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**Algorithmic algebra.**
*(English)*
Zbl 0804.13009

Texts and Monographs in Computer Science. Berlin: Springer-Verlag. xii, 416 p. DM 70.00; öS 546.00; sFr 70.00 /hc (1993).

This book is based on a graduate course in computer science taught in 1987. The following topics are covered: computational ideal theory, solving systems of polynomial equations, elimination theory, real algebra, as well as an introduction chapter and two chapters with the needed algebraic background. The book is selfcontained and the proofs are given with many details.

It is clear that this book is only an introduction to the topic and does not cover the many improvements that appeared in the last 7 years about for example the computation of Gröbner basis, polynomial solving, multivariate resultants and algorithms in real algebra. Choices had to be made to keep the content of a reasonable size and the complexity issues are not considered.

The choice of topics is excellent, there are many exercises and examples. It is a very useful book.

It is clear that this book is only an introduction to the topic and does not cover the many improvements that appeared in the last 7 years about for example the computation of Gröbner basis, polynomial solving, multivariate resultants and algorithms in real algebra. Choices had to be made to keep the content of a reasonable size and the complexity issues are not considered.

The choice of topics is excellent, there are many exercises and examples. It is a very useful book.

Reviewer: M.-F.Roy (Rennes)

### MSC:

13Pxx | Computational aspects and applications of commutative rings |

13-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to commutative algebra |

68-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to computer science |