Safe Haskell	Safe
Language	Haskell2010

Algebra.AD

Documentation

data D v c Source #

Constructors

D
Fields dValue :: !c dDerivs :: !(Map v c)

Instances

(Ord v, Ring c) => Module c (D v c) Source #
Methods (*^) :: c -> D v c -> D v c #
Eq c => Eq (D v c) Source #
Methods (==) :: D v c -> D v c -> Bool # (/=) :: D v c -> D v c -> Bool #
Ord c => Ord (D v c) Source #
Methods compare :: D v c -> D v c -> Ordering # (<) :: D v c -> D v c -> Bool # (<=) :: D v c -> D v c -> Bool # (>) :: D v c -> D v c -> Bool # (>=) :: D v c -> D v c -> Bool # max :: D v c -> D v c -> D v c # min :: D v c -> D v c -> D v c #
(Show v, Show c) => Show (D v c) Source #
Methods showsPrec :: Int -> D v c -> ShowS # show :: D v c -> String # showList :: [D v c] -> ShowS #
(Ord v, Additive c) => Additive (D v c) Source #
Methods (+) :: D v c -> D v c -> D v c # zero :: D v c # times :: Natural -> D v c -> D v c #
(AbelianAdditive c, Ord v) => AbelianAdditive (D v c) Source #

(Ord v, Group c) => Group (D v c) Source #
Methods (-) :: D v c -> D v c -> D v c # negate :: D v c -> D v c # mult :: Integer -> D v c -> D v c #
(Ord v, Ring c) => Multiplicative (D v c) Source #
Methods (*) :: D v c -> D v c -> D v c # one :: D v c # (^) :: D v c -> Natural -> D v c #
(Ord v, Ring c) => Ring (D v c) Source #
Methods fromInteger :: Integer -> D v c #
(Field c, Ord v) => Division (D v c) Source #
Methods recip :: D v c -> D v c # (/) :: D v c -> D v c -> D v c #
(Ord v, Ring c) => Module (D v c) (D v c) Source #
Methods (*^) :: D v c -> D v c -> D v c #

newtype E v c Source #

Constructors

E
Fields fromE :: (v -> D v c) -> D v c

Instances

(Ord v, Ring c) => Module c (E v c) Source #
Methods (*^) :: c -> E v c -> E v c #
(Ord v, Additive c) => Additive (E v c) Source #
Methods (+) :: E v c -> E v c -> E v c # zero :: E v c # times :: Natural -> E v c -> E v c #
(Ord v, Ring c) => AbelianAdditive (E v c) Source #

(Ord v, Group c) => Group (E v c) Source #
Methods (-) :: E v c -> E v c -> E v c # negate :: E v c -> E v c # mult :: Integer -> E v c -> E v c #
(Ord v, Ring c) => Multiplicative (E v c) Source #
Methods (*) :: E v c -> E v c -> E v c # one :: E v c # (^) :: E v c -> Natural -> E v c #
(Ord v, Ring c) => Ring (E v c) Source #
Methods fromInteger :: Integer -> E v c #
(Field c, Ord v) => Division (E v c) Source #
Methods recip :: E v c -> E v c # (/) :: E v c -> E v c -> E v c #
(Ord v, Ring c) => Module (E v c) (E v c) Source #
Methods (*^) :: E v c -> E v c -> E v c #

subst :: E v c -> (v -> E v c) -> E v c Source #

dVar :: forall v c. Ring c => v -> c -> D v c Source #

sqrtE :: forall t t1. (Floating t1, Ord t, Field t1) => E t t1 -> E t t1 Source #