APPLICATION OF GROEBNER BASIS FOR CONSTRUCTING PHASE DIAGRAMS USING CATASTROPHE THEORY METHODS

摘要

A method of constructing phase diagrams was developed, in which the Groebner basis and the ideal of the leading terms of the Groebner basis were used to find the polynomial quotient-ring in the gradient ideal. The eliminating ideal was applied to determine the syzygies between equivariant vector fields and to search for the stationary algebra of the quasi-homogeneous part.