Subsections

• Accessing the Defining Generators and Relations

Given straight-line programs u = [u_1, ..., u_m] and v = [v_1, ..., v_n] belonging to the same blackbox group G, return a straight-line program corresponding to the product of u and v. It is clear that the straight-line program [u_1, ..., u_m, v_1, ..., v_n, u_m v_n] satisfies the formal definition. In practice, the u_i and v_i need not be distinct, so the resulting program may be shorter.

Given an integer m and a straight-line program u, return the straight-line program corresponding to the m-th power of u.

u ^ v : GrpBBElt, GrpBBElt -> GrpBBElt

Given straight-line programs u and v, return the straight-line program corresponding to the conjugate of u by v.

Given a straight-line program u, return the number of multiplication, power or conjugate operations required to evaluate a homomorphism on u.

The functions described here provide access to basic information stored for a blackbox group G.

G . i : GrpBB, RngIntElt -> GrpBBElt

The i-th generator for G.

A set containing the generators for G.

Ngens(G) : GrpBB -> RngIntElt

The number of generators for B.

The parent group G of the straight-line program u.