Numeric.Coalgebra.Trigonometric

Documentation

class Trigonometric r where

Minimal complete definition

cos, sin

Methods

cos :: r

sin :: r

Instances

Trigonometric TrigBasis

Methods

cos :: TrigBasis

sin :: TrigBasis

Rig r => Trigonometric (Trig r)

Methods

cos :: Trig r

sin :: Trig r

Rig r => Trigonometric (TrigBasis -> r)

Methods

cos :: TrigBasis -> r

sin :: TrigBasis -> r

Trigonometric a => Trigonometric (Covector r a)

Methods

cos :: Covector r a

sin :: Covector r a

data TrigBasis

Constructors

Cos

Sin

Instances

Bounded TrigBasis

Methods

minBound :: TrigBasis

maxBound :: TrigBasis

Enum TrigBasis

Methods

succ :: TrigBasis -> TrigBasis

pred :: TrigBasis -> TrigBasis

toEnum :: Int -> TrigBasis

fromEnum :: TrigBasis -> Int

enumFrom :: TrigBasis -> [TrigBasis]

enumFromThen :: TrigBasis -> TrigBasis -> [TrigBasis]

enumFromTo :: TrigBasis -> TrigBasis -> [TrigBasis]

enumFromThenTo :: TrigBasis -> TrigBasis -> TrigBasis -> [TrigBasis]

Eq TrigBasis

Methods

(==) :: TrigBasis -> TrigBasis -> Bool

(/=) :: TrigBasis -> TrigBasis -> Bool

Data TrigBasis

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> TrigBasis -> c TrigBasis

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c TrigBasis

toConstr :: TrigBasis -> Constr

dataTypeOf :: TrigBasis -> DataType

dataCast1 :: Typeable (* -> *) t => (forall d. Data d => c (t d)) -> Maybe (c TrigBasis)

dataCast2 :: Typeable (* -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c TrigBasis)

gmapT :: (forall b. Data b => b -> b) -> TrigBasis -> TrigBasis

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> TrigBasis -> r

gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> TrigBasis -> r

gmapQ :: (forall d. Data d => d -> u) -> TrigBasis -> [u]

gmapQi :: Int -> (forall d. Data d => d -> u) -> TrigBasis -> u

gmapM :: Monad m => (forall d. Data d => d -> m d) -> TrigBasis -> m TrigBasis

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> TrigBasis -> m TrigBasis

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> TrigBasis -> m TrigBasis

Ord TrigBasis

Methods

compare :: TrigBasis -> TrigBasis -> Ordering

(<) :: TrigBasis -> TrigBasis -> Bool

(<=) :: TrigBasis -> TrigBasis -> Bool

(>) :: TrigBasis -> TrigBasis -> Bool

(>=) :: TrigBasis -> TrigBasis -> Bool

max :: TrigBasis -> TrigBasis -> TrigBasis

min :: TrigBasis -> TrigBasis -> TrigBasis

Read TrigBasis

Methods

readsPrec :: Int -> ReadS TrigBasis

readList :: ReadS [TrigBasis]

readPrec :: ReadPrec TrigBasis

readListPrec :: ReadPrec [TrigBasis]

Show TrigBasis

Methods

showsPrec :: Int -> TrigBasis -> ShowS

show :: TrigBasis -> String

showList :: [TrigBasis] -> ShowS

Ix TrigBasis

Methods

range :: (TrigBasis, TrigBasis) -> [TrigBasis]

index :: (TrigBasis, TrigBasis) -> TrigBasis -> Int

unsafeIndex :: (TrigBasis, TrigBasis) -> TrigBasis -> Int

inRange :: (TrigBasis, TrigBasis) -> TrigBasis -> Bool

rangeSize :: (TrigBasis, TrigBasis) -> Int

unsafeRangeSize :: (TrigBasis, TrigBasis) -> Int

Trigonometric TrigBasis

Methods

cos :: TrigBasis

sin :: TrigBasis

Distinguished TrigBasis

Methods

e :: TrigBasis

Complicated TrigBasis

Methods

i :: TrigBasis

MonadReader TrigBasis Trig

Methods

ask :: Trig TrigBasis

local :: (TrigBasis -> TrigBasis) -> Trig a -> Trig a

reader :: (TrigBasis -> a) -> Trig a

(Commutative k, Rng k) => Coalgebra k TrigBasis

Methods

comult :: (TrigBasis -> k) -> TrigBasis -> TrigBasis -> k

(Commutative k, Rng k) => Algebra k TrigBasis

Methods

mult :: (TrigBasis -> TrigBasis -> k) -> TrigBasis -> k

(Commutative k, Rng k) => Bialgebra k TrigBasis

(Commutative k, Rng k) => CounitalCoalgebra k TrigBasis

Methods

counit :: (TrigBasis -> k) -> k

(Commutative k, Rng k) => UnitalAlgebra k TrigBasis

Methods

unit :: k -> TrigBasis -> k

(Commutative k, Group k, InvolutiveSemiring k) => HopfAlgebra k TrigBasis

Methods

antipode :: (TrigBasis -> k) -> TrigBasis -> k

(Commutative k, Group k, InvolutiveSemiring k) => InvolutiveCoalgebra k TrigBasis

