Modern computer algebra / Joachim von zur Gathen, Jürgen Gerhard.

Format:

Book

Author/Creator:

Gathen, Joachim von zur, author.

Gerhard, Jürgen, 1967- author.

Language:

English

Subjects (All):

Algebra--Data processing.

Algebra.

Computer algorithms.

Computer science--Mathematics.

Computer science.

Physical Description:

1 online resource (xiii, 795 pages) : digital, PDF file(s).

Edition:

Third edition.

Place of Publication:

Cambridge : Cambridge University Press, 2013.

Language Note:

English

Summary:

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.

Contents:

1. Cyclohexane, cryptography, codes, and computer algebra

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

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

14. Factoring polynomials over finite fields

15. Hensel lifting and factoring polynomials

16. Short vectors in lattices

17. Applications of basis reduction

18. Primality testing

19. Factoring integers

20. Application: public key cryptography

21. Gröbner bases

22. Symbolic integration

23. Symbolic summation

24. Applications

25. Fundamental concepts.

Notes:

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Includes bibliographical references and index.

ISBN:

9781139856065

1-316-09077-9

1-107-24805-1

1-107-03903-7

1-139-85606-5

1-107-25054-4

1-107-24888-4

1-107-24971-6

OCLC:

843762781