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Modern Computer Algebra

3rd Edition

£82.00

  • Date Published: April 2013
  • availability: Available
  • format: Hardback
  • isbn: 9781107039032

£ 82.00
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Description
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Resources
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About the Authors
  • Computer algebra systems are now ubiquitous in all areas of science and engineering. This highly successful textbook, widely regarded as the 'bible of computer algebra', gives a thorough introduction to the algorithmic basis of the mathematical engine in computer algebra systems. Designed to accompany one- or two-semester courses for advanced undergraduate or graduate students in computer science or mathematics, its comprehensiveness and reliability has also made it an essential reference for professionals in the area. Special features include: detailed study of algorithms including time analysis; implementation reports on several topics; complete proofs of the mathematical underpinnings; and a wide variety of applications (among others, in chemistry, coding theory, cryptography, computational logic, and the design of calendars and musical scales). A great deal of historical information and illustration enlivens the text. In this third edition, errors have been corrected and much of the Fast Euclidean Algorithm chapter has been renovated.

    • Detailed algorithms with analysis, and complete proofs (none left to the reader)
    • Student-friendly with gentle introductions and overviews
    • Includes many illustrations and applications and much historical background
    • Solutions to selected exercises are available from the book's webpage
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    Reviews & endorsements

    Review of previous edition: 'Wow! What a beautifully produced book, and what a wealth of information.' Don Knuth, Stanford University

    Review of previous edition: '… this lively and exciting volume represents the state of the art in textbooks on computer algebra. Every student and instructor in this area will want a copy.' Jeffrey O. Shallit, Mathematical Reviews

    'I find the quality of this book really exceptional …' Zentralblatt für Mathematik

    'This book is a delight: I heartily recommend it.' Alistair Fitt, London Mathematical Society Newsletter

    'On each page I can feel [the authors'] thorough understanding and love for the subject and [their] uncompromising scholarship in presenting this story. A masterpiece.' Erich Kaltofen, North Carolina State University

    'I predict it will be a major success.' Steve Cook, University of Toronto

    'It's really an impressive work. I'm sure it will become a reference for computer algebra algorithms, and stay it for a long time. Such a reference book was really missing.' Paul Zimmermann, Universite de Nancy, France

    'I think it's a most successful balance of intuition, rigorous mathematics, interesting and beautiful applications and completeness. The extensive collection of exercises makes it into an ideal textbook for the use in a graduate course.' Ton Levelt, Radboud University Nijmegen

    'I have to say that not only can one apply the book as a flexible textbook for many courses, but its comprehensiveness and clear style also make it an excellent reference text for computer science researchers and grad[uate] students, and anyone else interested in developing exact solution codes.' Alexander Tzanov, Computing Reviews

    '… a polished introduction to algorithms for performing algebraic operations on a computer … The book is almost as interesting for the advanced mathematics (mostly in ring and ideal theory and in linear algebra) that is needed to develop the algorithms. It assumes familiarity with the fundamentals of these topics, but does include a 25-page appendix summarizing the needed background. It is well-equipped with exercises, ranging from numerical practice to extensions and variants on results in the body.' Allen Stenger, MAA Reviews

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    Product details

    • Edition: 3rd Edition
    • Date Published: April 2013
    • format: Hardback
    • isbn: 9781107039032
    • length: 808 pages
    • dimensions: 249 x 183 x 41 mm
    • weight: 1.77kg
    • contains: 55 b/w illus. 53 colour illus. 40 tables 560 exercises
    • availability: Available
  • Table of Contents

    Introduction
    1. Cyclohexane, cryptography, codes, and computer algebra
    Part I. Euclid:
    2. Fundamental algorithms
    3. The Euclidean Algorithm
    4. Applications of the Euclidean Algorithm
    5. Modular algorithms and interpolation
    6. The resultant and gcd computation
    7. Application: decoding BCH codes
    Part II. Newton:
    8. Fast multiplication
    9. Newton iteration
    10. Fast polynomial evaluation and interpolation
    11. Fast Euclidean Algorithm
    12. Fast linear algebra
    13. Fourier Transform and image compression
    Part III. Gauß:
    14. Factoring polynomials over finite fields
    15. Hensel lifting and factoring polynomials
    16. Short vectors in lattices
    17. Applications of basis reduction
    Part IV. Fermat:
    18. Primality testing
    19. Factoring integers
    20. Application: public key cryptography
    Part V. Hilbert:
    21. Gröbner bases
    22. Symbolic integration
    23. Symbolic summation
    24. Applications
    Appendix:
    25. Fundamental concepts
    Sources of illustrations
    Sources of quotations
    List of algorithms
    List of figures and tables
    References
    List of notation
    Index.

  • Resources for

    Modern Computer Algebra

    Joachim von zur Gathen, Jürgen Gerhard

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  • Authors

    Joachim von zur Gathen, Bonn-Aachen International Center for Information Technology
    Joachim von zur Gathen has a PhD from Universität Zürich and has taught at the University of Toronto and the University of Paderborn. He is currently a professor at the Bonn-Aachen International Center for Information Technology (B-IT) and the Department of Computer Science at Universität Bonn.

    Jürgen Gerhard, Maplesoft, Canada
    Jürgen Gerhard has a PhD from Universität Paderborn. He is now Director of Research at Maplesoft in Canada, where he leads research collaborations with partners in Canada, France, Russia, Germany, the USA and the UK, as well as a number of consulting projects for global players in the automotive industry.

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