# Documentation

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# `Type`::`Arithmetical`

Type representing arithmetical objects

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.

## Syntax

```testtype(`obj`, `Type::Arithmetical`)
```

## Description

`Type::Arithmetical` represents arithmetical objects.

In MuPAD®, arithmetical objects are objects that represent complex numbers if all identifiers in them also represent complex numbers. Arithmetical objects include numbers, most expressions, and elements of certain library domains. In particular, the latter include `rectform` objects and series expansions of domain type `Series::Puiseux`.

Certain infinite objects such as `dirac(0)`, `infinity`, or `complexInfinity` are also defined to be arithmetical expressions.

The following objects are not regarded as arithmetical objects:

This type does not represent a property: it cannot be used in `assume` to mark an identifier as an arithmetical object.

## Examples

### Example 1

The expression may represent a matrix if A and B are matrices, or it may represent a number if A and B are numbers. However, MuPAD regards identifiers as numbers: hence they commute with each other, and a product of identifiers represents a number, too:

`A^(-1) * B * A * B`

`testtype(%, Type::Arithmetical)`

### Example 2

Numbers and expressions are regarded as arithmetical objects:

```testtype(3 + I, Type::Arithmetical), testtype(x + sqrt(2) + I*PI, Type::Arithmetical), testtype(x/y + y/x, Type::Arithmetical)```

Equations and inequalities are not regarded as arithmetical objects:

```testtype(x^2 = 2, Type::Arithmetical), testtype(x <> 2, Type::Arithmetical), testtype(x < 2, Type::Arithmetical), testtype(x >= 2, Type::Arithmetical)```

Sets, lists, tables and arrays are not arithmetical:

```testtype({a, b, c}, Type::Arithmetical), testtype(array(1..1, [x]), Type::Arithmetical)```

Most domain objects such as matrices of some matrix domain are not arithmetical:

`testtype(Dom::Matrix()([[1, 2], [3, 4]]), Type::Arithmetical)`

## Parameters

 `obj` Any MuPAD object