A Simple Quantifier-free Formula of Positive Semidefinite Cyclic Ternary Quartic Forms

TL;DR

This paper presents a new, simplified quantifier-free formula for positive semidefinite cyclic ternary quartic forms, achieved through advanced algebraic methods, improving automatic derivation over previous approaches.

Contribution

The paper introduces a novel, explicit quantifier-free formula for a specific class of polynomial forms, advancing the automation and efficiency of algebraic inequality verification.

Findings

Derived a simple quantifier-free formula for the forms

Used complete discrimination systems and Maple15 tools

Achieved automatic derivation previously difficult with existing methods

Abstract

Quantifier elimination of positive semidefinite cyclic ternary quartic forms is studied in this paper. We solve the problem by the theory of complete discrimination systems, function \RealTriangularize in Maple15 and the so-called Criterions on Equality of Symmetric Inequalities method. The equivalent simple quantifier-free formula is proposed and is difficult to obtain automatically by previous methods or quantifier elimination tools.