Jet Ideals and Products of Ideals in Differential Rings
Sprache des Vortragstitels:
Kolchin Seminar in Differential Algebra
Sprache des Tagungstitel:
We will start with the following question emerged recently in the algorithmic studies of algebraic differential equation: assume that you have several ideals (not necessarily differential) in a differential algebra, how are the product of their derivatives and derivatives of their product related? This question turned out to be closely related to the classical membership problem for the differential ideal [x_1,...,x_n] in the algebra of differential polynomials in x_1, ..., x_n.
Both these questions can be approached using the jet schemes of the ideal (x_1,...,x_n) in the polynomial algebra in x_1,...,x_n. In the talk we will describe the structure of these jet schemes and use the obtained results to solve initial problems in differential algebra.