Details:
Title  On the topology of real algebraic plane curves.  Author(s)  JinSan Cheng, Sylvain Lazard, Luis Pe~naranda, Marc Pouget, Fabrice Rouillier  Type  Article in Journal  Abstract  We revisit the problem of computing the topology and geometry of a real algebraic plane curve. The topology is of prime interest but geometric information, such as the position of singular and critical points, is also relevant. A challenge is to compute efficiently this information for the given coordinate system even if the curve is not in generic position. Previous methods based on the cylindrical algebraic decomposition use subresultant sequences and computations with polynomials with algebraic coefficients. A novelty of our approach is to replace these tools by Gröbner basis computations and isolation with rational univariate representations. This has the advantage of avoiding computations with polynomials with algebraic coefficients, even in nongeneric positions. Our algorithm isolates critical points in boxes and computes a decomposition of the plane by rectangular boxes. This decomposition also induces a new approach for computing an arrangement of polylines isotopic to the input curve. We also present an analysis of the complexity of our algorithm. An implementation of our algorithm demonstrates its efficiency, in particular on highdegree nongeneric curves.  ISSN  16618270; 16618289/e 
URL 
http://link.springer.com/article/10.1007%2Fs1178601000443 
Language  English  Journal  Math. Comput. Sci.  Volume  4  Number  1  Pages  113137  Publisher  Springer (Birkh\"auser), Basel  Year  2010  Edition  0  Translation 
No  Refereed 
No 
