Cox–Zucker machine

In arithmetic geometry, the Cox–Zucker machine is an algorithm created by David A. Cox and Steven Zucker. This algorithm determines whether a given set of sections provides a basis (up to torsion) for the Mordell–Weil group of an elliptic surface E → S, where S is isomorphic to the projective line.

The algorithm was first published in the 1979 article "Intersection numbers of sections of elliptic surfaces" by Cox and Zucker and was later named the "Cox–Zucker machine" by Charles Schwartz in 1984.