We present Las Vegas algorithms for constructive recognition and constructive
membership testing of the Ree groups 2G_2(q) = Ree(q), where q = 3^{2m + 1} for
some m > 0, in their natural representations of degree 7. The input is a
generating set X.
The constructive recognition algorithm is polynomial time given a discrete
logarithm oracle. The constructive membership testing consists of a
pre-processing step, that only needs to be executed once for a given X, and a
main step. The latter is polynomial time, and the former is polynomial time
given a discrete logarithm oracle.
Implementations of the algorithms are available for the computer algebra
system MAGMA