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# Cox–Zucker machine

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.

References

Cox, D. A.; Zucker, S. (1979). "Intersection numbers of sections of elliptic surfaces". Invent. Math. 53: 1–44. doi:10.1007/BF01403189.

Schwartz, C. F. (1984). "A Mordell–Weil Group of Rank 8, and a Subgroup of Finite Index" (PDF). Nagoya Math J. 93: 17–26.

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