Math Parser Java Android C# .NET/MONO (.NET Framework, .NET Core, .NET Standard, .NET PCL, Xamarin.Android, Xamarin.iOS) CLS Library - a super easy, rich and flexible mathematical expression parser (expression evaluator, expression provided as plain text / strings) for JAVA and C#. Main features: rich built-in library of operators, constants, ma…
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mXparser - a super easy, rich and highly flexible Mathematical Expression Parser (Math Parser, Expression Evaluator) library for JAVA, Android and C# .NET.

### 20.11.2017: first 20000 downloads!
### 01.09.2017: first 15000 downloads!
### 04.05.2017: first 10000 downloads!
### 31.03.2016: first 1000 downloads!

02-mXparser-sin.gif

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

Supported frameworks

mXparser frameworks

  • JAVA: 1.5, 1.6, 1.7, 1.8
  • Android - tested with mxparser compiled using jdk 1.7
  • .NET / MONO: 2.0, 3.0, 3.5, 4.0, 4.5, 4.6, 4.7 (CLS)
  • .NET Core
  • .NET Standard, .NET PCL
  • Xamarin.Android
  • Xamarin.iOS

03-mXparser-sum.gif

JAVA intro

mXparser demo

C# intro

mXparser demo - csharp

Tutorial

mXparser tutorial

>>> Click to learn from examples <<<

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)

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mXparser in nutshell

You want simple calculator...

calc

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

πŸ‘

A calculator supporting parenthesis...

parenth

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

πŸ‘

You care about predefined constants...

const

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

πŸ‘

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();

πŸ‘

You enjoy using many built-in functions...

sinx

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

πŸ‘

You do not limit yourself to unary functions...

fun-variadic

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

πŸ‘

What about user defined arguments...

arg-free

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

πŸ‘

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();

πŸ‘

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();

πŸ‘

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

true-false

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

πŸ‘

And for binary relations as well!

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

πŸ‘

mXparser is cool! But this is only the begging, 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();

πŸ‘

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

prod

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

πŸ‘

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();

πŸ‘

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();

πŸ‘

And definite integrals as well...

int

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

πŸ‘

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();

πŸ‘

Recursion is your desire...

recur

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

πŸ‘

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()

πŸ‘

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

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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

Operators

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

Boolean Operators

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

Bitwise Operators

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

Binary Relations

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

Unary Functions

Key word Category Description Example Since
sin Unary Function Trigonometric sine function sin(x) 1.0
cos Unary Function Trigonometric cosine function cos(x) 1.0
tg Unary Function Trigonometric tangent function tg(x) 1.0
tan Unary Function Trigonometric tangent function tan(x) 1.0
ctg Unary Function Trigonometric cotangent function ctg(x) 1.0
cot Unary Function Trigonometric cotangent function cot(x) 1.0
ctan Unary Function Trigonometric cotangent function ctan(x) 1.0
sec Unary Function Trigonometric secant function sec(x) 1.0
csc Unary Function Trigonometric cosecant function csc(x) 1.0
cosec Unary Function Trigonometric cosecant function cosec(x) 1.0
asin Unary Function Inverse trigonometric sine function asin(x) 1.0
arsin Unary Function Inverse trigonometric sine function arsin(x) 1.0
arcsin Unary Function Inverse trigonometric sine function arcsin(x) 1.0
acos Unary Function Inverse trigonometric cosine function acos(x) 1.0
arcos Unary Function Inverse trigonometric cosine function arcos(x) 1.0
arccos Unary Function Inverse trigonometric cosine function arccos(x) 1.0
atg Unary Function Inverse trigonometric tangent function atg(x) 1.0
atan Unary Function Inverse trigonometric tangent function atan(x) 1.0
arctg Unary Function Inverse trigonometric tangent function arctg(x) 1.0
arctan Unary Function Inverse trigonometric tangent function arctan(x) 1.0
actg Unary Function Inverse trigonometric cotangent function actg(x) 1.0
acot Unary Function Inverse trigonometric cotangent function acot(x) 1.0
actan Unary Function Inverse trigonometric cotangent function actan(x) 1.0
arcctg Unary Function Inverse trigonometric cotangent function arcctg(x) 1.0
arccot Unary Function Inverse trigonometric cotangent function arccot(x) 1.0
arcctan Unary Function Inverse trigonometric cotangent function arcctan(x) 1.0
ln Unary Function Natural logarithm function (base e) ln(x) 1.0
log2 Unary Function Binary logarithm function (base 2) log2(x) 1.0
log10 Unary Function Common logarithm function (base 10) log10(x) 1.0
rad Unary Function Degrees to radians function rad(x) 1.0
exp Unary Function Exponential function exp(x) 1.0
sqrt Unary Function Squre root function sqrt(x) 1.0
sinh Unary Function Hyperbolic sine function sinh(x) 1.0
cosh Unary Function Hyperbolic cosine function cosh(x) 1.0
tgh Unary Function Hyperbolic tangent function tgh(x) 1.0
tanh Unary Function Hyperbolic tangent function tanh(x) 1.0
coth Unary Function Hyperbolic cotangent function coth(x) 1.0
ctgh Unary Function Hyperbolic cotangent function ctgh(x) 1.0
ctanh Unary Function Hyperbolic cotangent function ctanh(x) 1.0
sech Unary Function Hyperbolic secant function sech(x) 1.0
csch Unary Function Hyperbolic cosecant function csch(x) 1.0
cosech Unary Function Hyperbolic cosecant function cosech(x) 1.0
deg Unary Function Radians to degrees function deg(x) 1.0
abs Unary Function Absolut value function abs(x) 1.0
sgn Unary Function Signum function sgn(x) 1.0
floor Unary Function Floor function floor(x) 1.0
ceil Unary Function Ceiling function ceil(x) 1.0
not Unary Function Negation function not(x) 1.0
asinh Unary Function Inverse hyperbolic sine function asinh(x) 1.0
arsinh Unary Function Inverse hyperbolic sine function arsinh(x) 1.0
arcsinh Unary Function Inverse hyperbolic sine function arcsinh(x) 1.0
acosh Unary Function Inverse hyperbolic cosine function acosh(x) 1.0
arcosh Unary Function Inverse hyperbolic cosine function arcosh(x) 1.0
arccosh Unary Function Inverse hyperbolic cosine function arccosh(x) 1.0
atgh Unary Function Inverse hyperbolic tangent function atgh(x) 1.0
atanh Unary Function Inverse hyperbolic tangent function atanh(x) 1.0
arctgh Unary Function Inverse hyperbolic tangent function arctgh(x) 1.0
arctanh Unary Function Inverse hyperbolic tangent function arctanh(x) 1.0
acoth Unary Function Inverse hyperbolic cotangent function acoth(x) 1.0
actgh Unary Function Inverse hyperbolic cotangent function actgh(x) 1.0
actanh Unary Function Inverse hyperbolic cotangent function actanh(x) 1.0
arcoth Unary Function Inverse hyperbolic cotangent function arcoth(x) 1.0
arccoth Unary Function Inverse hyperbolic cotangent function arccoth(x) 1.0
arcctgh Unary Function Inverse hyperbolic cotangent function arcctgh(x) 1.0
arcctanh Unary Function Inverse hyperbolic cotangent function arcctanh(x) 1.0
asech Unary Function Inverse hyperbolic secant function asech(x) 1.0
arsech Unary Function Inverse hyperbolic secant function arsech(x) 1.0
arcsech Unary Function Inverse hyperbolic secant function arcsech(x) 1.0
acsch Unary Function Inverse hyperbolic cosecant function acsch(x) 1.0
arcsch Unary Function Inverse hyperbolic cosecant function arcsch(x) 1.0
arccsch Unary Function Inverse hyperbolic cosecant function arccsch(x) 1.0
acosech Unary Function Inverse hyperbolic cosecant function acosech(x) 1.0
arcosech Unary Function Inverse hyperbolic cosecant function arcosech(x) 1.0
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

