This online help node and the nodes below it describe the category of blackbox groups. The elements of a blackbox group are similar to straight-line programs and will be referred to as such in the following sections. A straight-line program is formally a sequence [s_1, s_2, ..., s_n] such that each s_i is one of the following:

• A generator of the blackbox group;
• A product s_j s_k, j<i, k<i;
• A power s_j^n, j<i;
• A conjugate s_j^(s_k), j<i, k<i.

The importance of such a category of groups is that storing a word as an expression tree allows much faster evaluation of homomorphisms given as the unique extension of a mapping of the generators into a group of any category, as common subexpressions may be computed once only, and powers or conjugates may be more efficiently computed in the target group than by a linear product of generators and their inverses.