"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.