Radical parametrizations of algebraic curves by adjoint curves

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• 作者：J. Rafael Sendra^a ; ^{rafael.sendra@uah.es"" rel=""nofollow} ; David Sevilla^b ; ¹ ; ^{david.sevilla@oeaw.ac.at"" rel=""nofollow} ;
• 关键词：Radical parametrization ; Parametrization by adjoint curves ; Offset curves ; Conchoids
• 刊名：Journal of Symbolic Computation
• 出版年：2011
• 出版时间：September 2011
• 年：2011
• 卷：46
• 期：9
• 页码：1030-1038
• 全文大小：246 K

文摘

We present algorithms for parametrizing by radicals an irreducible curve, not necessarily plane, when the genus is less than or equal to 4 and the curve is defined over an algebraically closed field of characteristic zero. In addition, we also present an algorithm for parametrizing by radicals any irreducible plane curve of degree d having at least a point of multiplicity d−r, with 1≤r≤4 and, as a consequence, every irreducible plane curve of degree d≤5 and every irreducible singular plane curve of degree 6.