RISC Forum
Abstract for diploma thesis of Christian Aistleitner
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.
