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^{[further explanation needed]} 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.^[1]

The algorithm was first published in the 1979 article "Intersection numbers of sections of elliptic surfaces" by Cox and Zucker^[2] and was later named the "Cox–Zucker machine" by Charles Schwartz in 1984.^[1]

Name origin

The name sounds similar to the obscenity "cocksucker". This was a deliberate choice by Cox and Zucker, who, as first-year graduate students at Princeton University in 1970, conceived of the idea of coauthoring a paper for the express purpose of enabling this joke. They followed through on it five years later, as members of the faculty at Rutgers University.^[3] 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."^[3]

See also

• Cox ring