ABSTRACT
This chapter is devoted to a more detailed introduction of the study of plane algebraic curves by using the methods developed in previous chapters, in particular, the local method introduced in CH.VI is essential for understanding singularities on curves, intersections of curves and the elementary function theory on curves. In CH.IV §5, CH.V and CH.VI §5 we have seen the power of Groebner basis in algebraic geometry. But there are other computational techniques prominently present in the theory of curves, some of are algebraic nature and some of are analytical type. We point out that there have been several algorithms for parametrizing a curve and for computing the linear space L(D) associated to a divisor D on a curve (see §5), in certain special cases. We will not introduce all techniques in this text but (as in CH.I §3), we refer the reader to the special issue (2,3)23(1997) of Journal of Symbolic Computation for some detailed discussion on this topic.
