# Wolfram Language & System 10.0 (2014)|Legacy Documentation

This is documentation for an earlier version of the Wolfram Language.
BUILT-IN WOLFRAM LANGUAGE SYMBOL

# AlgebraicNumber

AlgebraicNumber[θ,{c0,c1,,cn}]
represents the algebraic number in the field given by .

## DetailsDetails

• AlgebraicNumber objects in the same field are automatically combined by arithmetic operations.
• The generator θ can be any algebraic number, represented in terms of radicals or Root objects. The coefficients must be integers or rational numbers.
• AlgebraicNumber is automatically reduced so that θ is an algebraic integer, and the list of is of length equal to the degree of the minimal polynomial of θ.
• AlgebraicNumber objects are always treated as numeric quantities.
• N finds the approximate numerical value of an AlgebraicNumber object.
• Operations such as Abs, Re, Round, and Less can be used on AlgebraicNumber objects.
• RootReduce can be used to transform AlgebraicNumber objects into Root objects.
• A particular algebraic number can have many different representations as an AlgebraicNumber object. Each representation is characterized by the generator θ specified for the field.
• AlgebraicNumber objects representing integers or rational numbers are automatically reduced to explicit integer or rational form.

## ExamplesExamplesopen allclose all

### Basic Examples  (1)Basic Examples  (1)

Represent an algebraic number:

 Out[1]=

Do arithmetic:

 Out[2]=

Get a numerical approximation:

 Out[3]=