🔗 Cox-Zucker_machine

🔗 Mathematics

The Cox–Zucker machine is an algorithm created by David A. Cox and Steven Zucker. This algorithm determines if 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 paper "Intersection numbers of sections of elliptic surfaces" by Cox and Zucker, and it was later named the "Cox–Zucker machine" by Charles Schwartz in 1984. The name is a homophone for an obscenity, and this was a deliberate move by Cox and Zucker, who conceived of the idea of coauthoring a paper as graduate students at Princeton for the express purpose of enabling this joke, a joke they followed through on while professors at Rutgers five years later. As Cox explained in a memorial tribute to Zucker in Notices of the American Mathematical Society in 2021: "A few weeks after we met, we realized that we had to write a joint paper because the combination of our last names, in the usual alphabetical order, is remarkably obscene."