Some constructions for real algebraic curves

Authors:
E. Fortuna;P. Gianni;P. Parenti
Affiliations:
Dipartimento di Matematica, Università di Pisa, via Buonarroti 2, I56127 Pisa, Italy;Dipartimento di Matematica, Università di Pisa, via Buonarroti 2, I56127 Pisa, Italy;Dipartimento di Matematica, Università di Pisa, via Buonarroti 2, I56127 Pisa, Italy
Venue:
Journal of Symbolic Computation
Year:
2005

Citing 5
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Abstract

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. are fulfilled is given.