mXparser - a super easy, rich and highly flexible Mathematical Expression Parser (Math Parser, Expression Evaluator) library for JAVA, Android, C# .NET, TypeScript and JavaScript.
- Implied Multiplication, click to see usage example
- Unicode Math Symbols, click to see usage example
- Calculation Steps Register, 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
- Minor Bug fixing: 259, 258, 252, 261
- Regression tests refactoring
Install-Package MathParser.org-mXparser -Version 5.0.6
dotnet add package MathParser.org-mXparser --version 5.0.6
<PackageReference Include="MathParser.org-mXparser" Version="5.0.6"/>
<dependency>
<groupId>org.mariuszgromada.math</groupId>
<artifactId>MathParser.org-mXparser</artifactId>
<version>5.0.6</version>
</dependency>
implementation 'org.mariuszgromada.math:MathParser.org-mXparser:5.0.6'
implementation("org.mariuszgromada.math:MathParser.org-mXparser:5.0.6")
$ npm i mathparser.org-mxparser
- or consider donation: DONATION
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.
- 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
The tutorial consists of c.a. 140 live examples from over 30 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!
- Full help content
- In-line help searching
- Simple calculation
- Changing expression string
- Using operators
- Power function
- Using numbers in scientific notation
- Percent sign
- Leading zeros
- 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
- Binary relation “=”
- Binary relation “<“
- Boolean operator “OR”
- Boolean operator “AND”
- Unary function
- Binary function
- Function with 3 arguments
- Function with n-arguments
- Function with even number of arguments
- Defining constant – various options
- Dealing with free arguments
- Defining dependent arguments
- Implementing your own Argument Extension
- 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
- 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
- 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
- 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
- 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)
- General derivative
- Left / right derivative
- Derivative from more complex function
- Derivative – alternative syntax
- Integrals – calculating pi by integration sqrt(1-x^2)
- 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]
- 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
- Using built-in constants
- Estimating Moon gravitational acceleration
- Getting list of constants
- 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
- Example: 10 Millions / Kilo
- List of supported metric prefixes
- 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 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
- 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)
- Dependent argument as user defined random variable
- User defined function as user defined random variable – random walk example
- Bitwise unary complement
- Bitwise AND
- Bitwise exclusive OR
- Bitwise inclusive OR
- Signed left / right shift
- 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
- Binary number
- Octal number
- Hexadecimal number
- Unary number
- Unary zero
- Base 1 – 36 number literals
- Base N numeral system
- Fibonacci numbers using fast recursion
- 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)
- 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
- NaN in condition
- NaN symbol
- First non-NaN value
- Basic trigonometric function
- Inverse trigonometric function
- Using units of angle being in radians mode
- Simple Expression
- Dependent User Argument
- User Function
- Expression referencing User Argument and User Function
- Setting the verbose mode
- Syntax checking
- Lexical syntax checking
- Getting computing time
- Printing expression tokens
- Using tokens to print expression in a fancy way
- Playing with invalid tokens
- Removing built-in tokens
- Modifying built-in tokens
- Overriding built-in tokens
- 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
- 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
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.
- Units
- 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
- 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.
Expression e = new Expression("2+3");
e.calculate();
👍
Expression e = new Expression("2+(3-5)^2");
e.calculate();
👍
Expression e = new Expression("2*pi");
e.calculate();
👍
Constant tau = new Constant("tau = 2*pi");
Expression e = new Expression("3*tau", tau);
e.calculate();
👍
Expression e = new Expression("sin(2*pi)");
e.calculate();
👍
Expression e = new Expression("gcd(2,5,10,30)");
e.calculate();
👍
Argument x = new Argument("x = 5");
Expression e = new Expression("sin(x)", x);
e.calculate();
👍
Argument x = new Argument("x = 5");
Argument y = new Argument("y = 2*x", x);
Expression e = new Expression("sin(y)", y);
e.calculate();
👍
Argument x = new Argument("x = 5");
Expression e = new Expression("if(sin(x) > 5, 1, 0)", x);
e.calculate();
👍
Expression e = new Expression("5=6");
e.calculate();
👍
Expression e = new Expression("5 <= 6");
e.calculate();
👍
Expression e = new Expression("sum(i, 1, 10, 2*i^2 + pi)");
e.calculate();
👍
Expression e = new Expression("prod(i, 1, 5, i, 0.5)");
e.calculate();
👍
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();
👍
Argument x = new Argument("x = pi/2");
Expression e = new Expression("cos(x)-der(sin(x), x)", x);
e.calculate();
👍
Expression e = new Expression("2*int(sqrt(1-x^2), x, -1, 1)");
e.calculate();
👍
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();
👍
Function f = new Function("f(n) = if( n>0, n*f(n-1), 1)");
f.calculate()
👍
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()
👍
Expression e = new Expression("2+1/a");
e.checkSyntax();
mXparser.consolePrintln(e.getErrorMessage());
| 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 |
| Key word | Category | Description | Example | Since |
|---|---|---|---|---|
| + | Operator | Addition | a + b | 1.0 |
| - | Operator | Subtraction | a - b | 1.0 |
| * | Operator | Multiplication | a * b | 1.0 |
| × | Operator | Multiplication - unicode math symbol | a × b | 5.0 |
| ⨉ | Operator | Multiplication - unicode math symbol | a ⨉ b | 5.0 |
| ∙ | Operator | Multiplication - unicode math symbol | a ∙ b | 5.0 |
| / | Operator | Division | a / b | 1.0 |
| ÷ | Operator | Division - unicode math symbol | a ÷ b | 5.0 |
| ^ | Operator | Exponentiation | a^b | 1.0 |
| ! | Operator | Factorial | n! | 1.0 |
| # | Operator | Modulo function | a # b | 1.0 |
| % | Operator | Percentage | n% | 4.1 |
