Modern Computer Algebra

Author:   Joachim von zur Gathen ,  Jürgen Gerhard
Publisher:   Cambridge University Press
Edition:   3rd Revised edition
ISBN:  

9781107039032


Pages:   808
Publication Date:   25 April 2013
Format:   Hardback
Availability:   Manufactured on demand   Availability explained
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Modern Computer Algebra


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Full Product Details

Author:   Joachim von zur Gathen ,  Jürgen Gerhard
Publisher:   Cambridge University Press
Imprint:   Cambridge University Press
Edition:   3rd Revised edition
Dimensions:   Width: 18.30cm , Height: 4.10cm , Length: 24.90cm
Weight:   1.770kg
ISBN:  

9781107039032


ISBN 10:   1107039037
Pages:   808
Publication Date:   25 April 2013
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   Manufactured on demand   Availability explained
We will order this item for you from a manufactured on demand supplier.

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.

Reviews

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 fur 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 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


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 fur 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


Reviews of previous editions: 'Wow! What a beautifully produced book, and what a wealth of information.' Don Knuth, Stanford University, California '... 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 fur 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


Author Information

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 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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