  This paper designs an alogrithm to compute the minimal combinations of finite
sets in Euclidean spaces, and applys the algorithm of study the moment maps and
geometric invariant stability of hypersurfaces. The classical example of cubic
curves is repeated by the algorithm. Furhtermore the alogrithm works for cubic
surfaces. For given affinely indepdent subsets of monomials, the algorithm can
output the unique unstable points of the Morse strata if it exists. Also there
is a discussion on the affinely dependent sets of monomials.
