Partial algorithms for satellite unknowns determination

Abstract

The concept of satellite unknowns with respect to a set of selected unknowns in linear homogeneous differential systems was introduced earlier by the author of this paper, and an algorithm for satellite unknowns testing was proposed. On one of the stages of this algorithm, it is required to compare Picard–Vessiot extensions of two differential systems constructed in the course of the algorithm operation. The commonly accepted method of solving this problem, which is based on Hrushovski’s algorithm, has rather high algorithmic complexity, which hampers its use in practice. In the paper, some partial algorithms for satellite unknowns testing are described. These algorithms are not always applicable but have relatively low computational complexity and can be implemented in computer algebra systems.