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Magma
Computer • algebra
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Introduction
Construction of an SLP-Group and its Elements
Structure Constructors
NaturalBlackBoxGroup(H) : Grp -> GrpBB
Construction of an Element
Identity(G) : GrpBB -> GrpBBElt
Arithmetic with Elements
u * v : GrpBBElt, GrpBBElt -> GrpBBElt
u ^ m : GrpBBElt, RngIntElt -> GrpBBElt
u ^ v : GrpBBElt, GrpBBElt -> GrpBBElt
(u, v) : GrpBBElt, GrpBBElt -> GrpBBElt
Accessing the Defining Generators
G . i : GrpBB, RngIntElt -> GrpBBElt
Generators(G) : GrpBB -> { GrpBBElt }
NumberOfGenerators(G) : GrpBB -> RngIntElt
Operations on Elements
Equality and Comparison
u eq v : GrpBBElt, GrpBBElt -> BoolElt
u ne v : GrpBBElt, GrpBBElt -> BoolElt
Attributes of Elements
Parent(u) : GrpBBElt -> GrpBB
UnderlyingElement(u) : GrpBBElt -> GrpElt
Order(u) : GrpBBElt -> RngIntElt
Example
GrpBB_standard-gens (H70E1)
Set-Theoretic Operations
Membership and Equality
g in G : GrpBBElt, GrpBB -> BoolElt
Set Operations
PseudoRandom(G) : GrpBB -> GrpBBElt
Rep(G) : GrpBB -> GrpBBElt
Coercions Between Related Groups
G ! g : GrpBB, GrpBBElt -> GrpBBElt
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V2.28, 13 July 2023