| ^^ | Operator | Tetration (hyper-4, power tower, exponential tower) | a^^b | 4.2 |
| √ | Operator | Square root function represented as unary left operator - unicode math symbol | √x | 5.0 |
| ∛ | Operator | Cube root function represented as unary left operator - unicode math symbol | ∛x | 5.0 |
| ∜ | Operator | Fourth root function represented as unary left operator - unicode math symbol | ∜x | 5.0 |
| Key word | Category | Description | Example | Since |
|---|---|---|---|---|
| & | Boolean Operator | Logical conjunction (AND) | p & q | 1.0 |
| ∧ | Boolean Operator | Logical conjunction (AND) - unicode math symbol | p ∧ q | 5.0 |
| && | Boolean Operator | Logical conjunction (AND) | p && q | 1.0 |
| /\ | Boolean Operator | Logical conjunction (AND) | p /\ q | 1.0 |
| ⊼ | Boolean Operator | NAND - Sheffer stroke - unicode math symbol | p ⊼ q | 5.0 |
| ~& | Boolean Operator | NAND - Sheffer stroke | p ~& q | 1.0 |
| ~∧ | Boolean Operator | NAND - Sheffer stroke - unicode math symbol | p ~∧ q | 5.0 |
| ¬& | Boolean Operator | NAND - Sheffer stroke - unicode math symbol | p ¬& q | 5.0 |
| ¬∧ | Boolean Operator | NAND - Sheffer stroke - unicode math symbol | p ¬∧ q | 5.0 |
| ~&& | Boolean Operator | NAND - Sheffer stroke | p ~&& q | 1.0 |
| ~/\ | Boolean Operator | NAND - Sheffer stroke | p ~/\ q | 1.0 |
| ¬&& | Boolean Operator | NAND - Sheffer stroke - unicode math symbol | p ¬&& q | 5.0 |
| ¬/\ | Boolean Operator | NAND - Sheffer stroke - unicode math symbol | p ¬/\ q | 5.0 |
| | | Boolean Operator | Logical disjunction (OR) | p | q | 1.0 |
| ∨ | Boolean Operator | Logical disjunction (OR) - unicode math symbol | p ∨ q | 5.0 |
| || | Boolean Operator | Logical disjunction (OR) | p || q | 1.0 |
| \/ | Boolean Operator | Logical disjunction (OR) | p \/ q | 1.0 |
| ⊽ | Boolean Operator | Logical NOR - unicode math symbol | p ⊽ q | 5.0 |
| ~| | Boolean Operator | Logical NOR | p ~| q | 1.0 |
| ~∨ | Boolean Operator | Logical NOR - unicode math symbol | p ~∨ q | 5.0 |
| ¬| | Boolean Operator | Logical NOR - unicode math symbol | p ¬| q | 5.0 |
| ¬∨ | Boolean Operator | Logical NOR - unicode math symbol | p ¬∨ q | 5.0 |
| ~|| | Boolean Operator | Logical NOR | p ~|| q | 1.0 |
| ~\/ | Boolean Operator | Logical NOR | p ~\/ q | 1.0 |
| ¬|| | Boolean Operator | Logical NOR - unicode math symbol | p ¬|| q | 5.0 |
| ¬\/ | Boolean Operator | Logical NOR - unicode math symbol | p ¬\/ q | 5.0 |
| ⊻ | Boolean Operator | Exclusive or (XOR) - unicode math symbol | p ⊻ q | 5.0 |
| (+) | Boolean Operator | Exclusive or (XOR) | p (+) q | 1.0 |
| ⇒ | Boolean Operator | Implication (IMP) - unicode math symbol | p ⇒ q | 5.0 |
| --> | Boolean Operator | Implication (IMP) | p --> q | 1.0 |
| ⇐ | Boolean Operator | Converse implication (CIMP) - unicode math symbol | p ⇐ q | 5.0 |
| <-- | Boolean Operator | Converse implication (CIMP) | p <-- q | 1.0 |
| ⇏ | Boolean Operator | Material nonimplication (NIMP) - unicode math symbol | p ⇏ q | 5.0 |
| -/> | Boolean Operator | Material nonimplication (NIMP) | p -/> q | 1.0 |
| ⇍ | Boolean Operator | Converse nonimplication (CNIMP) - unicode math symbol | p ⇍ q | 5.0 |
| </- | Boolean Operator | Converse nonimplication (CNIMP) | p </- q | 1.0 |
| ⇔ | Boolean Operator | Logical biconditional (EQV) - unicode math symbol | p ⇔ q | 5.0 |
| <-> | Boolean Operator | Logical biconditional (EQV) | p <-> q | 1.0 |
| ~ | Boolean Operator | Negation | ~p | 1.0 |
| ¬ | Boolean Operator | Negation - unicode math symbol | ¬p | 5.0 |
| Key word | Category | Description | Example | Since |
|---|---|---|---|---|
| @~ | Bitwise Operator | Bitwise unary complement | @~a | 4.0 |
| @& | Bitwise Operator | Bitwise AND | a @& b | 4.0 |
| @^ | Bitwise Operator | Bitwise exclusive OR | a @^ b | 4.0 |
| @| | Bitwise Operator | Bitwise inclusive OR | a @| b | 4.0 |
| @<< | Bitwise Operator | Signed left shift | a @<< b | 4.0 |
| @>> | Bitwise Operator | Signed right shift | a @>> b | 4.0 |
| Key word | Category | Description | Example | Since |
|---|---|---|---|---|
| = | Binary Relation | Equality | a = b | 1.0 |
| == | Binary Relation | Equality | a == b | 1.0 |
| ≠ | Binary Relation | Inequation - unicode math symbol | a ≠ b | 5.0 |
| <> | Binary Relation | Inequation | a <> b | 1.0 |
| ~= | Binary Relation | Inequation | a ~= b | 1.0 |
| != | Binary Relation | Inequation | a != b | 1.0 |
| < | Binary Relation | Lower than | a < b | 1.0 |
| > | Binary Relation | Greater than | a > b | 1.0 |
| ≤ | Binary Relation | Lower or equal - unicode math symbol | a ≤ b | 5.0 |
| ⋜ | Binary Relation | Lower or equal - unicode math symbol | a ⋜ b | 5.0 |
| <= | Binary Relation | Lower or equal | a <= b | 1.0 |
| ≥ | Binary Relation | Greater or equal - unicode math symbol | a ≥ b | 5.0 |
| ⋝ | Binary Relation | Greater or equal - unicode math symbol | a ⋝ b | 5.0 |
| >= | Binary Relation | Greater or equal | a >= b | 1.0 |
| Key word | Category | Description | Example | Since |
|---|---|---|---|---|
| sin | Unary Function | Trigonometric sine function | sin(x) | 1.0 |
| cos | Unary Function | Trigonometric cosine function | cos(x) | 1.0 |
| tg | Unary Function | Trigonometric tangent function | tg(x) | 1.0 |
| tan | Unary Function | Trigonometric tangent function | tan(x) | 1.0 |
| ctg | Unary Function | Trigonometric cotangent function | ctg(x) | 1.0 |
| cot | Unary Function | Trigonometric cotangent function | cot(x) | 1.0 |
| ctan | Unary Function | Trigonometric cotangent function | ctan(x) | 1.0 |
| sec | Unary Function | Trigonometric secant function | sec(x) | 1.0 |
| csc | Unary Function | Trigonometric cosecant function | csc(x) | 1.0 |
| cosec | Unary Function | Trigonometric cosecant function | cosec(x) | 1.0 |
| asin | Unary Function | Inverse trigonometric sine function | asin(x) | 1.0 |
| arsin | Unary Function | Inverse trigonometric sine function | arsin(x) | 1.0 |
| arcsin | Unary Function | Inverse trigonometric sine function | arcsin(x) | 1.0 |
| acos | Unary Function | Inverse trigonometric cosine function | acos(x) | 1.0 |
| arcos | Unary Function | Inverse trigonometric cosine function | arcos(x) | 1.0 |
| arccos | Unary Function | Inverse trigonometric cosine function | arccos(x) | 1.0 |
| atg | Unary Function | Inverse trigonometric tangent function | atg(x) | 1.0 |
| atan | Unary Function | Inverse trigonometric tangent function | atan(x) | 1.0 |
| arctg | Unary Function | Inverse trigonometric tangent function | arctg(x) | 1.0 |
| arctan | Unary Function | Inverse trigonometric tangent function | arctan(x) | 1.0 |
