An algorithm for the construction of exceptional modules over tubular canonical algebras

Let Λ be a tubular canonical algebra of quiver type. We describe an algorithm, which for numerical data computes all regular exceptional Λ-modules, or more generally all indecomposable modules in exceptional tubes. The input for the algorithm is a quadruple consisting of the slope, the number of the tube, the quasi-socle and the quasi-length, the output are explicit matrices for the module with the data above.