{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,17]],"date-time":"2026-03-17T18:55:37Z","timestamp":1773773737612,"version":"3.50.1"},"reference-count":25,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2026,9,1]],"date-time":"2026-09-01T00:00:00Z","timestamp":1788220800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2026,9,1]],"date-time":"2026-09-01T00:00:00Z","timestamp":1788220800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2026,9,1]],"date-time":"2026-09-01T00:00:00Z","timestamp":1788220800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-017"},{"start":{"date-parts":[[2026,9,1]],"date-time":"2026-09-01T00:00:00Z","timestamp":1788220800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"},{"start":{"date-parts":[[2026,9,1]],"date-time":"2026-09-01T00:00:00Z","timestamp":1788220800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-012"},{"start":{"date-parts":[[2026,9,1]],"date-time":"2026-09-01T00:00:00Z","timestamp":1788220800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2026,9,1]],"date-time":"2026-09-01T00:00:00Z","timestamp":1788220800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-004"}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Journal of Symbolic Computation"],"published-print":{"date-parts":[[2026,9]]},"DOI":"10.1016\/j.jsc.2026.102566","type":"journal-article","created":{"date-parts":[[2026,2,20]],"date-time":"2026-02-20T16:28:47Z","timestamp":1771604927000},"page":"102566","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":0,"special_numbering":"C","title":["Gr\u00f6bner bases over polytopal affinoid algebras"],"prefix":"10.1016","volume":"136","author":[{"given":"Moulay","family":"Barkatou","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lucas","family":"Legrand","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4208-8349","authenticated-orcid":false,"given":"Tristan","family":"Vaccon","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"78","reference":[{"key":"10.1016\/j.jsc.2026.102566_br0190","series-title":"Proceedings of the 2024 International Symposium on Symbolic and Algebraic Computation","first-page":"188","article-title":"Gr\u00f6bner bases over polytopal affinoid algebras","author":"Barkatou","year":"2024"},{"key":"10.1016\/j.jsc.2026.102566_br0110","doi-asserted-by":"crossref","DOI":"10.1016\/j.jsc.2023.102224","article-title":"Massively parallel computation of tropical varieties, their positive part, and tropical Grassmannians","volume":"120","author":"Bendle","year":"2024","journal-title":"J. Symb. Comput."},{"issue":"1","key":"10.1016\/j.jsc.2026.102566_br0120","doi-asserted-by":"crossref","first-page":"54","DOI":"10.1016\/j.jsc.2006.02.004","article-title":"Computing tropical varieties","volume":"42","author":"Bogart","year":"2007","journal-title":"J. Symb. Comput."},{"key":"10.1016\/j.jsc.2026.102566_br0020","series-title":"ISSAC 2019 - International Symposium on Symbolic and Algebraic Computation","article-title":"Gr\u00f6bner bases over Tate algebras","author":"Caruso","year":"2019"},{"key":"10.1016\/j.jsc.2026.102566_br0140","series-title":"ISSAC'20","article-title":"Signature-based algorithms for Gr\u00f6bner bases over Tate algebras","author":"Caruso","year":"2020"},{"key":"10.1016\/j.jsc.2026.102566_br0150","series-title":"Proceedings of the 2021 on International Symposium on Symbolic and Algebraic Computation, ISSAC'21","first-page":"67","article-title":"On fglm algorithms with Tate algebras","author":"Caruso","year":"2021"},{"key":"10.1016\/j.jsc.2026.102566_br0160","series-title":"Proceedings of the 2022 International Symposium on Symbolic and Algebraic Computation, ISSAC'22","first-page":"489","article-title":"On polynomial ideals and overconvergence in Tate algebras","author":"Caruso","year":"2022"},{"key":"10.1016\/j.jsc.2026.102566_br0240","doi-asserted-by":"crossref","DOI":"10.1016\/j.jsc.2024.102416","article-title":"Topological closure of formal powers series ideals and application to topological rewriting theory","volume":"129","author":"Chenavier","year":"2025","journal-title":"J. Symb. Comput."},{"key":"10.1016\/j.jsc.2026.102566_br0250","series-title":"Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra","author":"Cox","year":"2025"},{"issue":"601","key":"10.1016\/j.jsc.2026.102566_br0010","doi-asserted-by":"crossref","first-page":"139","DOI":"10.1515\/CRELLE.2006.097","article-title":"Non-archimedean amoebas and tropical varieties","volume":"2006","author":"Einsiedler","year":"2006","journal-title":"J. Reine Angew. Math."