knots-0.1.0.0: Khovanov homology computations

Safe Haskell	None

Knots.Khovanov

Documentation

data PartitionComparison a Source

Constructors

Split (Set (Set a)) (Set a) (Set (Set a)) (Set a) (Set (Set a))
Merge (Set (Set a)) (Set a) (Set (Set a)) (Set a) (Set (Set a))

Instances

Eq a => Eq (PartitionComparison a)
Show a => Show (PartitionComparison a)

data ComparisonType Source

Constructors

TypeSplit
TypeMerge

split3 :: Ord a => Set a -> a -> a -> (Set a, Set a, Set a)Source

partitionComparison :: Ord a => Set (Set a) -> Set (Set a) -> PartitionComparison aSource

data MarkPosition Source

Constructors

None
MarkLeft Int
ReducedLeft
MarkMiddle Int
ReducedRight
MarkRight Int

Instances

Eq MarkPosition
Read MarkPosition
Show MarkPosition

markPosition :: Ord a => a -> PartitionComparison a -> MarkPosition Source

markPosition' :: Ord a => a -> Set (Set a) -> Set a -> Set (Set a) -> Set a -> Set (Set a) -> MarkPosition Source

toElMo :: Ord a => PartitionComparison a -> ElMo Source

morphism :: Ord a => Set Int -> Set Int -> Set (Set a) -> Set (Set a) -> ElMo Source

morphism_ :: Ord a => a -> Set Int -> Set Int -> Set (Set a) -> Set (Set a) -> (ElMo, MarkPosition)Source

toMorphism :: RingEq r => ElMo -> MarkPosition -> Morphism [B] rSource

padMorphism :: RingEq r => ComparisonType -> Int -> Int -> Int -> MarkPosition -> Morphism [B] rSource

khovanov :: Ord a => Maybe a -> PD a -> Map (Set Int, Set Int) (ElMo, MarkPosition)Source

khovanovLine :: [[[Int]]] -> [ElMo]Source