Algebra.Morphism.LinComb

Documentation

newtype LinComb x c

Normalised linear combinations as maps from variables to coefficients (zero coefficient never present in the map)

Constructors

LinComb (Map x c)

Instances

Scalable s a => Scalable s (LinComb k a)

Defined in Algebra.Morphism.LinComb

Methods

(*^) :: s -> LinComb k a -> LinComb k a

Foldable (LinComb x)

Defined in Algebra.Morphism.LinComb

Methods

fold :: Monoid m => LinComb x m -> m

foldMap :: Monoid m => (a -> m) -> LinComb x a -> m

foldMap' :: Monoid m => (a -> m) -> LinComb x a -> m

foldr :: (a -> b -> b) -> b -> LinComb x a -> b

foldr' :: (a -> b -> b) -> b -> LinComb x a -> b

foldl :: (b -> a -> b) -> b -> LinComb x a -> b

foldl' :: (b -> a -> b) -> b -> LinComb x a -> b

foldr1 :: (a -> a -> a) -> LinComb x a -> a

foldl1 :: (a -> a -> a) -> LinComb x a -> a

toList :: LinComb x a -> [a]

null :: LinComb x a -> Bool

length :: LinComb x a -> Int

elem :: Eq a => a -> LinComb x a -> Bool

maximum :: Ord a => LinComb x a -> a

minimum :: Ord a => LinComb x a -> a

sum :: Num a => LinComb x a -> a

product :: Num a => LinComb x a -> a

Traversable (LinComb x)

Defined in Algebra.Morphism.LinComb

Methods

traverse :: Applicative f => (a -> f b) -> LinComb x a -> f (LinComb x b)

sequenceA :: Applicative f => LinComb x (f a) -> f (LinComb x a)

mapM :: Monad m => (a -> m b) -> LinComb x a -> m (LinComb x b)

sequence :: Monad m => LinComb x (m a) -> m (LinComb x a)

Functor (LinComb x)

Defined in Algebra.Morphism.LinComb

Methods

fmap :: (a -> b) -> LinComb x a -> LinComb x b

(<$) :: a -> LinComb x b -> LinComb x a

(Show x, Show c) => Show (LinComb x c)

Defined in Algebra.Morphism.LinComb

Methods

showsPrec :: Int -> LinComb x c -> ShowS

show :: LinComb x c -> String

showList :: [LinComb x c] -> ShowS

(AbelianAdditive c, DecidableZero c, Ord x) => AbelianAdditive (LinComb x c)

Defined in Algebra.Morphism.LinComb

(AbelianAdditive c, DecidableZero c, Ord e) => Additive (LinComb e c)

Defined in Algebra.Morphism.LinComb

Methods

(+) :: LinComb e c -> LinComb e c -> LinComb e c

zero :: LinComb e c

times :: Natural -> LinComb e c -> LinComb e c

(AbelianAdditive c, Eq c, DecidableZero c, Ord e) => DecidableZero (LinComb e c)

Defined in Algebra.Morphism.LinComb

Methods

isZero :: LinComb e c -> Bool

(AbelianAdditive c, Group c, DecidableZero c, Ord e) => Group (LinComb e c)

Defined in Algebra.Morphism.LinComb

Methods

(-) :: LinComb e c -> LinComb e c -> LinComb e c

subtract :: LinComb e c -> LinComb e c -> LinComb e c

negate :: LinComb e c -> LinComb e c

mult :: Integer -> LinComb e c -> LinComb e c

(Eq x, Eq c) => Eq (LinComb x c)

Defined in Algebra.Morphism.LinComb

Methods

(==) :: LinComb x c -> LinComb x c -> Bool

(/=) :: LinComb x c -> LinComb x c -> Bool

(Ord x, Ord c) => Ord (LinComb x c)

Defined in Algebra.Morphism.LinComb

Methods

compare :: LinComb x c -> LinComb x c -> Ordering

(<) :: LinComb x c -> LinComb x c -> Bool

(<=) :: LinComb x c -> LinComb x c -> Bool

(>) :: LinComb x c -> LinComb x c -> Bool

(>=) :: LinComb x c -> LinComb x c -> Bool

max :: LinComb x c -> LinComb x c -> LinComb x c

min :: LinComb x c -> LinComb x c -> LinComb x c

fromLinComb :: LinComb x c -> Map x c

eval :: forall d x c v. Scalable d x => Additive x => (c -> d) -> (v -> x) -> LinComb v c -> x

normalise :: DecidableZero c => LinComb x c -> LinComb x c

toList :: LinComb k a -> [(k, a)]

var :: Multiplicative c => x -> LinComb x c

unsafeFromList :: Ord v => [(v, c)] -> LinComb v c

Convert from list without testing coefficients

fromList :: DecidableZero c => Additive c => Ord v => [(v, c)] -> LinComb v c

subst :: DecidableZero c => AbelianAdditive c => Scalable c c => Ord v => (x -> LinComb v c) -> LinComb x c -> LinComb v c

Substitution by evaluation

mapVars :: Ord x => (t -> x) -> LinComb t c -> LinComb x c

transform variables. coefficients are not touched

mulVarsMonotonic :: Multiplicative x => x -> LinComb x c -> LinComb x c

Multiplies elements, assuming multiplication is monotonous.

traverseVars :: Applicative f => Ord x => (v -> f x) -> LinComb v c -> f (LinComb x c)

transform variables with effect. coefficients are not touched

bitraverse :: Applicative f => Ord x => (v -> f x) -> (c -> f d) -> LinComb v c -> f (LinComb x d)

transform variables and coefficients with effect.