  Let C be an irreducible projective curve of degree d in Pn(K), where K is an
algebraically closed field, and let I be the associated homogeneous prime
ideal. We wish to compute generators for I, assuming we are given sufficiently
many points on the curve C. In particular if I can be generated by polynomials
of degree at most m and we are given md + 1 points on C, then we can find a set
of generators for I. We will show that a minimal set of generators of I can be
constructed in polynomial time. Our constructions are completely independent of
any notion of term ordering; this allows us the maximal freedom in performing
our constructions in order to improve the numerical stability. We also
summarize some classical results on bounds for the degrees of the generators of
our ideal in terms of the degree and genus of the curve.
