Safe Haskell	None

Knots.Morphism

Documentation

type Morphism b r = Graded (Lin b b r)Source

oo :: (Default b, Ord b, RingEq r) => Morphism b r -> Morphism b r -> Morphism b rSource

data B Source

Constructors

B1
Bx

Instances

Eq B
Ord B
Read B
Show B
NFData B

degreeB :: B -> Int Source

degree :: [B] -> Int Source

isB1 :: B -> Bool Source

basis :: Int -> [[B]]Source

b1 :: [B]Source

bx :: [B]Source

b11 :: [B]Source

bxx :: [B]Source

bx1 :: [B]Source

b1x :: [B]Source

b111 :: [B]Source

bxxx :: [B]Source

bxx1 :: [B]Source

bx1x :: [B]Source

bx11 :: [B]Source

b1xx :: [B]Source

b1x1 :: [B]Source

b11x :: [B]Source

mult :: RingEq r => Morphism [B] rSource

idB1 :: RingEq r => Morphism [B] rSource

idA :: RingEq r => Morphism [B] rSource

permReduced :: RingEq r => Morphism [B] rSource

perm :: RingEq r => Morphism [B] rSource

comultReducedRight :: RingEq r => Morphism [B] rSource

comultReducedLeft :: RingEq r => Morphism [B] rSource

comult :: RingEq r => Morphism [B] rSource

multReducedRight :: RingEq r => Morphism [B] rSource

multReducedLeft :: RingEq r => Morphism [B] rSource

backPermute :: RingEq r => Morphism [B] r -> Morphism [B] r -> Int -> Morphism [B] rSource

forwardPermute :: RingEq r => Morphism [B] r -> Morphism [B] r -> Int -> Morphism [B] rSource

type Complex' r = Map Int (Morphism (Set Int, [B]) r)Source

convert :: (Ord i, Ord b, Ord c, AbelianGroup r) => Lin b c (Map i r) -> Map i (Lin b c r)Source

toMatrix :: (Ord a, Ord b, AbelianGroup r) => Lin a b r -> ((Int, Int), [[r]])Source

toMatrices :: AbelianGroup r => Complex' r -> Map (Int, Int) ((Int, Int), [[r]])Source

isNullComplex' :: AbEq r => Complex' r -> Bool Source

isNullMorphism :: AbEq r => Morphism b r -> Bool Source

homology' :: Graded (Int, Int, Int) -> Graded (Int, Int, Int) -> Graded Int Source

homology :: Map Int (Graded (Int, Int, Int)) -> Map Int (Graded Int)Source

computeDims :: (Field r, Eq r, NFData r) => Complex' r -> Map Int (Graded (Int, Int, Int))Source

shiftGraded :: Graded a -> Graded aSource