atom module with rational and imaginary types and operations

1 files changed, 45 insertions, 0 deletions

diff --git a/src/atom.hs b/src/atom.hs
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+module Atom where
+
+
+data Atom
+    = ARational Float
+    | AImaginary Float
+
+infixl 6 +?
+(+?) :: Atom -> Atom -> Maybe Atom
+(ARational a) +? (ARational b) = Just $ ARational (a + b)
+(AImaginary a) +? (AImaginary b) = Just $ AImaginary (a + b)
+_ +? _ = Nothing
+
+infixl 6 -?
+(-?) :: Atom -> Atom -> Maybe Atom
+(ARational a) -? (ARational b) = Just $ ARational (a - b)
+(AImaginary a) -? (AImaginary b) = Just $ AImaginary (a - b)
+_ -? _ = Nothing
+
+infixl 7 *?
+(*?) :: Atom -> Atom -> Maybe Atom
+(ARational a) *? (ARational b) = Just $ ARational (a * b)
+(ARational a) *? (AImaginary b) = Just $ AImaginary (a * b)
+(AImaginary a) *? (AImaginary b) = (AImaginary (a * b)) ^? ARational 2
+_ *? _ = Nothing
+
+infixl 7 /?
+(/?) :: Atom -> Atom -> Maybe Atom
+_ /? (ARational 0) = Nothing
+(ARational a) /? (ARational b) = Just $ ARational (a / b)
+_ /? _ = Nothing
+
+infixr 8 ^?
+(^?) :: Atom -> Atom -> Maybe Atom
+(ARational a) ^? (ARational b) = Just $ ARational (a ** b)
+(AImaginary a) ^? (ARational 0) = Just $ ARational a
+(AImaginary a) ^? (ARational 1) = Just $ AImaginary a
+(AImaginary a) ^? (ARational 2) = Just $ ARational (-a)
+(AImaginary a) ^? (ARational 3) = Just $ AImaginary (-a)
+(AImaginary a) ^? (ARational b) = AImaginary a ^? (ARational (b - 4))
+_ ^? _ = Nothing
+
+instance Show Atom where
+    show (ARational r) = show r
+    show (AImaginary i) = show i ++ "i"