# Algebraics

represents the domain of algebraic numbers, as in xAlgebraics.

# Details

• Algebraic numbers are defined to be numbers that solve polynomial equations with rational coefficients.
• xAlgebraics evaluates immediately only for quantities x that are explicitly constructed from rational numbers, radicals, and Root objects, or are known to be transcendental.
• Simplify[exprAlgebraics] can be used to try to determine whether an expression corresponds to an algebraic number.
• Algebraics is output in TraditionalForm as . This typeset form can be input using algs.

# Examples

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## Basic Examples(4)

An algebraic number:

is not an algebraic number:

The square root of an algebraic number is an algebraic number:

Find algebraic solutions of an equation:

## Scope(4)

Test domain membership of a numeric expression:

Make domain membership assumptions:

Specify the default domain for Reduce and Resolve:

## Properties & Relations(3)

Algebraics contains Rationals, Integers, and Primes:

Algebraics is contained in Complexes:

Algebraics neither contains nor is contained in Reals:

## Possible Issues(1)

Some numbers are not yet known to be algebraic or not:

Wolfram Research (1999), Algebraics, Wolfram Language function, https://reference.wolfram.com/language/ref/Algebraics.html (updated 2017).

#### Text

Wolfram Research (1999), Algebraics, Wolfram Language function, https://reference.wolfram.com/language/ref/Algebraics.html (updated 2017).

#### CMS

Wolfram Language. 1999. "Algebraics." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2017. https://reference.wolfram.com/language/ref/Algebraics.html.

#### APA

Wolfram Language. (1999). Algebraics. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Algebraics.html

#### BibTeX

@misc{reference.wolfram_2024_algebraics, author="Wolfram Research", title="{Algebraics}", year="2017", howpublished="\url{https://reference.wolfram.com/language/ref/Algebraics.html}", note=[Accessed: 24-July-2024 ]}

#### BibLaTeX

@online{reference.wolfram_2024_algebraics, organization={Wolfram Research}, title={Algebraics}, year={2017}, url={https://reference.wolfram.com/language/ref/Algebraics.html}, note=[Accessed: 24-July-2024 ]}