Safe Haskell	None
Language	Haskell98

Numeric.Coalgebra.Trigonometric

Documentation

class Trigonometric r where Source #

Minimal complete definition

cos, sin

Methods

cos :: r Source #

sin :: r Source #

Instances

Trigonometric TrigBasis Source #
Methods cos :: TrigBasis Source # sin :: TrigBasis Source #
Rig r => Trigonometric (Trig r) Source #
Methods cos :: Trig r Source # sin :: Trig r Source #
Rig r => Trigonometric (TrigBasis -> r) Source #
Methods cos :: TrigBasis -> r Source # sin :: TrigBasis -> r Source #
Trigonometric a => Trigonometric (Covector r a) Source #
Methods cos :: Covector r a Source # sin :: Covector r a Source #

data TrigBasis Source #

Constructors

Cos
Sin

Instances

Bounded TrigBasis Source #
Methods minBound :: TrigBasis # maxBound :: TrigBasis #
Enum TrigBasis Source #
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 Source #
Methods (==) :: TrigBasis -> TrigBasis -> Bool # (/=) :: TrigBasis -> TrigBasis -> Bool #
Data TrigBasis Source #
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 Source #
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 Source #
Methods readsPrec :: Int -> ReadS TrigBasis # readList :: ReadS [TrigBasis] # readPrec :: ReadPrec TrigBasis # readListPrec :: ReadPrec [TrigBasis] #
Show TrigBasis Source #
Methods showsPrec :: Int -> TrigBasis -> ShowS # show :: TrigBasis -> String # showList :: [TrigBasis] -> ShowS #
Ix TrigBasis Source #
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 Source #
Methods cos :: TrigBasis Source # sin :: TrigBasis Source #
Distinguished TrigBasis Source #
Methods e :: TrigBasis Source #
Complicated TrigBasis Source #
Methods i :: TrigBasis Source #
MonadReader TrigBasis Trig Source #
Methods ask :: Trig TrigBasis # local :: (TrigBasis -> TrigBasis) -> Trig a -> Trig a # reader :: (TrigBasis -> a) -> Trig a #
(Commutative k, Rng k) => Coalgebra k TrigBasis Source #
Methods comult :: (TrigBasis -> k) -> TrigBasis -> TrigBasis -> k Source #
(Commutative k, Rng k) => Algebra k TrigBasis Source #
Methods mult :: (TrigBasis -> TrigBasis -> k) -> TrigBasis -> k Source #
(Commutative k, Rng k) => Bialgebra k TrigBasis Source #

(Commutative k, Rng k) => CounitalCoalgebra k TrigBasis Source #
Methods counit :: (TrigBasis -> k) -> k Source #
(Commutative k, Rng k) => UnitalAlgebra k TrigBasis Source #
Methods unit :: k -> TrigBasis -> k Source #
(Commutative k, Group k, InvolutiveSemiring k) => HopfAlgebra k TrigBasis Source #
Methods antipode :: (TrigBasis -> k) -> TrigBasis -> k Source #
(Commutative k, Group k, InvolutiveSemiring k) => InvolutiveCoalgebra k TrigBasis Source #
Methods coinv :: (TrigBasis -> k) -> TrigBasis -> k Source #
(Commutative k, Group k, InvolutiveSemiring k) => InvolutiveAlgebra k TrigBasis Source #
Methods inv :: (TrigBasis -> k) -> TrigBasis -> k Source #
Rig r => Trigonometric (TrigBasis -> r) Source #
Methods cos :: TrigBasis -> r Source # sin :: TrigBasis -> r Source #
Rig r => Distinguished (TrigBasis -> r) Source #
Methods e :: TrigBasis -> r Source #
Rig r => Complicated (TrigBasis -> r) Source #
Methods i :: TrigBasis -> r Source #

