Wolfram Language & System 10.3 (2015)|Legacy Documentation

This is documentation for an earlier version of the Wolfram Language.View current documentation (Version 11.2)


represents the algebraic number in the field given by .


  • 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.
Introduced in 2007