Bulletin of the Australian Mathematical Society

Research Article

The topological configuration of a real algebraic curve

Takis Sakkalisa1

a1 Department of Mathematical Sciences, Oakland University, Rochester MI 48309-4401, United States of America

Abstract

This paper presents an algorithm, motivated by Morse Theory, for the topological configuration of the components of a real algebraic curve {f(x, y) = 0}. The running time of the algorithm is O(n12 (d + log n)2 log n), where n, d are the degree and maximum coefficient size of f(x, y).

(Received January 31 1990)