Algebra.AD

Documentation

data D v c

Constructors

D

Fields

• dValue :: !c
• dDerivs :: !(Map v c)

Instances

(Ord v, Ring c) => Module c (D v c)

Methods

(*^) :: c -> D v c -> D v c

Eq c => Eq (D v c)

Methods

(==) :: D v c -> D v c -> Bool

(/=) :: D v c -> D v c -> Bool

Ord c => Ord (D v c)

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)

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)

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)

(Ord v, Group c) => Group (D v c)

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)

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)

Methods

fromInteger :: Integer -> D v c

(Field c, Ord v) => Division (D v c)

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)

Methods

(*^) :: D v c -> D v c -> D v c

newtype E v c

Constructors

E

Fields

• fromE :: (v -> D v c) -> D v c

Instances

(Ord v, Ring c) => Module c (E v c)

Methods

(*^) :: c -> E v c -> E v c

(Ord v, Additive c) => Additive (E v c)

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)

(Ord v, Group c) => Group (E v c)

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)

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)

Methods

fromInteger :: Integer -> E v c

(Field c, Ord v) => Division (E v c)

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)

Methods

(*^) :: E v c -> E v c -> E v c

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

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

var :: (Multiplicative c, Additive c, Ord v) => v -> E v c

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