Modern Computer Algebra

Modern Computer Algebra


Joachim von zur Gathen and Jürgen Gerhard.

b-it cosec,                                          Team Lead Mathematical Software,
University of Bonn, Germany.            Maplesoft, Canada.
Formerly both:
Textbook, 3rd edition, Cambridge University Press 2013 (publisher 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.
ISBN 978-1107039032.
808 pages, 55 b/w illustrations, 53 colour illustrations, 40 tables, 560 exercises.
(Second edition 2003: ISBN 978-0521826464.)
(First edition 1999: ISBN 0521641764.)



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

Addenda and corrigenda

Addenda and corrigenda, third and earlier editions (PDF as of 08 April 2016).

Stuff to download

  • GuidelineContents, Introduction, and Leitfaden (PDF). © Cambridge University Press 2003.
  • Cyclohexane illustrationThe cyclohexane computations (Maple worksheet). © Joachim von zur Gathen and Jürgen Gerhard 1999.
  • Complexity classesExercises to Chapter 25: Fundamental concepts (PDF). © Joachim von zur Gathen and Jürgen Gerhard 1999.
  • SolutionsSolutions to selected exercises (PDF). © Joachim von zur Gathen and Jürgen Gerhard 1999-2003.
  • Addenda & corrigendaAddenda and corrigenda, third and earlier edition (PDF as of 16 December 2013).
  • Addenda & corrigendaAddenda and corrigenda, second edition (PDF as of 31 January 2011).
  • Addenda & corrigendaAddenda and corrigenda second edition (PDFsorted by date PDFsorted by contributor PDF).
  • Addenda & corrigendaAddenda and corrigenda first edition (PDFsorted by date PDFsorted by contributor PDF).

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