represents the domain of algebraic numbers, as in x∈Algebraics.
Algebraics
represents the domain of algebraic numbers, as in x∈Algebraics.
Details
- Algebraic numbers are defined to be numbers that solve polynomial equations with rational coefficients.
- x∈Algebraics evaluates immediately only for quantities x that are explicitly constructed from rational numbers, radicals, and Root objects, or are known to be transcendental.
- Simplify [expr∈Algebraics] can be used to try to determine whether an expression corresponds to an algebraic number.
- Algebraics is output in TraditionalForm as TemplateBox[{}, Algebraics]. This typeset form can be input using algs.
Examples
open all close allBasic 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 :
TraditionalForm of formatting:
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:
Tech Notes
Related Guides
History
Introduced in 1999 (4.0) | Updated in 2017 (11.2)
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_2025_algebraics, author="Wolfram Research", title="{Algebraics}", year="2017", howpublished="\url{https://reference.wolfram.com/language/ref/Algebraics.html}", note=[Accessed: 04-January-2026]}
BibLaTeX
@online{reference.wolfram_2025_algebraics, organization={Wolfram Research}, title={Algebraics}, year={2017}, url={https://reference.wolfram.com/language/ref/Algebraics.html}, note=[Accessed: 04-January-2026]}