Modern Computer Algebra
Joachim von zur Gathen and Jürgen Gerhard
Research Group Algorithmic Mathematics
Department of Mathematics and Computer Science
University of Paderborn, Germany
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 twosemester 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. 1920
 Richard Fateman, Computing Reviews, October 1999, ACM, p. 472
 Jeffrey Shallit (from Mathematical Reviews)
 Maurice Mignotte (from Zentralblatt MATH)
 B. H. Matzat, ComputeralgebraRundbrief, Vol 27, October 2000, Fachgruppe Computeralgebra GIDMVGAMM, pp. 3536
 Robert Corless, ACM SIGSAM Bulletin, Vol 35, No. 1, March 2001, pp. 813
 R. Gregory Taylor, ACM SIGACT News, Vol 33, No. 3, September 2002, pp. 714
ISBN 0521826462
Price £ 40 (US $ 65).
xiv+786 pages, 132 figures and tables (54 colored), 102 algorithms, 563 exercises.
(First edition 1999: ISBN 0521641764.)
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 19992003

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
Useful computer algebra links
Author: Jürgen Gerhard, last change: 14 September 2003