Relations between Groebner bases, differential Groebner bases, and differential characteristic sets

While Gröbner bases classically focus on purely algebraic settings, Gröbner basis literature followed the general trend of the last decades to also incorporate differential settings, which resulted in the notion of differential Gröbner bases. In the differential setting, there is also the much older, but different notion of differential characteristec sets. Although those three methods of elimination theory are closely related, literature does not provide a comparison of those methods. The main contribution of this diploma thesis is such a comparison. Additionally, we give a presentation of Gröbner bases, differential Gröbner bases, and differential characteristic sets using a unified notation system that allows to easily identify and exhibit differences and matches between the different methods.