Ed Mosteig
Using Valuations to Compute Gröbner Bases
Classical computations of Gröbner bases rely upon initially
setting a term order that will be used in the division algorithm.
Alternatively, Sweedler suggested in a paper (1986) another method of
computing Gröbner bases by using valuations in place of term
orders. This talk will address the use of valuations and some of the
computational issues involved. As will be shown, all term orders can
be described by appropriate valuations, but there are many well behaved
valuations that have characteristics that are very different from term
orders. In the setting of a polynomial ring with two variables,
k[x,y], a description of some of the well-behaved valuations will be
given when k has characteristic zero. Lastly, we will demonstrate
some of the difficulties that arise when we shift our focus to fields
of positive charcteristic.