On the problem of computing intersections of fields

Description

Given the generators of two fields, and the relations they satisfy, we approach the problem of how to compute their intersection. We present a semi-algorithm that solves the problem when the fields are simple, that is, generated by one element each, and there is only one relation between their generators. It takes as input the relation, and outputs a generator of their intersection. The semi-algorithm may not terminate. Termination depends on a dynamical system on the curve defined by the relation. However, if the intersection is non-trivial, the semi-algorithm is guaranteed to terminate.

Period	19 Feb 2025
Event title	Differential Galois theories and transcendence
Event type	Conference
Location	FranceShow on map