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Titlebook: Computer Algebra; An Algorithm-Oriente Wolfram Koepf Textbook 2021 Springer Nature Switzerland AG 2021 Computer algebra textbook.Computer a

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发表于 2025-3-21 17:43:53 | 显示全部楼层 |阅读模式
书目名称Computer Algebra
副标题An Algorithm-Oriente
编辑Wolfram Koepf
视频video
概述Balances theoretical and practical aspects with an implementation-oriented approach.Guides readers through numerous hands-on tutorials to build practical skills and algorithmic thinking.Supports three
丛书名称Springer Undergraduate Texts in Mathematics and Technology
图书封面Titlebook: Computer Algebra; An Algorithm-Oriente Wolfram Koepf Textbook 2021 Springer Nature Switzerland AG 2021 Computer algebra textbook.Computer a
描述.This textbook offers an algorithmic introduction to the field of computer algebra. A leading expert in the field, the author guides readers through numerous hands-on tutorials designed to build practical skills and algorithmic thinking. This implementation-oriented approach equips readers with versatile tools that can be used to enhance studies in mathematical theory, applications, or teaching. Presented using .Mathematica. code, the book is fully supported by downloadable sessions in .Mathematica., .Maple., and .Maxima....Opening with an introduction to computer algebra systems and the basics of programming mathematical algorithms, the book goes on to explore integer arithmetic. A chapter on modular arithmetic completes the number-theoretic foundations, which are then applied to coding theory and cryptography. From here, the focus shifts to polynomial arithmetic and algebraic numbers, with modern algorithms allowing the efficient factorization of polynomials. The final chapters offer extensions into more advanced topics: simplification and normal forms, power series, summation formulas, and integration...Computer Algebra. is an indispensable resource for mathematics and computer
出版日期Textbook 2021
关键词Computer algebra textbook; Computer algebra reference; Maple algebra; Mathematica algebra; Maxima algebr
版次1
doihttps://doi.org/10.1007/978-3-030-78017-3
isbn_softcover978-3-030-78019-7
isbn_ebook978-3-030-78017-3Series ISSN 1867-5506 Series E-ISSN 1867-5514
issn_series 1867-5506
copyrightSpringer Nature Switzerland AG 2021
The information of publication is updating

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发表于 2025-3-21 23:58:08 | 显示全部楼层
1867-5506 ters offer extensions into more advanced topics: simplification and normal forms, power series, summation formulas, and integration...Computer Algebra. is an indispensable resource for mathematics and computer 978-3-030-78019-7978-3-030-78017-3Series ISSN 1867-5506 Series E-ISSN 1867-5514
发表于 2025-3-22 02:07:11 | 显示全部楼层
https://doi.org/10.1007/978-3-030-13431-0Before we discuss mathematical algorithms and their programming, we want to show the capabilities of a general computer algebra system such as . (The same questions can be also treated with the systems . and .,and the corresponding worksheets can be downloaded from .).
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https://doi.org/10.1007/978-3-030-13431-0The integers with their operations addition and multiplication . form a commutative ring with unity 1. Now, we would like to translate this algebraic structure to finite subsets of .. This is done by identification of certain elements in . that lie in common arithmetic progressions.
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Systems Engineering & ManagementIn the sequel (if not stated otherwise), we assume that . is a zero-divisor-free ring with unity 1. Such a ring is called an integral domain.
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https://doi.org/10.1007/978-1-4614-6663-5The aim of this chapter is the development of efficient algorithms for factorization in ℚ[.]. For this purpose, efficient factorization algorithms for ℤ.[.] are used which, of course, are interesting by themselves.
发表于 2025-3-23 09:10:59 | 显示全部楼层
https://doi.org/10.1007/978-1-4614-6663-5If we call a simplification command like ., ., . or . in ., then algebraic expressions are replaced by (hopefully) mathematically equivalent ones. Therefore the general question arises under which circumstances such transformations are possible and which types of simplifications can be executed.
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