# interval

Convert constant subexpressions to intervals

### Use only in the MuPAD Notebook Interface.

This functionality does not run in MATLAB.

## Syntax

```interval(`object`)
```

## Description

`interval(object)` converts all constant subexpressions of `object` to floating point intervals.

`interval` is the analogue of `float`. While the latter converts exact numbers and numerical expressions to floating-point approximations, `interval` converts numbers and numerical expressions to enclosing floating-point intervals.

If `object` is an arithmetical expression, `interval(object)` recursively descends into the subexpressions of `object` and replaces all integers,rationals, and floating point numbers as well as the constants CATALAN, EULER and PI by floating-point intervals enclosing them. Afterwards, the resulting expression is evaluated via interval arithmetic.

If `object` is not an arithmetical expression, `interval` returns the object unchanged.

## Examples

### Example 1

Only constant expressions such as numbers 1, , 0.123 + 4.5 i etc. and numerical expressions ```PI + sqrt(2)```, `sin(PI/24)` etc. are converted to floating-point intervals. Symbolic objects such as identifiers, indexed identifiers etc. are left untouched:

`interval(4*x[1] + PI*x[2]^2/sin(1) + 1/4)`

`interval(f(g(2 + x) + sin(1)*sqrt(PI)))`

### Example 2

The special MuPAD® constants CATALAN, EULER and PI can be converted to an enclosing floating-point interval:

`interval(CATALAN), interval(EULER), interval(PI)`

## Parameters

 `object` An arbitrary MuPAD object