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    Algebraic Number

    Basic definition

    An algebraic number is a number that is the root of some polynomial with integer coefficients. Algebraic numbers can be real or complex and need not be rational.

    Detailed definition

    If r is a root of a nonzero polynomial equation a_n x^n + a_(n - 1) x^(n - 1) + ... + a_1 x + a_0 = 0, where the a_is are integers (or equivalently, rational numbers) and r satisfies no similar equation of degree <n, then r is said to be an algebraic number of degree n. A number that is not algebraic is said to be transcendental. If r is an algebraic number and a_n = 1, then it is called an algebraic integer.

    Related terms

    algebraic integer | algebraic number minimal polynomial | algebraic number theory | Euclidean number | Hermite-Lindemann theorem | number field | Q^_ | radical integer | transcendental number

    Educational grade level

    college level

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