author = {Christian Aistleitner},
title = {{Relations between Groebner bases, differential Groebner bases, and differential characteristic sets}},
language = {english},
abstract = {While Groebner bases classically focus on purely algebraic settings, Groebner basis literature followed the general trend of the last decades to also incorporate differential settings, which resulted in the notion of differential Groebner bases. In the differential setting, there is also the much older, but different notion of differential characteristic 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 Groebner bases, differential Groebner bases, and differential characteristic sets using a unified notation system that allows to easily identify and exhibit differences and matches between the different methods.},
number = {11-02},
year = {2010},
month = {December},
sponsor = {Austrian Science Foundation (FWF) under the project DIFFOP (P20336-N18) and Doctoral Program "Computational Mathematics" (W1214), project DK11.},
length = {99},
type = {RISC Report Series},
institution = {Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz},
address = {Altenberger Straße 69, 4040 Linz, Austria},
issn = {2791-4267 (online)}