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We demonstrate the method by a systematic study of thousands of quartic surfaces (K3 surfaces) defined by sparse polynomials. The results are only supported by strong numerical evidence, yet the possibility of error is quantified in intrinsic terms, like the degree of curves generating the Picard group.<\/jats:p>","DOI":"10.1137\/18m122861x","type":"journal-article","created":{"date-parts":[[2019,11,5]],"date-time":"2019-11-05T11:55:10Z","timestamp":1572954910000},"page":"559-584","source":"Crossref","is-referenced-by-count":10,"title":["A Numerical Transcendental Method in Algebraic Geometry: Computation of Picard Groups and Related Invariants"],"prefix":"10.1137","volume":"3","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3756-0151","authenticated-orcid":true,"given":"Pierre","family":"Lairez","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7450-7494","authenticated-orcid":true,"given":"Emre Can","family":"Sert\u00f6z","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2019,11,5]]},"reference":[{"key":"atypb1","unstructured":"Elliptic Curves, Modular Forms and Cryptography\n                      , in Proceedings of the Advanced Instructional Workshop on Algebraic Number Theory, A. 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Costa,\n                      Effective Computations of Hasse-Weil Zeta Functions\n                      , ProQuest LLC, Ann Arbor, MI, Ph.D. Thesis, New York University, New York, 2015."},{"key":"atypb20","unstructured":"E. Costa, D. Harvey, and K. S. Kedlaya,\n                      Zeta Functions of Nondegenerate Hypersurfaces in Toric Varieties via cOntrolled Reduction in $p$-adic Cohomology\n                      , preprint,https:\/\/arxiv.org\/abs\/1806.00368, 2018."},{"key":"atypb21","doi-asserted-by":"publisher","DOI":"10.1090\/mcom\/3373"},{"key":"atypb22","doi-asserted-by":"crossref","unstructured":"B. Deconinck and M. S. 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