- algebraic number
- A real number that is the root of a polynomial equation. All rationals are algebraic (they are all roots of equations b x = a where a, b are integers). Reals that are not algebraic are called transcendental numbers.
Philosophy dictionary. Academic. 2011.
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algebraic number — n. a root of a polynomial equation with coefficients that are rational numbers … English World dictionary
Algebraic number — In mathematics, an algebraic number is a complex number that is a root of a non zero polynomial in one variable with rational (or equivalently, integer) coefficients. Complex numbers such as pi that are not algebraic are said to be transcendental … Wikipedia
algebraic number — Math. 1. a root of an algebraic equation with integral coefficients. 2. root1 (def. 10b). [1930 35] * * * real number for which there exists a polynomial equation with integer coefficients such that the given real number is a solution.… … Universalium
algebraic number — noun root of an algebraic equation with rational coefficients • Hypernyms: ↑irrational number, ↑irrational * * * noun : a root of an algebraic equation whose coefficients are rational * * * Math. 1. a root of an algebraic equation with integral… … Useful english dictionary
algebraic number — noun Date: 1904 a root of an algebraic equation with rational coefficients … New Collegiate Dictionary
algebraic number — al′gebra′ic num′ber n. 1) math. a root of an algebraic equation with integral coefficients 2) math. root I, 9), b) • Etymology: 1930–35 … From formal English to slang
algebraic number — noun A complex number that is a root of a polynomial equation with rational coefficients. Ant: transcendental number … Wiktionary
Algebraic number field — In mathematics, an algebraic number field (or simply number field) F is a finite (and hence algebraic) field extension of the field of rational numbers Q. Thus F is a field that contains Q and has finite dimension when considered as a vector… … Wikipedia
Algebraic number theory — In mathematics, algebraic number theory is a major branch of number theory which studies the algebraic structures related to algebraic integers. This is generally accomplished by considering a ring of algebraic integers O in an algebraic number… … Wikipedia
algebraic number theory — noun The subfield of number theory where algebraic numbers are studied using algebra … Wiktionary