"On Computing the Weierstrass Points of a Plane Algebraic Curve"

Mark Heiligman and Emil Volcheck*.
*Department of Defense
3120 Saint Paul St., Apt. B-205
Baltimore MD  21218
USA
E-mail:volcheck@acm.org


Abstract:

Weierstrass points are an important geometric feature of an algebraic curve.
We present an algorithm based on a classical construction to compute the
Weierstrass points of an absolutely irreducible plane algebraic curve
defined over a computable field of characteristic zero.  As a partial
complexity analysis, we show that critical steps of the algorithm are bounded
by $O(g^9 d^2)$ ground field operations, where $g$ is the genus
and $d$ the degree of the curve.