Modern Computer Algebra

Joachim von zur Gathen, Jurgen Gerhard

800 pages, parution le 04/07/2003 (2^eme édition)

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Résumé

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.

Sommaire

Cyclohexane, cryptography, codes and computer algebra
Euclid
- Fundamental algorithms
- The Euclidean algorithm
- Applications of the Euclidean algorithm
- Modular algorithms and interpolation
- The resultant and gcd computation
- Application: Decoding BCH codes
Newton
- Fast multiplication
- Newton iteration
- Fast polynomial evaluation and interpolation
- Fast Euclidean algorithm
- Fast linear algebra
- Fourier transform and image compression
Gauss
- Factoring polynomials over finite fields
- Hensel lifting and factoring polynomials
- Short vectors in lattices
- Applications of basis reduction
Fermat
- Primality testing
- Factoring integers
- Application: Public key cryptography
Hilbert
- Gröbner bases
- Symbolic integration
- Symbolic summation
- Applications
Appendix
- Fundamental concepts
- Sources of illustrations
- Sources of quotations
- List of algorithms
- List of figures and tables
- References
- List of notation
- Index

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	PAPIER
Éditeur(s)	Cambridge University Press
Auteur(s)	Joachim von zur Gathen, Jurgen Gerhard
Parution	04/07/2003
Édition	2^eme édition
Nb. de pages	800
Format	26 x 42
Couverture	Broché
Intérieur	Noir et Blanc
EAN13	9780521826464
ISBN13	978-0-521-82646-4