The Subideal Version of the SOI-Algorithm and Its Application

The coordinates of the empirical points are known with only limited precision, typically up to a permitted tolerance \(\varepsilon \). In this paper, we present an algorithm which computes stable border bases of the ideal \(I\cap J\), where I is the approximately vanishing ideal of an empirical point set, and J is the vanishing ideal of an exact point set. This algorithm is the subideal version of the SOI-Algorithm and it can be applied to the production allocation problem in the Algebraic Oil Research Project.