On the complexity of computing Grobner bases for weighted homogeneous systems

摘要

Solving polynomial systems arising from applications is frequently made easier by the structure of the systems. Weighted homogeneity (or quasi-homogeneity) is one example of such a structure: given a system of weights W = (w1, ... W-homogeneous polynomials are polynomials which are homogeneous w.r.t. the weighted degree deg (X-1(alpha 1)...X-n(alpha n)) = Sigma wi alpha i.