Modern Computer Algebra

Joachim Zur Gathen & Jürgen Gerhard "Modern Computer Algebra"
(Note: the cover image is from the 2nd. edition, it is just illustrative)
Publisher: Cambridge University Press | ISBN: 0521641764 | 1st. ed. 1999 | djvu | 767 pages | English | 10 MB
“Computer algebra systems are gaining importance in all areas of science and engineering. This textbook gives a thorough introduction to the algorithmic basis of the mathematical engine in computer algebra systems. It is designed to accompany one- or two-semester courses for advanced undergraduate or graduate students in computer science or mathematics. Its comprehensiveness and authority also make it an essential reference for professionals in the area.”

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.


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