| actg | Unary Function | Inverse trigonometric cotangent function | actg(x) | 1.0 |
| acot | Unary Function | Inverse trigonometric cotangent function | acot(x) | 1.0 |
| actan | Unary Function | Inverse trigonometric cotangent function | actan(x) | 1.0 |
| arcctg | Unary Function | Inverse trigonometric cotangent function | arcctg(x) | 1.0 |
| arccot | Unary Function | Inverse trigonometric cotangent function | arccot(x) | 1.0 |
| arcctan | Unary Function | Inverse trigonometric cotangent function | arcctan(x) | 1.0 |
| ln | Unary Function | Natural logarithm function (base e) | ln(x) | 1.0 |
| log2 | Unary Function | Binary logarithm function (base 2) | log2(x) | 1.0 |
| lg | Unary Function | Common logarithm function (base 10) | lg(x) | 5.0 |
| log10 | Unary Function | Common logarithm function (base 10) | log10(x) | 1.0 |
| rad | Unary Function | Degrees to radians function | rad(x) | 1.0 |
| exp | Unary Function | Exponential function | exp(x) | 1.0 |
| sqrt | Unary Function | Squre root function | sqrt(x) | 1.0 |
| sinh | Unary Function | Hyperbolic sine function | sinh(x) | 1.0 |
| cosh | Unary Function | Hyperbolic cosine function | cosh(x) | 1.0 |
| tgh | Unary Function | Hyperbolic tangent function | tgh(x) | 1.0 |
| tanh | Unary Function | Hyperbolic tangent function | tanh(x) | 1.0 |
| coth | Unary Function | Hyperbolic cotangent function | coth(x) | 1.0 |
| ctgh | Unary Function | Hyperbolic cotangent function | ctgh(x) | 1.0 |
| ctanh | Unary Function | Hyperbolic cotangent function | ctanh(x) | 1.0 |
| sech | Unary Function | Hyperbolic secant function | sech(x) | 1.0 |
| csch | Unary Function | Hyperbolic cosecant function | csch(x) | 1.0 |
| cosech | Unary Function | Hyperbolic cosecant function | cosech(x) | 1.0 |
| deg | Unary Function | Radians to degrees function | deg(x) | 1.0 |
| abs | Unary Function | Absolut value function | abs(x) | 1.0 |
| sgn | Unary Function | Signum function | sgn(x) | 1.0 |
| floor | Unary Function | Floor function | floor(x) | 1.0 |
| ceil | Unary Function | Ceiling function | ceil(x) | 1.0 |
| not | Unary Function | Negation function | not(x) | 1.0 |
| asinh | Unary Function | Inverse hyperbolic sine function | asinh(x) | 1.0 |
| arsinh | Unary Function | Inverse hyperbolic sine function | arsinh(x) | 1.0 |
| arcsinh | Unary Function | Inverse hyperbolic sine function | arcsinh(x) | 1.0 |
| acosh | Unary Function | Inverse hyperbolic cosine function | acosh(x) | 1.0 |
| arcosh | Unary Function | Inverse hyperbolic cosine function | arcosh(x) | 1.0 |
| arccosh | Unary Function | Inverse hyperbolic cosine function | arccosh(x) | 1.0 |
| atgh | Unary Function | Inverse hyperbolic tangent function | atgh(x) | 1.0 |
| atanh | Unary Function | Inverse hyperbolic tangent function | atanh(x) | 1.0 |
| arctgh | Unary Function | Inverse hyperbolic tangent function | arctgh(x) | 1.0 |
| arctanh | Unary Function | Inverse hyperbolic tangent function | arctanh(x) | 1.0 |
| acoth | Unary Function | Inverse hyperbolic cotangent function | acoth(x) | 1.0 |
| actgh | Unary Function | Inverse hyperbolic cotangent function | actgh(x) | 1.0 |
| actanh | Unary Function | Inverse hyperbolic cotangent function | actanh(x) | 1.0 |
| arcoth | Unary Function | Inverse hyperbolic cotangent function | arcoth(x) | 1.0 |
| arccoth | Unary Function | Inverse hyperbolic cotangent function | arccoth(x) | 1.0 |
| arcctgh | Unary Function | Inverse hyperbolic cotangent function | arcctgh(x) | 1.0 |
| arcctanh | Unary Function | Inverse hyperbolic cotangent function | arcctanh(x) | 1.0 |
| asech | Unary Function | Inverse hyperbolic secant function | asech(x) | 1.0 |
| arsech | Unary Function | Inverse hyperbolic secant function | arsech(x) | 1.0 |
| arcsech | Unary Function | Inverse hyperbolic secant function | arcsech(x) | 1.0 |
| acsch | Unary Function | Inverse hyperbolic cosecant function | acsch(x) | 1.0 |
| arcsch | Unary Function | Inverse hyperbolic cosecant function | arcsch(x) | 1.0 |
| arccsch | Unary Function | Inverse hyperbolic cosecant function | arccsch(x) | 1.0 |
| acosech | Unary Function | Inverse hyperbolic cosecant function | acosech(x) | 1.0 |
| arcosech | Unary Function | Inverse hyperbolic cosecant function | arcosech(x) | 1.0 |
| arccosech | Unary Function | Inverse hyperbolic cosecant function | arccosech(x) | 1.0 |
| Sa | Unary Function | Sinc function (normalized) | Sa(x) | 1.0 |
| sinc | Unary Function | Sinc function (normalized) | sinc(x) | 1.0 |
| Sinc | Unary Function | Sinc function (unnormalized) | Sinc(x) | 1.0 |
| Bell | Unary Function | Bell number | Bell(n) | 1.0 |
| Luc | Unary Function | Lucas number | Luc(n) | 1.0 |
| Fib | Unary Function | Fibonacci number | Fib(n) | 1.0 |
| harm | Unary Function | Harmonic number | harm(n) | 1.0 |
| ispr | Unary Function | Prime number test (is number a prime?) | ispr(n) | 2.3 |
| Pi | Unary Function | Prime-counting function - Pi(x) | Pi(n) | 2.3 |
| Ei | Unary Function | Exponential integral function (non-elementary special function) - usage example: Ei(x) | Ei(x) | 2.3 |
| li | Unary Function | Logarithmic integral function (non-elementary special function) - usage example: li(x) | li(x) | 2.3 |
| Li | Unary Function | Offset logarithmic integral function (non-elementary special function) - usage example: Li(x) | Li(x) | 2.3 |
| erf | Unary Function | Gauss error function (non-elementary special function) - usage example: 2 + erf(x) | erf(x) | 3.0 |
| erfc | Unary Function | Gauss complementary error function (non-elementary special function) - usage example: 1 - erfc(x) | erfc(x) | 3.0 |
| erfInv | Unary Function | Inverse Gauss error function (non-elementary special function) - usage example: erfInv(x) | erfInv(x) | 3.0 |
| erfcInv | Unary Function | Inverse Gauss complementary error function (non-elementary special function) - usage example: erfcInv(x) | erfcInv(x) | 3.0 |
| ulp | Unary Function | Unit in The Last Place - ulp(0.1) | ulp(x) | 3.0 |
| isNaN | Unary Function | Returns true = 1 if value is a Not-a-Number (NaN), false = 0 otherwise - usage example: isNaN(x) | isNaN(x) | 4.1 |
| ndig10 | Unary Function | Number of digits in numeral system with base 10 | ndig10(x) | 4.1 |
| nfact | Unary Function | Prime decomposition - number of distinct prime factors | nfact(x) | 4.1 |
| arcsec | Unary Function | Inverse trigonometric secant | arcsec(x) | 4.1 |
| arccsc | Unary Function | Inverse trigonometric cosecant | arccsc(x) | 4.1 |
| Gamma | Unary Function | Gamma special function Γ(s) | Gamma(x) | 4.2 |
| LambW0 | Unary Function | Lambert-W special function, principal branch 0, also called the omega function or product logarithm | LambW0(x) | 4.2 |
