caa a22 4500 463203097 CHVBK 20180405153117.0 cr unu---uuuuu 170326e20070201xx s 000 0 eng 10.1007/s00200-006-0032-7 doi (NATIONALLICENCE)springer-10.1007/s00200-006-0032-7 Plotting missing points and branches of real parametric curves [Elektronische Daten] [Carlos Andradas, Tomás Recio] This paper is devoted to the study (from the theoretic and algorithmic point of view) of the existence of points and branches non-reachable by a parametric representation of a rational algebraic curve (in n-dimensional space) either over the field of complex numbers or over the field of real numbers. In particular, we generalize some of the results on missing points in (J. Symbolic Comput. 33, 863-885, 2002) to the case of space curves. Moreover, we introduce for the first time and we solve the case of missing branches. Another novelty is the emphasis on topological conditions over the curve for the existence of missing points and branches. Finally, we would like to point out that, by developing an "ad hoc” and simplified theory of valuations for the case of parametric curves, we approach in a new and unified way the analysis of the missing points and branches, and the proposal of the algorithmic solution to these problems. Springer-Verlag, 2006 Parametric curves nationallicence Normal parametrization nationallicence Branches nationallicence Valuation rings nationallicence Andradas Carlos Departamento de Álgebra, Universidad Complutense, 28040, Madrid, Spain aut Recio Tomás Departamento de Matemáticas, Universidad de Cantabria, 39071, Santander, Spain aut Applicable Algebra in Engineering, Communication and Computing Springer-Verlag 18/1-2(2007-02-01), 107-126 0938-1279 18:1-2<107 2007 18 200 https://doi.org/10.1007/s00200-006-0032-7 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00200-006-0032-7 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Andradas Carlos Departamento de Álgebra, Universidad Complutense, 28040, Madrid, Spain aut NATIONALLICENCE 700 1- Recio Tomás Departamento de Matemáticas, Universidad de Cantabria, 39071, Santander, Spain aut NATIONALLICENCE 773 0- Applicable Algebra in Engineering, Communication and Computing Springer-Verlag 18/1-2(2007-02-01), 107-126 0938-1279 18:1-2<107 2007 18 200 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer