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.[1]

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

References

Schwartz, Charles F. (1984). "A Mordell–Weil Group of Rank 8, and a Subgroup of Finite Index". Nagoya Mathematical Journal. 93: 17–26. doi:10.1017/S0027763000020705. MR 0738915. Zbl 0504.14031.
Cox, David A.; Zucker, Steven (1979-02-01). "Intersection numbers of sections of elliptic surfaces". Inventiones mathematicae. 53 (1): 1–44. doi:10.1007/BF01403189. ISSN 0020-9910.

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[Schwartz-1984-1] Schwartz, Charles F. (1984). "A Mordell–Weil Group of Rank 8, and a Subgroup of Finite Index". Nagoya Mathematical Journal. 93: 17–26. doi:10.1017/S0027763000020705. MR 0738915. Zbl 0504.14031.

[2] Cox, David A.; Zucker, Steven (1979-02-01). "Intersection numbers of sections of elliptic surfaces". Inventiones mathematicae. 53 (1): 1–44. doi:10.1007/BF01403189. ISSN 0020-9910.