About this product

Product Identifiers

PublisherCambridge University Press

ISBN-100521641764

ISBN-139780521641760

eBay Product ID (ePID)1007927

Product Key Features

Number of Pages771 Pages

Publication NameModern Computer Algebra

LanguageEnglish

Publication Year1999

SubjectGeneral, Algebra / General

TypeTextbook

AuthorJürgen Gerhard, Joachim Von Zur Gathen

Subject AreaMathematics, Computers

FormatHardcover

Dimensions

Item Height1.6 in

Item Weight59.4 Oz

Item Length10 in

Item Width7.1 in

Additional Product Features

Intended AudienceScholarly & Professional

LCCN99-232072

Dewey Edition21

Reviews‘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 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, '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, ‘… a welcome survey of a fast-gorwing and toical area of modern mathematics and computer science.’European Maths Society Journal, '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, '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, '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, ' â€¦ 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, ' ... 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, 'Wow! What a beautifully produced book, and what a wealth of information! Also written in perfect idiomatic English by two German authors'Don Knuth, '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 welcome survey of a fast-gorwing and toical area of modern mathematics and computer science.' European Maths Society Journal, '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 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, ' ... 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, ' â€¦ 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 â€¦ aesthetically beautiful, with the color plots and multitudes of epigraphs for each chapter.' Todd Moon, '... a welcome survey of a fast-gorwing and toical area of modern mathematics and computer science.'European Maths Society Journal, '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 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, ' â€¦ 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, ‘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, '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 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, ‘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, ' ... 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, ' ... 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, ‘ … 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, 'â€¦ a welcome survey of a fast-gorwing and toical area of modern mathematics and computer science.' European Maths Society Journal, ‘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

IllustratedYes

Dewey Decimal512/.00285

Table Of ContentIntroduction; 1. Cyclohexane, cryptography, codes, and computer algebra; 2. Fundamental algorithms; 3. The Euclidean algorithm; 4. Applications of the Euclidean algorithm; 5. Interpolation and modular algorithms; 6. The resultant and gcd computation; 7. Application: decoding BCH codes; 8. Fast multiplication; 9. Newton iteration; 10. Fast polynomial evaluation and interpolation; 11. Fast Euclidean algorithm; 12. Fast linear algebra; 13. Fourier transforms, signal processing, 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 testing; 19. Factoring integers; 20. Application: public key cryptography; 21. Gröbner bases; 22. Symbolic integration; 23. Symbolic summation; 24. Applications; 25. Fundamental concepts; References.

SynopsisComputer 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., 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.

LC Classification NumberQA155.7.E4 Z87 1999