},{"key":"10.1016\/j.jsc.2026.102566_br0080","author":"Friedenberg"},{"key":"10.1016\/j.jsc.2026.102566_br0200","doi-asserted-by":"crossref","DOI":"10.1007\/b105283","article-title":"Polytopes, Rings, and K-Theory","author":"Gubeladze","year":"2009"},{"issue":"2","key":"10.1016\/j.jsc.2026.102566_br0060","doi-asserted-by":"crossref","first-page":"321","DOI":"10.1007\/s00222-007-0048-z","article-title":"Tropical varieties for non-archimedean analytic spaces","volume":"169","author":"Gubler","year":"2007","journal-title":"Invent. Math."},{"issue":"2","key":"10.1016\/j.jsc.2026.102566_br0090","doi-asserted-by":"crossref","first-page":"377","DOI":"10.1007\/s00222-007-0049-y","article-title":"The Bogomolov conjecture for totally degenerate abelian varieties","volume":"169","author":"Gubler","year":"2007","journal-title":"Invent. Math."},{"key":"10.1016\/j.jsc.2026.102566_br0220","doi-asserted-by":"crossref","DOI":"10.1017\/9781009127684","article-title":"p-adic Differential Equations","author":"Kedlaya","year":"2022"},{"key":"10.1016\/j.jsc.2026.102566_br0230","series-title":"The Art of Computer Programming, Volume 1: Fundamental Algorithms","author":"Knuth","year":"1997"},{"key":"10.1016\/j.jsc.2026.102566_br0210","series-title":"Bases de Gr\u00f6bner dans les alg\u00e8bres polyh\u00e9drales","author":"Legrand","year":"2025"},{"key":"10.1016\/j.jsc.2026.102566_br0130","series-title":"Introduction to Tropical Geometry, vol. 161","author":"Maclagan","year":"2015"},{"issue":"4","key":"10.1016\/j.jsc.2026.102566_br0100","doi-asserted-by":"crossref","first-page":"783","DOI":"10.1007\/s10208-019-09430-2","article-title":"Computing tropical varieties over fields with valuation","volume":"20","author":"Markwig","year":"2020","journal-title":"Found. Comput. Math."},{"key":"10.1016\/j.jsc.2026.102566_br0030","doi-asserted-by":"crossref","first-page":"271","DOI":"10.1007\/s002000050108","article-title":"Gr\u00f6bner bases for ideals in Laurent polynomial rings and their application to systems of difference equations","volume":"9","author":"Pauer","year":"1999","journal-title":"Appl. Algebra Eng. Commun. Comput."},{"issue":"6","key":"10.1016\/j.jsc.2026.102566_br0070","doi-asserted-by":"crossref","first-page":"3192","DOI":"10.1016\/j.aim.2012.02.003","article-title":"Tropical analytic geometry, Newton polygons, and tropical intersections","volume":"229","author":"Rabinoff","year":"2012","journal-title":"Adv. Math."},{"key":"10.1016\/j.jsc.2026.102566_br0050","doi-asserted-by":"crossref","first-page":"425","DOI":"10.1007\/BF01231568","article-title":"Rev\u00eatements de la droite affine en caract\u00e9ristique p> 0 et conjecture d'Abhyankar","volume":"116","author":"Raynaud","year":"1994","journal-title":"Invent. Math."},{"issue":"4","key":"10.1016\/j.jsc.2026.102566_br0040","doi-asserted-by":"crossref","first-page":"257","DOI":"10.1007\/BF01403307","article-title":"Rigid analytic spaces","volume":"12","author":"Tate","year":"1971","journal-title":"Invent. Math."},{"key":"10.1016\/j.jsc.2026.102566_br0180","author":"The Sage Developers"},{"key":"10.1016\/j.jsc.2026.102566_br0170","series-title":"ISSAC'23","first-page":"517","article-title":"Universal analytic Gr\u00f6bner bases and tropical geometry","author":"Vaccon","year":"2023"}],"container-title":["Journal of Symbolic Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0747717126000143?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0747717126000143?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2026,3,17]],"date-time":"2026-03-17T16:05:30Z","timestamp":1773763530000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0747717126000143"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,9]]},"references-count":25,"alternative-id":["S0747717126000143"],"URL":"https:\/\/doi.org\/10.1016\/j.jsc.2026.102566","relation":{},"ISSN":["0747-7171"],"issn-type":[{"value":"0747-7171","type":"print"}],"subject":[],"published":{"date-parts":[[2026,9]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"Gr\u00f6bner bases over polytopal affinoid algebras","name":"articletitle","label":"Article Title"},{"value":"Journal of Symbolic Computation","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.jsc.2026.102566","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2026 Published by Elsevier Ltd.","name":"copyright","label":"Copyright"}],"article-number":"102566"}}