This is machine translation

Translated by Microsoft
Mouseover text to see original. Click the button below to return to the English verison of the page.

Note: This page has been translated by MathWorks. Please click here
To view all translated materals including this page, select Japan from the country navigator on the bottom of this page.

..., hull

Convert to a floating-point interval

MuPAD® notebooks are not recommended. Use MATLAB® live scripts instead.

MATLAB live scripts support most MuPAD functionality, though there are some differences. For more information, see Convert MuPAD Notebooks to MATLAB Live Scripts.


l ... r


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:

DIGITS, Pref::floatFormat, and Pref::trailingZeroes.

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.


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:


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



l, r, object

Arbitrary MuPAD objects

Return Values

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

Overloaded By


See Also

MuPAD Domains

MuPAD Functions

Was this topic helpful?