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# ..., hull

Convert to a floating-point interval

### Use only in the MuPAD Notebook Interface.

This functionality does not run in MATLAB.

## Syntax

```l ... r
hull(object)
```

## Description

hull(object) returns a floating-point interval enclosing object.

l ... r is equivalent to hull(l, r).

hull converts numerical and interval expressions to numerical intervals of type DOM_INTERVAL. It accepts lists and sets of numerical expressions or intervals as well as numerical expressions, intervals, and set-theoretic functions of intervals and sets.

Infinities are displayed using RD_INF for infinity and RD_NINF for -infinity.

hull is mapped recursively to the operands of any expression given—but for subexpressions, lists and sets are not accepted. Identifiers are replaced by intervals, respecting a certain subset of properties. Cf. Example 3. Likewise, function calls and domain elements not overloading hull are converted to the interval representing the complex plane.

The output of floating-point intervals is influenced by the same parameters as the output of floating-point numbers:

## Environment Interactions

The function is sensitive to the environment variable DIGITS which determines the numerical working precision.

Each sub-object of object can be evaluated multiple times and must not have any side-effects.

## Examples

### Example 1

hull returns an interval enclosing its arguments. You can also use the operator ... instead of the function call:

`hull(0, PI) = 0 ... PI`

Infinities are displayed using RD_NINF for - ∞ and RD_INF for infinity:

`hull(-infinity, 9/7), hull({1/4, 9/7, infinity})`

Please note that any number whose absolute value is larger than MuPAD® can store in a float is considered infinite:

`hull(0, 1e100000000)^4`

### Example 2

Inversion of intervals may lead to unions of intervals. If these are not required, you may use hull to unify them:

`1/(-1 ... 1); hull(%)`

### Example 3

The application of hull to an identifier without a value returns an interval representing the complex plane:

`delete x:  hull(x)`

Certain properties are respected during this conversion:

```assume(x > 0): hull(x);
delete x:```

This way, you can enclose the values of an expression:

`hull(sin(abs(x)))`

Calls to "unknown" functions are regarded as potentially returning the complex plane:

`hull(f(x))`

## Parameters

 l, r, object Arbitrary MuPAD objects

## Return Values

floating-point interval, the empty set, or FAIL.