Methods

coinv :: (TrigBasis -> k) -> TrigBasis -> k

(Commutative k, Group k, InvolutiveSemiring k) => InvolutiveAlgebra k TrigBasis

Methods

inv :: (TrigBasis -> k) -> TrigBasis -> k

Rig r => Trigonometric (TrigBasis -> r)

Methods

cos :: TrigBasis -> r

sin :: TrigBasis -> r

Rig r => Distinguished (TrigBasis -> r)

Methods

e :: TrigBasis -> r

Rig r => Complicated (TrigBasis -> r)

Methods

i :: TrigBasis -> r

data Trig a

Constructors

Trig a a

Instances

Monad Trig

Methods

(>>=) :: Trig a -> (a -> Trig b) -> Trig b

(>>) :: Trig a -> Trig b -> Trig b

return :: a -> Trig a

fail :: String -> Trig a

Functor Trig

Methods

fmap :: (a -> b) -> Trig a -> Trig b

(<$) :: a -> Trig b -> Trig a

Applicative Trig

Methods

pure :: a -> Trig a

(<*>) :: Trig (a -> b) -> Trig a -> Trig b

liftA2 :: (a -> b -> c) -> Trig a -> Trig b -> Trig c

(*>) :: Trig a -> Trig b -> Trig b

(<*) :: Trig a -> Trig b -> Trig a

Foldable Trig

Methods

fold :: Monoid m => Trig m -> m

foldMap :: Monoid m => (a -> m) -> Trig a -> m

foldr :: (a -> b -> b) -> b -> Trig a -> b

foldr' :: (a -> b -> b) -> b -> Trig a -> b

foldl :: (b -> a -> b) -> b -> Trig a -> b

foldl' :: (b -> a -> b) -> b -> Trig a -> b

foldr1 :: (a -> a -> a) -> Trig a -> a

foldl1 :: (a -> a -> a) -> Trig a -> a

toList :: Trig a -> [a]

null :: Trig a -> Bool

length :: Trig a -> Int

elem :: Eq a => a -> Trig a -> Bool

maximum :: Ord a => Trig a -> a

minimum :: Ord a => Trig a -> a

sum :: Num a => Trig a -> a

product :: Num a => Trig a -> a

Traversable Trig

Methods

traverse :: Applicative f => (a -> f b) -> Trig a -> f (Trig b)

sequenceA :: Applicative f => Trig (f a) -> f (Trig a)

mapM :: Monad m => (a -> m b) -> Trig a -> m (Trig b)

sequence :: Monad m => Trig (m a) -> m (Trig a)

Distributive Trig

Methods

distribute :: Functor f => f (Trig a) -> Trig (f a)

collect :: Functor f => (a -> Trig b) -> f a -> Trig (f b)

distributeM :: Monad m => m (Trig a) -> Trig (m a)

collectM :: Monad m => (a -> Trig b) -> m a -> Trig (m b)

Representable Trig

Associated Types

type Rep (Trig :: * -> *) :: *

Methods

tabulate :: (Rep Trig -> a) -> Trig a

index :: Trig a -> Rep Trig -> a

Traversable1 Trig

Methods

traverse1 :: Apply f => (a -> f b) -> Trig a -> f (Trig b)

sequence1 :: Apply f => Trig (f b) -> f (Trig b)

Foldable1 Trig

Methods

fold1 :: Semigroup m => Trig m -> m

foldMap1 :: Semigroup m => (a -> m) -> Trig a -> m

toNonEmpty :: Trig a -> NonEmpty a

Apply Trig

Methods

(<.>) :: Trig (a -> b) -> Trig a -> Trig b

(.>) :: Trig a -> Trig b -> Trig b

(<.) :: Trig a -> Trig b -> Trig a

Bind Trig

Methods

(>>-) :: Trig a -> (a -> Trig b) -> Trig b

join :: Trig (Trig a) -> Trig a

MonadReader TrigBasis Trig

Methods

ask :: Trig TrigBasis

local :: (TrigBasis -> TrigBasis) -> Trig a -> Trig a

reader :: (TrigBasis -> a) -> Trig a

RightModule r s => RightModule r (Trig s)

Methods

(*.) :: Trig s -> r -> Trig s

LeftModule r s => LeftModule r (Trig s)