| LambW1 | Unary Function | Lambert-W special function, branch -1, also called the omega function or product logarithm | LambW1(x) | 4.2 |
| sgnGamma | Unary Function | Signum of Gamma special function, Γ(s) | sgnGamma(x) | 4.2 |
| logGamma | Unary Function | Log Gamma special function, lnΓ(s) | logGamma(x) | 4.2 |
| diGamma | Unary Function | Digamma function as the logarithmic derivative of the Gamma special function, ψ(x) | diGamma(x) | 4.2 |
| rStud | Unary Function | Random variable - Student's t-distribution | rStud(v) | 5.0 |
| rChi2 | Unary Function | Random variable - Chi-squared distribution | rChi2(k) | 5.0 |
| Key word | Category | Description | Example | Since |
|---|---|---|---|---|
| log | Binary Function | Logarithm function | log(a, b) | 1.0 |
| mod | Binary Function | Modulo function | mod(a, b) | 1.0 |
| C | Binary Function | Binomial coefficient function, number of k-combinations that can be drawn from n-elements set | C(n, k) | 1.0 |
| nCk | Binary Function | Binomial coefficient function, number of k-combinations that can be drawn from n-elements set | nCk(n, k) | 4.2 |
| Bern | Binary Function | Bernoulli numbers | Bern(m, n) | 1.0 |
| Stirl1 | Binary Function | Stirling numbers of the first kind | Stirl1(n, k) | 1.0 |
| Stirl2 | Binary Function | Stirling numbers of the second kind | Stirl2(n, k) | 1.0 |
| Worp | Binary Function | Worpitzky number | Worp(n, k) | 1.0 |
| Euler | Binary Function | Euler number | Euler(n, k) | 1.0 |
| KDelta | Binary Function | Kronecker delta | KDelta(i, j) | 1.0 |
| EulerPol | Binary Function | EulerPol | EulerPol(m, x) | 1.0 |
| Harm | Binary Function | Harmonic number | Harm(x, n) | 1.0 |
| rUni | Binary Function | Random variable - Uniform continuous distribution U(a,b), usage example: 2*rUni(2,10) | rUni(a, b) | 3.0 |
| rUnid | Binary Function | Random variable - Uniform discrete distribution U{a,b}, usage example: 2*rUnid(2,100) | rUnid(a, b) | 3.0 |
| round | Binary Function | Half-up rounding, usage examples: round(2.2, 0) = 2, round(2.6, 0) = 3, round(2.66,1) = 2.7 | round(x, n) | 3.0 |
| rNor | Binary Function | Random variable - Normal distribution N(m,s) m - mean, s - stddev, usage example: 3*rNor(0,1) | rNor(mean, stdv) | 3.0 |
| ndig | Binary Function | Number of digits representing the number in numeral system with given base | ndig(number, base) | 4.1 |
| dig10 | Binary Function | Digit at position 1 ... n (left -> right) or 0 ... -(n-1) (right -> left) - base 10 numeral system | dig10(num, pos) | 4.1 |
| factval | Binary Function | Prime decomposition - factor value at position between 1 ... nfact(n) - ascending order by factor value | factval(number, factorid) | 4.1 |
| factexp | Binary Function | Prime decomposition - factor exponent / multiplicity at position between 1 ... nfact(n) - ascending order by factor value | factexp(number, factorid) | 4.1 |
| root | Binary Function | N-th order root of a number | root(rootorder, number) | 4.1 |
| GammaL | Binary Function | Lower incomplete gamma special function, γ(s,x) | GammaL(s, x) | 4.2 |
| GammaU | Binary Function | Upper incomplete Gamma special function, Γ(s,x) | GammaU(s, x) | 4.2 |
| GammaP | Binary Function | Lower regularized P gamma special function, P(s,x) | GammaP(s, x) | 4.2 |
| GammaRegL | Binary Function | Lower regularized P gamma special function, P(s,x) | GammaRegL(s, x) | 4.2 |
| GammaQ | Binary Function | Upper regularized Q Gamma special function, Q(s,x) | GammaQ(s, x) | 4.2 |
| GammaRegU | Binary Function | Upper regularized Q Gamma special function, Q(s,x) | GammaRegU(s, x) | 4.2 |
| nPk | Binary Function | Number of k-permutations that can be drawn from n-elements set | nPk(n, k) | 4.2 |
| Beta | Binary Function | The Beta special function B(x,y), also called the Euler integral of the first kind | Beta(x, y) | 4.2 |
| logBeta | Binary Function | The Log Beta special function ln B(x,y), also called the Log Euler integral of the first kind, ln B(x,y) | logBeta(x, y) | 4.2 |
| pStud | Binary Function | Probability distribution function - Student's t-distribution | pStud(x, v) | 5.0 |
| cStud | Binary Function | Cumulative distribution function - Student's t-distribution | cStud(x, v) | 5.0 |
| qStud | Binary Function | Quantile function (inverse cumulative distribution function) - Student's t-distribution | qStud(p, v) | 5.0 |
| pChi2 | Binary Function | Probability distribution function - Chi-squared distribution | pChi2(x, k) | 5.0 |
| cChi2 | Binary Function | Cumulative distribution function - Chi-squared distribution | cChi2(x, k) | 5.0 |
| qChi2 | Binary Function | Quantile function (inverse cumulative distribution function) - Chi-squared distribution | qChi2(p, k) | 5.0 |
| Key word | Category | Description | Example | Since |
|---|---|---|---|---|
| if | 3-args Function | If function | if(cond, expr-if-true, expr-if-false) | 1.0 |
| chi | 3-args Function | Characteristic function for x in (a,b) | chi(x, a, b) | 1.0 |
| CHi | 3-args Function | Characteristic function for x in [a,b] | CHi(x, a, b) | 1.0 |
| Chi | 3-args Function | Characteristic function for x in [a,b) | Chi(x, a, b) | 1.0 |
| cHi | 3-args Function | Characteristic function for x in (a,b] | cHi(x, a, b) | 1.0 |
| pUni | 3-args Function | Probability distribution function - Uniform continuous distribution U(a,b) | pUni(x, a, b) | 3.0 |
| cUni | 3-args Function | Cumulative distribution function - Uniform continuous distribution U(a,b) | cUni(a, a, b) | 3.0 |
| qUni | 3-args Function | Quantile function (inverse cumulative distribution function) - Uniform continuous distribution U(a,b) | qUni(q, a, b) | 3.0 |
| pNor | 3-args Function | Probability distribution function - Normal distribution N(m,s) | pNor(x, mean, stdv) | 3.0 |
| cNor | 3-args Function | Cumulative distribution function - Normal distribution N(m,s) | cNor(x, mean, stdv) | 3.0 |
| qNor | 3-args Function | Quantile function (inverse cumulative distribution function) | qNor(q, mean, stdv) | 3.0 |
| dig | 3-args Function | Digit at position 1 ... n (left -> right) or 0 ... -(n-1) (right -> left) - numeral system with given base | dig(num, pos, base) | 4.1 |
| BetaInc | 3-args Function | The incomplete beta special function B(x; a, b), also called the incomplete Euler integral of the first kind | BetaInc(x, a, b) | 4.2 |
| BetaI | 3-args Function | The regularized incomplete beta (or regularized beta) special function I(x; a, b), also called the regularized incomplete Euler integral of the first kind | BetaI(x, a, b) | 4.2 |
