Polynomial Algorithms in Computer Algebra

1. Front Matter

   Pages i-viii

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2. Introduction

   • Franz Winkler

   Pages 1-25

3. Arithmetic in basic domains

   • Franz Winkler

   Pages 26-50

4. Computing by homomorphic images

   • Franz Winkler

   Pages 51-81

5. Greatest common divisors of polynomials

   • Franz Winkler

   Pages 82-111

6. 5 Factorization of polynomials

   • Franz Winkler

   Pages 112-150

7. Decomposition of polynomials

   • Franz Winkler

   Pages 151-156

8. Linear algebra—solving linear systems

   • Franz Winkler

   Pages 157-171

9. The method of Gröbner bases

   • Franz Winkler

   Pages 172-203

10. Quantifier elimination in real closed fields

    • Franz Winkler

    Pages 204-214

11. 10 Indefinite summation

    • Franz Winkler

    Pages 215-223

12. Parametrization of algebraic curves

    • Franz Winkler

    Pages 224-236

13. Back Matter

    Pages 237-279

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For several years now I have been teaching courses in computer algebra at the Universitat Linz, the University of Delaware, and the Universidad de Alcala de Henares. In the summers of 1990 and 1992 I have organized and taught summer schools in computer algebra at the Universitat Linz. Gradually a set of course notes has emerged from these activities. People have asked me for copies of the course notes, and different versions of them have been circulating for a few years. Finally I decided that I should really take the time to write the material up in a coherent way and make a book out of it. Here, now, is the result of this work. Over the years many students have been helpful in improving the quality of the notes, and also several colleagues at Linz and elsewhere have contributed to it. I want to thank them all for their effort, in particular I want to thank B. Buchberger, who taught me the theory of Grabner bases nearly two decades ago, B. F. Caviness and B. D. Saunders, who first stimulated my interest in various problems in computer algebra, G. E. Collins, who showed me how to compute in algebraic domains, and J. R. Sendra, with whom I started to apply computer algebra methods to problems in algebraic geometry. Several colleagues have suggested improvements in earlier versions of this book. However, I want to make it clear that I am responsible for all remaining mistakes.

• algebra
• algorithm
• algorithms
• complexity
• computer
• computer algebra
• computer science
• data structures
• algorithm analysis and problem complexity

• Research Institute for Symbolic Computation, Johannes-Kepler-University Linz, Linz, Austria

  Franz Winkler

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