Number.GaloisField2p32m5

This number type is intended for tests of functions over fields, where the field elements need constant space. This way we can provide a Storable instance. For Rational this would not be possible.

However, be aware that sums of non-zero elements may yield zero. Thus division is not always defined, where it is for rational numbers.

Documentation

>>> import qualified Number.GaloisField2p32m5 as GF
>>> import qualified Algebra.Laws as Laws
>>> import Test.QuickCheck ((==>))
>>> import NumericPrelude.Numeric
>>> import NumericPrelude.Base
>>> import Prelude ()
>>> 
>>> gf :: GF.T -> GF.T
>>> gf = id

newtype T

Laws.identity (+) zero . gf

Laws.commutative (+) . gf

Laws.associative (+) . gf

Laws.inverse (+) negate zero . gf

\x -> Laws.inverse (+) (x-) (gf x)

Laws.identity (*) one . gf

Laws.commutative (*) . gf

Laws.associative (*) . gf

\y -> gf y /= zero ==> Laws.inverse (*) recip one y

\y x -> gf y /= zero ==> Laws.inverse (*) (x/) x y

Constructors

Cons

Fields

• decons :: Word32

Instances

Eq T

Defined in Number.GaloisField2p32m5

Methods

(==) :: T -> T -> Bool

(/=) :: T -> T -> Bool

Show T

Defined in Number.GaloisField2p32m5

Methods

showsPrec :: Int -> T -> ShowS

show :: T -> String

showList :: [T] -> ShowS

Arbitrary T

Defined in Number.GaloisField2p32m5

Methods

arbitrary :: Gen T

shrink :: T -> [T]

Storable T

Defined in Number.GaloisField2p32m5

Methods

sizeOf :: T -> Int

alignment :: T -> Int

peekElemOff :: Ptr T -> Int -> IO T

pokeElemOff :: Ptr T -> Int -> T -> IO ()

peekByteOff :: Ptr b -> Int -> IO T

pokeByteOff :: Ptr b -> Int -> T -> IO ()

peek :: Ptr T -> IO T

poke :: Ptr T -> T -> IO ()

C T

Defined in Number.GaloisField2p32m5

Methods

zero :: T

(+) :: T -> T -> T

(-) :: T -> T -> T

negate :: T -> T

C T

Defined in Number.GaloisField2p32m5

Methods

isZero :: T -> Bool

C T

Defined in Number.GaloisField2p32m5

Methods

(*) :: T -> T -> T

one :: T

fromInteger :: Integer -> T

(^) :: T -> Integer -> T

C T

Defined in Number.GaloisField2p32m5

Methods

(/) :: T -> T -> T

recip :: T -> T

fromRational' :: Rational -> T

(^-) :: T -> Integer -> T

C T T

Defined in Number.GaloisField2p32m5

Methods

(*>) :: T -> T -> T

appPrec :: Int

base :: C a => a

lift2 :: (Word64 -> Word64 -> Word64) -> T -> T -> T

lift2Integer :: (Int64 -> Int64 -> Int64) -> T -> T -> T