| BetaReg | 3-args Function | The regularized incomplete beta (or regularized beta) special function I(x; a, b), also called the regularized incomplete Euler integral of the first kind | BetaReg(x, a, b) | 4.2 |
| Key word | Category | Description | Example | Since |
|---|---|---|---|---|
| iff | Variadic Function | If function | iff(cond-1, expr-1; ... ; cond-n, expr-n) | 1.0 |
| min | Variadic Function | Minimum function | min(a1, ..., an) | 1.0 |
| max | Variadic Function | Maximum function | max(a1, ..., an) | 1.0 |
| ConFrac | Variadic Function | Continued fraction | ConFrac(a1, ..., an) | 1.0 |
| ConPol | Variadic Function | Continued polynomial | ConPol(a1, ..., an) | 1.0 |
| gcd | Variadic Function | Greatest common divisor | gcd(a1, ..., an) | 1.0 |
| lcm | Variadic Function | Least common multiple | lcm(a1, ..., an) | 1.0 |
| add | Variadic Function | Summation operator | add(a1, ..., an) | 2.4 |
| multi | Variadic Function | Multiplication | multi(a1, ..., an) | 2.4 |
| mean | Variadic Function | Mean / average value | mean(a1, ..., an) | 2.4 |
| var | Variadic Function | Bias-corrected sample variance | var(a1, ..., an) | 2.4 |
| std | Variadic Function | Bias-corrected sample standard deviation | std(a1, ..., an) | 2.4 |
| rList | Variadic Function | Random number from given list of numbers | rList(a1, ..., an) | 3.0 |
| coalesce | Variadic Function | Returns the first non-NaN value | coalesce(a1, ..., an) | 4.1 |
| or | Variadic Function | Logical disjunction (OR) - variadic | or(a1, ..., an) | 4.1 |
| and | Variadic Function | Logical conjunction (AND) - variadic | and(a1, ..., an) | 4.1 |
| xor | Variadic Function | Exclusive or (XOR) - variadic | xor(a1, ..., an) | 4.1 |
| argmin | Variadic Function | Arguments / indices of the minima | argmin(a1, ..., an) | 4.1 |
| argmax | Variadic Function | Arguments / indices of the maxima | argmax(a1, ..., an) | 4.1 |
| med | Variadic Function | The sample median | med(a1, ..., an) | 4.1 |
| mode | Variadic Function | Mode - the value that appears most often | mode(a1, ..., an) | 4.1 |
| base | Variadic Function | Returns number in given numeral system base represented by list of digits | base(b, d1, ..., dn) | 4.1 |
| ndist | Variadic Function | Number of distinct values | ndist(v1, ..., vn) | 4.1 |
| Key word | Category | Description | Example | Since |
|---|---|---|---|---|
| ∑ | Calculus Operator | Summation operator - SIGMA - unicode math symbol | ∑(i, from, to, expr, ) | 5.0 |
| Σ | Calculus Operator | Summation operator - SIGMA - unicode math symbol | Σ(i, from, to, expr, ) | 5.0 |
| sum | Calculus Operator | Summation operator - SIGMA | sum(i, from, to, expr, ) | 1.0 |
| ∏ | Calculus Operator | Product operator - PI - unicode math symbol | ∏(i, from, to, expr, ) | 5.0 |
| ℿ | Calculus Operator | Product operator - PI - unicode math symbol | ℿ(i, from, to, expr, ) | 5.0 |
| Π | Calculus Operator | Product operator - PI - unicode math symbol | Π(i, from, to, expr, ) | 5.0 |
| prod | Calculus Operator | Product operator - PI | prod(i, from, to, expr, ) | 1.0 |
| ∫ | Calculus Operator | Definite integral operator - unicode math symbol | ∫(expr, arg, from, to) | 5.0 |
| int | Calculus Operator | Definite integral operator | int(expr, arg, from, to) | 1.0 |
| ∂ | Calculus Operator | Derivative operator - unicode math symbol | ∂(expr, arg, ) | 5.0 |
| der | Calculus Operator | Derivative operator | der(expr, arg, ) | 1.0 |
| ∂- | Calculus Operator | Left derivative operator - unicode math symbol | ∂-(expr, arg, ) | 5.0 |
| der- | Calculus Operator | Left derivative operator | der-(expr, arg, ) | 1.0 |
| ∂+ | Calculus Operator | Right derivative operator - unicode math symbol | ∂+(expr, arg, ) | 5.0 |
| der+ | Calculus Operator | Right derivative operator | der+(expr, arg, ) | 1.0 |
| dern | Calculus Operator | n-th derivative operator | dern(expr, n, arg) | 1.0 |
| ∆ | Calculus Operator | Forward difference operator - unicode math symbol | ∆(expr, arg, ) | 5.0 |
| Δ | Calculus Operator | Forward difference operator - unicode math symbol | Δ(expr, arg, ) | 5.0 |
| diff | Calculus Operator | Forward difference operator | diff(expr, arg, ) | 1.0 |
| ∇ | Calculus Operator | Backward difference operator - unicode math symbol | ∇(expr, arg, ) | 5.0 |
| difb | Calculus Operator | Backward difference operator | difb(expr, arg, ) | 1.0 |
| avg | Calculus Operator | Average operator | avg(i, from, to, expr, ) | 2.4 |
| vari | Calculus Operator | Bias-corrected sample variance operator | vari(i, from, to, expr, ) | 2.4 |
| stdi | Calculus Operator | Bias-corrected sample standard deviation operator | stdi(i, from, to, expr, ) | 2.4 |
| mini | Calculus Operator | Minimum value | mini(i, from, to, expr, ) | 2.4 |
| maxi | Calculus Operator | Maximum value | maxi(i, from, to, expr, ) | 2.4 |
| solve | Calculus Operator | f(x) = 0 equation solving, function root finding | solve(expr, arg, from, to) | 4.0 |
| Key word | Category | Description | Example | Since |
|---|---|---|---|---|
| [Uni] | Random Variable | Random variable - Uniform continuous distribution U(0,1) | [Uni] | 3.0 |
| [Int] | Random Variable | Random variable - random integer | [Int] | 3.0 |
| [Int1] | Random Variable | Random variable - random integer - Uniform discrete distribution U{-10^1, 10^1} | [Int1] | 3.0 |
| [Int2] | Random Variable | Random variable - random integer - Uniform discrete distribution U{-10^2, 10^2} | [Int2] | 3.0 |
| [Int3] | Random Variable | Random variable - random integer - Uniform discrete distribution U{-10^3, 10^3} | [Int3] | 3.0 |
| [Int4] | Random Variable | Random variable - random integer - Uniform discrete distribution U{-10^4, 10^4} | [Int4] | 3.0 |
| [Int5] | Random Variable | Random variable - random integer - Uniform discrete distribution U{-10^5, 10^5} | [Int5] | 3.0 |
| [Int6] | Random Variable | Random variable - random integer - Uniform discrete distribution U{-10^6, 10^6} | [Int6] | 3.0 |
| [Int7] | Random Variable | Random variable - random integer - Uniform discrete distribution U{-10^7, 10^7} | [Int7] | 3.0 |
| [Int8] | Random Variable | Random variable - random integer - Uniform discrete distribution U{-10^8, 10^8} | [Int8] | 3.0 |
| [Int9] | Random Variable | Random variable - random integer - Uniform discrete distribution U{-10^9, 10^9} | [Int9] | 3.0 |
| [nat] | Random Variable | Random variable - random natural number including 0 | [nat] | 3.0 |
| [nat1] | Random Variable | Random variable - random natural number including 0 - Uniform discrete distribution U{0, 10^1} | [nat1] | 3.0 |
