000			02859nam a22001817a 4500
005			20240926100217.0
008			240926b |||||||| |||| 00| 0 eng d
020			_a9781107039032
082			_a512.002 _bGAT
100			_a Gathen,Joachim von zur
245			_aModern Computer Algebra _cJoachim von zur Gathen
250			_a3RD
260			_aLondon _bCambridge _c2013
300			_a795p
505			_tIntroduction 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.
520			_aComputer 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
942			_2ddc _cBK
999			_c2424 _d2424