[Fall 1998
Colloquiums]
[Department Homepage]
DEPARTMENT OF MATHEMATICS AND STATISTICS
OAKLAND UNIVERSITY
ROCHESTER, MICHIGAN 48309
Hyungju Alan Park
Department of Mathematics and Statistics
Oakland University
Effective computation of singularities
of
affine parametric curves
Abstract
For a plane curve parametrized by x = f(t) and y
= g(t) over a field of characteristic zero, Abhyankar developed
the notion of Taylor resultant in order to find its singularities without
knowing its defining polynomial. This concept was generalized as D-resultant
by J. Yu and van den Essen, which works over an arbitrary field. In this
talk, we extend this to a curve in affine n-space parametrized by x1
= f1(t), . . . , xn = fn(t). This approach
compares to the usual approach of computing the ideal of the curve first.
After a brief introduction to the tools of symbolic computation, some computational
examples worked out by symbolic computation packages will also be presented.
372 Science and Engineering Building
Thursday, December 10, 1998
3:004:00 P.M.
Refreshments at 2:303:00 P.M. in Room 368, Science and Engineering Building