Modern Computer Algebra - ISBN:0521641764

Modern Computer Algebra

Date: 30 April 2011, 10:49

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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. Grobner 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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