Computing the Newton polytope of the discriminant from the fiber polytope. The finite \(\mathcal{S}\)-determinacy of singularities in positive characteristic \(\mathcal{S}=\mathcal{R}_{\mathcal{G}},\mathcal{R}_{\mathcal{A}}, \mathcal{K}_{\mathcal{G}},\mathcal{K}_{\mathcal{A}}\) 