  The research described in this note aims at solving the constructive
membership problem for the class of quasisimple classical groups. Our
algorithms are developed in the black-box group model; that is, they do not
require specific characteristics of the representations in which the input
groups are given. The elements of a black-box group are represented, not
necessarily uniquely, as bit strings of uniform length. We assume the existence
of oracles to compute the product of two elements, the inverse of an element,
and to test if two strings represent the same element. Solving the constructive
membership problem for a black-box group $G$ requires to write every element of
$G$ as a word in a given generating set. In practice we write the elements of
$G$ as straight-line programs (SLPs) which can be viewed as a compact way of
writing words.