| [nat2] | Random Variable | Random variable - random natural number including 0 - Uniform discrete distribution U{0, 10^2} | [nat2] | 3.0 |
| [nat3] | Random Variable | Random variable - random natural number including 0 - Uniform discrete distribution U{0, 10^3} | [nat3] | 3.0 |
| [nat4] | Random Variable | Random variable - random natural number including 0 - Uniform discrete distribution U{0, 10^4} | [nat4] | 3.0 |
| [nat5] | Random Variable | Random variable - random natural number including 0 - Uniform discrete distribution U{0, 10^5} | [nat5] | 3.0 |
| [nat6] | Random Variable | Random variable - random natural number including 0 - Uniform discrete distribution U{0, 10^6} | [nat6] | 3.0 |
| [nat7] | Random Variable | Random variable - random natural number including 0 - Uniform discrete distribution U{0, 10^7} | [nat7] | 3.0 |
| [nat8] | Random Variable | Random variable - random natural number including 0 - Uniform discrete distribution U{0, 10^8} | [nat8] | 3.0 |
| [nat9] | Random Variable | Random variable - random natural number including 0 - Uniform discrete distribution U{0, 10^9} | [nat9] | 3.0 |
| [Nat] | Random Variable | Random variable - random natural number | [Nat] | 3.0 |
| [Nat1] | Random Variable | Random variable - random natural number - Uniform discrete distribution U{1, 10^1} | [Nat1] | 3.0 |
| [Nat2] | Random Variable | Random variable - random natural number - Uniform discrete distribution U{1, 10^2} | [Nat2] | 3.0 |
| [Nat3] | Random Variable | Random variable - random natural number - Uniform discrete distribution U{1, 10^3} | [Nat3] | 3.0 |
| [Nat4] | Random Variable | Random variable - random natural number - Uniform discrete distribution U{1, 10^4} | [Nat4] | 3.0 |
| [Nat5] | Random Variable | Random variable - random natural number - Uniform discrete distribution U{1, 10^5} | [Nat5] | 3.0 |
| [Nat6] | Random Variable | Random variable - random natural number - Uniform discrete distribution U{1, 10^6} | [Nat6] | 3.0 |
| [Nat7] | Random Variable | Random variable - random natural number - Uniform discrete distribution U{1, 10^7} | [Nat7] | 3.0 |
| [Nat8] | Random Variable | Random variable - random natural number - Uniform discrete distribution U{1, 10^8} | [Nat8] | 3.0 |
| [Nat9] | Random Variable | Random variable - random natural number - Uniform discrete distribution U{1, 10^9} | [Nat9] | 3.0 |
| [Nor] | Random Variable | Random variable - Normal distribution N(0,1) | [Nor] | 3.0 |
| Key word | Category | Description | Example | Since |
|---|---|---|---|---|
| π | Constant Value | Pi, Archimedes' constant or Ludolph's number - unicode math symbol | π | 5.0 |
| ℼ | Constant Value | Pi, Archimedes' constant or Ludolph's number - unicode math symbol | ℼ | 5.0 |
| pi | Constant Value | Pi, Archimedes' constant or Ludolph's number | pi | 1.0 |
| e | Constant Value | Napier's constant, or Euler's number, base of Natural logarithm | e | 1.0 |
| ℯ | Constant Value | Napier's constant, or Euler's number, base of Natural logarithm - unicode math symbol | ℯ | 5.0 |
| ⅇ | Constant Value | Napier's constant, or Euler's number, base of Natural logarithm - unicode math symbol | ⅇ | 5.0 |
| [gam] | Constant Value | Euler-Mascheroni constant | [gam] | 1.0 |
| [phi] | Constant Value | Golden ratio | [phi] | 1.0 |
| [PN] | Constant Value | Plastic constant | [PN] | 1.0 |
| [B*] | Constant Value | Embree-Trefethen constant | [B*] | 1.0 |
| [F'd] | Constant Value | Feigenbaum constant alfa | [F'd] | 1.0 |
| [F'a] | Constant Value | Feigenbaum constant delta | [F'a] | 1.0 |
| [C2] | Constant Value | Twin prime constant | [C2] | 1.0 |
| [M1] | Constant Value | Meissel-Mertens constant | [M1] | 1.0 |
| [B2] | Constant Value | Brun's constant for twin primes | [B2] | 1.0 |
| [B4] | Constant Value | Brun's constant for prime quadruplets | [B4] | 1.0 |
| [BN'L] | Constant Value | de Bruijn-Newman constant | [BN'L] | 1.0 |
| [Kat] | Constant Value | Catalan's constant | [Kat] | 1.0 |
| [K*] | Constant Value | Landau-Ramanujan constant | [K*] | 1.0 |
| [K.] | Constant Value | Viswanath's constant | [K.] | 1.0 |
| [B'L] | Constant Value | Legendre's constant | [B'L] | 1.0 |
| [RS'm] | Constant Value | Ramanujan-Soldner constant | [RS'm] | 1.0 |
| [EB'e] | Constant Value | Erdos-Borwein constant | [EB'e] | 1.0 |
| [Bern] | Constant Value | Bernstein's constant | [Bern] | 1.0 |
| [GKW'l] | Constant Value | Gauss-Kuzmin-Wirsing constant | [GKW'l] | 1.0 |
| [HSM's] | Constant Value | Hafner-Sarnak-McCurley constant | [HSM's] | 1.0 |
| [lm] | Constant Value | Golomb-Dickman constant | [lm] | 1.0 |
| [Cah] | Constant Value | Cahen's constant | [Cah] | 1.0 |
| [Ll] | Constant Value | Laplace limit | [Ll] | 1.0 |
| [AG] | Constant Value | Alladi-Grinstead constant | [AG] | 1.0 |
| [L*] | Constant Value | Lengyel's constant | [L*] | 1.0 |
| [L.] | Constant Value | Levy's constant | [L.] | 1.0 |
| [Dz3] | Constant Value | Apery's constant | [Dz3] | 1.0 |
| [A3n] | Constant Value | Mills' constant | [A3n] | 1.0 |
| [Bh] | Constant Value | Backhouse's constant | [Bh] | 1.0 |
| [Pt] | Constant Value | Porter's constant | [Pt] | 1.0 |
| [L2] | Constant Value | Lieb's square ice constant | [L2] | 1.0 |
| [Nv] | Constant Value | Niven's constant | [Nv] | 1.0 |
| [Ks] | Constant Value | Sierpinski's constant | [Ks] | 1.0 |
| [Kh] | Constant Value | Khinchin's constant | [Kh] | 1.0 |
| [FR] | Constant Value | Fransen-Robinson constant | [FR] | 1.0 |
| [La] | Constant Value | Landau's constant | [La] | 1.0 |
| [P2] | Constant Value | Parabolic constant | [P2] | 1.0 |
| [Om] | Constant Value | Omega constant | [Om] | 1.0 |
| [MRB] | Constant Value | MRB constant | [MRB] | 1.0 |
| [li2] | Constant Value | li(2) - Logarithmic integral function at x=2 | [li2] | 2.3 |
| [EG] | Constant Value | Gompertz constant | [EG] | 2.3 |
| Key word | Category | Description | Example | Since |
|---|---|---|---|---|
| [c] | Constant Value | <Physical Constant> Light speed in vacuum [m/s] (m=1, s=1) | [c] | 4.0 |
| [G.] | Constant Value | <Physical Constant> Gravitational constant (m=1, kg=1, s=1)] | [G.] | 4.0 |
| [g] | Constant Value | <Physical Constant> Gravitational acceleration on Earth [m/s^2] (m=1, s=1) | [g] | 4.0 |
| [hP] | Constant Value | <Physical Constant> Planck constant (m=1, kg=1, s=1) | [hP] | 4.0 |
| [h-] | Constant Value | <Physical Constant> Reduced Planck constant / Dirac constant (m=1, kg=1, s=1)] | [h-] | 4.0 |
| [lP] | Constant Value | <Physical Constant> Planck length [m] (m=1) | [lP] | 4.0 |
