Arithmetic with Elements

u * v : GrpSLPElt, GrpSLPElt -> GrpSLPElt

Given straight-line programs u = [u₁, ..., u_m] and v = [v₁, ..., v_n] belonging to the same SLP-group G, return a straight-line program corresponding to the product of u and v. It is clear that the straight-line program [u₁, ..., u_m, v₁, ..., 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.

u ^ m : GrpSLPElt, RngIntElt -> GrpSLPElt

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 : GrpSLPElt, GrpSLPElt -> GrpSLPElt

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

# u : GrpSLPElt -> RngIntElt

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

Accessing the Defining Generators and Relations

The functions described here provide access to basic information stored for an SLP-group G.

G . i : GrpSLP, RngIntElt -> GrpSLPElt

The i-th generator for G.

Generators(G) : GrpSLP -> { GrpSLPElt }

A set containing the generators for G.

NumberOfGenerators(G) : GrpSLP -> RngIntElt

Ngens(G) : GrpSLP -> RngIntElt

The number of generators for B.

Parent(u) : GrpSLPElt -> GrpSLP

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