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AlgebraicNumber

AlgebraicNumber[

, {c₀, c₁, ..., c_n}]
represents the algebraic number in the field

given by

.

MORE INFORMATION

AlgebraicNumber objects in the same field are automatically combined by arithmetic operations.

The generator can be any algebraic number, represented in terms of radicals or Root objects. The coefficients c_i must be integers or rational numbers.

AlgebraicNumber is automatically reduced so that is an algebraic integer, and the list of c_i is of length equal to the degree of the minimal polynomial of .

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 specified for the field.

AlgebraicNumber objects representing integers or rational numbers are automatically reduced to explicit integer or rational form.

Basic Examples (1)

Represent an algebraic number:

Do arithmetic:

Get a numerical approximation:

Applications (2)

Properties & Relations (5)

Possible Issues (1)

Root AlgebraicNumberPolynomial ToNumberField Algebraics RootReduce MinimalPolynomial Extension AlgebraicIntegerQ AlgebraicUnitQ AlgebraicNumberTrace AlgebraicNumberNorm

Algebraic Number Fields

Algebraic Numbers

Algebraic Number Theory

Number Theory

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