Computing the real variety of an ideal

Abstract

Solving systems of polynomial equations is a classical problem of mathematics with an emerging number of modern applications, such as coding theory, robotics, computational statistics, etc. Its importance is reflected by the broad literature that deals with algorithms, ranging from numerical continuation methods to exact methods based e.g. on Gröbner or border bases; see e.g. the monograph [1] and the references therein. However in many practical applications one is only interested in real solutions. The literature tailored to the problem of real solving systems of polynomials is by far not as broad.