algebraic number


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Related to algebraic number: Algebraic number field, Algebraic number theory

algebraic number

n.
A number that is a root of a polynomial equation with rational coefficients.

algebraic number

n
(Mathematics) any number that is a root of a polynomial equation having rational coefficients such as √2 but not π. Compare transcendental number

al′gebra′ic num′ber


n.
1. a root of an algebraic equation with integral coefficients.
[1930–35]
ThesaurusAntonymsRelated WordsSynonymsLegend:
Noun1.algebraic number - root of an algebraic equation with rational coefficientsalgebraic number - root of an algebraic equation with rational coefficients
irrational, irrational number - a real number that cannot be expressed as a rational number
Translations
References in periodicals archive ?
Dubickas, On the degree of a linear form in conjugates of an algebraic number, Illinois J.
Prerequisites are algebraic geometry, algebraic number theory, and some group cohomology.
Particularly, we bring symmetries, computational- and complexity theoretic aspects, and connections with algebraic number theory, -geometry, and -combinatorics into play in novel ways.
Neukirch Algebraic Number Theory Springer- Verlag Inc.
Akiyama, Cubic Pisot units with finite beta expansions, Algebraic Number Theory and Diophantine Analysis, (2000), pp.
Eleven contributions are selected from the eight working groups in the areas of elliptic surfaces and the Mahler measure, analytic number theory, number theory in functions fields and algebraic geometry over finite fields, arithmetic algebraic geometry, K-theory and algebraic number theory, arithmetic geometry, modular forms, and arithmetic intersection theory.
Proved by the work of French mathematician Jean-Pierre Serre (who has made fundamental contributions to algebraic topology, algebraic geometry, and algebraic number theory) and American mathematician John Torrence Tate, Jr.
Our main results (Theorem 5 and Proposition 7) may seem surprising as we might expect that any algebraic number would be computable in our setting.
Let a, b, c > 0 and u be a real algebraic number.
Stan, Florin, University of Illinois, Urbana-Champaign, Trace problems in algebraic number fields and applications to characters of finite groups.
Ten chapters cover algebraic number theory and quadratic fields; ideal theory; binary quadratic forms; Diophantine approximation; arithmetic functions; p-adic analysis; Dirichlet characters, density, and primes in progression; applications to Diophantine equations; elliptic curves; and modular forms.
In these cases, [rho] is an algebraic number of degree 2 (e.

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