FINITELY PRESENTED SEMIGROUPS
Acknowledgements
Introduction
The Construction of Free Semigroups and their Elements
Structure Constructors
Element Constructors
Elementary Operators for Words
Multiplication and Exponentiation
The Length of a Word
Equality and Comparison
Specification of a Presentation
Relations
Presentations
Accessing the Defining Generators and Relations
Subsemigroups, Ideals and Quotients
Subsemigroups and Ideals
Quotients
Extensions
Elementary Tietze Transformations
String Operations on Words
Introduction
The Construction of Free Semigroups and their Elements
Structure Constructors
FreeSemigroup(n) : RngIntElt -> SgpFP
FreeMonoid(n) : RngIntElt -> MonFP
Example SgpFP_FreeSemigroup (H86E1)
Element Constructors
S ! [i1, ... is] : SgpFP, [RngIntElt] -> SgpFPElt
Id(M) : MonFP -> MonFPElt
Elementary Operators for Words
Multiplication and Exponentiation
u * v : SgpFPElt, SgpFPElt -> SgpFPElt
u ^ n : SgpFPElt, RngIntElt -> SgpFPElt
G ! Q : SgpFP, [ SgpFPElt ] -> SgpFPElt
The Length of a Word
# u : SgpFPElt -> RngIntElt
Equality and Comparison
u eq v : SgpFPElt, SgpFPElt -> BoolElt
u ne v : SgpFPElt, SgpFPElt -> BoolElt
u lt v : SgpFPElt, SgpFPElt -> BoolElt
u le v : SgpFPElt, SgpFPElt -> BoolElt
u ge v : SgpFPElt, SgpFPElt -> BoolElt
u gt v : SgpFPElt, SgpFPElt -> BoolElt
IsOne(u) : MonFPElt -> BoolElt
Specification of a Presentation
Relations
w1 = w2 : SgpFPElt, SgpFPElt -> Rel
LHS(r) : Rel -> SgpFPElt
RHS(r) : Rel -> SgpFPElt
Presentations
Semigroup< generators | relations > : SgpFPElt, ..., SgpFPElt, Rel, ...Rel -> SgpFP
Monoid< generators | relations > : MonFPElt, ..., MonFPElt, Rel, ..., Rel -> MonFP
Example SgpFP_Monoid (H86E2)
Accessing the Defining Generators and Relations
S . i : SgpFP, RngIntElt -> SgpFPElt
Generators(S) : SgpFP -> { SgpFPElt }
NumberOfGenerators(S) : SgpFP -> RngIntElt
Parent(u) : SgpFPElt -> SgpFP
Relations(S) : SgpFP -> [ Rel ]
Subsemigroups, Ideals and Quotients
Subsemigroups and Ideals
sub<S | L1, ..., Lr> : SgpFP, SgpFPElt, ..., SgpFPElt -> SgpFP
ideal<S | L1, ..., Lr> : SgpFP, SgpFPElt, ..., SgpFPElt -> SgpFPIdl
lideal<G | L1, ..., Lr> : SgpFP, SgpFPElt, ..., SgpFPElt -> SgpFPIdl
rideal<G | L1, ..., Lr> : SgpFP, SgpFPElt, ..., SgpFPElt -> SgpFPIdl
Quotients
quo< F | relations > : SgpFP, Rel, ..., Rel -> SgpFP
Extensions
DirectProduct(R, S) : SgpFP, SgpFP -> SgpFP
FreeProduct(R, S) : SgpFP, SgpFP -> SgpFP
Elementary Tietze Transformations
AddRelation(S, r) : SgpFP, Rel -> SgpFP
DeleteRelation(S, r) : SgpFP, Rel -> SgpFP
DeleteRelation(S, i) : SgpFP, RngIntElt -> SgpFP
ReplaceRelation(S, r1, r2) : SgpFP, Rel, Rel -> SgpFP
ReplaceRelation(S, i, r) : SgpFP, RngIntElt, Rel -> SgpFP
AddGenerator(S) : SgpFP -> SgpFP
AddGenerator(S, w) : SgpFP, SgpFPElt -> SgpFP
DeleteGenerator(S, y) : SgpFP, SgpFPElt -> SgpFP
String Operations on Words
Eliminate(u, x, v) : SgpFPElt, SgpFPElt, SgpFPElt -> SgpFPElt
Match(u, v, f) : SgpFPElt, SgpFPElt, RngIntElt -> BoolElt, RngIntElt
Random(S, m, n) : SgpFP, RngIntElt, RngIntElt -> SgpFPElt
RotateWord(u, n) : SgpFPElt, RngIntElt -> SgpFPElt
Substitute(u, f, n, v) : SgpFPElt, RngIntElt, SgpFPElt, RngIntElt -> SgpFPElt
Subword(u, f, n) : SgpFPElt, RngIntElt, RngIntElt -> SgpFPElt
ElementToSequence(u) : SgpFPElt -> [ SgpFPElt ]
[Next][Prev] [Right] [____] [Up] [Index] [Root]
|