Extended Euclidean Algorithm and CRT Algorithm

• Autorzy: Hiroyuki Okazaki , Yosiki Aoki , Yasunari Shidama
• Języki publikacji: EN

Abstrakty

EN

In this article we formalize some number theoretical algorithms, Euclidean Algorithm and Extended Euclidean Algorithm [9]. Besides the a gcd b, Extended Euclidean Algorithm can calculate a pair of two integers (x, y) that holds ax + by = a gcd b. In addition, we formalize an algorithm that can compute a solution of the Chinese remainder theorem by using Extended Euclidean Algorithm. Our aim is to support the implementation of number theoretic tools. Our formalization of those algorithms is based on the source code of the NZMATH, a number theory oriented calculation system developed by Tokyo Metropolitan University [8].

• Wydawca: De Gruyter Open
• Czasopismo: Formalized Mathematics
• Rocznik: 2012
• Tom: 20
• Numer: 2
• Strony: 175-179

Daty

wydano

2012-12-01

online

2013-02-02

Twórcy

autor

Hiroyuki Okazaki

• Shinshu University, Nagano, Japan

autor

Yosiki Aoki

• Shinshu University, Nagano, Japan

autor

Yasunari Shidama

• Shinshu University, Nagano, Japan

Bibliografia

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• [8] NZMATH development Group. http://tnt.math.se.tmu.ac.jp/nzmath/.
• [9] Donald E. Knuth. Art of Computer Programming. Volume 2: Seminumerical Algorithms, 3rd Edition, Addison-Wesley Professional, 1997.
• [10] Rafał Kwiatek and Grzegorz Zwara. The divisibility of integers and integer relative primes. Formalized Mathematics, 1(5):829-832, 1990.
• [11] Andrzej Trybulec. Tuples, projections and Cartesian products. Formalized Mathematics, 1(1):97-105, 1990.
• [12] Michał J. Trybulec. Integers. Formalized Mathematics, 1(3):501-505, 1990.
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Identyfikatory

DOI

10.2478/v10037-012-0020-2