Applications of Polynomial Systems

There is no doubt that systems of polynomials are at the core of many mathematical models, with applications in mechanics, networks, economics, biology, and many other fields. The goal of this volume is to present some of these applications, through specific examples. 

 

This book is not suitable as a textbook, or as a self-contained introduction to any of the topics exposed: the theory is not systematically developed, and many proofs and definitions are omitted. Rather, as stated in the preface: “the hope is that the brief presentation provided here inspires you to learn more”, and the reader is referred to the comprehensive bibliography (371 items).

 

The first two chapters introduce the history of elimination theory and numerical algebraic geometry. The remaining 3 chapters deal with applications: geometric modeling, rigidity theory, and chemical reaction networks. 

 

Rigidity theory studies the possible motions of frameworks built from bars and joints in 2 and 3-dimensional space. I found this chapter quite enjoyable to read, especially because of the rich and unexpected connections with topics like matroid theory and graphical Gaussian models. 

I did not find in the book a justification for the selection of the applications, whether it was based on personal taste or on the richness of connections with other branches of mathematics. 

 

In any case, in my opinion, this is not a book to read ‘linearly’, chapter after chapter; I think it is more useful to just pick some parts, the ones that are closer to the reader’s interests.

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Fabio Mainardi (fabio.mainardi@rd.nestle.com) is a mathematician working as a senior data scientist at Nestlé Research, Switzerland. His mathematical interests are number theory, functional analysis, discrete mathematics and probability.