Safe Haskell	Safe-Inferred
Language	Haskell2010

Algebra.Morphism.Affine

Synopsis

data Affine x c = Affine c (LinComb x c)
splitVar :: Ord x => Additive c => x -> Affine x c -> (c, Affine x c)
solve :: (Ord scalar, Eq scalar, Field scalar, Ord x, DecidableZero scalar) => x -> Affine x scalar -> Either (Affine x scalar) (Bool, Affine x scalar)
constant :: (AbelianAdditive c, DecidableZero c) => Ord x => c -> Affine x c
isConstant :: Eq c => Ord x => DecidableZero c => Affine x c -> Either x c
var :: Multiplicative c => Additive c => v -> Affine v c
eval :: forall x c v. (Additive x, Scalable x x) => (c -> x) -> (v -> x) -> Affine v c -> x
subst :: (Ord x, AbelianAdditive c, DecidableZero c, Multiplicative c) => (v -> Affine x c) -> Affine v c -> Affine x c
mapVars :: Ord x => (v -> x) -> Affine v c -> Affine x c
traverseVars :: Ord x => Applicative f => (v -> f x) -> Affine v c -> f (Affine x c)

Documentation

data Affine x c Source #

Constructors

Affine c (LinComb x c)

Instances

Instances details

Multiplicative c => Scalable c (Affine x c) Source #
Instance details Defined in Algebra.Morphism.Affine Methods (*^) :: c -> Affine x c -> Affine x c Source #
Functor (Affine x) Source #
Instance details Defined in Algebra.Morphism.Affine Methods fmap :: (a -> b) -> Affine x a -> Affine x b # (<$) :: a -> Affine x b -> Affine x a #
(Show c, Show x) => Show (Affine x c) Source #
Instance details Defined in Algebra.Morphism.Affine Methods showsPrec :: Int -> Affine x c -> ShowS # show :: Affine x c -> String # showList :: [Affine x c] -> ShowS #
(Ord x, AbelianAdditive c, DecidableZero c) => AbelianAdditive (Affine x c) Source #
Instance details Defined in Algebra.Morphism.Affine
(Ord x, AbelianAdditive c, DecidableZero c) => Additive (Affine x c) Source #
Instance details Defined in Algebra.Morphism.Affine Methods (+) :: Affine x c -> Affine x c -> Affine x c Source # zero :: Affine x c Source # times :: Natural -> Affine x c -> Affine x c Source #
(Ord x, AbelianAdditive c, Group c, DecidableZero c) => Group (Affine x c) Source #
Instance details Defined in Algebra.Morphism.Affine Methods (-) :: Affine x c -> Affine x c -> Affine x c Source # subtract :: Affine x c -> Affine x c -> Affine x c Source # negate :: Affine x c -> Affine x c Source # mult :: Integer -> Affine x c -> Affine x c Source #
(Eq c, Eq x) => Eq (Affine x c) Source #
Instance details Defined in Algebra.Morphism.Affine Methods (==) :: Affine x c -> Affine x c -> Bool # (/=) :: Affine x c -> Affine x c -> Bool #
(Ord c, Ord x) => Ord (Affine x c) Source #
Instance details Defined in Algebra.Morphism.Affine Methods compare :: Affine x c -> Affine x c -> Ordering # (<) :: Affine x c -> Affine x c -> Bool # (<=) :: Affine x c -> Affine x c -> Bool # (>) :: Affine x c -> Affine x c -> Bool # (>=) :: Affine x c -> Affine x c -> Bool # max :: Affine x c -> Affine x c -> Affine x c # min :: Affine x c -> Affine x c -> Affine x c #

splitVar :: Ord x => Additive c => x -> Affine x c -> (c, Affine x c) Source #

solve :: (Ord scalar, Eq scalar, Field scalar, Ord x, DecidableZero scalar) => x -> Affine x scalar -> Either (Affine x scalar) (Bool, Affine x scalar) Source #

solve x f solves the equation f == 0 for x. Let f = k x + e. If k == 0, return Left e. Otherwise, x and return Right -e/k. (The value of x)

constant :: (AbelianAdditive c, DecidableZero c) => Ord x => c -> Affine x c Source #

Constant affine expression

isConstant :: Eq c => Ord x => DecidableZero c => Affine x c -> Either x c Source #

var :: Multiplicative c => Additive c => v -> Affine v c Source #

eval :: forall x c v. (Additive x, Scalable x x) => (c -> x) -> (v -> x) -> Affine v c -> x Source #

subst :: (Ord x, AbelianAdditive c, DecidableZero c, Multiplicative c) => (v -> Affine x c) -> Affine v c -> Affine x c Source #

mapVars :: Ord x => (v -> x) -> Affine v c -> Affine x c Source #

traverseVars :: Ord x => Applicative f => (v -> f x) -> Affine v c -> f (Affine x c) Source #