Results 1 to 10 of about 373,045 (181)
Semi-algebraic Ramsey numbers [PDF]
Journal of Combinatorial Theory, Series B, 2014 Given a finite point set $P \subset \mathbb{R}^d$, a $k$-ary semi-algebraic relation $E$ on $P$ is the set of $k$-tuples of points in $P$, which is determined by a finite number of polynomial equations and inequalities in $kd$ real variables.
Suk, Andrew
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Algebraic values of sines and cosines and their arguments
Lietuvos Matematikos Rinkinys, 2021 The article introduces the reader to some amazing properties of trigonometric functions. It turns out that if the values of the arguments of the functions sin x, cos x, tg x and ctg x, expressed in radians, are algebraic numbers, then the values of these
Edmundas Mazėtis +1 more
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Experimental Mathematics, 2022 We study the geometry of algebraic numbers in the complex plane, and their Diophantine approximation, aided by extensive computer visualization. Motivated by these images, called algebraic starscapes, we describe the geometry of the map from the coefficient space of polynomials to the root space, focussing on the quadratic and cubic cases. The geometry
Edmund Harriss +2 more
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Remarks on the approximation to an algebraic number by algebraic numbers. [PDF]
Michigan Mathematical Journal, 1986 Die Verff. wenden eine in zwei früheren Arbeiten [vgl. \textit{E. Bombieri}, Acta Math. 148, 255-296 (1982; Zbl 0505.10015) und Verff., J. Reine Angew. Math. 342, 173-196 (1983; Zbl 0516.10024)] entwickelte Methode an, um eine algebraische Zahl durch algebraische Zahlen aus einem passenden reellen algebraischen Zahlkörper effektiv abzuschätzen.
Bombieri, E., Mueller, J.
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Fractional parts of powers of real algebraic numbers
Comptes Rendus. Mathématique, 2022 Let $\alpha $ be a real algebraic number greater than $1$. We establish an effective lower bound for the distance between an integral power of $\alpha $ and its nearest integer.
Bugeaud, Yann
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Algebraic Numbers of the form αT with α Algebraic and T Transcendental
Mathematics, 2020 Let α≠1 be a positive real number and let P(x) be a non-constant rational function with algebraic coefficients. In this paper, in particular, we prove that the set of algebraic numbers of the form αP(T), with T transcendental, is dense in some open ...
Štěpán Hubálovský, Eva Trojovská
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Formal proofs in real algebraic geometry: from ordered fields to quantifier elimination [PDF]
Logical Methods in Computer Science, 2012 This paper describes a formalization of discrete real closed fields in the Coq proof assistant. This abstract structure captures for instance the theory of real algebraic numbers, a decidable subset of real numbers with good algorithmic properties.
Assia Mahboubi, Cyril Cohen
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On the Degree of Product of Two Algebraic Numbers
Mathematics, 2023 A triplet (a,b,c) of positive integers is said to be product-feasible if there exist algebraic numbers α, β and γ of degrees (over Q) a, b and c, respectively, such that αβγ=1.
Lukas Maciulevičius
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Denumerability of the Algebraic Numbers
Davao Research Journal, 2000 An algebraic number is a real number that is a root of a polynomial equation anXn + an-1Xn-1…+a0 where ai are integers. In this paper, using the fact that a polynomial equation of degree n has at most n roots, together with some results, the ...
Marleonie Bauyot
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Formalized Mathematics, 2016 Summary This article provides definitions and examples upon an integral element of unital commutative rings. An algebraic number is also treated as consequence of a concept of “integral”. Definitions for an integral closure, an algebraic integer and a transcendental numbers [14], [1], [10] and [7] are included as well.
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