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GHC 10.0.0.20260917 · lts/ghc-10.0.x · 8fef28d · 2026-11-02

Modulenumeric-prelude-0.4.4Haskell98

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.

Synopsis
Example9 expressions
import qualified Number.GaloisField2p32m5 as GFimport qualified Algebra.Laws as Lawsimport Test.QuickCheck ((==>))import NumericPrelude.Numericimport NumericPrelude.Baseimport Prelude ()gf :: GF.T -> GF.Tgf = id
newtypenewtype T
Source#
Property
Laws.identity (+) zero . gf
Property
Laws.commutative (+) . gf
Property
Laws.associative (+) . gf
Property
Laws.inverse (+) negate zero . gf
Property
\x -> Laws.inverse (+) (x-) (gf x)
Property
Laws.identity (*) one . gf
Property
Laws.commutative (*) . gf
Property
Laws.associative (*) . gf
Property
\y -> gf y /= zero ==> Laws.inverse (*) recip one y
Property
\y x -> gf y /= zero ==> Laws.inverse (*) (x/) x y

Constructors

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