  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.
