algebraic number

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Related to Algebraic numbers: Transcendental numbers

algebraic number

n.
A number that is a root of a polynomial equation with rational coefficients.
American Heritage® Dictionary of the English Language, Fifth Edition. Copyright © 2016 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.

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
Collins English Dictionary – Complete and Unabridged, 12th Edition 2014 © HarperCollins Publishers 1991, 1994, 1998, 2000, 2003, 2006, 2007, 2009, 2011, 2014

al′gebra′ic num′ber


n.
1. a root of an algebraic equation with integral coefficients.
[1930–35]
Random House Kernerman Webster's College Dictionary, © 2010 K Dictionaries Ltd. Copyright 2005, 1997, 1991 by Random House, Inc. All rights reserved.
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
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His topics are integers, modular arithmetic, quadratic reciprocity and primitive roots, secrets, arithmetic functions, algebraic numbers, rational and irrational numbers, diophantine equations, elliptic curves, dynamical systems, and polynomials.
The proofs of the theorems are completely self-contained except for several simple observations which follow from some earlier results on additive and multiplicative relations with conjugate algebraic numbers. Specifically, we shall use the fact that, e.g., by [1, Theorem 4], for any n [greater than or equal to] 3 distinct algebraic numbers [[alpha].sub.1], ..., [[alpha].sub.n] conjugate over Q we have
In the role of "the most irrational numbers" was proposed algebraic numbers, which are roots of equation
Although our model is very general and allows to compute a large set of numbers, some algebraic numbers as "simple" (on a computational point of view) as 1/5 are not computable.
of Science and Technology, China) introduce the Diophantine distribution theory of algebraic numbers as analogue of the value distribution theory of Nevanlinna theory.
* High-performance arithmetic for algebraic numbers is presented in Mathematica 5.
Those irrational numbers that cannot serve as solutions are called transcendental numbers (from Latin words meaning "to climb beyond," since they climb beyond the algebraic numbers to further heights).

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