{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,3]],"date-time":"2026-06-03T03:05:45Z","timestamp":1780455945579,"version":"3.54.1"},"reference-count":39,"publisher":"American Mathematical Society (AMS)","issue":"302","license":[{"start":{"date-parts":[[2017,1,14]],"date-time":"2017-01-14T00:00:00Z","timestamp":1484352000000},"content-version":"am","delay-in-days":366,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"funder":[{"DOI":"10.13039\/501100000038","name":"Natural Sciences and Engineering Research Council of Canada","doi-asserted-by":"publisher","award":["4168"],"award-info":[{"award-number":["4168"]}],"id":[{"id":"10.13039\/501100000038","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>We investigate the computation and applications of rational invariants of the linear action of a finite abelian group in the nonmodular case. By diagonalization, such a group action can be described by integer matrices of orders and exponents. We make use of integer linear algebra to compute a minimal generating set of invariants along with the substitution needed to rewrite any invariant in terms of this generating set. In addition, we show how to construct a minimal generating set that consists only of polynomial invariants. As an application, we provide a symmetry reduction scheme for polynomial systems whose solution set is invariant by a finite abelian group action. Finally, we also provide an algorithm to find such symmetries given a polynomial system.<\/p>","DOI":"10.1090\/mcom\/3076","type":"journal-article","created":{"date-parts":[[2015,5,27]],"date-time":"2015-05-27T10:44:05Z","timestamp":1432723445000},"page":"3029-3050","source":"Crossref","is-referenced-by-count":16,"title":["Computation of invariants of finite abelian groups"],"prefix":"10.1090","volume":"85","author":[{"given":"Evelyne","family":"Hubert","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"George","family":"Labahn","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"14","published-online":{"date-parts":[[2016,1,14]]},"reference":[{"key":"1","isbn-type":"print","doi-asserted-by":"publisher","first-page":"20","DOI":"10.1145\/2442829.2442837","article-title":"Computing Puiseux series for algebraic surfaces","author":"Adrovic, Danko","year":"2012","ISBN":"https:\/\/id.crossref.org\/isbn\/9781450312691"},{"issue":"2","key":"2","doi-asserted-by":"publisher","first-page":"304","DOI":"10.1287\/moor.26.2.304.10555","article-title":"Cutting planes and the elementary closure in fixed dimension","volume":"26","author":"Bockmayr, Alexander","year":"2001","journal-title":"Math. 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