  Let R be a commutative ring with 1. For every homogeneous polynomial
f(X_0,X_1,X_2) in R[X_0,X_1,X_2] of degree d <= 25, we find a explicit linear
Pfaffian R-representation of f. We describe an empirical method that leads us
to find such R-representations. This generalizes and constitutes an alternative
proof (up to degree 25) of a result due to A. Beauville [Bea] about the
existence of linear Pfaffian K-representations for any smooth plane curve of
degree d >= 2, where K is an algebraically closed field of characteristic zero.
