Some constructions for real algebraic curves

• Autores: Elisabetta Fortuna, P. Parenti, P. Gianni
• Localización: Journal of symbolic computation, ISSN 0747-7171, Vol. 40, Nº 4, 2005, págs. 1169-1179
• Idioma: inglés
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• Resumen

  • We address two basic questions for real algebraic curves. The first one is how to decide whether a real algebraic curve in the n-projective space contains some real point. We present an algorithm that reduces the original question to deciding whether the zero-set of a zero-dimensional ideal contains real points. The second part of the paper is devoted to giving necessary and sufficient conditions for the existence of a real line disjoint from a given real plane algebraic curve. An algorithm for testing whether these conditions are fulfilled is given.