Modern computer algebra [E-Book] / Joachim von zur Gathen, Jürgen Gerhard.
Gathen, Joachim von zur, (author)
Gerhard, Jürgen, (author)
Third edition.
Cambridge : Cambridge University Press, 2013
1 online resource (xiii, 795 pages)
englisch
9781107039032
9781139856065
Full Text
Table of 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.