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Modern computer algebra
Computer algebra systems are gaining more and more 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 un...
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| Auteurs principaux : | , |
|---|---|
| Format : | Livre |
| Langue : | anglais |
| Titre complet : | Modern computer algebra / Joachim von zur Gathen and Jürgen Gerhard |
| Publié : |
Cambridge :
Cambridge University Press
, 1999, cop. 1999 |
| Description matérielle : | 1 vol. (XIII-753 p.) |
| Sujets : |
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| 200 | 1 | |a Modern computer algebra |b Texte imprimé |f Joachim von zur Gathen and Jürgen Gerhard | |
| 210 | |a Cambridge |c Cambridge University Press |d 1999, cop. 1999 | ||
| 215 | |a 1 vol. (XIII-753 p.) |c ill. en noir et en coul., couv. ill. en coul. |d 26 cm | ||
| 320 | |a Bibliogr. p. 698-727. Index | ||
| 330 | |a Computer algebra systems are gaining more and more 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 means that it is 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 (among others 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 enlivens the text. (4e de couv.) | ||
| 359 | 2 | |b Introduction |c 1, Cyclohexane, cryptography, codes, and computer algebra |b I, Euclid |c 2, Fundamental algorithms |c 3, The euclidean algorithm |c 4, Application of the euclidean algorithm |c 5, Modular algorithms and interpolation |c 6, The resultant and ged computation |c 7, Application : decoding BCH codes |b II, Newton |c 8, Fast multiplication |c 9, Newton iteration |c 10, Fast polynomial evaluation and interpolation |c 11, Fast euclidan algorithm |c 12, Fast linear algebra |c 13, Fourier transform and image compression |b III, Gaub |c 14, Factoring polynomials over finite fields |c 15, Hensel lifting and factoring polynomials |c 16, Short vectors in lattices |c 17, Applications of basis reduction |b IV, Fermat |c 18, Primality testing |c 19, Factoring integers |c 20, Application : public key cryptography |b V, Hilbert |c 21, Gröbner bases |c 22, Symbolic integration |c 23, Symbolic summation |c 24, Applications |b Appendix |c 25, Fundamental concepts | |
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