Computer Algebra Systems Are Now Ubiquitous In All Areas Of Science And Engineering. This Highly Successful Textbook, Widely Regarded As The Bible Of Computer Algebra, Gives A Thorough Introduction To The Algorithmic Basis Of The Mathematical Engine In Computer Algebra Systems. Designed To Accompany One- Or Two- Semester Courses For Advanced Undergraduate Or Graduate Students In Computer Science Or Mathematics, Its Comprehensiveness And Reliability Has Also Made It An Essential Reference For Professionals In The Area. Special Features Include: Detailed Study Of Algorithms Including Time Analysis; Implementation Reports On Several Topics; Complete Proofs Of The Mathematical Underpinnings; And A Wide Variety Of Applications (among Others, In Chemistry, Coding Theory, Crytopgraphy, Computational Logic, And The Design Of Calendars And Musical Scales). A Great Deal Of Historical Information And Illustration Enlivens The Text. 1. Cyclohexane, Cryptography, Codes, And Computer Algebra -- 2. Fundamental Algorithms -- 3. The Euclidean Algorithm -- 4. Applications Of The Euclidean Algorithm -- 5. Modular Algorithms And Interpolation -- 6. The Resultant And Ged Computation -- 7. Application: Decoding Bcd Codes -- 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 -- 14. Factoring Polynomials Over Finite Fields -- 15. Hensel Lifting And Factoring Polynomials -- 16. Short Vectors In Lattices -- 17. Applications Of Basis Reduction -- 18. Primality -- 19. Factoring Integers -- 20. Application: Public Key Cryptography -- 21. Gröbner Bases -- 22. Symbolic Integration -- 23. Symbolic Summation -- 24. Applications -- 25. Fundamental Concepts . Joachim Von Zur Gathen, Jürgen Gerhard. Includes Bibliographical References (p. 734-767) And Index.