New in: 5.1.20The mathematics filter operators allow numerical calculations to be performed within filters.

# Using mathematics operators

The mathematics operators interpret their arguments as numbers according to the following rules:

- Any non-numeric characters after a valid number are ignored (e.g.
`28px`

is interpreted as the number 28) - If the argument cannot be interpreted as a number, the value 0 is used (e.g.
`foo`

is interpreted as the number 0) - The special values
`Infinity`

and`-Infinity`

can be used to represent positive and negative infinity respectively

The mathematics operators take three different forms:

**Unary operators**apply an operation to each number in the input list (e.g. negate, truncate, sign)`=1 =2 =3 =4 +[negate[]]`

evaluates to`-1`

`-2`

`-3`

`-4`

`=1.2 =2.4 =3.6 =4.8 +[trunc[]]`

evaluates to`1`

`2`

`3`

`4`

`=1.2 =2.4 =3.6 =4.8 +[round[]]`

evaluates to`1`

`2`

`4`

`5`

**Binary operators**apply an operation and operand to each number in the input list (e.g. add, multiply, remainder)`=1 =2 =3 =4 +[add[3]]`

evaluates to`4`

`5`

`6`

`7`

`=1 =2 =3 =4 +[multiply[8]]`

evaluates to`8`

`16`

`24`

`32`

**Reducing operators**apply an operation to all of the numbers in the input list, returning a single result (e.g. sum, product)`=1 =2 =3 =4 +[sum[]]`

evaluates to`10`

`=1 =2 =3 =4 +[product[]]`

evaluates to`24`

`=1 =2 =3 =4 +[average[]]`

evaluates to`2.5`

# Operations Combination

Operations can be combined by concatenating them while merging the inner `][`

characters.

`[[355]divide[113]fixed[5]]`

evaluates to`3.14159`

`[range[100]sum[]divide[100]]`

evaluates to`50.5`

`[tag[HelloThere]get[text]length[]sum[]]`

evaluates to`10375`

Complex operations will sometimes need to be split up into separate filters. For example, to compute the average length of the text field of tiddlers tagged "HelloThere":

```
<$set name="number-of-tiddlers" value={{{ [tag[HelloThere]count[]] }}}>
Average length of <$text text=<<number-of-tiddlers>>/> tiddlers tagged <<tag "HelloThere">>: <$text text={{{ [tag[HelloThere]get[text]length[]sum[]divide<number-of-tiddlers>fixed[3]] }}}/>
</$set>
```

That renders as:

Average length of 8 tiddlers tagged

: 1296.875# Mathematics Operators list

Operator | Purpose |
---|---|

abs | calculate the absolute value of a list of numbers |

acos | calculate the arccosine value (in radians) of a list of numbers |

add | treating each input title as a number, add to each the numeric value of the operand |

asin | calculate the arcsine value (in radians) of a list of numbers |

atan | calculate the arctangent value (in radians) of a list of numbers |

atan2 | returns the angle in the plane (in radians) between the positive x-axis and the ray from (0,0) to the point (x,y), for [`Y` ]atan2[`X` ] |

average | treating each input title as a number, compute their arithmetic mean |

ceil | rounds a list of numbers up to the next largest integer |

compare | filter the input by comparing each item against the operand |

cos | calculate the cosine value of a list of angles (given in radians) |

divide | treating each input title as a number, divide them by the numeric value of the operand |

exponential | convert each number to exponential notation with `N` digits |

fixed | convert each number to fixed point notation with `N` digits after the decimal point |

floor | rounds a list of numbers to the largest integer less than or equal to each number |

log | treating each input title as a number, return its logarithm with base equal to the numeric value of the operand if specified, otherwise base `e` |

max | treating each input title as a number, take the maximum of its value and the numeric value of the operand |

maxall | find the largest of a list of numbers |

median | treating each input title as a number, compute their median value |

min | treating each input title as a number, take the minimum of its value and the numeric value of the operand |

minall | find the smallest of a list of numbers |

multiply | treating each input title as a number, multiply it by the numeric value of the operand |

negate | calculate the negation of a list of numbers |

power | treating each input title as a number, raise it to the power of the numeric value of the operand |

precision | convert each number to a string with `N` significant digits |

product | produce the product of the input numbers |

remainder | treating each input title as a number, return the remainder when divided by the numeric value of the operand |

round | rounds a list of numbers to the nearest integer |

sign | return -1, 0 or 1 for a list of numbers according to whether each number is negative, zero, or positive |

sin | calculate the sine value of a list of angles (given in radians) |

standard-deviation | treating each input title as a number, compute their standard-deviation |

subtract | treating each input title as a number, subtract from each the numeric value of the operand |

sum | produce the sum of the input numbers |

tan | calculate the tangent value of a list of angles (given in radians) |

trunc | truncates a list of numbers to their integer part, removing any fractional part |

untrunc | rounds a list of numbers to the next integer with largest absolute value, that is, away from zero |

variance | treating each input title as a number, compute their variance |