit	[day]	4.0	Day - Unit of time [s] (s=1) - Unit
[week]	Unit	[week]	4.0	Week - Unit of time [s] (s=1) - Unit
[yearj]	Unit	[yearj]	4.0	Julian year = 365.25 days - Unit of time [s] (s=1) - Unit

Units of mass

Keyword	Type	Syntax	Since	Description
[kg]	Unit	[kg]	4.0	Kilogram - Unit of mass [kg] (kg=1) - Unit
[gr]	Unit	[gr]	4.0	Gram - Unit of mass [kg] (kg=1) - Unit
[mg]	Unit	[mg]	4.0	Milligram - Unit of mass [kg] (kg=1) - Unit
[dag]	Unit	[dag]	4.0	Decagram - Unit of mass [kg] (kg=1) - Unit
[t]	Unit	[t]	4.0	Tonne - Unit of mass [kg] (kg=1) - Unit
[oz]	Unit	[oz]	4.0	Ounce - Unit of mass [kg] (kg=1) - Unit
[lb]	Unit	[lb]	4.0	Pound - Unit of mass [kg] (kg=1) - Unit

Units of information

Keyword	Type	Syntax	Since	Description
[b]	Unit	[b]	4.0	Bit - Unit of information [bit] (bit=1) - Unit
[kb]	Unit	[kb]	4.0	Kilobit - Unit of information [bit] (bit=1) - Unit
[Mb]	Unit	[Mb]	4.0	Megabit - Unit of information [bit] (bit=1) - Unit
[Gb]	Unit	[Gb]	4.0	Gigabit - Unit of information [bit] (bit=1) - Unit
[Tb]	Unit	[Tb]	4.0	Terabit - Unit of information [bit] (bit=1) - Unit
[Pb]	Unit	[Pb]	4.0	Petabit - Unit of information [bit] (bit=1) - Unit
[Eb]	Unit	[Eb]	4.0	Exabit - Unit of information [bit] (bit=1) - Unit
[Zb]	Unit	[Zb]	4.0	Zettabit - Unit of information [bit] (bit=1) - Unit
[Yb]	Unit	[Yb]	4.0	Yottabit - Unit of information [bit] (bit=1) - Unit
[B]	Unit	[B]	4.0	Byte - Unit of information [bit] (bit=1) - Unit
[kB]	Unit	[kB]	4.0	Kilobyte - Unit of information [bit] (bit=1) - Unit
[MB]	Unit	[MB]	4.0	Megabyte - Unit of information [bit] (bit=1) - Unit
[GB]	Unit	[GB]	4.0	Gigabyte - Unit of information [bit] (bit=1) - Unit
[TB]	Unit	[TB]	4.0	Terabyte - Unit of information [bit] (bit=1) - Unit
[PB]	Unit	[PB]	4.0	Petabyte - Unit of information [bit] (bit=1) - Unit
[EB]	Unit	[EB]	4.0	Exabyte - Unit of information [bit] (bit=1) - Unit
[ZB]	Unit	[ZB]	4.0	Zettabyte - Unit of information [bit] (bit=1) - Unit
[YB]	Unit	[YB]	4.0	Yottabyte - Unit of information [bit] (bit=1) - Unit

Units of energy

Keyword	Type	Syntax	Since	Description
[J]	Unit	[J]	4.0	Joule - Unit of energy [J] (m=1, kg=1, s=1) - Unit
[eV]	Unit	[eV]	4.0	Electronovolt - Unit of energy [J] (m=1, kg=1, s=1) - Unit
[keV]	Unit	[keV]	4.0	Kiloelectronovolt - Unit of energy [J] (m=1, kg=1, s=1) - Unit
[MeV]	Unit	[MeV]	4.0	Megaelectronovolt - Unit of energy [J] (m=1, kg=1, s=1) - Unit
[GeV]	Unit	[GeV]	4.0	Gigaelectronovolt - Unit of energy [J] (m=1, kg=1, s=1) - Unit
[TeV]	Unit	[TeV]	4.0	Teraelectronovolt - Unit of energy [J] (m=1, kg=1, s=1) - Unit

Units of speed

Keyword	Type	Syntax	Since	Description
[m/s]	Unit	[m/s]	4.0	Meter per second - Unit of speed [m/s] (m=1, s=1) - Unit
[km/h]	Unit	[km/h]	4.0	Kilometer per hour - Unit of speed [m/s] (m=1, s=1) - Unit
[mi/h]	Unit	[mi/h]	4.0	Mile per hour - Unit of speed [m/s] (m=1, s=1) - Unit
[knot]	Unit	[knot]	4.0	Knot - Unit of speed [m/s] (m=1, s=1) - Unit

Units of acceleration

Keyword	Type	Syntax	Since	Description
[m/s2]	Unit	[m/s2]	4.0	Meter per square second - Unit of acceleration [m/s²] (m=1, s=1) - Unit
[km/h2]	Unit	[km/h2]	4.0	Kilometer per square hour - Unit of acceleration [m/s²] (m=1, s=1) - Unit
[mi/h2]	Unit	[mi/h2]	4.0	Mile per square hour - Unit of acceleration [m/s²] (m=1, s=1) - Unit

Units of angle

Keyword	Type	Syntax	Since	Description
[rad]	Unit	[rad]	4.0	Radian - Unit of angle [rad] (rad=1) - Unit
[deg]	Unit	[deg]	4.0	Degree of arc - Unit of angle [rad] (rad=1) - Unit
[']	Unit	[']	4.0	Minute of arc - Unit of angle [rad] (rad=1) - Unit
['']	Unit	['']	4.0	Second of arc - Unit of angle [rad] (rad=1) - Unit

Other parser symbols

Keyword	Type	Syntax	Since	Description
(	Parser symbol	( ... )	1.0	Left parentheses - Parser symbol
)	Parser symbol	( ... )	1.0	Right parentheses - Parser symbol
,	Parser symbol	(a1, ... ,an)	1.0	Comma (function parameters) - Parser symbol
;	Parser symbol	(a1; ... ;an)	1.0	Semicolon (function parameters) - Parser symbol
	Parser symbol		4.2	Blank (whitespace) character - Parser symbol

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Best regards, Mariusz Gromada