Title: A NEW ALGORITHM FOR FINDING RATIONAL FIRST
INTEGRALS OF POLYNOMIAL VECTOR FIELDS

Authors: ANTONI FERRAGUT AND HECTOR GIACOMINI

Abstract: We present a new method to compute rational first integrals
of a planar polynomial vector field. The algorithm is in general much
faster than the usual methods and also allows to compute the remarkable
curves associated to the rational first integral of the system.

1991 Mathematics Subject Classification. 34C05, 34A34, 34C14.
Key words and phrases. Polynomial vector field, Rational first integral, Remarkable
curve.

The first author is partially supported by a MEC/FEDER grant MTM2005-06098-
C02-1 and by a CIRIT grant 2005SGR-00550.