Abstract :
In this paper, combined elimination techniques are applied to establish relations among center conditions for certain cubic differential systems initially investigated by Kukles in 1944. The obtained relations clarify recent rediscoveries of some known conditions of Cherkas. The computational difficulties of establishing the complete center conditions for Kukles’ system, a problem that is still open, are illustrated by interactive elimination. Some generated polynomial systems that need be solved are made available electronically for other developers to test elimination algorithms and their implementations.
