Modern Computer Algebra

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Modern Computer Algebra Vital Source e-bog

Joachim von zur Gathen og Jürgen Gerhard

(2013)

Cambridge University Press

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Joachim von zur Gathen og Jürgen Gerhard

(2013)

Sprog: Engelsk

Cambridge University Press

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3. Udgave
Vital Source searchable e-book (Reflowable pages)
Udgiver: Cambridge University Press (April 2013)
Forfattere: Joachim von zur Gathen og Jürgen Gerhard
ISBN: 9781107241879

Beskrivelse
Om e-bogen

Computer algebra systems are now ubiquitous in all areas of science and engineering. This highly successful textbook, widely regarded as the 'bible of computer algebra', gives a thorough introduction to the algorithmic basis of the mathematical engine in computer algebra systems. Designed to accompany one- or two-semester courses for advanced undergraduate or graduate students in computer science or mathematics, its comprehensiveness and reliability has also made 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; and a wide variety of applications (among others, in chemistry, coding theory, cryptography, computational logic, and the design of calendars and musical scales). A great deal of historical information and illustration enlivens the text. In this third edition, errors have been corrected and much of the Fast Euclidean Algorithm chapter has been renovated.

Licens varighed:
Bookshelf online: 5 år fra købsdato.
Bookshelf appen: ubegrænset dage fra købsdato.

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Detaljer om varen

Hardback: 808 sider
Udgiver: Cambridge University Press (April 2013)
Forfattere: Joachim von zur Gathen og Jürgen Gerhard
ISBN: 9781107039032

Beskrivelse
Indhold

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. Gröbner 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.