{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,20]],"date-time":"2026-02-20T07:50:36Z","timestamp":1771573836977,"version":"3.50.1"},"reference-count":7,"publisher":"Association for Computing Machinery (ACM)","issue":"3","license":[{"start":{"date-parts":[[2021,9,1]],"date-time":"2021-09-01T00:00:00Z","timestamp":1630454400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Commun. Comput. Algebra"],"published-print":{"date-parts":[[2021,9]]},"abstract":"<jats:p>We introduce a new method for finding a non-realizability certificate of a simplicial sphere \u03a3. It enables us to prove for the first time the non-realizability of a balanced 2-neighborly 3-sphere by Zheng, a family of highly neighborly centrally symmetric spheres by Novik and Zheng, and several combinatorial prismatoids introduced by Criado and Santos.<\/jats:p>\n          <jats:p>The method, implemented in the polymake framework, uses integer programming to find a monomial combination of classical 3-term Pl\u00fccker relations that must be positive in any realization of \u03a3; but since this combination should also vanish identically, the realization cannot exist.<\/jats:p>\n          <jats:p>Previous approaches by Firsching, implemented using SCIP, and by Gouveia, Macchia and Wiebe, implemented using Singular and Macaulay2, are not able to process these examples.<\/jats:p>","DOI":"10.1145\/3511528.3511533","type":"journal-article","created":{"date-parts":[[2022,1,12]],"date-time":"2022-01-12T17:07:13Z","timestamp":1642007233000},"page":"82-86","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":1,"title":["Large final polynomials from integer programming"],"prefix":"10.1145","volume":"55","author":[{"given":"Julian","family":"Pfeifle","sequence":"first","affiliation":[{"name":"Universitat Polit\u00e8cnica de Catalunya, Barcelona, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2022,1,12]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1080\/10586458.2019.1641766"},{"key":"e_1_2_1_2_1","series-title":"DMV Sem","first-page":"43","volume-title":"Polytopes---combinatorics and computation (Oberwolfach","author":"Gawrilow Ewgenij","year":"1997","unstructured":"[GJ00] Ewgenij Gawrilow and Michael Joswig . polymake: a framework for analyzing convex polytopes . In Polytopes---combinatorics and computation (Oberwolfach , 1997 ), volume 29 of DMV Sem ., pages 43 -- 73 . Birkh\u00e4user , Basel , 2000. [GJ00] Ewgenij Gawrilow and Michael Joswig. polymake: a framework for analyzing convex polytopes. In Polytopes---combinatorics and computation (Oberwolfach, 1997), volume 29 of DMV Sem., pages 43--73. Birkh\u00e4user, Basel, 2000."},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1016\/0097-3165(95)90070-5"},{"key":"e_1_2_1_4_1","volume-title":"Highly neighborly centrally symmetric spheres","author":"Novik Isabella","year":"2019","unstructured":"[NZ19] Isabella Novik and Hailun Zheng . Highly neighborly centrally symmetric spheres , 2019 . [NZ19] Isabella Novik and Hailun Zheng. Highly neighborly centrally symmetric spheres, 2019."},{"key":"e_1_2_1_5_1","doi-asserted-by":"publisher","DOI":"10.4007\/annals.2012.176.1.7"},{"key":"e_1_2_1_6_1","first-page":"1","volume-title":"Ear decomposition and balanced neighborly simplicial manifolds. Electron. J. Comb., 27(1):research paper","author":"Zheng Hailun","unstructured":"[Zhe20a] Hailun Zheng . Ear decomposition and balanced neighborly simplicial manifolds. Electron. J. Comb., 27(1):research paper p 1 .10, 17, 2020. [Zhe20a] Hailun Zheng. Ear decomposition and balanced neighborly simplicial manifolds. Electron. J. Comb., 27(1):research paper p1.10, 17, 2020."},{"key":"e_1_2_1_7_1","volume-title":"personal communication","author":"Zheng Hailun","year":"2020","unstructured":"[Zhe20b] Hailun Zheng . personal communication , 2020 . [Zhe20b] Hailun Zheng. personal communication, 2020."}],"container-title":["ACM Communications in Computer Algebra"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3511528.3511533","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/3511528.3511533","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,17]],"date-time":"2025-06-17T17:51:04Z","timestamp":1750182664000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3511528.3511533"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,9]]},"references-count":7,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2021,9]]}},"alternative-id":["10.1145\/3511528.3511533"],"URL":"https:\/\/doi.org\/10.1145\/3511528.3511533","relation":{},"ISSN":["1932-2240"],"issn-type":[{"value":"1932-2240","type":"print"}],"subject":[],"published":{"date-parts":[[2021,9]]},"assertion":[{"value":"2022-01-12","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}