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Titlebook: Computational Algebraic Number Theory; Michael E. Pohst Book 1993 Springer Basel AG 1993 Algebra.coding theory.cryptography.finite field.g

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發(fā)表于 2025-3-21 16:39:26 | 只看該作者 |倒序瀏覽 |閱讀模式
書目名稱Computational Algebraic Number Theory
編輯Michael E. Pohst
視頻videohttp://file.papertrans.cn/233/232089/232089.mp4
叢書名稱Oberwolfach Seminars
圖書封面Titlebook: Computational Algebraic Number Theory;  Michael E. Pohst Book 1993 Springer Basel AG 1993 Algebra.coding theory.cryptography.finite field.g
描述Computational algebraic number theory has been attracting broad interest in the last few years due to its potential applications in coding theory and cryptography. For this reason, the Deutsche Mathematiker Vereinigung initiated an introductory graduate seminar on this topic in Düsseldorf. The lectures given there by the author served as the basis for this book which allows fast access to the state of the art in this area. Special emphasis has been placed on practical algorithms - all developed in the last five years - for the computation of integral bases, the unit group and the class group of arbitrary algebraic number fields. Contents: Introduction ? Topics from finite fields ? Arithmetic and polynomials ? Factorization of polynomials ? Topics from the geometry of numbers ? Hermite normal form ? Lattices ? Reduction ? Enumeration of lattice points ? Algebraic number fields ? Introduction ? Basic Arithmetic ? Computation of an integral basis ? Integral closure ? Round-Two-Method ? Round-Four-Method ? Computation of the unit group ? Dirichlet‘s unit theorem and a regulator bound ? Two methods for computing r independent units ? Fundamental unit computation ? Computation of the cla
出版日期Book 1993
關(guān)鍵詞Algebra; coding theory; cryptography; finite field; geometry; mathematics; number theory
版次1
doihttps://doi.org/10.1007/978-3-0348-8589-8
isbn_softcover978-3-7643-2913-6
isbn_ebook978-3-0348-8589-8Series ISSN 1661-237X Series E-ISSN 2296-5041
issn_series 1661-237X
copyrightSpringer Basel AG 1993
The information of publication is updating

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沙發(fā)
發(fā)表于 2025-3-21 20:43:47 | 只看該作者
Topics from finite fields, and . a . of ., i.e. .. = 〈.〉. In general, arithmetic in . will be done by using two representations for its elements .:(i).,(ii)..Then addition and subtraction is done by the first, multiplication and division by the second representation. Thus all we need are two tables allowing to switch from on
板凳
發(fā)表于 2025-3-22 03:46:22 | 只看該作者
Topics from the geometry of numbers,ater chapters. All results can be easily generalized to principal entire rings . For practical calculations, however, we need a Euclidean division algorithm in . for the computation of the greatest common divisor of two elements. Proofs of Lemmata 1.1, 1.2, 1.6, 1.7 and Theorem 1.3, 1.5 for principa
地板
發(fā)表于 2025-3-22 05:29:40 | 只看該作者
Algebraic number fields,called the . of .. Clearly, ?(.) = . ? ?[.].(.)?[.], and the successive powers l, .,…, .. form a basis of . over ?. For describing the arithmetic in . we will need the counterpart of the rational integers in . These integers of . are defined as those elements of . which are .., i.e. zeros of monic n
5#
發(fā)表于 2025-3-22 09:19:18 | 只看該作者
Computation of an integral basis,… until .. = .. for some . ∈ ?.. Prom our considerations in chapter III we know that . is in ?. since that quotient equals the absolute value of the determinant of a transition matrix from a basis of .. to a basis of ... Prom chapters III, IV we recall that ∣d(.)∣ = .(..)., ∣..∣ = .(..).. Since with
6#
發(fā)表于 2025-3-22 16:14:51 | 只看該作者
7#
發(fā)表于 2025-3-22 19:47:08 | 只看該作者
Book 1993ion ? Basic Arithmetic ? Computation of an integral basis ? Integral closure ? Round-Two-Method ? Round-Four-Method ? Computation of the unit group ? Dirichlet‘s unit theorem and a regulator bound ? Two methods for computing r independent units ? Fundamental unit computation ? Computation of the cla
8#
發(fā)表于 2025-3-22 23:46:36 | 只看該作者
9#
發(fā)表于 2025-3-23 03:18:47 | 只看該作者
Introduction,olving non-linear Diophantine equations, in factoring with the number field sieve and in carrying out numerical experiments in number fields. We illustrate their importance by two introductory examples.
10#
發(fā)表于 2025-3-23 05:57:31 | 只看該作者
https://doi.org/10.1007/978-1-4615-7918-2olving non-linear Diophantine equations, in factoring with the number field sieve and in carrying out numerical experiments in number fields. We illustrate their importance by two introductory examples.
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