  The Poincar\'e series of a ring associated to a plane curve was defined by
Campillo, Delgado, and Gusein-Zade. This series, defined through the value
semigroup of the curve, encodes the topological information of the curve. In
this paper we extend the definition of Poincar\'e series to the class of good
semigroup ideals, to which value semigroups of curves belong. Using this
definition we generalize a result of Pol: under suitable assumptions, given
good semigroup ideals E and K, with K canonical, the Poincar\'e series of K-E
is symmetric to the Poincar\'e series of E.
