The Category of Automatic Groups
The Construction of an Automatic Group
Construction of an Automatic Group
AutomaticGroup(F: parameters) : GrpFP -> GrpAtc
Example GrpAtc_AutomaticGroup (H35E1)
Modifying Limits
AutomaticGroup(F: parameters) : GrpFP -> GrpAtc
SetVerbose("KBMAG", v) : MonStgElt, RngIntElt ->
Example GrpAtc_AutomaticGroup-3 (H35E2)
Example GrpAtc_AutomaticGroup-4 (H35E3)
Accessing Group Information
G . i : GrpRWS, RngIntElt -> GrpRWSElt
Generators(G) : GrpRWS -> [GrpRWSElt]
NumberOfGenerators(G) : GrpRWS -> RngIntElt
Example GrpAtc_BasicAccess (H35E4)
Properties of an Automatic Group
IsFinite(G) : GrpRWS -> BoolElt, RngIntElt
Order(G) : GrpRWS -> RngIntElt
Example GrpAtc_Order (H35E5)
Example GrpAtc_Order-2 (H35E6)
Construction of a Word
G ! [ i_1, ..., i_s ] : GrpAtc, [ RngIntElt ] -> GrpAtcElt
Identity(G) : GrpAtc -> GrpAtcElt
Parent(w) : GrpAtcElt -> GrpAtc
Example GrpAtc_Words (H35E7)
Operations on Elements
u * v : GrpRWSElt, GrpRWSElt -> GrpRWSElt
u / v : GrpRWSElt, GrpRWSElt -> GrpRWSElt
u ^ n : GrpRWSElt, RngIntElt -> GrpRWSElt
u ^ v : GrpRWSElt, GrpRWSElt -> GrpRWSElt
Inverse(w) : GrpRWSElt -> GrpRWSElt
(u, v) : GrpRWSElt, GrpRWSElt -> GrpRWSElt
(u_1, ..., u_r) : GrpRWSElt, ..., GrpRWSElt -> GrpRWSElt
u eq v : GrpRWSElt, GrpRWSElt -> BoolElt
u ne v : GrpRWSElt, GrpRWSElt -> BoolElt
IsId(w) : GrpRWSElt -> BoolElt
# u : GrpRWSElt -> RngIntElt
ElementToSequence(u) : GrpRWSElt -> [ RngIntElt ]
Example GrpAtc_Arithmetic (H35E8)
Construction of Homomorphisms
hom< A -> G | S > : Struct , Struct -> Map
Set Operations
Random(G, n) : GrpAtc, RngIntElt -> GrpAtcElt
Random(G) : GrpAtc -> GrpAtcElt
Representative(G) : GrpAtc -> GrpAtcElt
Set(G, a, b) : GrpAtc, RngIntElt, RngIntElt -> SetEnum
Set(G) : GrpAtc -> SetEnum
Seq(G, a, b) : GrpAtc, RngIntElt, RngIntElt -> SeqEnum
Seq(G) : GrpAtc -> SeqEnum
Example GrpAtc_Set (H35E9)
The Growth Function
GrowthFunction(G) : GrpAtc -> FldFunRatElt