Joachim von zur Gathen, Jürgen GerhardCambridge University PressEdition: 3, 4/25/2013EAN 9781107039032, ISBN10: 1107039037Hardcover, 808 pages, 24.9 x 18.3 x 4.1 cmLanguage: EnglishComputer 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.Introduction1. Cyclohexane, cryptography, codes, and computer algebraPart I. Euclid2. Fundamental algorithms3. The Euclidean Algorithm4. Applications of the Euclidean Algorithm5. Modular algorithms and interpolation6. The resultant and gcd computation7. Applicationdecoding BCH codesPart II. Newton8. Fast multiplication9. Newton iteration10. Fast polynomial evaluation and interpolation11. Fast Euclidean Algorithm12. Fast linear algebra13. Fourier Transform and image compressionPart III. Gauß14. Factoring polynomials over finite fields15. Hensel lifting and factoring polynomials16. Short vectors in lattices17. Applications of basis reductionPart IV. Fermat18. Primality testing19. Factoring integers20. Applicationpublic key cryptographyPart V. Hilbert21. Gröbner bases22. Symbolic integration23. Symbolic summation24. ApplicationsAppendix25. Fundamental conceptsSources of illustrationsSources of quotationsList of algorithmsList of figures and tablesReferencesList of notationIndex.Reviews of previous editions: 'Wow! What a beautifully produced book, and what a wealth of information.' Don Knuth, Stanford University
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