In order to parametrize an algebraic ’ curve of genus zero, one usually faces the problem of finding rational points on it. This problem can be reduced to find rational points on a (birationally equivalent) conic. In this paper, we deal with a method of computing such a rational point on a conic from its defining equation (we are only interested in exact, i. e. symbolic solutions). The method will then be extended to work over the rational function field too. This problem arises in the parametrization of surfaces over Q.Contents
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