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TitleDetecting real singularities of a space curve from a real rational parametrization
Author(s) R. Rubio, J.M. Serradilla, M.P. Vélez
TypeArticle in Journal
AbstractIn this paper we give an algorithm that detects real singularities, including singularities at infinity, and counts local branches and multiplicities of real rational curves in the affine n -space without knowing an implicitization. The main idea behind this is a generalization of the D -resultant (see [van den Essen, A., Yu, J.-T., 1997. The D -resultant, singularities and the degree of unfaithfulness. Proc. Amer. Math. Soc. 25 (3), 689695]) to n rational functions. This allows us to find all real parameters corresponding to the real singularities between the solutions of a system of polynomials in one variable.
KeywordsAlgebraic curves, Rational parametrizations, Singular points, Generalized resultants
ISSN0747-7171
URL http://www.sciencedirect.com/science/article/pii/S0747717108001405
LanguageEnglish
JournalJournal of Symbolic Computation
Volume44
Number5
Pages490 - 498
Year2009
NoteSpanish National Conference on Computer Algebra
Edition0
Translation No
Refereed No
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