## Documentation |

Convert to a floating-point interval

This functionality does not run in MATLAB.

l...rhull(object)

`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:

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.

`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

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(%)

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))

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