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# listlib::insert

Insert an element into a list

### Use only in the MuPAD Notebook Interface.

This functionality does not run in MATLAB.

## Syntax

```listlib::insert(list, element, <function>)
```

## Description

listlib::insert(list, element) inserts element into list.

With the function listlib::insert any element can be inserted into any list.

With the third optional argument a function can be given that compare the elements of the list with the element to insert and therewith determines the position, the element is inserted. 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 list as first argument and the given element as second argument, until it returns FALSE. Then the given element is inserted into the list in front of the last proved element (see Example 2).

 Note:   The list must be ordered with regard to the order function, otherwise the element 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

Insert 3 into the given ordered list:

`listlib::insert([1, 2, 4, 5, 6], 3)`

Insert 3 into the given descending ordered list. The insert function represents and preserves the order of the list:

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

Because identifiers cannot be ordered by _less, another function must be given, e.g., the function that represents the systems internal order:

`listlib::insert([a, b, d, e, f], c, sysorder)`

### Example 2

Because no function is given as third argument, the function _less is used. _less is called: _less(1, 3), _less(2, 3), _less(4, 3) and then 3 is inserted in front of 4:

`listlib::insert([1, 2, 4], 3)`

If the list is not ordered right, then the insert position could be wrong:

`listlib::insert([4, 1, 2], 3)`

### Example 3

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 expression x*2 is inserted at the "right" place in the list:

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

## Parameters

 list MuPAD® list element MuPAD expression to insert function Function that determines the insert position

## Return Values

Given list enlarged with the inserted element