Solving Polynomial Equation Systems I: The Kronecker-Duval Philosophy

This is an excellent book for readers interested in algebraic methods. A part of the content will not be new to most of them; its usefulness lies in the fact that so much is brought together in one book. In the first part of the book, the author describes the Kronecker-Duval approach to the solution of systems of polynomial equations. The second part contains a discussion of factorisation of polynomials. The author says: “It is my firm belief that the best way of understanding a theory and an algorithm is to verify it through computation …” Accordingly, the book contains 52 numerical examples provided with solutions and 27 programs. I enjoyed the author’s language enormously. The author’s words from the preface “the number of hidden mistakes in a draft is always larger than the number of the found ones” are true. I spotted a few, e.g., in Theorem 5.2.3 as well as in Theorem 5.5.6, one has to add the assumption that the degree of considered polynomials is at least one. This criticism of the text is a little more than a quibble and, in any case, is greatly outweighed by its virtues.

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