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

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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 accompa...

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Bibliographic Details
Main Authors: Gathen, Joachim von zur (Author), Gerhard, Jürgen, 1967- (Author)
Language:English
Published: Cambridge : Cambridge University Press, 2013.
Edition:Third edition.
Subjects:
Computer science > Mathematics.
Algebra > Data processing.
Computer algorithms.
Physical Description:xiii, 795 pages : illustrations (black and white, and colour) ; 26 cm
Format: Book
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.