Deciding Nonnegativity of Polynomials by MAPLE
Lu Yang, Bican Xia
TL;DR
This paper demonstrates how to use Maple's RealRootClassification tool to effectively determine the nonnegativity of polynomials under various constraints, providing practical guidance and examples.
Contribution
It offers a user guide with tricks for applying Maple's RealRootClassification to prove polynomial nonnegativity, enhancing computational algebra techniques.
Findings
Effective use of Maple's RealRootClassification for polynomial nonnegativity
Practical examples illustrating the method's application
Tips and tricks for improved tool usage
Abstract
There have been some effective tools for solving (constant/parametric) semi-algebraic systems in Maple's library RegularChains since Maple 13. By using the functions of the library, e.g., RealRootClassfication, one can prove and discover polynomial inequalities. This paper is more or less a user guide on using RealRootClassfication to prove the nonnegativity of polynomials. We show by examples how to use this powerful tool to prove a polynomial is nonnegative under some polynomial inequality and/or equation constraints. Some tricks for using the tool are also provided.
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Taxonomy
TopicsPolynomial and algebraic computation · Advanced Numerical Analysis Techniques · Logic, programming, and type systems