Modern Computer Algebra

Joachim von zur Gathen has a PhD from Universität Zürich and has taught at the University of Toronto and the University of Paderborn. He is currently a professor at the Bonn-Aachen International Center for Information Technology (B-IT) and the Department of Computer Science at Universität Bonn. Jürgen Gerhard has a PhD from Universität Paderborn. He is now Director of Research at Maplesoft in Canada, where he leads research collaborations with partners in Canada, France, Russia, Germany, the USA and the UK, as well as a number of consulting projects for global players in the automotive industry.

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.