Description
Book Synopsis
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 th
Trade Review
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
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.
