Copyright | Adam Saltz |
---|---|
License | BSD3 |
Maintainer | saltz.adam@gmail.com |
Stability | experimental |
Safe Haskell | None |
Language | Haskell2010 |
Longer description to come.
- type ArcLabel = Int
- type Height = Int
- type BraidIndex = Int
- type ArtinGen = Int
- newtype NameNode = NameNode (Node ArcLabel)
- identity :: BraidIndex -> Diagram B
- identityAt :: BraidIndex -> ArcLabel -> Diagram B
- negativeCrossing :: Diagram B
- positiveCrossing :: Diagram B
- cupCap :: Diagram B
- cupCapLevelAt :: BraidIndex -> ArcLabel -> ArtinGen -> Diagram B
- artin :: BraidIndex -> ArtinGen -> Diagram B
- drawBraid :: Braid -> Diagram B
- drawBraidClosure :: Braid -> Diagram B
- resolutionD :: Int -> BraidIndex -> ArtinGen -> Diagram B
- resolutionAt :: Int -> BraidIndex -> ArtinGen -> Height -> Diagram B
- resolveD :: Resolution -> Braid -> Diagram B
- resolveClosureD :: Resolution -> Braid -> Diagram B
- cubeOfResolutionsD :: Braid -> Map Resolution (Diagram B)
- cubeOfResolutionsClosureD :: Braid -> Map Resolution (Diagram B)
- printCube :: Map [Int] (Diagram B) -> Diagram B
- bigGeneratorD :: Braid -> AlgGen -> Map [Int] (Diagram B)
- generatorD :: Braid -> Generator -> Diagram B
- markIn :: Diagram B -> Component -> Sign -> Diagram B -> Diagram B
Documentation
type BraidIndex = Int Source
identity :: BraidIndex -> Diagram B Source
The identity braid of index index
.
identityAt :: BraidIndex -> ArcLabel -> Diagram B Source
The identity braid of index index
with arc names starting at lastlabel + 1
.
negativeCrossing :: Diagram B Source
A negative crossing.
positiveCrossing :: Diagram B Source
Draws a positive crossing.
cupCapLevelAt :: BraidIndex -> ArcLabel -> ArtinGen -> Diagram B Source
A cup-cap combo with names starting at lastLabel + 1
.
artin :: BraidIndex -> ArtinGen -> Diagram B Source
The k
th Artin generator of the braid group on n
strands.
To draw the inverse of the k
th generator, use -k
.
drawBraidClosure :: Braid -> Diagram B Source
Draws a braid closure.
resolutionD :: Int -> BraidIndex -> ArtinGen -> Diagram B Source
Draws the r
resolution of the k
th Artin generator in the n
strand braid group.
To draw the inverse of the k
th generator, use -k
.
resolutionAt :: Int -> BraidIndex -> ArtinGen -> Height -> Diagram B Source
Draws the r
resolution of the k
th Artin generator in the n
strand braid group with names starting at lastLabel + 1
.
To draw the inverse of the k
th generator, use -k
.
resolveClosureD :: Resolution -> Braid -> Diagram B Source
Draws the closure of the braid b
resolved according to rs
.
cubeOfResolutionsD :: Braid -> Map Resolution (Diagram B) Source
A Map
from Resolution
s to a diagram of the corresponding resolution of the braid b
.
cubeOfResolutionsClosureD :: Braid -> Map Resolution (Diagram B) Source
A Map
from Resolution
s to a diagram of the corresponding resolution of the closure of the braid b
.
printCube :: Map [Int] (Diagram B) -> Diagram B Source
Prints Map
s like the output of cubeOfResolutionsD
and `cubeOfResolutionsClosureD.`
bigGeneratorD :: Braid -> AlgGen -> Map [Int] (Diagram B) Source
Diagrams for an AlgGen
indexed by their resolutions.
generatorD :: Braid -> Generator -> Diagram B Source
Diagram for a single Generator
-- mostly exists to be called by bigGeneratorD
.