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.
Successful advanced textbook and reference on computer algebra for computer scientists and mathematicians.
From reviews of the first edition: 'Wow! What a beautifully produced book, and what a wealth of information.' Don Knuth 'This book is a delight: I heartily recommend it.' London Mathematical Society Newsletter 'I predict it will be a major success.' Steve Cook 'I predict it will be a major success.' Steve Cook 'I find the quality of this book really exceptional ...'. Zentralblatt fur Mathematik '... this lively and exciting volume represents the state of the art in textbooks on computer algebra. Every student and instructor in this area will want a copy.' Mathematical Reviews
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