| Titre : |
Modern computer algebra |
| Type de document : |
texte imprimé |
| Auteurs : |
Joachim VON ZUR GATHEN, Auteur ; Jurgen GERHARD, Auteur |
| Editeur : |
Cambridge university press |
| Année de publication : |
1999 |
| Importance : |
753 p. |
| Format : |
25 cm. |
| ISBN/ISSN/EAN : |
978-0-521-64176-0 |
| Note générale : |
Index. |
| Langues : |
Anglais (eng) |
| Catégories : |
MATHÉMATIQUES:Algébre
|
| Index. décimale : |
04-03 Algébre |
| 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 |
Modern computer algebra [texte imprimé] / Joachim VON ZUR GATHEN, Auteur ; Jurgen GERHARD, Auteur . - Cambridge university press, 1999 . - 753 p. ; 25 cm. ISBN : 978-0-521-64176-0 Index. Langues : Anglais ( eng)
| Catégories : |
MATHÉMATIQUES:Algébre
|
| Index. décimale : |
04-03 Algébre |
| 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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