{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,20]],"date-time":"2025-10-20T10:24:15Z","timestamp":1760955855418},"reference-count":8,"publisher":"World Scientific Pub Co Pte Lt","issue":"07","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Algebra Comput."],"published-print":{"date-parts":[[2018,11]]},"abstract":"<jats:p> In this paper, we characterize the classification of unimodal maps from the plane to the plane with respect to [Formula: see text]-equivalence given by Rieger in terms of invariants. We recall the classification over an algebraically closed field of characteristic [Formula: see text]. On the basis of this characterization, we present an algorithm to compute the type of the unimodal maps from the plane to the plane without computing the normal form and also give its implementation in the computer algebra system Singular. <\/jats:p>","DOI":"10.1142\/s0218196718500534","type":"journal-article","created":{"date-parts":[[2018,7,24]],"date-time":"2018-07-24T05:47:01Z","timestamp":1532411221000},"page":"1199-1208","source":"Crossref","is-referenced-by-count":6,"title":["Recognition of unimodal map germs from the plane to the plane by invariants"],"prefix":"10.1142","volume":"28","author":[{"given":"Saima","family":"Aslam","sequence":"first","affiliation":[{"name":"Department of Mathematics, Government College University, Faisalabad, Pakistan"}]},{"given":"Muhammad Ahsan","family":"Binyamin","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Government College University, Faisalabad, Pakistan"}]},{"given":"Gerhard","family":"Pfister","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of Kaiserslautern, Germany"}]}],"member":"219","published-online":{"date-parts":[[2018,10,15]]},"reference":[{"issue":"2","key":"S0218196718500534BIB001","first-page":"135","volume":"61","author":"Afzal D.","year":"2018","journal-title":"Bull. Math. Soc. Sci. Roumanie"},{"key":"S0218196718500534BIB002","doi-asserted-by":"publisher","DOI":"10.1142\/S0219498817501997"},{"key":"S0218196718500534BIB003","doi-asserted-by":"publisher","DOI":"10.1088\/0951-7715\/10\/1\/017"},{"key":"S0218196718500534BIB005","volume-title":"A Singular Introduction to Commutative Algebra","author":"Greuel G.-M.","year":"2007","edition":"2"},{"key":"S0218196718500534BIB006","doi-asserted-by":"publisher","DOI":"10.1016\/j.topol.2016.01.011"},{"key":"S0218196718500534BIB007","doi-asserted-by":"publisher","DOI":"10.1007\/BF02684889"},{"key":"S0218196718500534BIB008","doi-asserted-by":"publisher","DOI":"10.1112\/jlms\/s2-36.2.351"},{"key":"S0218196718500534BIB009","doi-asserted-by":"publisher","DOI":"10.14492\/hokmj\/1285766004"}],"container-title":["International Journal of Algebra and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0218196718500534","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T12:16:29Z","timestamp":1565180189000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218196718500534"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,10,15]]},"references-count":8,"journal-issue":{"issue":"07","published-online":{"date-parts":[[2018,10,15]]},"published-print":{"date-parts":[[2018,11]]}},"alternative-id":["10.1142\/S0218196718500534"],"URL":"https:\/\/doi.org\/10.1142\/s0218196718500534","relation":{},"ISSN":["0218-1967","1793-6500"],"issn-type":[{"value":"0218-1967","type":"print"},{"value":"1793-6500","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,10,15]]}}}