# Polynomial Algorithms in Computer Algebra

• Franz Winkler
Textbook

Part of the Texts and Monographs in Symbolic Computation book series (TEXTSMONOGR)

1. Front Matter
Pages i-viii
2. Franz Winkler
Pages 1-25
3. Franz Winkler
Pages 26-50
4. Franz Winkler
Pages 51-81
5. Franz Winkler
Pages 82-111
6. Franz Winkler
Pages 112-150
7. Franz Winkler
Pages 151-156
8. Franz Winkler
Pages 157-171
9. Franz Winkler
Pages 172-203
10. Franz Winkler
Pages 204-214
11. Franz Winkler
Pages 215-223
12. Franz Winkler
Pages 224-236
13. Back Matter
Pages 237-279

### Introduction

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.

### Keywords

algebra algorithm algorithms complexity computer computer algebra computer science

#### Authors and affiliations

• Franz Winkler
• 1
1. 1.Research Institute for Symbolic ComputationJohannes-Kepler-University LinzLinzAustria

### Bibliographic information

• DOI https://doi.org/10.1007/978-3-7091-6571-3