# Documentation

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# Dom::Integer

Ring of integer numbers

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Dom::Integer(x)

## Description

Dom::Integer is the ring of integer numbers represented by elements of the domain DOM_INT.

Elements of Dom::Integer are usually not created explicitly. However, if one creates elements using the usual syntax, it is checked whether the input is an integer number. This means that Dom::Integer is a façade domain which creates elements of domain type DOM_INT.

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

Dom::Integer 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::Integer. Methods described below are those implemented by Dom::Integer.

Dom::Numerical

## Examples

### Example 1

Creating some integer numbers using Dom::Integer. This example also shows that Dom::Integer is a façade domain.

Dom::Integer(2); domtype(%)

Dom::Integer(2/3)
Error: The arguments are invalid. [Dom::Integer::new]

### Example 2

By tracing the method Dom::Integer::testtypeDom we can see the interaction between testtype and Dom::Integer::testtypeDom.

prog::trace(Dom::Integer::testtypeDom):
delete x:
testtype(x, Dom::Integer);
testtype(3, Dom::Integer);
prog::untrace(Dom::Integer::testtypeDom):
enter Dom::Integer::testtypeDom(x, Dom::Integer)
computed FALSE

enter Dom::Integer::testtypeDom(3, Dom::Integer)
computed TRUE

## Parameters

 x An integer

## Methods

expand all

#### Mathematical Methods

associates(x, y)

_divide(x, y)

_divides(x, y)

euclideanDegree(x)

factor(x)

gcd(x1, x2, …)

gcdex(x, y)

_invert(x)

irreducible(x)

isUnit(x)

lcm(x1, x2, …)

quo(x, y)

random()

random(n)

random(m .. n)

This methods returns a random number between 0 and n - 1.

This methods returns a random number between m and n.

rem(x, y)

unitNormal(x)

unitNormalRep(x)

#### Conversion Methods

convert(x)

convert_to(x, T)

The following domains are allowed for T: DOM_INT, Dom::Integer, Dom::Rational, DOM_FLOAT, Dom::Float and Dom::Numerical.

testtype(x, T)

Usually, this method is called from the function testtype and not directly by the user. Example 2 demonstrates this behavior.