Arithmetic with Elements

Contents

u * v : GrpSLPElt, GrpSLPElt -> GrpSLPElt
Given straight-line programs u = [u1, ..., um] and v = [v1, ..., vn] 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, ..., um, v1, ..., vn, um vn] satisfies the formal definition. In practice, the ui and vi 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.
V2.28, 13 July 2023