The Category of Automatic Groups
The Construction of an Automatic Group
Construction of an Automatic Group
AutomaticGroup(F: parameters) : GrpFP -> GrpAtc
Example GrpAtc_AutomaticGroup (H75E1)
Modifying Limits
AutomaticGroup(F: parameters) : GrpFP -> GrpAtc
SetVerbose("KBMAG", v) : MonStgElt, RngIntElt ->
Example GrpAtc_AutomaticGroup-3 (H75E2)
Example GrpAtc_AutomaticGroup-4 (H75E3)
Accessing Group Information
G . i : GrpRWS, RngIntElt -> GrpRWSElt
Generators(G) : GrpRWS -> [GrpRWSElt]
NumberOfGenerators(G) : GrpRWS -> RngIntElt
Example GrpAtc_BasicAccess (H75E4)
FPGroup(G) : GrpAtc -> GrpFP, Map
WordAcceptor(G) : GrpAtc -> Rec
WordAcceptorSize(G) : GrpAtc -> RngIntElt, RngIntElt
WordDifferenceAutomaton(G) : GrpAtc -> Rec
WordDifferenceSize(G) : GrpAtc -> RngIntElt, RngIntElt
WordDifferences(G) : GrpAtc -> SeqEnum
GeneratorOrder(G) : GrpAtc -> SeqEnum
Properties of an Automatic Group
IsFinite(G) : GrpRWS -> BoolElt, RngIntElt
Order(G) : GrpRWS -> RngIntElt
Example GrpAtc_Order (H75E5)
Example GrpAtc_Order-2 (H75E6)
Construction of a Word
G ! [ i1, ..., is ] : GrpAtc, [ RngIntElt ] -> GrpAtcElt
Identity(G) : GrpAtc -> GrpAtcElt
Parent(w) : GrpAtcElt -> GrpAtc
Example GrpAtc_Words (H75E7)
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
(u1, ..., ur) : 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 (H75E8)
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 (H75E9)
The Growth Function
GrowthFunction(G) : GrpAtc -> FldFunRatElt
Example GrpAtc_GrowthFunction (H75E10)
Bibliography
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Version: V2.19 of
Mon Dec 17 14:40:36 EST 2012