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Computer • algebra
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Introduction
Construction of an SLP-Group and its Elements
Structure Constructors
SLPGroup(n) : RngIntElt -> GrpSLP
Example
GrpSLP_SLPGroup (H83E1)
Construction of an Element
Identity(G) : GrpSLP -> GrpSLPElt
Arithmetic with Elements
u * v : GrpSLPElt, GrpSLPElt -> GrpSLPElt
u ^ m : GrpSLPElt, RngIntElt -> GrpSLPElt
u ^ v : GrpSLPElt, GrpSLPElt -> GrpSLPElt
# u : GrpSLPElt -> RngIntElt
Accessing the Defining Generators and Relations
G . i : GrpSLP, RngIntElt -> GrpSLPElt
Generators(G) : GrpSLP -> { GrpSLPElt }
NumberOfGenerators(G) : GrpSLP -> RngIntElt
Parent(u) : GrpSLPElt -> GrpSLP
Addition of Extra Generators
AddRedundantGenerators(G, Q) : GrpSLP, [ GrpSLPElt ] -> GrpSLP
Creating Homomorphisms
hom< G -> H | L: parameters> : GrpSLP, Grp -> Map
Evaluate(u, Q) : GrpSLPElt, [ GrpElt ] -> GrpElt
Example
GrpSLP_ConstructingHomomorphisms (H83E2)
Operations on Elements
Equality and Comparison
u eq v : GrpSLPElt, GrpSLPElt -> BoolElt
u ne v : GrpSLPElt, GrpSLPElt -> BoolElt
Set-Theoretic Operations
Membership and Equality
g in G : GrpSLPElt, GrpSLP -> BoolElt
g notin G : GrpSLPElt, GrpSLP -> BoolElt
S subset G : { GrpSLPElt } , GrpSLP -> BoolElt
S notsubset G : { GrpSLPElt } , GrpSLP -> BoolElt
Set Operations
RandomProcess(G) : GrpSLP -> Process
Random(P) : Process -> GrpSLPElt
Rep(G) : GrpSLP -> GrpSLPElt
Example
GrpSLP_HomomorphismSpeed (H83E3)
Coercions Between Related Groups
G ! g : GrpSLP, GrpSLPElt -> GrpSLPElt
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V2.28, 13 July 2023