Computer algebra systems are gaining 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 also make it 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. For the new edition, errors have been corrected, the text has been smoothed and updated, and new sections on greatest common divisors and symbolic integration have been added.
Rezensionen / Stimmen
From reviews of the first edition: 'Wow! What a beautifully produced book, and what a wealth of information.' Don Knuth 'This book is a delight: I heartily recommend it.' London Mathematical Society Newsletter 'I predict it will be a major success.' Steve Cook, University of Toronto 'I find the quality of this book really exceptional ...'. Zentralblatt fuer Mathematik '... this lively and exciting volume represents the state of the art in textbooks on computer algebra. Every student and instructor in this area will want a copy.' Mathematical Reviews
Auflage
Sprache
Verlagsort
Zielgruppe
Für Beruf und Forschung
Für höhere Schule und Studium
Editions-Typ
Illustrationen
Worked examples or Exercises; 29 Tables, unspecified; 54 Line drawings, color
Maße
Höhe: 256 mm
Breite: 182 mm
Dicke: 42 mm
Gewicht
ISBN-13
978-0-521-82646-4 (9780521826464)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Klassifikation
Autor*in
Universitaet-Gesamthochschule Paderborn, Germany
Universitaet-Gesamthochschule Paderborn, Germany
Introduction; 1. Cyclohexane, cryptography, codes and computer algebra; Part I. Euclid: 2. Fundamental algorithms; 3. The Euclidean algorithm; 4. Applications of the Euclidean algorithm; 5. Modular algorithms and interpolation; 6. The resultant and gcd computation; 7. Application: decoding BCH codes; Part II. Newton: 8. Fast multiplication; 9. Newton iteration; 10. Fast polynomial evaluation and interpolation; 11. Fast Euclidean algorithm; 12. Fast linear algebra; 13. Fourier Transform and image compression; Part III. Gauss: 14. Factoring polynomials over finite fields; 15. Hensel lifting and factoring polynomials; 16. Short vectors in lattices; 17. Applications of basis reduction; Part IV. Fermat: 18. Primality testing; 19. Factoring integers; 20. Application: public key cryptography; Part V. Hilbert: 21. Groebner bases; 22. Symbolic integration; 23. Symbolic summation; 24. Applications; Appendix: 25. Fundamental concepts; Sources of illustrations; Sources of quotations; List of algorithms; List of figures and tables; References; List of notation; Index.
