Math.Algebra.Field.Static

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

Documentation

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

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 F97

type Characteristic F97 = 97

type Characteristic F89

type Characteristic F89 = 89

type Characteristic F83

type Characteristic F83 = 83

type Characteristic F79

type Characteristic F79 = 79

type Characteristic F73

type Characteristic F73 = 73

type Characteristic F71

type Characteristic F71 = 71

type Characteristic F7

type Characteristic F7 = 7

type Characteristic F67

type Characteristic F67 = 67

type Characteristic F61

type Characteristic F61 = 61

type Characteristic F59

type Characteristic F59 = 59

type Characteristic F53

type Characteristic F53 = 53

type Characteristic F5

type Characteristic F5 = 5

type Characteristic F47

type Characteristic F47 = 47

type Characteristic F43

type Characteristic F43 = 43

type Characteristic F41

type Characteristic F41 = 41

type Characteristic F37

type Characteristic F37 = 37

type Characteristic F31

type Characteristic F31 = 31

type Characteristic F3

type Characteristic F3 = 3

type Characteristic F29

type Characteristic F29 = 29

type Characteristic F23

type Characteristic F23 = 23

type Characteristic F2

type Characteristic F2 = 2

type Characteristic F19

type Characteristic F19 = 19

type Characteristic F17

type Characteristic F17 = 17

type Characteristic F13

type Characteristic F13 = 13

type Characteristic F11

type Characteristic F11 = 11

type Characteristic (ExtensionField k poly)

type Characteristic (ExtensionField k poly) = Characteristic k

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

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

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

Instances

type PolyDegree ConwayF9

type PolyDegree ConwayF9 = 2

type PolyDegree ConwayF8

type PolyDegree ConwayF8 = 3

type PolyDegree ConwayF4

type PolyDegree ConwayF4 = 2

type PolyDegree ConwayF32

type PolyDegree ConwayF32 = 5

type PolyDegree ConwayF27

type PolyDegree ConwayF27 = 3

type PolyDegree ConwayF25

type PolyDegree ConwayF25 = 2

type PolyDegree ConwayF16

type PolyDegree ConwayF16 = 4

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

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

Instances

type Size (Fp p)

type Size (Fp p) = Characteristic (Fp p)

type Size (ExtensionField fp poly)

type Size (ExtensionField fp poly) = (^) (Characteristic fp) (PolyDegree poly)