1 files changed, 64 insertions, 0 deletions
diff --git a/src/equation.hs b/src/equation.hs
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+++ b/src/equation.hs
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+module Equation where
+
+import Numeric.Natural
+import Data.List
+
+
+data Equation = Equation { left :: Polynomial, right :: Polynomial }
+type Polynomial = [Term]
+data Term = Term { coefficient :: Float, exponent :: Natural }
+
+instance Eq Term where
+    (Term _ e1) == (Term _ e2) = e1 == e2
+
+instance Ord Term where
+    compare (Term _ e1) (Term _ e2) = compare e1 e2
+
+instance Show Term where
+    show (Term c e) = show c ++ " * X^" ++ show e
+
+instance Show Equation where
+    show (Equation l r) = showPolynomial l ++ " = " ++ showPolynomial r
+        where showPolynomial [] = "0"
+              showPolynomial p  = intercalate " + " (map show p)
+
+equationMap :: (Polynomial -> Polynomial) -> Equation -> Equation
+equationMap f (Equation l r) = Equation (f l) (f r)
+
+degree :: Polynomial -> Natural
+degree p = Equation.exponent (maximum p)
+
+reduce :: Equation -> Equation
+reduce equ = Equation (merge (left stdForm) (right stdForm)) []
+    where stdForm = equationMap (\a -> (reducePolynomial $ sort a)) equ
+          merge [] rs = rs
+          merge ls [] = ls
+          merge (l:ls) (r:rs)
+            | l == r = (subTerm l r) : merge ls rs
+            | l < r  = l : merge ls (r:rs)
+            | r < l  = r : merge (l:ls) rs
+            where subTerm (Term c1 e) (Term c2 _) = Term (c1 - c2) e
+          reducePolynomial []         = []
+          reducePolynomial [t]        = [t]
+          reducePolynomial (t1:t2:ts)
+            | t1 == t2  = (addTerm t1 t2) : reducePolynomial ts
+            | otherwise = t1 : reducePolynomial (t2:ts)
+            where addTerm (Term c1 e) (Term c2 _) = Term (c1 + c2) e
+
+solveDegree2 :: Float -> Float -> Float -> [Float]
+solveDegree2 a b c
+    | phi < 0   = []
+    | phi == 0  = [(-b) / (2.0 * a)]
+    | phi > 0   = [ (-b + sqrt phi) / (2.0 * a)
+                  , (-b - sqrt phi) / (2.0 * a)
+                  ]
+    where phi = b ^ 2 - 4.0 * a * c
+
+solveDegree1 :: Float -> Float -> Float
+solveDegree1 b c = -c / b
+
+solve :: Polynomial -> [Float]
+solve [t0]         = []
+solve [t0, t1]     = [solveDegree1 (coefficient t1) (coefficient t0)]
+solve [t0, t1, t2] = solveDegree2 (coefficient t2) (coefficient t1) (coefficient t0)
+solve _            = undefined