{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T15:36:35Z","timestamp":1776785795203,"version":"3.51.2"},"reference-count":15,"publisher":"American Mathematical Society (AMS)","issue":"255","license":[{"start":{"date-parts":[[2007,3,31]],"date-time":"2007-03-31T00:00:00Z","timestamp":1175299200000},"content-version":"am","delay-in-days":365,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>A problem concerning the perturbation of roots of a system of homogeneous algebraic equations is investigated. The question of conservation and decomposition of a multiple root into simple roots are discussed. The main theorem on the conservation of the number of roots of a deformed (not necessarily homogeneous) algebraic system is proved by making use of a homotopy connecting initial roots of the given system and roots of a perturbed system. Hereby we give an estimate on the size of perturbation that does not affect the number of roots. Further on we state the existence of a slightly deformed system that has the same number of real zeros as the original system in taking the multiplicities into account. We give also a result about the decomposition of multiple real roots into simple real roots.<\/p>","DOI":"10.1090\/s0025-5718-06-01847-3","type":"journal-article","created":{"date-parts":[[2006,5,24]],"date-time":"2006-05-24T14:43:01Z","timestamp":1148481781000},"page":"1383-1402","source":"Crossref","is-referenced-by-count":1,"title":["On perturbation of roots of homogeneous algebraic systems"],"prefix":"10.1090","volume":"75","author":[{"given":"S.","family":"Tanab\u00e9","sequence":"first","affiliation":[]},{"given":"M.","family":"Vrahatis","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2006,3,31]]},"reference":[{"key":"1","volume-title":"Topologie","author":"Alexandroff, Paul","year":"1965"},{"key":"2","series-title":"Monographs in Mathematics","isbn-type":"print","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-5154-5","volume-title":"Singularities of differentiable maps. Vol. I","volume":"82","author":"Arnol\u2032d, V. 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