Methods

(.*) :: r -> Trig s -> Trig s

Eq a => Eq (Trig a)

Methods

(==) :: Trig a -> Trig a -> Bool

(/=) :: Trig a -> Trig a -> Bool

Data a => Data (Trig a)

Methods

gfoldl :: (forall d b. Data d => c (d -> b) -> d -> c b) -> (forall g. g -> c g) -> Trig a -> c (Trig a)

gunfold :: (forall b r. Data b => c (b -> r) -> c r) -> (forall r. r -> c r) -> Constr -> c (Trig a)

toConstr :: Trig a -> Constr

dataTypeOf :: Trig a -> DataType

dataCast1 :: Typeable (* -> *) t => (forall d. Data d => c (t d)) -> Maybe (c (Trig a))

dataCast2 :: Typeable (* -> * -> *) t => (forall d e. (Data d, Data e) => c (t d e)) -> Maybe (c (Trig a))

gmapT :: (forall b. Data b => b -> b) -> Trig a -> Trig a

gmapQl :: (r -> r' -> r) -> r -> (forall d. Data d => d -> r') -> Trig a -> r

gmapQr :: (r' -> r -> r) -> r -> (forall d. Data d => d -> r') -> Trig a -> r

gmapQ :: (forall d. Data d => d -> u) -> Trig a -> [u]

gmapQi :: Int -> (forall d. Data d => d -> u) -> Trig a -> u

gmapM :: Monad m => (forall d. Data d => d -> m d) -> Trig a -> m (Trig a)

gmapMp :: MonadPlus m => (forall d. Data d => d -> m d) -> Trig a -> m (Trig a)

gmapMo :: MonadPlus m => (forall d. Data d => d -> m d) -> Trig a -> m (Trig a)

Read a => Read (Trig a)

Methods

readsPrec :: Int -> ReadS (Trig a)

readList :: ReadS [Trig a]

readPrec :: ReadPrec (Trig a)

readListPrec :: ReadPrec [Trig a]

Show a => Show (Trig a)

Methods

showsPrec :: Int -> Trig a -> ShowS

show :: Trig a -> String

showList :: [Trig a] -> ShowS

Idempotent r => Idempotent (Trig r)

Abelian r => Abelian (Trig r)

Partitionable r => Partitionable (Trig r)

Methods

partitionWith :: (Trig r -> Trig r -> r) -> Trig r -> NonEmpty r

Additive r => Additive (Trig r)

Methods

(+) :: Trig r -> Trig r -> Trig r

sinnum1p :: Natural -> Trig r -> Trig r

sumWith1 :: Foldable1 f => (a -> Trig r) -> f a -> Trig r

Monoidal r => Monoidal (Trig r)

Methods

zero :: Trig r

sinnum :: Natural -> Trig r -> Trig r

sumWith :: Foldable f => (a -> Trig r) -> f a -> Trig r

(Commutative k, Rng k) => Semiring (Trig k)

(Commutative k, Rng k) => Multiplicative (Trig k)

Methods

(*) :: Trig k -> Trig k -> Trig k

pow1p :: Trig k -> Natural -> Trig k

productWith1 :: Foldable1 f => (a -> Trig k) -> f a -> Trig k

Group r => Group (Trig r)

Methods

(-) :: Trig r -> Trig r -> Trig r

negate :: Trig r -> Trig r

subtract :: Trig r -> Trig r -> Trig r

times :: Integral n => n -> Trig r -> Trig r

(Commutative k, Ring k) => Unital (Trig k)

Methods

one :: Trig k

pow :: Trig k -> Natural -> Trig k

productWith :: Foldable f => (a -> Trig k) -> f a -> Trig k

(Commutative k, Rng k) => Commutative (Trig k)

(Commutative r, Rng r, InvolutiveSemiring r) => InvolutiveSemiring (Trig r)

(Commutative r, Rng r, InvolutiveMultiplication r) => InvolutiveMultiplication (Trig r)

Methods

adjoint :: Trig r -> Trig r

(Commutative r, Ring r) => Rig (Trig r)

Methods

fromNatural :: Natural -> Trig r

(Commutative r, Ring r) => Ring (Trig r)

Methods

fromInteger :: Integer -> Trig r

Rig r => Trigonometric (Trig r)

Methods

cos :: Trig r

sin :: Trig r

Rig r => Distinguished (Trig r)

Methods

e :: Trig r

Rig r => Complicated (Trig r)

Methods

i :: Trig r

(Commutative r, Rng r) => RightModule (Trig r) (Trig r)

Methods

(*.) :: Trig r -> Trig r -> Trig r

(Commutative r, Rng r) => LeftModule (Trig r) (Trig r)

Methods

(.*) :: Trig r -> Trig r -> Trig r

type Rep Trig

type Rep Trig = TrigBasis