Classification of gap functions with degree 4

In algebraic geometry, gap functions are useful tools in the study of singularities of curves. It is thus desirable to have a classification of gap functions with arbitrary degrees. Gap functions with degrees 1 and 2 are known classically and Buczyński, Ilten, Ventura have classified gap functions with degree 3. In this thesis, building on the results of Buczyński, Ilten, Ventura, we present an algorithm that computes gap functions with arbitrary dimensions and degrees. After implementing the algorithm in Maple, we classify all 4 dimensional gap functions, which can help study all the curve singularities with delta invariant 4.