Binary Functions

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

3-args Functions

Key word Category Description Example Since
if 3-args Function If function if( cond, expr-if-true, expr-if-false ) 1.0
chi 3-args Function Characteristic function for x in (a,b) chi(x, a, b) 1.0
CHi 3-args Function Characteristic function for x in [a,b] CHi(x, a, b) 1.0
Chi 3-args Function Characteristic function for x in [a,b) Chi(x, a, b) 1.0
cHi 3-args Function Characteristic function for x in (a,b] cHi(x, a, b) 1.0
pUni 3-args Function Probability distribution function - Uniform continuous distribution U(a,b) pUni(x, a, b) 3.0
cUni 3-args Function Cumulative distribution function - Uniform continuous distribution U(a,b) cUni(x, a, b) 3.0
qUni 3-args Function Quantile function (inverse cumulative distribution function) - Uniform continuous distribution U(a,b) qUni(q, a, b) 3.0
pNor 3-args Function Probability distribution function - Normal distribution N(m,s) pNor(x, mean, stdv) 3.0
cNor 3-args Function Cumulative distribution function - Normal distribution N(m,s) cNor(x, mean, stdv) 3.0
qNor 3-args Function Quantile function (inverse cumulative distribution function) qNor(q, mean, stdv) 3.0
dig 3-args Function Digit at position 1 ... n (left -> right) or 0 ... -(n-1) (right -> left) - numeral system with given base dig(num, pos, base) 4.1

Variadic Functions

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

Calculus Operators / Iterated Operators

Key word Category Description Example Since
sum Calculus Operator Summation operator - SIGMA sum( i, from, to, expr , ) 1.0
prod Calculus Operator Product operator - PI prod( i, from, to, expr , ) 1.0
int Calculus Operator Definite integral operator int( expr, arg, from, to ) 1.0
der Calculus Operator Derivative operator der( expr, arg, ) 1.0
der- Calculus Operator Left derivative operator der-( expr, arg, ) 1.0
der+ Calculus Operator Right derivative operator der+( expr, arg, ) 1.0
dern Calculus Operator n-th derivative operator dern( expr, n, arg ) 1.0
diff Calculus Operator Forward difference operator diff( expr, arg, ) 1.0
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, a, b ) 4.0

Random Variables

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

Mathematical Constants

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

Physical Constant

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

Astronomical Constant

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

Metric prefixes

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

Units of length

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

Units of area

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

Units of volume

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

Units of time

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

Units of mass

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

Units of information

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

Units of energy

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

Units of speed

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

Units of acceleration

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

Units of angle

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

Other parser symbols

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

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Best regards, Mariusz Gromada