represents the domain of algebraic numbers, as in xAlgebraics.


  • 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 TemplateBox[{}, Algebraics]. This typeset form can be input using algs.


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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:

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:

Introduced in 1999
Updated in 2017