Braiddiagrams

Longer description to come.

Documentation

type ArcLabel = Int

type Height = Int

type BraidIndex = Int

type ArtinGen = Int

newtype NameNode

A newtype wrapper for Node to create an IsName instance.

Constructors

NameNode (Node ArcLabel)

Instances

Eq NameNode

Ord NameNode

Show NameNode

IsName NameNode

identity :: BraidIndex -> Diagram B

The identity braid of index index.

identityAt :: BraidIndex -> ArcLabel -> Diagram B

The identity braid of index index with arc names starting at lastlabel + 1.

negativeCrossing :: Diagram B

A negative crossing.

positiveCrossing :: Diagram B

Draws a positive crossing.

cupCap :: Diagram B

A cup-cap combo.

cupCapLevelAt :: BraidIndex -> ArcLabel -> ArtinGen -> Diagram B

A cup-cap combo with names starting at lastLabel + 1.

artin :: BraidIndex -> ArtinGen -> Diagram B

The kth Artin generator of the braid group on n strands. To draw the inverse of the kth generator, use -k.

drawBraid :: Braid -> Diagram B

Draws a braid.

drawBraidClosure :: Braid -> Diagram B

Draws a braid closure.

resolutionD :: Int -> BraidIndex -> ArtinGen -> Diagram B

Draws the r resolution of the kth Artin generator in the n strand braid group. To draw the inverse of the kth generator, use -k.

resolutionAt :: Int -> BraidIndex -> ArtinGen -> Height -> Diagram B

Draws the r resolution of the kth Artin generator in the n strand braid group with names starting at lastLabel + 1. To draw the inverse of the kth generator, use -k.

resolveD :: Resolution -> Braid -> Diagram B

Draws the braid b resolved according to rs.

resolveClosureD :: Resolution -> Braid -> Diagram B

Draws the closure of the braid b resolved according to rs.

cubeOfResolutionsD :: Braid -> Map Resolution (Diagram B)

A Map from Resolutions to a diagram of the corresponding resolution of the braid b.

cubeOfResolutionsClosureD :: Braid -> Map Resolution (Diagram B)

A Map from Resolutions to a diagram of the corresponding resolution of the closure of the braid b.

printCube :: Map [Int] (Diagram B) -> Diagram B

Prints Maps like the output of cubeOfResolutionsD and `cubeOfResolutionsClosureD.`

bigGeneratorD :: Braid -> AlgGen -> Map [Int] (Diagram B)

Diagrams for an AlgGen indexed by their resolutions.

generatorD :: Braid -> Generator -> Diagram B

Diagram for a single Generator -- mostly exists to be called by bigGeneratorD.

markIn :: Diagram B -> Component -> Sign -> Diagram B -> Diagram B

Marks a component of diagram.