module Numeric.Rig.Characteristic
( Characteristic(..)
, charInt
, charWord
, frobenius
) where
import Data.Int
import Data.Word
import Data.Proxy
import Numeric.Rig.Class
import Numeric.Ring.Endomorphism
import Numeric.Natural.Internal
import Numeric.Monoid.Multiplicative
import Prelude hiding ((^))
class Rig r => Characteristic r where
char :: Proxy r -> Natural
frobenius :: Characteristic r => End r
frobenius = End $ \r -> r `pow` char (ofRing r)
ofRing :: r -> Proxy r
ofRing _ = Proxy
charInt :: (Integral s, Bounded s) => Proxy s -> Natural
charInt p = 2 * fromIntegral (maxBound `asProxyTypeOf` p) + 2
charWord :: (Whole s, Bounded s) => Proxy s -> Natural
charWord p = toNatural (maxBound `asProxyTypeOf` p) + 1
instance Characteristic Bool where char _ = 0
instance Characteristic Integer where char _ = 0
instance Characteristic Natural where char _ = 0
instance Characteristic Int where char = charInt
instance Characteristic Int8 where char = charInt
instance Characteristic Int16 where char = charInt
instance Characteristic Int32 where char = charInt
instance Characteristic Int64 where char = charInt
instance Characteristic Word where char = charWord
instance Characteristic Word8 where char = charWord
instance Characteristic Word16 where char = charWord
instance Characteristic Word32 where char = charWord
instance Characteristic Word64 where char = charWord
instance Characteristic () where char _ = 1
instance (Characteristic a, Characteristic b) => Characteristic (a,b) where
char p = char (a p) `lcm` char (b p) where
a :: Proxy (a,b) -> Proxy a
a _ = Proxy
b :: Proxy (a,b) -> Proxy b
b _ = Proxy
instance (Characteristic a, Characteristic b, Characteristic c) => Characteristic (a,b,c) where
char p = char (a p) `lcm` char (b p) `lcm` char (c p) where
a :: Proxy (a,b,c) -> Proxy a
a _ = Proxy
b :: Proxy (a,b,c) -> Proxy b
b _ = Proxy
c :: Proxy (a,b,c) -> Proxy c
c _ = Proxy
instance (Characteristic a, Characteristic b, Characteristic c, Characteristic d) => Characteristic (a,b,c,d) where
char p = char (a p) `lcm` char (b p) `lcm` char (c p) `lcm` char (d p) where
a :: Proxy (a,b,c,d) -> Proxy a
a _ = Proxy
b :: Proxy (a,b,c,d) -> Proxy b
b _ = Proxy
c :: Proxy (a,b,c,d) -> Proxy c
c _ = Proxy
d :: Proxy (a,b,c,d) -> Proxy d
d _ = Proxy
instance (Characteristic a, Characteristic b, Characteristic c, Characteristic d, Characteristic e) => Characteristic (a,b,c,d,e) where
char p = char (a p) `lcm` char (b p) `lcm` char (c p) `lcm` char (d p) `lcm` char (e p) where
a :: Proxy (a,b,c,d,e) -> Proxy a
a _ = Proxy
b :: Proxy (a,b,c,d,e) -> Proxy b
b _ = Proxy
c :: Proxy (a,b,c,d,e) -> Proxy c
c _ = Proxy
d :: Proxy (a,b,c,d,e) -> Proxy d
d _ = Proxy
e :: Proxy (a,b,c,d,e) -> Proxy e
e _ = Proxy