We use the ring structure of R to compute the remaining relations of R as an k-algebra. This is done using the techniques introduced in [I. Stenger, A structure result for Gorenstein algebras of odd codimension. J. Algebra, 589:173–187, 2022]. The ideal IX defines the canonical model of a numerical Godeaux surface X embedded in the weighted projective space ℙ(22,34,44,53). The ring R = Sbig/IX is the canonical ring of X.
Up to now, this procedure involves several smaller Hom-computations which are very time consuming.