Safe Haskell	None

AronSymbolicAlgebra

Synopsis

data Fraction a
- = X
- | Constf a
- | (Fraction a) :+: (Fraction a)
- | (Fraction a) :*: (Fraction a)
- | (Fraction a) :/: (Fraction a)
- | Apply Func (Fraction a)
data Func
- = Cos
- | Sin
- | Tan
- | Log
- | Exp
- | Asin
- | Acos
- | Atan
eval :: Floating a => Fraction a -> a -> a
calculator :: Floating a => Func -> a -> a
cheatsheet :: Floating a => Func -> Fraction a
simplify :: (Eq a, Floating a) => Fraction a -> Fraction a
rewrite :: (Fractional a, Eq a) => Fraction a -> Fraction a
diff :: (Eq a, Floating a) => Fraction a -> Fraction a
diffS :: (Eq a, Floating a) => Fraction a -> Fraction a

Documentation

data Fraction a Source #

Constructors

X
Constf a
(Fraction a) :+: (Fraction a) infixl 6
(Fraction a) :*: (Fraction a) infixl 7
(Fraction a) :/: (Fraction a) infixl 7
Apply Func (Fraction a)

Instances

Instances details

Eq a => Eq (Fraction a) Source #
Instance details Defined in AronSymbolicAlgebra Methods (==) :: Fraction a -> Fraction a -> Bool (/=) :: Fraction a -> Fraction a -> Bool
Floating a => Floating (Fraction a) Source #
Instance details Defined in AronSymbolicAlgebra Methods pi :: Fraction a exp :: Fraction a -> Fraction a log :: Fraction a -> Fraction a sqrt :: Fraction a -> Fraction a (**) :: Fraction a -> Fraction a -> Fraction a logBase :: Fraction a -> Fraction a -> Fraction a sin :: Fraction a -> Fraction a cos :: Fraction a -> Fraction a tan :: Fraction a -> Fraction a asin :: Fraction a -> Fraction a acos :: Fraction a -> Fraction a atan :: Fraction a -> Fraction a sinh :: Fraction a -> Fraction a cosh :: Fraction a -> Fraction a tanh :: Fraction a -> Fraction a asinh :: Fraction a -> Fraction a acosh :: Fraction a -> Fraction a atanh :: Fraction a -> Fraction a log1p :: Fraction a -> Fraction a expm1 :: Fraction a -> Fraction a log1pexp :: Fraction a -> Fraction a log1mexp :: Fraction a -> Fraction a
Fractional a => Fractional (Fraction a) Source #
Instance details Defined in AronSymbolicAlgebra Methods (/) :: Fraction a -> Fraction a -> Fraction a recip :: Fraction a -> Fraction a fromRational :: Rational -> Fraction a
Num a => Num (Fraction a) Source #
Instance details Defined in AronSymbolicAlgebra Methods (+) :: Fraction a -> Fraction a -> Fraction a (-) :: Fraction a -> Fraction a -> Fraction a (*) :: Fraction a -> Fraction a -> Fraction a negate :: Fraction a -> Fraction a abs :: Fraction a -> Fraction a signum :: Fraction a -> Fraction a fromInteger :: Integer -> Fraction a
Show a => Show (Fraction a) Source #
Instance details Defined in AronSymbolicAlgebra Methods showsPrec :: Int -> Fraction a -> ShowS show :: Fraction a -> String showList :: [Fraction a] -> ShowS

data Func Source #

Constructors

Cos
Sin
Tan
Log
Exp
Asin
Acos
Atan

Instances

Instances details

Eq Func Source #
Instance details Defined in AronSymbolicAlgebra Methods (==) :: Func -> Func -> Bool (/=) :: Func -> Func -> Bool
Show Func Source #
Instance details Defined in AronSymbolicAlgebra Methods showsPrec :: Int -> Func -> ShowS show :: Func -> String showList :: [Func] -> ShowS

eval :: Floating a => Fraction a -> a -> a Source #

calculator :: Floating a => Func -> a -> a Source #

cheatsheet :: Floating a => Func -> Fraction a Source #

simplify :: (Eq a, Floating a) => Fraction a -> Fraction a Source #

rewrite :: (Fractional a, Eq a) => Fraction a -> Fraction a Source #

  rewrite (f :*: (g :*: h)) = rewrite (f :*: g) :*: rewrite h 
  rewrite (f :+: (g :+: h)) = rewrite (f :+: g) :+: rewrite h 
  rewrite (f :/: Constf 1) = f 
  rewrite (Constf a :*: Constf b) = Constf (a * b)
  rewrite (Constf a :+: Constf b) = Constf (a + b)
  rewrite (f :*: Constf a) = Constf a :*: f 
  rewrite (Constf a :*: f :+: Constf b :*: g) | f == g = rewrite (Constf a :+: Constf b) :*: rewrite f 
                                              | otherwise = rewrite (Constf a :*: f) :+: rewrite (Constf b :*: g) 

  rewrite (Apply func (Constf a)) = Constf (calculator func a)
  rewrite (f :+: g) = Constf 1 :*: f :+: Constf 1 :*: g 
  rewrite (f :*: g) = rewrite f :*: rewrite g
  rewrite (f :: g) = rewrite f :: rewrite g
  rewrite f = f

diff :: (Eq a, Floating a) => Fraction a -> Fraction a Source #

diffS :: (Eq a, Floating a) => Fraction a -> Fraction a Source #