| [mP] | Constant Value | <Physical Constant> Planck mass [kg] (kg=1) | [mP] | 4.0 |
| [tP] | Constant Value | <Physical Constant> Planck time [s] (s=1) | [tP] | 4.0 |
| [true] | Constant Value | Boolean True represented as double, [true] = 1 | [true] | 4.1 |
| [false] | Constant Value | Boolean False represented as double, [false] = 0 | [false] | 4.1 |
| [NaN] | Constant Value | Not-a-Number | [NaN] | 4.1 |
| Key word | Category | Description | Example | Since |
|---|---|---|---|---|
| [ly] | Constant Value | <Astronomical Constant> Light year [m] (m=1) | [ly] | 4.0 |
| [au] | Constant Value | <Astronomical Constant> Astronomical unit [m] (m=1) | [au] | 4.0 |
| [pc] | Constant Value | <Astronomical Constant> Parsec [m] (m=1) | [pc] | 4.0 |
| [kpc] | Constant Value | <Astronomical Constant> Kiloparsec [m] (m=1) | [kpc] | 4.0 |
| [Earth-R-eq] | Constant Value | <Astronomical Constant> Earth equatorial radius [m] (m=1) | [Earth-R-eq] | 4.0 |
| [Earth-R-po] | Constant Value | <Astronomical Constant> Earth polar radius [m] (m=1) | [Earth-R-po] | 4.0 |
| [Earth-R] | Constant Value | <Astronomical Constant> Earth mean radius (m=1) | [Earth-R] | 4.0 |
| [Earth-M] | Constant Value | <Astronomical Constant> Earth mass [kg] (kg=1) | [Earth-M] | 4.0 |
| [Earth-D] | Constant Value | <Astronomical Constant> Earth-Sun distance - semi major axis [m] (m=1) | [Earth-D] | 4.0 |
| [Moon-R] | Constant Value | <Astronomical Constant> Moon mean radius [m] (m=1) | [Moon-R] | 4.0 |
| [Moon-M] | Constant Value | <Astronomical Constant> Moon mass [kg] (kg=1) | [Moon-M] | 4.0 |
| [Moon-D] | Constant Value | <Astronomical Constant> Moon-Earth distance - semi major axis [m] (m=1) | [Moon-D] | 4.0 |
| [Solar-R] | Constant Value | <Astronomical Constant> Solar mean radius [m] (m=1) | [Solar-R] | 4.0 |
| [Solar-M] | Constant Value | <Astronomical Constant> Solar mass [kg] (kg=1) | [Solar-M] | 4.0 |
| [Mercury-R] | Constant Value | <Astronomical Constant> Mercury mean radius [m] (m=1) | [Mercury-R] | 4.0 |
| [Mercury-M] | Constant Value | <Astronomical Constant> Mercury mass [kg] (kg=1) | [Mercury-M] | 4.0 |
| [Mercury-D] | Constant Value | <Astronomical Constant> Mercury-Sun distance - semi major axis [m] (m=1) | [Mercury-D] | 4.0 |
| [Venus-R] | Constant Value | <Astronomical Constant> Venus mean radius [m] (m=1) | [Venus-R] | 4.0 |
| [Venus-M] | Constant Value | <Astronomical Constant> Venus mass [kg] (kg=1) | [Venus-M] | 4.0 |
| [Venus-D] | Constant Value | <Astronomical Constant> Venus-Sun distance - semi major axis [m] (m=1) | [Venus-D] | 4.0 |
| [Mars-R] | Constant Value | <Astronomical Constant> Mars mean radius [m] (m=1) | [Mars-R] | 4.0 |
| [Mars-M] | Constant Value | <Astronomical Constant> Mars mass [kg] (kg=1) | [Mars-M] | 4.0 |
| [Mars-D] | Constant Value | <Astronomical Constant> Mars-Sun distance - semi major axis [m] (m=1) | [Mars-D] | 4.0 |
| [Jupiter-R] | Constant Value | <Astronomical Constant> Jupiter mean radius [m] (m=1) | [Jupiter-R] | 4.0 |
| [Jupiter-M] | Constant Value | <Astronomical Constant> Jupiter mass [kg] (kg=1) | [Jupiter-M] | 4.0 |
| [Jupiter-D] | Constant Value | <Astronomical Constant> Jupiter-Sun distance - semi major axis [m] (m=1) | [Jupiter-D] | 4.0 |
| [Saturn-R] | Constant Value | <Astronomical Constant> Saturn mean radius [m] (m=1) | [Saturn-R] | 4.0 |
| [Saturn-M] | Constant Value | <Astronomical Constant> Saturn mass [kg] (kg=1) | [Saturn-M] | 4.0 |
| [Saturn-D] | Constant Value | <Astronomical Constant> Saturn-Sun distance - semi major axis [m] (m=1) | [Saturn-D] | 4.0 |
| [Uranus-R] | Constant Value | <Astronomical Constant> Uranus mean radius [m] (m=1) | [Uranus-R] | 4.0 |
| [Uranus-M] | Constant Value | <Astronomical Constant> Uranus mass [kg] (kg=1) | [Uranus-M] | 4.0 |
| [Uranus-D] | Constant Value | <Astronomical Constant> Uranus-Sun distance - semi major axis [m] (m=1) | [Uranus-D] | 4.0 |
| [Neptune-R] | Constant Value | <Astronomical Constant> Neptune mean radius [m] (m=1) | [Neptune-R] | 4.0 |
| [Neptune-M] | Constant Value | <Astronomical Constant> Neptune mass [kg] (kg=1) | [Neptune-M] | 4.0 |
| [Neptune-D] | Constant Value | <Astronomical Constant> Neptune-Sun distance - semi major axis [m] (m=1) | [Neptune-D] | 4.0 |
| Key word | Category | Description | Example | Since |
|---|---|---|---|---|
| [%] | Unit | <Ratio, Fraction> Percentage = 0.01 | [%] | 4.0 |
| [%%] | Unit | <Ratio, Fraction> Promil, Per mille = 0.001 | [%%] | 4.0 |
| [Y] | Unit | <Metric Constant> Septillion / Yotta = 10^24 | [Y] | 4.0 |
| [sept] | Unit | <Metric Constant> Septillion / Yotta = 10^24 | [sept] | 4.0 |
| [Z] | Unit | <Metric Constant> Sextillion / Zetta = 10^21 | [Z] | 4.0 |
| [sext] | Unit | <Metric Constant> Sextillion / Zetta = 10^21 | [sext] | 4.0 |
| [E] | Unit | <Metric Constant> Quintillion / Exa = 10^18 | [E] | 4.0 |
| [quint] | Unit | <Metric Constant> Quintillion / Exa = 10^18 | [quint] | 4.0 |
| [P] | Unit | <Metric Constant> Quadrillion / Peta = 10^15 | [P] | 4.0 |
| [quad] | Unit | <Metric Constant> Quadrillion / Peta = 10^15 | [quad] | 4.0 |
| [T] | Unit | <Metric Constant> Trillion / Tera = 10^12 | [T] | 4.0 |
| [tril] | Unit | <Metric Constant> Trillion / Tera = 10^12 | [tril] | 4.0 |
| [G] | Unit | <Metric Constant> Billion / Giga = 10^9 | [G] | 4.0 |
| [bil] | Unit | <Metric Constant> Billion / Giga = 10^9 | [bil] | 4.0 |
| [M] | Unit | <Metric Constant> Million / Mega = 10^6 | [M] | 4.0 |
| [mil] | Unit | <Metric Constant> Million / Mega = 10^6 | [mil] | 4.0 |
| [k] | Unit | <Metric Constant> Thousand / Kilo = 10^3 | [k] | 4.0 |
| [th] | Unit | <Metric Constant> Thousand / Kilo = 10^3 | [th] | 4.0 |
| [hund] | Unit | <Metric Constant> Hundred / Hecto = 10^2 | [hund] | 4.0 |
| [hecto] | Unit | <Metric Constant> Hundred / Hecto = 10^2 | [hecto] | 4.0 |
| [ten] | Unit | <Metric Constant> Ten / Deca = 10 | [ten] | 4.0 |
| [deca] | Unit | <Metric Constant> Ten / Deca = 10 | [deca] | 4.0 |
| [deci] | Unit | <Metric Constant> Tenth / Deci = 0.1 | [deci] | 4.0 |
| [centi] | Unit | <Metric Constant> Hundredth / Centi = 0.01 | [centi] | 4.0 |
| [milli] | Unit | <Metric Constant> Thousandth / Milli = 0.001 | [milli] | 4.0 |
| [mic] | Unit | <Metric Constant> Millionth / Micro = 10^-6 | [mic] | 4.0 |
| [n] | Unit | <Metric Constant> Billionth / Nano = 10^-9 | [n] | 4.0 |
| [p] | Unit | <Metric Constant> Trillionth / Pico = 10^-12 | [p] | 4.0 |
| [f] | Unit | <Metric Constant> Quadrillionth / Femto = 10^-15 | [f] | 4.0 |
| [a] | Unit | <Metric Constant> Quintillionth / Atoo = 10^-18 | [a] | 4.0 |
| [z] | Unit | <Metric Constant> Sextillionth / Zepto = 10^-21 | [z] | 4.0 |
