Some constructions for real algebraic curves

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.