# listlib::merge

Merging two ordered lists

### Use only in the MuPAD Notebook Interface.

This functionality does not run in MATLAB.

## Syntax

```listlib::merge(`list1`, `list2`, <`function`>)
```

## Description

`listlib::merge(list1, list2)` merges both lists into one list.

With the third optional argument a function can be given that compare the elements of the lists and therewith determines the order of the elements. The given function is called with two elements and have to return `TRUE`, if the two elements are in the right order, otherwise `FALSE` (see next paragraph).

The given function is called step by step with an element of the first list as first argument and an element of the second list as second argument, until it returns `FALSE`. Then the element of the second list is inserted into the first list in front of the last proved element (see Example 2).

 Note:   The lists must be ordered with regard to the order function, otherwise the elements could be inserted at the wrong place.

If no third argument is given the function `_less` is used. If no order of the elements with regard to `_less` is defined, a function must be given, otherwise an error appears. The system function `sysorder` always can be used.

## Examples

### Example 1

Merging two ascending ordered lists:

`listlib::merge([1, 3, 5, 7], [2, 4, 6, 8])`

Merging two descending ordered lists:

`listlib::merge([7, 5, 3, 1], [8, 6, 4, 2], _not@_less)`

### Example 2

The following example shows, how expressions can be ordered by a user defined priority. This order is given by the function named `priority`, which returns a smaller number, when the expression has a type with higher priority:

```priority := X -> contains(["_power", "_mult", "_plus"], type(X)): priority(x^2), priority(x + 2)```

The function `sortfunc` returns `TRUE`, if the both given arguments are in the right order, i.e., the first argument has a higher (or equal) priority than the second argument:

```sortfunc := (X, Y) -> bool(priority(Y) > priority(X)): sortfunc(x^2, x + 2), sortfunc(x + 2, x*2)```

Now the both lists are merged with regard to the given priority:

`listlib::merge([x^y, x*2, -y], [x^2, x*y, x + y], sortfunc)`

`delete priority, sortfunc:`

## Parameters

 `list1`, `list2` A MuPAD® list `function` A function that determines the merging order

## Return Values

Ordered list that contains the elements of both lists