- Introduction
- Constructing and Accessing Braid Groups
- Creating Elements of a Braid Group
- Representative(B) : GrpBrd -> GrpBrdElt
- Identity(B) : GrpBrd -> GrpBrdElt
- FundamentalElement(B: parameters) : GrpBrd -> GrpBrdElt
- Generators(B: parameters) : GrpBrd -> [ GrpBrd ]
- B . i : GrpBrd, RngIntElt -> GrpBrdElt
- B . T : GrpBrd, Tup -> GrpBrdElt
- B ! [ i1, ..., ik ] : GrpBrd, [ RngIntElt ] -> GrpBrdElt
- B ! [ T1, ..., Tk ] : GrpBrd, [ Tup ] -> GrpBrdElt
- B p : GrpBrd, GrpPermElt -> GrpBrdElt
- B ! [ p1, ...,pk ]: GrpBrd, [ GrpPermElt ] -> GrpBrdElt
- B T : GrpBrd, Tup -> GrpBrdElt
- IsProductOfParallelDescendingCycles(p) : GrpPermElt -> BoolElt
- Random(B, r, s, m, n: parameters) : GrpBrd, RngIntElt, RngIntElt, RngIntElt, RngIntElt -> GrpBrdElt
- Random(B, m, n: parameters) : GrpBrd, RngIntElt, RngIntElt -> GrpBrdElt
- Example GrpBrd_Constructor (H80E1)
- Working with Elements of a Braid Group
- Accessing Information
- Computing Normal Forms of Elements
- Arithmetic Operators and Functions for Elements
- u * v : GrpBrdElt, GrpBrdElt -> GrpBrdElt
- u *:= v : GrpBrdElt, GrpBrdElt ->
- u / v : GrpBrdElt, GrpBrdElt -> GrpBrdElt
- u /:= v : GrpBrdElt, GrpBrdElt ->
- u ^ n : GrpBrdElt, RngIntElt -> GrpBrdElt
- u ^:= n : GrpBrdElt, RngIntElt ->
- u ^ v : GrpBrdElt, GrpBrdElt -> GrpBrdElt
- u ^:= v : GrpBrdElt, GrpBrdElt ->
- Inverse(u) : GrpBrdElt -> GrpBrdElt
- Inverse(~u) : GrpBrdElt ->
- LeftConjugate(u, v) : GrpBrdElt, GrpBrdElt -> GrpBrdElt
- LeftConjugate(~u, v) : GrpBrdElt, GrpBrdElt -> GrpBrdElt
- LeftDiv(u, v) : GrpBrdElt, GrpBrdElt -> GrpBrdElt
- LeftDiv(u, ~v) : GrpBrdElt, GrpBrdElt -> GrpBrdElt
- Cycle(u: parameters) : GrpBrdElt -> GrpBrdElt
- Cycle(~u: parameters) : GrpBrdElt ->
- Decycle(u: parameters) : GrpBrdElt -> GrpBrdElt
- Decycle(~u: parameters) : GrpBrdElt ->
- Example GrpBrd_Arithmetic (H80E4)
- Boolean Predicates for Elements
- u in B : GrpBrdElt, GrpBrd -> BoolElt
- u notin B : GrpBrdElt, GrpBrd -> BoolElt
- IsEmptyWord(u: parameters) : GrpBrdElt -> BoolElt
- AreIdentical(u, v: parameters) : GrpBrdElt, GrpBrdElt -> BoolElt
- IsSimple(u: parameters) : GrpBrdElt -> BoolElt
- IsSuperSummitRepresentative(u: parameters) : GrpBrdElt -> BoolElt
- IsUltraSummitRepresentative(u: parameters) : GrpBrdElt -> BoolElt
- IsIdentity(u: parameters) : GrpBrdElt -> BoolElt
- u eq v : GrpBrdElt, GrpBrdElt -> BoolElt
- u ne v : GrpBrdElt, GrpBrdElt -> BoolElt
- u ≤v : GrpBrdElt, GrpBrdElt -> BoolElt
- u ≥v : GrpBrdElt, GrpBrdElt -> BoolElt
- IsConjugate(u, v: parameters) : GrpBrdElt, GrpBrdElt -> BoolElt, GrpBrdElt
- Example GrpBrd_Boolean (H80E5)
- Lattice Operations
- Invariants of Conjugacy Classes
- PositiveConjugates(u: parameters) : GrpBrdElt -> SetIndx
- SuperSummitRepresentative(u: parameters) : GrpBrdElt -> GrpBrdElt, GrpBrdElt
- SuperSummitSet(u: parameters) : GrpBrdElt -> SetIndx
- UltraSummitRepresentative(u: parameters) : GrpBrdElt -> GrpBrdElt, GrpBrdElt
- UltraSummitSet(u: parameters) : GrpBrdElt -> SetIndx
- Example GrpBrd_Conjugates (H80E7)
- Computing Class Invariants Interactively
- Computing Minimal Simple Elements
- MinimalElementConjugatingToPositive(x, s: parameters) : GrpBrdElt, GrpBrdElt -> GrpBrdElt
- MinimalElementConjugatingToSuperSummit(x, s: parameters) : GrpBrdElt, GrpBrdElt -> GrpBrdElt
- MinimalElementConjugatingToUltraSummit(x, s: parameters) : GrpBrdElt, GrpBrdElt -> GrpBrdElt
- Transport(x, s: parameters) : GrpBrdElt, GrpBrdElt -> GrpBrdElt
- Pullback(x, s: parameters) : GrpBrdElt, GrpBrdElt -> GrpBrdElt
- Example GrpBrd_MinimalSimpleElements (H80E9)
- Homomorphisms
- Bibliography
V2.28, 13 July 2023