VerifyRealRoots

Introduction

VerifyRealRoots is a MATLAB package for computing real verified solutions of polynomial systems of equations and inequalities. Two algorithms are provided for verifying the existence of real solutions of polynomial systems. The first one is based on the critical point method and the homotopy continuation method, and the second one is based on the low-rank moment matrix completion method.

Examples

Kissing number problem
Polynomial systems of equations
Polynomial systems of equations and inequalities

Reference

Zhengfeng Yang, Lihong Zhi and Yijun Zhu, Verified Error Bounds for Real Solutions of Positive-dimensional Polynomial Systems, in Proceedings of the 38th International Symposium on Symbolic and Algebraic Computation, 2013, pp371--378, ACM Press.

Zhengfeng Yang, Hanrui Zhao, Lihong Zhi. VerifyRealRoots: A Matlab Package for Computing Verified Real Solutions of Polynomials Systems of Equations and Inequalities, Journal of Systems Science and Complexity, 2023: 1-18.