Modern computer algebra

著者

書誌事項

Modern computer algebra

Joachim von zur Gathen, Jürgen Gerhard

Cambridge University Press, 2003

2nd ed

  • : hardback

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注記

Previous ed.: 1999

Includes bibliographical references (p. 724-757) and index

内容説明・目次

内容説明

Computer algebra systems are gaining 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 also make 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; a wide variety of applications (among others, in chemistry, coding theory, cryptography, computational logic, and the design of calendars and musical scales). Some of this material has never appeared before in book form. For the new edition, errors have been corrected, the text has been smoothed and updated, and new sections on greatest common divisors and symbolic integration have been added.

目次

  • 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. Groebner 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.

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