AlgebraicNumber

AlgebraicNumber[θ,{c0,c1,,cn}]

represents the algebraic number in the field given by .

Details

  • 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 ci must be integers or rational numbers.
  • AlgebraicNumber is automatically reduced so that θ is an algebraic integer, and the list of ci 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.

Examples

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Basic Examples  (1)

Represent an algebraic number:

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Do arithmetic:

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Get a numerical approximation:

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Scope  (7)

Applications  (2)

Properties & Relations  (5)

Possible Issues  (1)

See Also

Root  AlgebraicNumberPolynomial  ToNumberField  Algebraics  RootReduce  MinimalPolynomial  Extension  AlgebraicIntegerQ  AlgebraicUnitQ  AlgebraicNumberTrace  AlgebraicNumberNorm

Tutorials

Introduced in 2007
(6.0)