  The Function Field Sieve algorithm is dedicated to computing discrete
logarithms in a finite field GF(q^n), where q is small an prime power. The
scope of this article is to select good polynomials for this algorithm by
defining and measuring the size property and the so-called root and
cancellation properties. In particular we present an algorithm for rapidly
testing a large set of polynomials. Our study also explains the behaviour of
inseparable polynomials, in particular we give an easy way to see that the
algorithm encompass the Coppersmith algorithm as a particular case.
