Insert an element into a list
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listlib::insert(list
, element
, <function
>)
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.
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)
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)
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)

MuPAD^{®} list 

MuPAD expression to insert 

Function that determines the insert position 
Given list enlarged with the inserted element