data Trig a Source #

Constructors

Trig a a

Instances

Monad Trig Source #
Methods (>>=) :: Trig a -> (a -> Trig b) -> Trig b # (>>) :: Trig a -> Trig b -> Trig b # return :: a -> Trig a # fail :: String -> Trig a #
Functor Trig Source #
Methods fmap :: (a -> b) -> Trig a -> Trig b # (<$) :: a -> Trig b -> Trig a #
Applicative Trig Source #
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 Source #
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 Source #
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 Source #
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 Source #
Associated Types type Rep (Trig :: * -> ) :: # Methods tabulate :: (Rep Trig -> a) -> Trig a # index :: Trig a -> Rep Trig -> a #
Traversable1 Trig Source #
Methods traverse1 :: Apply f => (a -> f b) -> Trig a -> f (Trig b) # sequence1 :: Apply f => Trig (f b) -> f (Trig b) #
Foldable1 Trig Source #
Methods fold1 :: Semigroup m => Trig m -> m # foldMap1 :: Semigroup m => (a -> m) -> Trig a -> m # toNonEmpty :: Trig a -> NonEmpty a #
Apply Trig Source #
Methods (<.>) :: Trig (a -> b) -> Trig a -> Trig b # (.>) :: Trig a -> Trig b -> Trig b # (<.) :: Trig a -> Trig b -> Trig a #
Bind Trig Source #
Methods (>>-) :: Trig a -> (a -> Trig b) -> Trig b # join :: Trig (Trig a) -> Trig a #
MonadReader TrigBasis Trig Source #
Methods ask :: Trig TrigBasis # local :: (TrigBasis -> TrigBasis) -> Trig a -> Trig a # reader :: (TrigBasis -> a) -> Trig a #
RightModule r s => RightModule r (Trig s) Source #
Methods (*.) :: Trig s -> r -> Trig s Source #
LeftModule r s => LeftModule r (Trig s) Source #
Methods (.*) :: r -> Trig s -> Trig s Source #
Eq a => Eq (Trig a) Source #
Methods (==) :: Trig a -> Trig a -> Bool # (/=) :: Trig a -> Trig a -> Bool #
Data a => Data (Trig a) Source #
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) Source #
Methods readsPrec :: Int -> ReadS (Trig a) # readList :: ReadS [Trig a] # readPrec :: ReadPrec (Trig a) # readListPrec :: ReadPrec [Trig a] #
Show a => Show (Trig a) Source #
Methods showsPrec :: Int -> Trig a -> ShowS # show :: Trig a -> String # showList :: [Trig a] -> ShowS #
Idempotent r => Idempotent (Trig r) Source #

Abelian r => Abelian (Trig r) Source #

Partitionable r => Partitionable (Trig r) Source #
Methods partitionWith :: (Trig r -> Trig r -> r) -> Trig r -> NonEmpty r Source #
Additive r => Additive (Trig r) Source #
Methods (+) :: Trig r -> Trig r -> Trig r Source # sinnum1p :: Natural -> Trig r -> Trig r Source # sumWith1 :: Foldable1 f => (a -> Trig r) -> f a -> Trig r Source #
Monoidal r => Monoidal (Trig r) Source #
Methods zero :: Trig r Source # sinnum :: Natural -> Trig r -> Trig r Source # sumWith :: Foldable f => (a -> Trig r) -> f a -> Trig r Source #
(Commutative k, Rng k) => Semiring (Trig k) Source #

(Commutative k, Rng k) => Multiplicative (Trig k) Source #
Methods (*) :: Trig k -> Trig k -> Trig k Source # pow1p :: Trig k -> Natural -> Trig k Source # productWith1 :: Foldable1 f => (a -> Trig k) -> f a -> Trig k Source #
Group r => Group (Trig r) Source #
Methods (-) :: Trig r -> Trig r -> Trig r Source # negate :: Trig r -> Trig r Source # subtract :: Trig r -> Trig r -> Trig r Source # times :: Integral n => n -> Trig r -> Trig r Source #
(Commutative k, Ring k) => Unital (Trig k) Source #
Methods one :: Trig k Source # pow :: Trig k -> Natural -> Trig k Source # productWith :: Foldable f => (a -> Trig k) -> f a -> Trig k Source #
(Commutative k, Rng k) => Commutative (Trig k) Source #

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

(Commutative r, Rng r, InvolutiveMultiplication r) => InvolutiveMultiplication (Trig r) Source #
Methods adjoint :: Trig r -> Trig r Source #
(Commutative r, Ring r) => Rig (Trig r) Source #
Methods fromNatural :: Natural -> Trig r Source #
(Commutative r, Ring r) => Ring (Trig r) Source #
Methods fromInteger :: Integer -> Trig r Source #
Rig r => Trigonometric (Trig r) Source #
Methods cos :: Trig r Source # sin :: Trig r Source #
Rig r => Distinguished (Trig r) Source #
Methods e :: Trig r Source #
Rig r => Complicated (Trig r) Source #
Methods i :: Trig r Source #
(Commutative r, Rng r) => RightModule (Trig r) (Trig r) Source #
Methods (*.) :: Trig r -> Trig r -> Trig r Source #
(Commutative r, Rng r) => LeftModule (Trig r) (Trig r) Source #
Methods (.*) :: Trig r -> Trig r -> Trig r Source #
type Rep Trig Source #
type Rep Trig = TrigBasis