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检索条件"主题词=Euclidean algorithm"
533 条 记 录,以下是21-30 订阅
排序:
The Polynomial euclidean algorithm and the Linear Equation AX plus BY = gcd(A, B)
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MATHEMATICAL INTELLIGENCER 2017年 第1期39卷 22-25页
作者: Effinger, Gove Mullen, Gary L. Skidmore Coll Dept Math & Comp Sci Saratoga Springs NY 12866 USA Penn State Univ Dept Math University Pk PA 16802 USA
The article discusses the polynomial version of the euclidean algorithm and the solutions to the linear equation AX + BY = gcd (A,B) over a finite field. Topics include how the polynomial euclidean solution of linear ... 详细信息
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Bezoutians, euclidean algorithm, and orthogonal polynomials
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ANNALS OF COMBINATORICS 2005年 第3期9卷 301-319页
作者: Lascoux, Alain Pragacz, Piotr Univ Marne Vallee CNRS Inst Gaspard Monge F-77454 Marne La Vallee France Nankai Univ Ctr Combinator LMPC Tianjin 300071 Peoples R China Polish Acad Sci Inst Math PL-00956 Warsaw Poland
We prove a quadratic expression for the Bezoutian of two univariate polynomials in terms of the remainders for the euclidean algorithm. In case of two polynomials of the same degree, or of consecutive degrees, this al... 详细信息
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Euclid Meets Bezout: Intersecting Algebraic Plane Curves with the euclidean algorithm
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AMERICAN MATHEMATICAL MONTHLY 2010年 第3期117卷 250-260页
作者: Hilmar, Jan Smyth, Chris Univ Edinburgh Sch Math Edinburgh EH9 3JZ Midlothian Scotland Univ Edinburgh Maxwell Inst Math Sci Edinburgh EH9 3JZ Midlothian Scotland
Finding the intersection point of two lines in the plane is easy. But doing the same for a pair of algebraic plane curves is more difficult, not least because each point on both curves may be a multiple intersection p... 详细信息
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On the euclidean algorithm of polynomials
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IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES 2001年 第5期E84A卷 1261-1265页
作者: Futa, Y Nagao, K Matsushita Elect Ind Co Ltd Kadoma Osaka 5718501 Japan Kanto Gakuin Univ Yokohama Kanagawa 2368501 Japan
In order to compute gcd of polynomials, the euclidean algorithm is used. We estimate the complexities of known euclidean algorithms. Further, we propose a heuristic euclidean algorithm. This is faster than ordinary me... 详细信息
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Lattice reduction using a euclidean algorithm
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ACTA CRYSTALLOGRAPHICA A-FOUNDATION AND ADVANCES 2017年 第1期73卷 61-68页
作者: Mujica, A. Univ La Laguna Dept Fis Tenerife 38200 Spain Univ La Laguna MALTA Consolider Team Inst Univ Mat & Nanotecnol Tenerife 38200 Spain
The need to reduce a periodic structure given in terms of a large supercell and associated lattice generators arises frequently in different fields of application of crystallography, in particular in the ab initio the... 详细信息
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The 2-stage euclidean algorithm and the restricted Nagata's pairwise algorithm
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JOURNAL OF ALGEBRA 2011年 第1期348卷 1-13页
作者: Chen, Ching-An Leu, Ming-Guang Natl Cent Univ Dept Math Chungli 32054 Taiwan
As with euclidean rings and rings admitting a restricted Nagata's pairwise algorithm, we will give an internal characterization of 2-stage euclidean rings. Applying this characterization we are capable of providin... 详细信息
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ON THE euclidean algorithm: RHYTHM WITHOUT RECURSION
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BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY 2023年 第3期107卷 361-367页
作者: Morrill, Thomas Trine Univ Sch Arts & Sci Angola IN 46703 USA
A modified form of Euclid's algorithm has gained popularity among musical composers following Toussaint's 2005 survey of so-called euclidean rhythms in world music. We offer a method to easily calculate Euclid... 详细信息
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A rigorous version of RP Brent's model for the binary euclidean algorithm
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ADVANCES IN MATHEMATICS 2016年 290卷 73-143页
作者: Morris, Ian D. Univ Surrey Dept Math Guildford GU2 7XH Surrey England
The binary euclidean algorithm is a modification of the classical euclidean algorithm for computation of greatest common divisors which avoids ordinary integer division in favour of division by powers of two only. The... 详细信息
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The euclidean algorithm and the Linear Diophantine Equation ax plus by = gcd(a, b)
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AMERICAN MATHEMATICAL MONTHLY 2013年 第6期120卷 562-564页
作者: Rankin, S. A. Univ Western Ontario Dept Math London ON N6A 5B7 Canada
In this note, we prove that for any positive integers a and b, with d = gcd(a, b), among all integral solutions to the equation ax + by = d, the solution (x(0), y(0)) that is provided by the euclidean algorithm lies n... 详细信息
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The mean number of steps in the euclidean algorithm with least absolute value remainders
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MATHEMATICAL NOTES 2009年 第1-2期85卷 142-145页
作者: Ustinov, A. V. Russian Acad Sci Far E Div Khabarovsk Branch Inst Appl Math Moscow 117901 Russia
A letter to the editor is presented regarding the mean number of steps in the euclidean algorithm.
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