计算数论
外观
在数学和计算机科学领域中,计算数论(英语:computational number theory,或称为算法数论(英语:algorithmic number theory),是伴随着电子计算机的产生而产生的,借助于高性能计算机的计算能力来研究和解决数论和算术几何问题,如素数判定、整数分解算法,计算丢番图方程的解,算术几何的显式方法等[1]。它广泛应用于密码学,如RSA算法,椭圆曲线密码学,后量子密码学,并用于研究数论中的猜想和开放性问题,如黎曼猜想,贝赫和斯维讷通-戴尔猜想,Abc猜想,谷山-志村猜想,佐藤-泰特猜想,朗兰兹纲领等[1][2][3]
软件包
[编辑]延伸阅读
[编辑]- Eric Bach; Jeffrey Shallit. Algorithmic Number Theory, Volume 1: Efficient Algorithms. MIT Press. 1996 [2020-09-23]. ISBN 0-262-02405-5. (原始内容存档于2021-09-30).
- David M. Bressoud. Factorisation and Primality Testing
. Springer-Verlag. 1989. ISBN 0-387-97040-1.
- Joe P. Buhler; Peter Stevenhagen (编). Algorithmic Number Theory: Lattices, Number Fields, Curves and Cryptography. MSRI Publications 44. Cambridge University Press. 2008. ISBN 978-0-521-20833-8. Zbl 1154.11002.
- Henri Cohen. A Course In Computational Algebraic Number Theory. Graduate Texts in Mathematics 138. Springer-Verlag. 1993. ISBN 0-387-55640-0. doi:10.1007/978-3-662-02945-9.
- Henri Cohen. Advanced Topics in Computational Number Theory. Graduate Texts in Mathematics 193. Springer-Verlag. 2000. ISBN 0-387-98727-4. doi:10.1007/978-1-4419-8489-0.
- Henri Cohen. Number Theory – Volume I: Tools and Diophantine Equations. Graduate Texts in Mathematics 239. Springer-Verlag. 2007. ISBN 978-0-387-49922-2. doi:10.1007/978-0-387-49923-9.
- Henri Cohen. Number Theory – Volume II: Analytic and Modern Tools. Graduate Texts in Mathematics 240. Springer-Verlag. 2007. ISBN 978-0-387-49893-5. doi:10.1007/978-0-387-49894-2.
- Richard Crandall; Carl Pomerance. Prime Numbers: A Computational Perspective. Springer-Verlag. 2001. ISBN 0-387-94777-9. doi:10.1007/978-1-4684-9316-0.
- Hans Riesel. Prime Numbers and Computer Methods for Factorization. Progress in Mathematics 126 second. Birkhäuser. 1994. ISBN 0-8176-3743-5. Zbl 0821.11001.
- Victor Shoup. A Computational Introduction to Number Theory and Algebra. Cambridge University Press. 2012. ISBN 9781139165464. doi:10.1017/CBO9781139165464.
- Samuel S. Wagstaff, Jr. The Joy of Factoring. American Mathematical Society. 2013 [2020-09-23]. ISBN 978-1-4704-1048-3. (原始内容存档于2020-07-28).
参考
[编辑]- ^ 1.0 1.1 Carl Pomerance, Timothy Gowers , 编, Computational Number Theory (PDF), The Princeton Companion to Mathematics (Princeton University Press), 2009 [2020-09-23], (原始内容存档 (PDF)于2022-03-24)
- ^ Eric Bach; Jeffrey Shallit. Algorithmic Number Theory, Volume 1: Efficient Algorithms. MIT Press. 1996. ISBN 0-262-02405-5.
- ^ Henri Cohen. A Course In Computational Algebraic Number Theory. Graduate Texts in Mathematics 138. Springer-Verlag. 1993. ISBN 0-387-55640-0. doi:10.1007/978-3-662-02945-9.
链接
[编辑]维基共享资源上的相关多媒体资源:Computational number theory
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