represents the domain of algebraic numbers, as in x∈Algebraics.
- 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 . This typeset form can be input using algs.
Examplesopen allclose all
Basic Examples (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:
Wolfram Research (1999), Algebraics, Wolfram Language function, https://reference.wolfram.com/language/ref/Algebraics.html (updated 2017).
Wolfram Language. 1999. "Algebraics." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2017. https://reference.wolfram.com/language/ref/Algebraics.html.
Wolfram Language. (1999). Algebraics. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Algebraics.html