Modern Computer Algebra

Textbook, 2nd edition, Cambridge University Press 2003 (US site).

Computer algebra systems are gaining more and more importance in all areas of science and engineering. This textbook gives a thorough introduction to the algorithmic basis of the mathematical engine in computer algebra systems.

It is designed to accompany one- or two-semester courses for advanced undergraduate or graduate students in computer science or mathematics. Its comprehensiveness and authority make it also 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; a wide variety of applications (among others, in chemistry, coding theory, cryptography, computational logic, and the design of calendars and musical scales). Some of this material has never appeared before in book form. Finally, a great deal of historical information and illustration enlivens the text.

Besides many corrections and updates, Chapters 3 (Euclidean Algorithm), 15 (Hensel lifting), and 22 (Symbolic integration) were revised and extended in the 2nd edition.

Opinions ...

Reviews:

• Alistair Fitt, LMS Newsletter, October 1999, London Mathematical Society, pp. 19-20
• Richard Fateman, Computing Reviews, October 1999, ACM, p. 472
• Jeffrey Shallit (from Mathematical Reviews)
• Maurice Mignotte (from Zentralblatt MATH)
• B. H. Matzat, Computeralgebra-Rundbrief, Vol 27, October 2000, Fachgruppe Computeralgebra GI-DMV-GAMM, pp. 35-36
• Robert Corless, ACM SIGSAM Bulletin, Vol 35, No. 1, March 2001, pp. 8-13
• R. Gregory Taylor, ACM SIGACT News, Vol 33, No. 3, September 2002, pp. 7-14

Stuff to download

• Contents, Introduction, and Leitfaden (postscript 147k, gzipped 50k), © Cambridge University Press 2003

• The cyclohexane computations (Maple worksheet), © Joachim von zur Gathen and Jürgen Gerhard 1999

• Exercises to Chapter 25: Fundamental concepts (postscript 407k, gzipped 102k), © Joachim von zur Gathen and Jürgen Gerhard 1999

• Solutions to selected exercises (postscript 1300k, gzipped 427k), © Joachim von zur Gathen and Jürgen Gerhard 1999-2003

• Addenda and corrigenda 2009, second edition (PDF, PostScript)

• Addenda and corrigenda second edition (postscript 223k, gzipped 82k), sorted by date (postscript, gzipped), sorted by contributor (postscript, gzipped)

• Addenda and corrigenda first edition (postscript 426k, gzipped 155k), sorted by date (postscript, gzipped), sorted by contributor (postscript, gzipped)

Gallery

• Cyclohexane conformations

• Musical scales

• Fast multiplication

• Newton iteration

• Polynomial factorization

• Elliptic curves

• A robot

• The twisted cubic