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This paper designs an alogrithm to compute the minimal combinations of finitesets in Euclidean spaces, and applys the algorithm of study the moment maps andgeometric invariant stability of hypersurfaces. The classical example of cubiccurves is repeated by the algorithm. Furhtermore the alogrithm works for cubicsurfaces. For given affinely indepdent subsets of monomials, the algorithm canoutput the unique unstable points of the Morse strata if it exists. Also thereis a discussion on the affinely dependent sets of monomials.

Algorithms And Programming On The Minimal Combinations Of Weights Of Projective Hypersurfaces