The procedure computes first the quasi-singular locus of the variety in weighted projective space. Afterwards the image of the variety under the 6-uple embedding of ℙ(2,2,3,3,3,3) into ℙ13 is determined and the points in the quasi-smooth locus are checked for smoothness. Usually, the ideal I defines a surface in the weighted projective obtained by our construction method.
The computation of the quasi-smooth locus of the surfaces obtained by our construction is usually very time consuming.