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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.5.2.0 (2023-01-29): Orion: Improvement and standardization of descriptions and messages. Definition of your own translations. Exporting help in multiple formats. Clones for thread safe.

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

Package installation

Nuget - Packgae Manager

Install-Package MathParser.org-mXparser -Version 5.2.0

Nuget – .NET CLI

dotnet add package MathParser.org-mXparser --version 5.2.0

Nuget – Package Reference

<PackageReference Include="MathParser.org-mXparser" Version="5.2.0"/>

Maven - Dependency

<dependency>
    <groupId>org.mariuszgromada.math</groupId>
    <artifactId>MathParser.org-mXparser</artifactId>
    <version>5.2.0</version>
</dependency>

Maven - Gradle

implementation 'org.mariuszgromada.math:MathParser.org-mXparser:5.2.0'

Maven – Gradle (Kotlin)

implementation("org.mariuszgromada.math:MathParser.org-mXparser:5.2.0")

NPM

$ npm i mathparser.org-mxparser

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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

mXparser 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

mXparser demo

C# intro

mXparser demo - csharp

TypeScript intro

mXparser demo - TypeScript

Main functionalities:

High flexibility functionalities

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)

paypal

mXparser in nutshell

You want simple calculator...

calc

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

👍

A calculator supporting parenthesis...

parenth

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

👍

You care about predefined constants...

const

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

👍

You need to define your own constants...

const-user

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

👍

You enjoy using many built-in functions...

sinx

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

👍

You do not limit yourself to unary functions...

fun-variadic

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

👍

What about user defined arguments...

arg-free

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

👍

You are considering dependent arguments...

arg-dep

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

👍

You need to apply some logic...

if-then

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

👍

Yes, you are right, there is a support for Boolean algebra!

true-false

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

👍

And for binary relations as well!

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

👍

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

You want to play with iterated operators...

sum

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

👍

You want to iterate differently by not necessarily whole numbes...

prod

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

👍

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();

👍

You still want more fun with calculus operations, i.e. differentiation...

der

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

👍

And definite integrals as well...

int

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

👍

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

user defined functions...

fun-user

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();

👍

Recursion is your desire...

recur

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

👍

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()

👍

If anything above matches you then mXparser is a good choice!

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

syntax

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
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
Constant value 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
Constant value 5.0 Napier's or Euler's number (base of Natural logarithm) - Mathematical constant e - Constant value - Unicode math symbol
Constant value 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

Did you find mXparser useful? If yes:

INFIMA

Best regards, Mariusz Gromada



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