Computer algebra systems are gaining more and more importance in all areas of science and engineering. This textbook gives a thorough introduction to the subject, which is the 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. However its comprehensiveness and authority will mean it will be an essential reference also for professionals in the area. Special features include: detailed study of algorithmics including time analysis; implementation reports on several topics; complete proofs of the mathematical underpinnings; a wide variety of applications (including in chemistry, coding theory, cryptography, 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 is included.
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Book Description
Editorial Reviews
Review
' ... a most fascinating and readable survey of methods that are used by modern Computer Algebra Systems (CAS's). This book is a delight; I heartly recommend it (a) to anybody who has any interest at all in how their CAS works and (b) to anybody who enjoys seeing elegant and rigorous mathematics applied to practical problems.' Alistair Fitt, University of Southampton
'Wow! What a beautifully produced book, and what a wealth of information! Also written in perfect idiomatic English by two German authors' Don Knuth
' ... a pleasure to read. I predict it will be a major success.' Steve Cook
'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.' Paul Zimmermann
'This book is a delight; I heartily recommend it to anybody who has interest at all in how their CAS works and anybody who enjoys seeing elegant and rigorous mathematics applied to practical problems.' Alistair Fitt
'On each page I can feel thorough understanding and love for the subject and uncompromising scholarship in presenting its story. A masterpiece.' Erich Kaltofen
' ... a wonderful book! I am working my way through it (for what will probably be the first of many times), and am very pleased with it ... aesthetically beautiful, with the color plots and multitudes of epigraphs for each chapter.' Todd Moon
' ... it looks stunning! ...' Hendrik Lenstra
' ... 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
'The style is very clear. The arguments are very precise. In my opinion, the level of presentation is convenient for graduate students, some parts are quite readable for good undergraduate students. The typography and the quality of illustration of this Cambridge book are splendid. To conclude, I find the quality of this book really exceptional, this is certainly an excellent source on the state of the art in computer algebra.' Maurice Mignottte, Zbl. MATH
'... a welcome survey of a fast-gorwing and toical area of modern mathematics and computer science.' European Maths Society Journal
'Wow! What a beautifully produced book, and what a wealth of information! Also written in perfect idiomatic English by two German authors' Don Knuth
' ... a pleasure to read. I predict it will be a major success.' Steve Cook
'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.' Paul Zimmermann
'This book is a delight; I heartily recommend it to anybody who has interest at all in how their CAS works and anybody who enjoys seeing elegant and rigorous mathematics applied to practical problems.' Alistair Fitt
'On each page I can feel thorough understanding and love for the subject and uncompromising scholarship in presenting its story. A masterpiece.' Erich Kaltofen
' ... a wonderful book! I am working my way through it (for what will probably be the first of many times), and am very pleased with it ... aesthetically beautiful, with the color plots and multitudes of epigraphs for each chapter.' Todd Moon
' ... it looks stunning! ...' Hendrik Lenstra
' ... 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
'The style is very clear. The arguments are very precise. In my opinion, the level of presentation is convenient for graduate students, some parts are quite readable for good undergraduate students. The typography and the quality of illustration of this Cambridge book are splendid. To conclude, I find the quality of this book really exceptional, this is certainly an excellent source on the state of the art in computer algebra.' Maurice Mignottte, Zbl. MATH
'... a welcome survey of a fast-gorwing and toical area of modern mathematics and computer science.' European Maths Society Journal
Book Description
Computer algebra systems are gaining more and more importance in all areas of science and engineering. This textbook gives a thorough introduction to the subject. It is designed as a textbook for students in computer science or mathematics. However its comprehensiveness and authority will mean it will be an essential reference also for professionals in the area.
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Most Helpful Customer Reviews
5 of 5 people found the following review helpful:
5.0 out of 5 stars
Very nice,
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This review is from: Modern Computer Algebra (Hardcover)
This is a very nicely written text, comprehensive in what it aims to cover. The illustrations are plentiful and very helpful. The material is mostly self-contained and presented in a novel way (Fermat, Euler, Hilbert each have their own groups of sections!).
