@inbook{fe0a845c34364135a2f2eb7ec2b238d7,
title = "Solving polynomial systems",
abstract = "This chapter considers the known techniques to solve (systems of) nonlinear polynomial equations. After giving a historical overview of the topic, we describe algorithms to solve univariate polynomials of high degree. The remainder of the chapter deals with algorithms to solve systems of nonlinear multivariate polynomials. We describe the XL algorithm, give a short introduction into the theory of Gr{\"o}bner bases and present the most important algorithms to compute these bases. After analyzing the complexity of these algorithms against various types of multivariate polynomial systems, we end this chapter by giving an overview of the known algorithms used to solve over and underdetermined systems of multivariate quadratic equations.",
author = "Jintai Ding and Albrecht Petzoldt and Schmidt, {Dieter S.}",
note = "Publisher Copyright: {\textcopyright} Springer Science+Business Media, LLC, part of Springer Nature 2020.",
year = "2020",
doi = "10.1007/978-1-0716-0987-3_8",
language = "English",
series = "Advances in Information Security",
publisher = "Springer",
pages = "185--248",
booktitle = "Advances in Information Security",
}