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VerifyRealRoots: A Matlab Package for Computing Verified Real Solutions of Polynomials Systems of Equations and Inequalities

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Abstract

VerifyRealRoots is a Matlab package for computing and verifying real solutions of polynomial systems of equations and inequalities. It calls Bertini or MMCRSolver for finding approximate real solutions and then applies AINLSS to verify the existence of a regular solution of a polynomial system or applies AINLSS2 (AIVISS) to verify the existence of a double solution (a singular solution of an arbitrary multiplicity) of a slightly perturbed polynomial system.

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Authors and Affiliations

  1. Shanghai Key Laboratory of Trustworthy Computing, East China Normal University, Shanghai, 200062, China

    Zhengfeng Yang & Hanrui Zhao

  2. Key Laboratory of Mathematics Mechanization, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China

    Lihong Zhi

  3. University of Chinese Academy of Sciences, Beijing, 100049, China

    Lihong Zhi

Authors
  1. Zhengfeng Yang
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  2. Hanrui Zhao
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  3. Lihong Zhi
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Corresponding authors

Correspondence to Zhengfeng Yang, Hanrui Zhao or Lihong Zhi.

Additional information

This research is supported by the National Key Research Project of China under Grant No. 2018YFA0306702, and the National Natural Science Foundation of China under Grant Nos. 12171159, 12071467 and 61772203, and Shanghai Trusted Industry Internet Software Collaborative Innovation Center.

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Yang, Z., Zhao, H. & Zhi, L. VerifyRealRoots: A Matlab Package for Computing Verified Real Solutions of Polynomials Systems of Equations and Inequalities. J Syst Sci Complex 36, 866–883 (2023). https://doi.org/10.1007/s11424-023-1406-7

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  • DOI: https://doi.org/10.1007/s11424-023-1406-7

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