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.

1 type

4 values

Example9 expressions

>>> 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

newtypenewtype T

Property

prop> Laws.identity (+) zero . gf

Property

prop> Laws.commutative (+) . gf

Property

prop> Laws.associative (+) . gf

Property

prop> Laws.inverse (+) negate zero . gf

Property

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

Property

prop> Laws.identity (*) one . gf

Property

prop> Laws.commutative (*) . gf

Property

prop> Laws.associative (*) . gf

Property

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

Property

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

Constructors

Cons
- decons :: Word32

Instances9Eq, Show, Storable, Arbitrary, C, …

Eq TDefined in numeric-prelude-0.4.4 · Number.GaloisField2p32m5
Show TDefined in numeric-prelude-0.4.4 · Number.GaloisField2p32m5
Storable TDefined in numeric-prelude-0.4.4 · Number.GaloisField2p32m5
Arbitrary TDefined in numeric-prelude-0.4.4 · Number.GaloisField2p32m5
C TDefined in numeric-prelude-0.4.4 · Number.GaloisField2p32m5
C TDefined in numeric-prelude-0.4.4 · Number.GaloisField2p32m5
C TDefined in numeric-prelude-0.4.4 · Number.GaloisField2p32m5
C TDefined in numeric-prelude-0.4.4 · Number.GaloisField2p32m5
C T TDefined in numeric-prelude-0.4.4 · Number.GaloisField2p32m5