Computer algebra an algorithm-oriented introduction / [electronic resource] :

• 作者： Koepf, Wolfram.
• 其他作者：
  • SpringerLink (Online service)
• 其他題名：
  • Computeralgebra.
  • Springer undergraduate texts in mathematics and technology.
• 出版： Cham : Springer International Publishing :Imprint: Springer
• 叢書名： Springer undergraduate texts in mathematics and technology,
• 主題： Algebra--Data processing. , Computer science--Mathematics. , Computer algorithms. , Algebra. , Symbolic and Algebraic Manipulation. , Algorithms. , Mathematical Software.
• ISBN： 9783030780173 (electronic bk.) 、 9783030780166 (paper)
• FIND@SFXID: CGU
• 資料類型: 電子書
• 內容註: 1. Introduction to Computer Algebra -- 2. Programming in Computer Algebra Systems -- 3. Number Systems and Integer Arithmetic -- 4. Modular Arithmetic -- 5. Coding Theory and Cryptography -- 6. Polynomial Arithmetic -- 7. Algebraic Numbers -- 8. Factorization in Polynomial Rings -- 9. Simplification and Normal Forms -- 10. Power Series -- 11. Algorithmic Summation -- 12. Algorithmic Integration -- References -- List of Symbols -- Mathematica List of Keywords -- Index.
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• 摘要註: 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 science students new to the field. Numerous examples illustrate algorithms and their implementation throughout, with online support materials to encourage hands-on exploration. Prerequisites are minimal, with only a knowledge of calculus and linear algebra assumed. In addition to classroom use, the elementary approach and detailed index make this book an ideal reference for algorithms in computer algebra.
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