Copyright	(c) Wanja Chresta 2018
License	GPL-3
Maintainer	wanja dit hs at chrummibei dot ch
Stability	experimental
Portability	POSIX
Safe Haskell	None
Language	Haskell2010

Math.Algebra.Field.Static

Description

Some finite field parameters are missing from HaskellForMaths implementation. Here, we add type classes to add these parameters to the type level.

Synopsis

type family Characteristic (f :: *) :: Nat
char :: forall c f. (KnownNat c, c ~ Characteristic f) => Proxy f -> Int
type family PolyDegree (f :: *) :: Nat
type family Size (f :: *) :: Nat

Documentation

type family Characteristic (f :: *) :: Nat Source #

The characteristic of a finite field on the type level. The characteristic is: For any element x in the field f with characteristic c, we have: c * x = x + x + .. + x (c times) = 0

Instances

type Characteristic F2 Source #
Instance details Defined in Math.Algebra.Field.Static type Characteristic F2 = 2
type Characteristic F3 Source #
Instance details Defined in Math.Algebra.Field.Static type Characteristic F3 = 3
type Characteristic F5 Source #
Instance details Defined in Math.Algebra.Field.Static type Characteristic F5 = 5
type Characteristic F7 Source #
Instance details Defined in Math.Algebra.Field.Static type Characteristic F7 = 7
type Characteristic F11 Source #
Instance details Defined in Math.Algebra.Field.Static type Characteristic F11 = 11
type Characteristic F13 Source #
Instance details Defined in Math.Algebra.Field.Static type Characteristic F13 = 13
type Characteristic F17 Source #
Instance details Defined in Math.Algebra.Field.Static type Characteristic F17 = 17
type Characteristic F19 Source #
Instance details Defined in Math.Algebra.Field.Static type Characteristic F19 = 19
type Characteristic F23 Source #
Instance details Defined in Math.Algebra.Field.Static type Characteristic F23 = 23
type Characteristic F29 Source #
Instance details Defined in Math.Algebra.Field.Static type Characteristic F29 = 29
type Characteristic F31 Source #
Instance details Defined in Math.Algebra.Field.Static type Characteristic F31 = 31
type Characteristic F37 Source #
Instance details Defined in Math.Algebra.Field.Static type Characteristic F37 = 37
type Characteristic F41 Source #
Instance details Defined in Math.Algebra.Field.Static type Characteristic F41 = 41
type Characteristic F43 Source #
Instance details Defined in Math.Algebra.Field.Static type Characteristic F43 = 43
type Characteristic F47 Source #
Instance details Defined in Math.Algebra.Field.Static type Characteristic F47 = 47
type Characteristic F53 Source #
Instance details Defined in Math.Algebra.Field.Static type Characteristic F53 = 53
type Characteristic F59 Source #
Instance details Defined in Math.Algebra.Field.Static type Characteristic F59 = 59
type Characteristic F61 Source #
Instance details Defined in Math.Algebra.Field.Static type Characteristic F61 = 61
type Characteristic F67 Source #
Instance details Defined in Math.Algebra.Field.Static type Characteristic F67 = 67
type Characteristic F71 Source #
Instance details Defined in Math.Algebra.Field.Static type Characteristic F71 = 71
type Characteristic F73 Source #
Instance details Defined in Math.Algebra.Field.Static type Characteristic F73 = 73
type Characteristic F79 Source #
Instance details Defined in Math.Algebra.Field.Static type Characteristic F79 = 79
type Characteristic F83 Source #
Instance details Defined in Math.Algebra.Field.Static type Characteristic F83 = 83
type Characteristic F89 Source #
Instance details Defined in Math.Algebra.Field.Static type Characteristic F89 = 89
type Characteristic F97 Source #
Instance details Defined in Math.Algebra.Field.Static type Characteristic F97 = 97
type Characteristic (ExtensionField k poly) Source #
Instance details Defined in Math.Algebra.Field.Static type Characteristic (ExtensionField k poly) = Characteristic k

char :: forall c f. (KnownNat c, c ~ Characteristic f) => Proxy f -> Int Source #

Characteristic of a field. It takes a finite field type in the proxy value and gives the characteristic. This is done using type families To support new finite field types, you need to add a type instance for the type family Characteristic.

type family PolyDegree (f :: *) :: Nat Source #

Type family which gives the degree of a polynomial type. This is used to extract type level information from Extension

Instances

type PolyDegree ConwayF4 Source #
Instance details Defined in Math.Algebra.Field.Static type PolyDegree ConwayF4 = 2
type PolyDegree ConwayF8 Source #
Instance details Defined in Math.Algebra.Field.Static type PolyDegree ConwayF8 = 3
type PolyDegree ConwayF9 Source #
Instance details Defined in Math.Algebra.Field.Static type PolyDegree ConwayF9 = 2
type PolyDegree ConwayF16 Source #
Instance details Defined in Math.Algebra.Field.Static type PolyDegree ConwayF16 = 4
type PolyDegree ConwayF25 Source #
Instance details Defined in Math.Algebra.Field.Static type PolyDegree ConwayF25 = 2
type PolyDegree ConwayF27 Source #
Instance details Defined in Math.Algebra.Field.Static type PolyDegree ConwayF27 = 3
type PolyDegree ConwayF32 Source #
Instance details Defined in Math.Algebra.Field.Static type PolyDegree ConwayF32 = 5

type family Size (f :: *) :: Nat Source #

Type family which gives the size of a field, i.e. the number of elements of a finite field.

Instances

type Size (Fp p) Source #
Instance details Defined in Math.Algebra.Field.Static type Size (Fp p) = Characteristic (Fp p)
type Size (ExtensionField fp poly) Source #
Instance details Defined in Math.Algebra.Field.Static type Size (ExtensionField fp poly) = Characteristic fp ^ PolyDegree poly