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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 陳其誠 | |
| dc.contributor.author | Ying-Jen Tseng | en |
| dc.contributor.author | 曾膺任 | zh_TW |
| dc.date.accessioned | 2021-05-13T08:39:37Z | - |
| dc.date.available | 2016-03-08 | |
| dc.date.available | 2021-05-13T08:39:37Z | - |
| dc.date.copyright | 2016-03-08 | |
| dc.date.issued | 2016 | |
| dc.date.submitted | 2016-02-14 | |
| dc.identifier.citation | Agrawal, Manindra; Kayal, Neeraj; Saxena, Nitin, PRIMES is in P, Annals of Mathematics 160, 2(2004), 781-793.
Agrawal, Manindra; Kayal, Neeraj; Saxena, Nitin, PRIMES is in P, Preprint, (2002). Crandall, R. and Pomerance, C. Prime Numbers: A Computational Perspective, 2nd ed. New York: Springer-Verlag, 2005. Granville, A., It Is Easy to Determine Whether a Given Integer Is Prime, Bull. Amer. Math. Soc.42, 3-38, 2005. M.Nair, On Cheybyshev-type inequalities for primes, Amer. Math. Monthly, 89:126-129, 1982. E. Fouvry, Theorem de Brun-Titchmarsh; application au theoreme de Fermat, Invent. Math.,79:383-407, 1985. R. Lidl and H. Niederreiter, Introduction to finite fields and their applications, Cambridge University Press, 1986. Joachim von zur Gathen and Jurgen Gerhard, Modern Computer Algebra. Cambridge University Press, 1999. M.Ram Murty, Problems in Algebraic Number Theory, 2nd ed. Springer-Verlag, 2004. H. W. Lenstra Jr. and Carl Pomerance, Primality testing with Gaussian periods, preliminary version July 20, 2005. D. Bernstein, Proving primality in essentially quartic time. http://cr.yp.to/ntheory.html#quartic DEPARTMENT OF MATHEMATICS, NATIONAL TAIWAN UNIVERSITY, TAIPEI 10764, TAIWAN E-mail address: r01221030@ntu.edu.tw | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/3978 | - |
| dc.description.abstract | 本文研究由M. Agrawal, N. Kayal and N. Saxena 提出的第一個多項式時間確定型的質數判定演算法，經過H. Lenstra Jr.等人的建議修改後的版本”PRIMES is in P”(2004)，並補充了一些原文裡證明細節。 | zh_TW |
| dc.description.abstract | We take a exposition at the paper “PRIMES is in P” by M. Agrawal, N. Kayal and N. Saxena (2004), in which they used Lenstra's idea and made a revision of their earlier version. We also present some details in the proof. | en |
| dc.description.provenance | Made available in DSpace on 2021-05-13T08:39:37Z (GMT). No. of bitstreams: 1 ntu-105-R01221030-1.pdf: 347538 bytes, checksum: b61c07b56301d860c0bb402ebdc5bf60 (MD5) Previous issue date: 2016 | en |
| dc.description.tableofcontents | 口試委員會審定書……………………………………………i
誌謝……………………………………………………………………ii 中文摘要…………………………………………………………iii 英文摘要……………………………………………………………iv 第一章 簡介………………………………………………………1 第二章 算法的根源…………………………………………2 引理 2.0.1………………………………………………………2 第三章 演算法…………………………………………………3 第四章 演算法的正確性………………………………3 定理 1. ……………………………………………………………3 引理 4.0.2 ……………………………………………………3 引理 4.0.3………………………………………………………4 定理 2…………………………………………………………………4 第五章 演算法的時間雜度分析…………………8 定理 3. ……………………………………………………………8 引理 5.0.4………………………………………………………9 定理 4…………………………………………………………………9 參考文獻…………………………………………………………10 | |
| dc.language.iso | en | |
| dc.title | 多項式時間確定型質數判定演算法的研究 | zh_TW |
| dc.title | On the AKS Algorithm | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 104-1 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 陳君明,呂育道 | |
| dc.subject.keyword | 質數,演算法,多項式時間,確定型,質數判定, | zh_TW |
| dc.subject.keyword | prime number,algorithm,polynomial time,deterministic,primality test, | en |
| dc.relation.page | 11 | |
| dc.rights.note | 同意授權(全球公開) | |
| dc.date.accepted | 2016-02-15 | |
| dc.contributor.author-college | 理學院 | zh_TW |
| dc.contributor.author-dept | 數學研究所 | zh_TW |
| 顯示於系所單位： | 數學系 | |
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