## Operators

`+`

,`-`

,`*`

,`/`

Basic calculations (Add, Subtract, Multiply, Divide)- Support for:
`:`

and`÷`

(Division) and`×`

(Multiplication)

- Support for:
`^`

Exponent;`2^3 = 8`

`%`

Modulo, Returns the remainder of an integer division:`5 % 2 = 1`

`!`

Factorial;`5! = 1 * 2 * 3 * 4 * 5 = 120`

## Functions

### Number-based functions

`sqrt(x)`

: Square Root;`sqrt(9) = 3`

`nrt(n,x)`

: n-th Root;`nrt(3,8) = ∛8 = 2`

`sin(x)`

,`cos(x)`

,`tan(x)`

: Trigonometric functions*`arcsin(x)`

,`arccos(x)`

,`arctan(x)`

: Trigonometric arcus functions*`log(a,x)`

: Logarithm based`a`

;`log(10, 100) = 2`

`ln(x)`

: Natural logarithm (log based*e*);`ln(42) = log(e, 42)`

`e(x)`

: Exponential function with base*e*);`e(1)`

≈ 2.71828;`e(2)`

≈ 2.71828²`abs(x)`

: absolute value, converts negative values into positive values:`abs(-3) = 3`

`floor(x)`

: Rounds the value down to next integer value:`floor(2.8) = 2`

`ceil(x)`

: Rounds the value up to next integer value:`ceil(2.2) = 3`

`sgn(x)`

: Returns the sign of a number,`-1`

for negative values,`1`

for positive and`0`

for`0`

`min(x, y)`

: Returns the smallest number of the argument list;`min(23, 12, 42) = 12`

`max(x, y)`

: Returns the biggest number of the argument list;`max(23, 12, 42) = 42`

`cs(x)`

: Returns the cross sum of given numbers;`cs(99) = 18`

,`cs(99, 88) = 16`

`csi(x)`

: Returns the iterated cross sum of given numbers;`cs(99) = 9`

,`cs(99, 88) = 7`

`nth(x, n)`

: Returns the`n`

-th number (decimal sign counts!);`nth(1234, 2) = 2`

;`nth(1234.5, 6) = 5`

`nth(x, s, e)`

: Returns the`s`

-th until`e`

-th number (decimal sign counts!);`nth(1234, 2, 4) = 234`

;`nth(1234.5, 2, 6) = 234.5`

Note, that all decimal values need to be inserted with a **dot as decimal character**. Other way round, a function may return a dot-delimited decimal value, which could yield unexpected results in your entire formula.

### Text-based functions

: Returns the sum of alphabet values of a text;`bww(x)`

,`av(x)`

`av(ABCXYZ) = 1 + 2 + 3 + 24 + 25 + 26 = 81`

: Returns the number of characters of a text;`len(x)`

`len(ABCXYZ) = 6`

## Constants

`pi`

: ~3.1415926…`phi`

: Golden Ratio, ~1.61803…`ln10`

: Natural logarithm of 10;`= ln(10)`

`ln2`

: Natural logarithm of 2;`= ln(2)`

`log10e`

: Logarithm based 10 of*e*;`= log(10, e)`

`log2e`

: Logarithm based 2 of*e*;`= log(2, e)`

`sqrt2`

: Square Root of 2;`= sqrt(2)`

`sqrt1_2`

: Square Root of 1/2;`= sqrt(1/2)`