This is the best treatment I've seen for lattice basis reduction (a topic treated in many other texts) as well as for polynomial factoring over fields (Cantor Zassenhaus) and other topics. I've read parts of this book that were irrelevant for my research simply because the book is a joy to read. Highly recommended to anyone with an interest and some degree of mathematical maturity. The only drawback is that my edition has a number of typos, some serious (however the authors do provide an online corrigenda).
7 of 11 people found the following review helpful:
4.0 out of 5 stars
MCA - very adequate book on computer algebra topics,
By gilgamash (cologne, Germany) - See all my reviews
This review is from: Modern Computer Algebra (Hardcover)
Covering a lot of topics on "Computer Algebra" this book is a fine workout. Many mathematical proofs are provided and most subjects are explained and outlined very accurately. Only sometimes things can not as easily be seen as the author clames. The homepage of Mr. von zur Gathen provides a postscript file with corrections and additions and even more one containing solutions to many of the given exercises.
3 of 10 people found the following review helpful:
4.0 out of 5 stars
State-of-the-art in CAS,
By Luca De Santis (Avezzano, AQ Italy) - See all my reviews
This review is from: Modern Computer Algebra (Hardcover)
I am a C programmer and this book was fundamental to introduce myself in the field of computer algebra systems (CAS). It's very well structured and at the state-of-the-art in that discipline. The only remarks is about the strong presence of author's mother-tongue influences in some English phrases.
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Inside This Book
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First Sentence:
Little is known about the person of Euclid ( , c. 320-c. 275 BC). Read the first page Key Phrases - Capitalized Phrases (CAPs): (learn more)
Fourier Transform, Chinese Remainder Algorithm, Chinese Remainder Theorem, Discrete Cosine Transform, Prove Lemma, Unique Factorization Domain, Carl Friedrich, Chinese Remainder Problem, Las Vegas, Victor Shoup, Augustus De Morgan, Extended Riemann Hypothesis, Monte Carlo, Compute the Fourier, Emmy Noether, Hendrik Lenstra, James Joseph Sylvester, Multifactor Hensel, Sesame Street, William Shanks New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Little is known about the person of Euclid ( , c. 320-c. 275 BC). Read the first page Key Phrases - Capitalized Phrases (CAPs): (learn more)
Fourier Transform, Chinese Remainder Algorithm, Chinese Remainder Theorem, Discrete Cosine Transform, Prove Lemma, Unique Factorization Domain, Carl Friedrich, Chinese Remainder Problem, Las Vegas, Victor Shoup, Augustus De Morgan, Extended Riemann Hypothesis, Monte Carlo, Compute the Fourier, Emmy Noether, Hendrik Lenstra, James Joseph Sylvester, Multifactor Hensel, Sesame Street, William Shanks New!
Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 100
books:
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55
books
cite this book:
See all 55 books citing this book
- Cryptology and Computational Number Theory (Proceedings of Symposia in Applied Mathematics) by Carl Pomerance on 5 pages
- Men of Mathematics (Touchstone Books) by E.T. Bell on 4 pages
- Computer Science: A Breadth-First Approach with C by John Impagliazzo in Back Matter (1), Back Matter (2), and Back Matter (3)
- Don Quixote (English Picture Readers) by Miguel De Cervantes Saavedra on page 82, and Back Matter
- Disquisitiones Arithmeticae by Carl F. Gauss on page 348, and Back Matter
See all 100 books this book cites
- Selected Areas in Cryptography: 12th International Workshop, SAC 2005, Kingston, ON, Canada, August 11-12, 2005, Revised Selected Papers (Lecture Notes in Computer Science / Security and Cryptology) by Bart Preneel on page 81, and Back Matter
- Computing with Maple (Chapman Hall/CRC Mathematics Series) by Francis Wright on page 5, and Back Matter
- Comprehensive Mathematics for Computer Scientists 1 by Guerino B. Mazzola in Back Matter (1), and Back Matter (2)
- Computeralgebra (Springer-Lehrbuch Masterclass) (German Edition) by Michael Kaplan on page 4, and Back Matter
- Secure Communicating Systems: Design, Analysis, and Implementation by Michael R. A. Huth in Back Matter
See all 55 books citing this book
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