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Polynomial Equations: Theory and Practice

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Polynomial Optimization, Moments, and Applications

Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 206))

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Abstract

Solving polynomial equations is a subtask of polynomial optimization. This chapter introduces systems of such equations and the main approaches for solving them. We discuss critical point equations, algebraic varieties, and solution counts. The theory is illustrated by many examples using different software packages.

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Acknowledgements

This chapter is based on an introductory lecture given at the workshop Solving polynomial equations and applications organized at CWI, Amsterdam in October 2022. I thank Monique Laurent for involving me in this workshop, and all other speakers and attendants for making it a success. I was supported by a Veni grant from the Netherlands Organisation for Scientific Research (NWO).

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Authors and Affiliations

  1. Centrum Wiskunde & Informatica (CWI), Amsterdam, The Netherlands

    Simon Telen

  2. Present Address: Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany

    Simon Telen

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  1. Simon Telen
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Correspondence to Simon Telen .

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Editors and Affiliations

  1. University of Birmingham, Birmingham, UK

    Michal Kočvara

  2. Aromath, Inria at Université Côte d’Azur, Sophia Antipolis, France

    Bernard Mourrain

  3. UiT The Arctic University of Norway, Tromsø, Norway

    Cordian Riener

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Telen, S. (2023). Polynomial Equations: Theory and Practice. In: Kočvara, M., Mourrain, B., Riener, C. (eds) Polynomial Optimization, Moments, and Applications. Springer Optimization and Its Applications, vol 206. Springer, Cham. https://doi.org/10.1007/978-3-031-38659-6_8

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