{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T05:53:26Z","timestamp":1776837206505,"version":"3.51.2"},"reference-count":25,"publisher":"American Mathematical Society (AMS)","issue":"344","license":[{"start":{"date-parts":[[2024,5,8]],"date-time":"2024-05-08T00:00:00Z","timestamp":1715126400000},"content-version":"am","delay-in-days":366,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["1913119"],"award-info":[{"award-number":["1913119"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["1527193"],"award-info":[{"award-number":["1527193"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["1913119"],"award-info":[{"award-number":["1913119"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["1527193"],"award-info":[{"award-number":["1527193"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>We establish how the coefficients of a sparse polynomial system influence the sum (or the trace) of its zeros. As an application, we develop numerical tests for verifying whether a set of solutions to a sparse system is complete. These algorithms extend the classical trace test in numerical algebraic geometry. Our results rely on both the analysis of the structure of sparse resultants as well as an extension of Esterov\u2019s results on monodromy groups of sparse systems.<\/p>","DOI":"10.1090\/mcom\/3849","type":"journal-article","created":{"date-parts":[[2023,3,29]],"date-time":"2023-03-29T09:13:40Z","timestamp":1680081220000},"page":"2893-2922","source":"Crossref","is-referenced-by-count":5,"title":["Sparse trace tests"],"prefix":"10.1090","volume":"92","author":[{"given":"Taylor","family":"Brysiewicz","sequence":"first","affiliation":[]},{"given":"Michael","family":"Burr","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2023,5,8]]},"reference":[{"issue":"3","key":"1","first-page":"1","article-title":"The number of roots of a system of equations","volume":"9","author":"Bernstein, D. N.","year":"1975","journal-title":"Funkcional. 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