{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,22]],"date-time":"2026-04-22T07:47:50Z","timestamp":1776844070004,"version":"3.51.2"},"reference-count":13,"publisher":"World Scientific Pub Co Pte Lt","issue":"08","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2010,12]]},"abstract":"<jats:p> In this paper we analyze the problem of deciding the normality (i.e. the surjectivity) of a rational parametrization of a surface [Formula: see text]. The problem can be approached by means of elimination theory techniques, providing a proper close subset [Formula: see text] where surjectivity needs to be analyzed. In general, these direct approaches are unfeasible because [Formula: see text] is very complicated and its elements computationally hard to manipulate. Motivated by this fact, we study ad hoc computational alternative methods that simplifies [Formula: see text]. For this goal, we introduce the notion of pseudo-normality, a concept that provides necessary conditions for a parametrization for being normal. Also, we provide an algorithm for deciding the pseudo-normality. Finally, we state necessary and sufficient conditions on a pseudo-normal parametrization to be normal. As a consequence, certain types of parametrizations are shown to be always normal. For instance, pseudo-normal polynomial parametrizations are normal. Moreover, for certain class of parametrizations, we derive an algorithm for deciding the normality. <\/jats:p>","DOI":"10.1142\/s0218196710005972","type":"journal-article","created":{"date-parts":[[2010,12,28]],"date-time":"2010-12-28T10:27:42Z","timestamp":1293532062000},"page":"977-990","source":"Crossref","is-referenced-by-count":8,"title":["A FIRST APPROACH TOWARDS NORMAL PARAMETRIZATIONS OF ALGEBRAIC SURFACES"],"prefix":"10.1142","volume":"20","author":[{"given":"S.","family":"P\u00c9REZ-D\u00cdAZ","sequence":"first","affiliation":[{"name":"Dpto. de Matem\u00e1ticas, Facultad de Ciencias, Universidad de Alcal\u00e1, Madrid, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"J. R.","family":"SENDRA","sequence":"additional","affiliation":[{"name":"Dpto. de Matem\u00e1ticas, Facultad de Ciencias, Universidad de Alcal\u00e1, Madrid, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"C.","family":"VILLARINO","sequence":"additional","affiliation":[{"name":"Dpto. de Matem\u00e1ticas, Facultad de Ciencias, Universidad de Alcal\u00e1, Madrid, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2012,4,30]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1007\/s00200-006-0032-7"},{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1142\/S0218195995000180"},{"key":"rf3","first-page":"125","volume":"1","author":"Chou S. C.","journal-title":"Int. J. Comput. Geom. 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