Huang, Z.Y., England, M., Davenport, J.H. and Paulson, L.C. (2016) Using Machine Learning to Decide When to Precondition Cylindrical Algebraic Decomposition with Groebner Bases. 2016 18th International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC), Timisoara, 24-27 September 2016.
https://doi.org/10.1109/SYNASC.2016.020

has been cited by the following article:

• TITLE: Solve the Polynomial Functions Conditional Extreme by Applying the Groebner Basis Method

  AUTHORS: Junyu Luo, Shengzhen Ding

  KEYWORDS: Groebner Basis, Polynomial Equations, Conditional Extremum

  JOURNAL NAME: Open Journal of Applied Sciences, Vol.12 No.11, November 25, 2022

  ABSTRACT: In this paper, an algebraic method which is based on the groebner bases theory is proposed to solve the polynomial functions conditional extreme. Firstly, we describe how to solve conditional extreme value problems by establishing Lagrange functions and calculating the differential equations derived from the Lagrange functions. Then, by solving the single variable polynomials in the groebner basis, the solution of polynomial equations could be derived successively. We overcome the high number of variables and constraints in the extreme value problem. Finally, this paper illustrates the calculation process of this method through the general procedures and examples in solving questions of conditional extremum of polynomial function.