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`contains`

Test if an entry exists in a container

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contains(`s`

,`object`

) contains(`l`

,`object`

, <`i`

>) contains(`t`

,`object`

)

`contains(s, object)`

tests if `object`

is
an element of the set `s`

.

`contains(l, object)`

returns the index of `object`

in
the list `l`

.

`contains(t, object)`

tests if the array, table,
or domain `t`

has an entry corresponding to the index `object`

.

`contains`

is a fast membership test for the MuPAD^{®} basic
container data types. For lists and sets, `contains`

searches
the elements for the given object. However, for arrays, tables, and domains, `contains`

searches
the indices.

`contains`

works syntactically, i.e., mathematically
equivalent objects are considered to be equal only if they are syntactically
identical. `contains`

does *not* represent
elementhood in the mathematical sense. See Example 2.

`contains`

does not descend recursively into
subexpressions; use `has`

to
achieve this. See Example 3.

`contains(s, object)`

returns `TRUE`

if `object`

is
an element of the set `s`

.
Otherwise, it returns `FALSE`

.

`contains(l, object)`

returns the position
of `object`

in the list `l`

as
a positive integer if `object`

is an entry of `l`

.
Otherwise, the return value is `0`

. If more than
one entry of `l`

is equal to `object`

,
then the index of the first occurrence is returned.

By passing a third argument `i`

to `contains`

,
you can specify a position in the list where the search is to start.
Then, entries with index less than `i`

are not taken
into account. If `i`

is out of range, then the return
value is `0`

.

`contains(t, object)`

returns `TRUE`

if
the array, table,
or domain `t`

has
an entry corresponding to the index `object`

. Otherwise,
it returns `FALSE`

.
Cf. Example 6.

`contains`

may be used to test if a set contains a given element:

contains({a, b, c}, a), contains({a, b, c}, 2)

`contains`

works syntactically, i.e., mathematically
equivalent objects are considered to be equal only if they are syntactically
identical. In this example `contains`

returns `FALSE`

since ```
y*(x
+ 1)
```

and `y*x + y`

are different representations
of the same mathematical expression:

contains({y*(x + 1)}, y*x + y)

Elementhood in the mathematical sense is represented by the
operator `in`

:

simplify(y*x + y in {y*(x+1)}, condition)

`contains`

does not descend recursively into
the operands of its first argument. In the following example, `c`

is
not an element of the set, and therefore `FALSE`

is returned:

contains({a, b, c + d}, c)

If you want to test whether a given expression is contained *somewhere
inside* a complex expression, please use `has`

:

has({a, b, c + d}, c)

`contains`

applied to a `list`

returns the position
of the specified object in the list:

contains([a, b, c], b)

If the list does not contain the object, `0`

is
returned:

contains([a, b, c], d)

`contains`

returns the position of the first
occurrence of the given object in the list if it occurs more than
once:

l := [a, b, a, b]: contains(l, b)

A starting position for the search may be given as optional third argument:

contains(l, b, 1), contains(l, b, 2), contains(l, b, 3), contains(l, b, 4)

If the third argument is out of range, then the return value
is `0`

:

contains(l, b, -1), contains(l, b, 0), contains(l, b, 5)

For tables, `contains`

returns `TRUE`

if
the second argument is a valid index in the table. The entries stored
in the table are not considered:

t := table(13 = value): contains(t, 13), contains(t, value)

Similarly, `contains`

tests if an `array`

has
a value for a given index. The array `a`

has a value
corresponding to the index `(1, 1)`

, but none for
the index `(1, 2)`

:

a := array(1..3, 1..2, (1, 1) = x, (2, 1) = PI): contains(a, (1, 1)), contains(a, (1, 2))

`contains`

is not intended for testing if an
array contains a given value:

contains(a, PI)

Error: Index dimension does not match. [array]

Even if the dimensions match, the index must not be out of range:

contains(a, (4, 4))

Error: Invalid argument. [array]

`contains`

may be used to test, whether a domain has the
specified `slot`

:

T := newDomain("T"): T::index := value: contains(T, index), contains(T, value)

There is no entry corresponding to the slot `index`

in `T`

.
Please keep in mind that the syntax `T::index`

is
equivalent to `slot(T, "index" )`

:

contains(T, "index")

Users can overload`contains`

for
their own domains.
For illustration, we create a new domain `T`

and
supply it with an `"contains"`

slot, which tests
is the set of entries of an element contains the given value `idx`

:

T := newDomain("T"): T::contains := (e, idx) -> contains({extop(e)}, idx):

If we now call `contains`

with an object of
domain type `T`

, the slot routine `T::contains`

is
invoked:

e := new(T, 1, 2): contains(e, 2), contains(e, 3)

For sets, arrays, tables, or domains, `contains`

returns
one of the Boolean values `TRUE`

or `FALSE`

. For lists, the
return value is a nonnegative integer.

` l`

, `s`

, ` t`

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