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Titlebook: A Course in Computational Algebraic Number Theory; Henri Cohen Textbook 1993 Springer-Verlag GmbH Germany, part of Springer Nature 1993 Al

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期刊全称A Course in Computational Algebraic Number Theory
影响因子2023Henri Cohen
视频video
发行地址Immediate bestselling graduate textbook
学科分类Graduate Texts in Mathematics
图书封面Titlebook: A Course in Computational Algebraic Number Theory;  Henri Cohen Textbook 1993 Springer-Verlag GmbH Germany, part of Springer Nature 1993 Al
影响因子With the advent of powerful computing tools and numerous advances in math­ ematics, computer science and cryptography, algorithmic number theory has become an important subject in its own right. Both external and internal pressures gave a powerful impetus to the development of more powerful al­ gorithms. These in turn led to a large number of spectacular breakthroughs. To mention but a few, the LLL algorithm which has a wide range of appli­ cations, including real world applications to integer programming, primality testing and factoring algorithms, sub-exponential class group and regulator algorithms, etc ... Several books exist which treat parts of this subject. (It is essentially impossible for an author to keep up with the rapid pace of progress in all areas of this subject.) Each book emphasizes a different area, corresponding to the author‘s tastes and interests. The most famous, but unfortunately the oldest, is Knuth‘s Art of Computer Programming, especially Chapter 4. The present book has two goals. First, to give a reasonably comprehensive introductory course in computational number theory. In particular, although we study some subjects in great detail, others are only men
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0072-5285 and cryptography, algorithmic number theory has become an important subject in its own right. Both external and internal pressures gave a powerful impetus to the development of more powerful al­ gorithms. These in turn led to a large number of spectacular breakthroughs. To mention but a few, the LLL
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Global Culture and Sport Serieso implement them, at least in unoptimized form. The reader who wants to implement these methods in a more optimized form is urged to read the abundant literature after reading this chapter, before doing so.
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African Feminisms and Justice on the Ground,in particular the Birch and Swinnerton-Dyer conjecture) were direct consequences of number-theoretical experiments. This lends further support to the claim that number theory, even in its sophisticated areas, is an experimental as well as a theoretical science.
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A Theoretical Research Frameworkple, solving a linear system of equations is such a problem. Apart from stability considerations, such problems and algorithms can be solved by a single algorithm independently of the base field (or more generally of the base ring if we work with modules). Those algorithms will naturally be called .
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