Tables of Contents for Modern Computer Algebra

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Chapter/Section Title

Page #

Page Count

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. Grö

bner 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.