The Construction of Free Semigroups and their Elements
Structure Constructors
FreeSemigroup(n) : RngIntElt -> SgpFP
FreeMonoid(n) : RngIntElt -> MonFP
Example SgpFP_FreeSemigroup (H77E1)
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 (H77E2)
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 ]
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Version: V2.19 of
Mon Dec 17 14:40:36 EST 2012