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The Cox-Zucker machine

“A Mordell-Weil Group of Rank 8, and a Subgroup of Finite Index,” Charles F. Schwartz, Nagoya Math Journal, vol. 93, 1984, pp. 17-26. (Thanks to Rodrigo Trevino and Don Troop for bringing this to our attention.)

The author, who is at Rider College in Lawrenceville, New Jersey, makes reference to the following paper, which was written by two Rutgers University mathematicians: “Intersection Numbers of Sections of Elliptic Surfaces,” David A. Cox (who is now at Amherst College) and Steven Zucker (who is now at Johns Hopkins University), Inventiones Mathematicae, vol. 53, 1979, pp. 1-44( The Schwartz paper is notable for its Section 1, which begins:

1. The algorithm of Cox and Zucker (AKA, The Cox-Zucker Machine)
The purpose of this section is to provide, not a complete description of the algorithm of Cox and Zucker, but rather, a brief summary of their technique.

(That’s an excerpt from the article “Boys Will Be Boys,” published in AIR 14:3.)

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