Modern Computer Algebra

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.

Joachim von zur Gathen has a PhD from Universitat Zurich 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 Universitat Bonn. Jurgen Gerhard has a PhD from Universitat 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.

Reviews of previous editions: 'Wow! What a beautifully produced book, and what a wealth of information.' Don Knuth, Stanford University '... 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.' Jeffrey O. Shallit, Mathematical Reviews 'I find the quality of this book really exceptional ...' Zentralblatt fur Mathematik 'This book is a delight: I heartily recommend it.' Alistair Fitt, London Mathematical Society Newsletter 'On each page I can feel [the authors'] thorough understanding and love for the subject and [their] uncompromising scholarship in presenting this story. A masterpiece.' Erich Kaltofen, North Carolina State University 'I predict it will be a major success.' Steve Cook, University of Toronto 'It's really an impressive work. I'm sure it will become a reference for computer algebra algorithms, and stay it for a long time. Such a reference book was really missing.' Paul Zimmermann, Universite de Nancy, France 'I think it's a most successful balance of intuition, rigorous mathematics, interesting and beautiful applications and completeness. The extensive collection of exercises makes it into an ideal textbook for the use in a graduate course.' Ton Levelt, Radboud University Nijmegen