# Documentation

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# `Dom`::`FloatIV`

The “field” of Floating Point Intervals

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## Syntax

```Dom::FloatIV(`x, …`)
```

## Description

`Dom::FloatIV` is the inclusion algebra of (finite unions of) rectangular intervals in the complex plane.

`Dom::FloatIV` is the domain of kernel intervals of type `DOM_INTERVAL`.

`Dom::FloatIV` has category `Cat::Field` out of pragmatism. This domain actually is not a field because, for example, there is no additive inverse of `1...2`.

Elements of `Dom::FloatIV` are usually not created explicitly. The syntax given above is equivalent to an `interval` call, with no check to ensure that the result is in fact an interval, it could, for example, also be an expression with all numerical coefficients replaced by intervals. Apart from this behavior of the constructor and the `"convert"` slot, `Dom::FloatIV` is a façade domain for elements of domain type `DOM_INTERVAL`.

Viewed as a differential ring `Dom::FloatIV` is trivial, it contains constants only.

`Dom::FloatIV` has the domain `Dom::Numerical` as its super domain, i.e., it inherits each method which is defined by `Dom::Numerical` and not re-implemented by `Dom::FloatIV`. Methods described below are those implemented by `Dom::FloatIV`.

## Superdomain

`Dom::Numerical`

## Axioms

`Ax::canonicalRep`, `Ax::systemRep`, `Ax::efficientOperation``("_divide")`, `Ax::efficientOperation``("_invert")`, `Ax::efficientOperation``("_mult")`, `Ax::efficientOperation``("_plus")`

## Parameters

 `x, …` MuPAD® expressions

## Methods

expand all

#### Mathematical Methods

`Im(iv)`

`Re(iv)`

`abs(iv)`

`arccos(iv)`

`arccosh(iv)`

`arccot(iv)`

`arccoth(iv)`

`arccsc(iv)`

`arccsch(iv)`

`arcsec(iv)`

`arcsech(iv)`

`arcsin(iv)`

`arcsinh(iv)`

`arctan(iv)`

`arctanh(iv)`

`arg(iv)`

`beta(iv)`

`ceil(iv)`

`center(iv)`

`cos(iv)`

`cosh(iv)`

`cot(iv)`

`coth(iv)`

`csc(iv)`

`dirac(iv)`

`exp(iv)`

`floor(iv)`

`gamma(iv)`

`ln(iv)`

`mag(iv)`

`mig(iv)`

`random()`

`round(iv)`

`sec(iv)`

`sign(iv)`

`sin(iv)`

`sinh(iv)`

`sqrt(iv)`

`tan(iv)`

`tanh(iv)`

`trunc(iv)`

`width(x)`

#### Conversion Methods

`convert(x)`

`testtype(x, T)`

Usually, this method is called from the function `testtype` and not directly by the user.