| [y] | Unit | <Metric Constant> Septillionth / Yocto = 10^-24 | [y] | 4.0 |
| Key word | Category | Description | Example | Since |
|---|---|---|---|---|
| [m] | Unit | <Unit of length> Metre / Meter (m=1) | [m] | 4.0 |
| [km] | Unit | <Unit of length> Kilometre / Kilometer (m=1) | [km] | 4.0 |
| [cm] | Unit | <Unit of length> Centimetre / Centimeter (m=1) | [cm] | 4.0 |
| [mm] | Unit | <Unit of length> Millimetre / Millimeter (m=1) | [mm] | 4.0 |
| [inch] | Unit | <Unit of length> Inch (m=1) | [inch] | 4.0 |
| [yd] | Unit | <Unit of length> Yard (m=1) | [yd] | 4.0 |
| [ft] | Unit | <Unit of length> Feet (m=1) | [ft] | 4.0 |
| [mile] | Unit | <Unit of length> Mile (m=1) | [mile] | 4.0 |
| [nmi] | Unit | <Unit of length> Nautical mile (m=1) | [nmi] | 4.0 |
| Key word | Category | Description | Example | Since |
|---|---|---|---|---|
| [m2] | Unit | <Unit of area> Square metre / Square meter (m=1) | [m2] | 4.0 |
| [cm2] | Unit | <Unit of area> Square centimetre / Square centimeter (m=1) | [cm2] | 4.0 |
| [mm2] | Unit | <Unit of area> Square millimetre / Square millimeter (m=1) | [mm2] | 4.0 |
| [are] | Unit | <Unit of area> Are (m=1) | [are] | 4.0 |
| [ha] | Unit | <Unit of area> Hectare (m=1) | [ha] | 4.0 |
| [acre] | Unit | <Unit of area> Acre (m=1) | [acre] | 4.0 |
| [km2] | Unit | <Unit of area> Square kilometre / Square kilometer (m=1) | [km2] | 4.0 |
| Key word | Category | Description | Example | Since |
|---|---|---|---|---|
| [mm3] | Unit | <Unit of volume> Cubic millimetre / Cubic millimeter (m=1) | [mm3] | 4.0 |
| [cm3] | Unit | <Unit of volume> Cubic centimetre / Cubic centimeter (m=1) | [cm3] | 4.0 |
| [m3] | Unit | <Unit of volume> Cubic metre / Cubic meter (m=1) | [m3] | 4.0 |
| [km3] | Unit | <Unit of volume> Cubic kilometre / Cubic kilometer (m=1) | [km3] | 4.0 |
| [ml] | Unit | <Unit of volume> Millilitre / Milliliter (m=1) | [ml] | 4.0 |
| [l] | Unit | <Unit of volume> Litre / Liter (m=1) | [l] | 4.0 |
| [gall] | Unit | <Unit of volume> Gallon (m=1) | [gall] | 4.0 |
| [pint] | Unit | <Unit of volume> Pint (m=1) | [pint] | 4.0 |
| Key word | Category | Description | Example | Since |
|---|---|---|---|---|
| [s] | Unit | <Unit of time> Second (s=1) | [s] | 4.0 |
| [ms] | Unit | <Unit of time> Millisecond (s=1) | [ms] | 4.0 |
| [min] | Unit | <Unit of time> Minute (s=1) | [min] | 4.0 |
| [h] | Unit | <Unit of time> Hour (s=1) | [h] | 4.0 |
| [day] | Unit | <Unit of time> Day (s=1) | [day] | 4.0 |
| [week] | Unit | <Unit of time> Week (s=1) | [week] | 4.0 |
| [yearj] | Unit | <Unit of time> Julian year = 365.25 days (s=1) | [yearj] | 4.0 |
| Key word | Category | Description | Example | Since |
|---|---|---|---|---|
| [kg] | Unit | <Unit of mass> Kilogram (kg=1) | [kg] | 4.0 |
| [gr] | Unit | <Unit of mass> Gram (kg=1) | [gr] | 4.0 |
| [mg] | Unit | <Unit of mass> Milligram (kg=1) | [mg] | 4.0 |
| [dag] | Unit | <Unit of mass> Decagram (kg=1) | [dag] | 4.0 |
| [t] | Unit | <Unit of mass> Tonne (kg=1) | [t] | 4.0 |
| [oz] | Unit | <Unit of mass> Ounce (kg=1) | [oz] | 4.0 |
| [lb] | Unit | <Unit of mass> Pound (kg=1) | [lb] | 4.0 |
| Key word | Category | Description | Example | Since |
|---|---|---|---|---|
| [b] | Unit | <Unit of information> Bit (bit=1) | [b] | 4.0 |
| [kb] | Unit | <Unit of information> Kilobit (bit=1) | [kb] | 4.0 |
| [Mb] | Unit | <Unit of information> Megabit (bit=1) | [Mb] | 4.0 |
| [Gb] | Unit | <Unit of information> Gigabit (bit=1) | [Gb] | 4.0 |
| [Tb] | Unit | <Unit of information> Terabit (bit=1) | [Tb] | 4.0 |
| [Pb] | Unit | <Unit of information> Petabit (bit=1) | [Pb] | 4.0 |
| [Eb] | Unit | <Unit of information> Exabit (bit=1) | [Eb] | 4.0 |
| [Zb] | Unit | <Unit of information> Zettabit (bit=1) | [Zb] | 4.0 |
| [Yb] | Unit | <Unit of information> Yottabit (bit=1) | [Yb] | 4.0 |
| [B] | Unit | <Unit of information> Byte (bit=1) | [B] | 4.0 |
| [kB] | Unit | <Unit of information> Kilobyte (bit=1) | [kB] | 4.0 |
| [MB] | Unit | <Unit of information> Megabyte (bit=1) | [MB] | 4.0 |
| [GB] | Unit | <Unit of information> Gigabyte (bit=1) | [GB] | 4.0 |
| [TB] | Unit | <Unit of information> Terabyte (bit=1) | [TB] | 4.0 |
| [PB] | Unit | <Unit of information> Petabyte (bit=1) | [PB] | 4.0 |
| [EB] | Unit | <Unit of information> Exabyte (bit=1) | [EB] | 4.0 |
| [ZB] | Unit | <Unit of information> Zettabyte (bit=1) | [ZB] | 4.0 |
| [YB] | Unit | <Unit of information> Yottabyte (bit=1) | [YB] | 4.0 |
| Key word | Category | Description | Example | Since |
|---|---|---|---|---|
| [J] | Unit | <Unit of energy> Joule (m=1, kg=1, s=1) | [J] | 4.0 |
| [eV] | Unit | <Unit of energy> Electronovolt (m=1, kg=1, s=1) | [eV] | 4.0 |
| [keV] | Unit | <Unit of energy> Kiloelectronovolt (m=1, kg=1, s=1) | [keV] | 4.0 |
| [MeV] | Unit | <Unit of energy> Megaelectronovolt (m=1, kg=1, s=1) | [MeV] | 4.0 |
| [GeV] | Unit | <Unit of energy> Gigaelectronovolt (m=1, kg=1, s=1) | [GeV] | 4.0 |
| [TeV] | Unit | <Unit of energy> Teraelectronovolt (m=1, kg=1, s=1) | [TeV] | 4.0 |
| Key word | Category | Description | Example | Since |
|---|---|---|---|---|
| [m/s] | Unit | <Unit of speed> Metre / Meter per second (m=1, s=1) | [m/s] | 4.0 |
| [km/h] | Unit | <Unit of speed> Kilometre / Kilometer per hour (m=1, s=1) | [km/h] | 4.0 |
| [mi/h] | Unit | <Unit of speed> Mile per hour (m=1, s=1) | [mi/h] | 4.0 |
| [knot] | Unit | <Unit of speed> Knot (m=1, s=1) | [knot] | 4.0 |
| Key word | Category | Description | Example | Since |
|---|---|---|---|---|
| [m/s2] | Unit | <Unit of acceleration> Metre / Meter per square second (m=1, s=1) | [m/s2] | 4.0 |
| [km/h2] | Unit | <Unit of acceleration> Kilometre / Kilometer per square hour (m=1, s=1) | [km/h2] | 4.0 |
| [mi/h2] | Unit | <Unit of acceleration> Mile per square hour (m=1, s=1) | [mi/h2] | 4.0 |
| Key word | Category | Description | Example | Since |
|---|---|---|---|---|
| [rad] | Unit | <Unit of angle> Radian (rad=1) | [rad] | 4.0 |
| [deg] | Unit | <Unit of angle> Degree of arc (rad=1) | [deg] | 4.0 |
| ['] | Unit | <Unit of angle> Minute of arc (rad=1) | ['] | 4.0 |
| [''] | Unit | <Unit of angle> Second of arc (rad=1) | [''] | 4.0 |
| Key word | Category | Description | Example | Since |
|---|---|---|---|---|
| ( | Parser Symbol | Left parentheses | ( ... ) | 1.0 |
| ) | Parser Symbol | Right parentheses | ( ... ) | 1.0 |
| , | Parser Symbol | Comma (function parameters) | (a1, ... ,an) | 1.0 |
| ; | Parser Symbol | Semicolon (function parameters) | (a1; ... ;an) | 1.0 |
| Parser Symbol | Blank (whitespace) character | 4.2 |
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