{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,5]],"date-time":"2026-01-05T22:14:51Z","timestamp":1767651291424,"version":"3.41.2"},"reference-count":1,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","license":[{"start":{"date-parts":[[2015,12,2]],"date-time":"2015-12-02T00:00:00Z","timestamp":1449014400000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/arxiv.org\/licenses\/nonexclusive-distrib\/1.0"}],"funder":[{"DOI":"10.13039\/501100000780","name":"European Commission","doi-asserted-by":"crossref","award":["294962"],"award-info":[{"award-number":["294962"]}],"id":[{"id":"10.13039\/501100000780","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"abstract":"<jats:p>We investigate choice principles in the Weihrauch lattice for finite sets on\nthe one hand, and convex sets on the other hand. Increasing cardinality and\nincreasing dimension both correspond to increasing Weihrauch degrees. Moreover,\nwe demonstrate that the dimension of convex sets can be characterized by the\ncardinality of finite sets encodable into them. Precisely, choice from an n+1\npoint set is reducible to choice from a convex set of dimension n, but not\nreducible to choice from a convex set of dimension n-1. Furthermore we consider\nsearching for zeros of continuous functions. We provide an algorithm producing\n3n real numbers containing all zeros of a continuous function with up to n\nlocal minima. This demonstrates that having finitely many zeros is a strictly\nweaker condition than having finitely many local extrema. We can prove 3n to be\noptimal.<\/jats:p>","DOI":"10.2168\/lmcs-11(4:6)2015","type":"journal-article","created":{"date-parts":[[2016,11,21]],"date-time":"2016-11-21T13:46:40Z","timestamp":1479736000000},"source":"Crossref","is-referenced-by-count":10,"title":["Finite choice, convex choice and finding roots"],"prefix":"10.46298","volume":"Volume 11, Issue 4","author":[{"given":"St\u00e9phane Le","family":"Roux","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0173-3295","authenticated-orcid":false,"given":"Arno","family":"Pauly","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"25203","published-online":{"date-parts":[[2015,12,2]]},"reference":[{"key":"934:not-found"}],"container-title":["Logical Methods in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/lmcs.episciences.org\/1607\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/lmcs.episciences.org\/1607\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,4,11]],"date-time":"2023-04-11T20:07:44Z","timestamp":1681243664000},"score":1,"resource":{"primary":{"URL":"https:\/\/lmcs.episciences.org\/1607"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,12,2]]},"references-count":1,"URL":"https:\/\/doi.org\/10.2168\/lmcs-11(4:6)2015","relation":{"is-same-as":[{"id-type":"arxiv","id":"1302.0380","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.1302.0380","asserted-by":"subject"}],"is-referenced-by":[{"id-type":"arxiv","id":"1206.4809","asserted-by":"subject"},{"id-type":"doi","id":"10.1142\/s0219061319500041","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arxiv.1206.4809","asserted-by":"subject"}]},"ISSN":["1860-5974"],"issn-type":[{"type":"electronic","value":"1860-5974"}],"subject":[],"published":{"date-parts":[[2015,12,2]]},"article-number":"1607"}}