HaskellForMaths-0.4.8: Combinatorics, group theory, commutative algebra, non-commutative algebra

Safe Haskell	None
Language	Haskell98

Math.Algebra.Field.Extension

Documentation

newtype UPoly a Source

Constructors

UP [a]

Instances

Eq a => Eq (UPoly a)
(Eq a, Num a) => Num (UPoly a)
Ord a => Ord (UPoly a)
(Eq a, Show a, Num a) => Show (UPoly a)

x :: UPoly Integer Source

showUP :: (Show a, Num a, Eq a) => [Char] -> [a] -> [Char] Source

toUPoly :: (Num a, Eq a) => [a] -> UPoly a Source

(<+>) :: (Num a, Eq a) => [a] -> [a] -> [a] Source

(<*>) :: (Num t, Eq t) => [t] -> [t] -> [t] Source

convert :: (Num a, Eq a) => UPoly Integer -> UPoly a Source

deg :: UPoly a -> Int Source

lt :: UPoly a -> a Source

monomial :: Num a => a -> Int -> UPoly a Source

quotRemUP :: (Eq k, Fractional k) => UPoly k -> UPoly k -> (UPoly k, UPoly k) Source

modUP :: (Fractional k, Eq k) => UPoly k -> UPoly k -> UPoly k Source

extendedEuclidUP :: (Fractional k, Eq k) => UPoly k -> UPoly k -> (UPoly k, UPoly k, UPoly k) Source

class PolynomialAsType k poly where Source

Methods

pvalue :: (k, poly) -> UPoly k Source

data ExtensionField k poly Source

Constructors

Instances

Eq k => Eq (ExtensionField k poly)
(Eq k, Fractional k, PolynomialAsType k poly) => Fractional (ExtensionField k poly)
(Eq k, Fractional k, PolynomialAsType k poly) => Num (ExtensionField k poly)
Ord k => Ord (ExtensionField k poly)
(Eq k, Show k, Num k) => Show (ExtensionField k poly)
(FinSet fp, Eq fp, Num fp, PolynomialAsType fp poly) => FinSet (ExtensionField fp poly)
(FiniteField k, PolynomialAsType k poly) => FiniteField (ExtensionField k poly)

(/>) :: (Fractional t, Eq t) => t -> UPoly t -> UPoly t Source

embed :: (Num k, Eq k) => UPoly Integer -> ExtensionField k poly Source

polys :: (Num a1, Num a, Eq a1, Eq a) => a1 -> [a] -> [UPoly a] Source

data ConwayF4 Source

Instances

PolynomialAsType F2 ConwayF4

type F4 = ExtensionField F2 ConwayF4 Source

f4 :: [F4] Source

a4 :: F4 Source

data ConwayF8 Source

Instances

PolynomialAsType F2 ConwayF8

type F8 = ExtensionField F2 ConwayF8 Source

f8 :: [F8] Source

a8 :: F8 Source

data ConwayF9 Source

Instances

PolynomialAsType F3 ConwayF9

type F9 = ExtensionField F3 ConwayF9 Source

f9 :: [F9] Source

a9 :: F9 Source

data ConwayF16 Source

Instances

PolynomialAsType F2 ConwayF16

type F16 = ExtensionField F2 ConwayF16 Source

f16 :: [F16] Source

a16 :: F16 Source

data ConwayF25 Source

Instances

PolynomialAsType F5 ConwayF25

type F25 = ExtensionField F5 ConwayF25 Source

f25 :: [F25] Source

a25 :: F25 Source

data ConwayF27 Source

Instances

PolynomialAsType F3 ConwayF27

type F27 = ExtensionField F3 ConwayF27 Source

f27 :: [F27] Source

a27 :: F27 Source

data ConwayF32 Source

Instances

PolynomialAsType F2 ConwayF32

type F32 = ExtensionField F2 ConwayF32 Source

f32 :: [F32] Source

a32 :: F32 Source

frobeniusAut :: FiniteField a => a -> a Source

degree :: [a] -> Int Source

data Sqrt a Source

Constructors

Instances

IntegerAsType n => PolynomialAsType Q (Sqrt n)

type QSqrt2 = ExtensionField Q (Sqrt T2) Source

sqrt2 :: QSqrt2 Source

type QSqrt3 = ExtensionField Q (Sqrt T3) Source

sqrt3 :: QSqrt3 Source

type QSqrt5 = ExtensionField Q (Sqrt T5) Source

sqrt5 :: QSqrt5 Source

type QSqrt7 = ExtensionField Q (Sqrt T7) Source

sqrt7 :: QSqrt7 Source

type QSqrtMinus1 = ExtensionField Q (Sqrt TMinus1) Source

i :: QSqrtMinus1 Source

type QSqrtMinus2 = ExtensionField Q (Sqrt (M TMinus1 T2)) Source

sqrtminus2 :: QSqrtMinus2 Source

type QSqrtMinus3 = ExtensionField Q (Sqrt (M TMinus1 T3)) Source

sqrtminus3 :: QSqrtMinus3 Source

type QSqrtMinus5 = ExtensionField Q (Sqrt (M TMinus1 T5)) Source

sqrtminus5 :: QSqrtMinus5 Source

conjugate :: ExtensionField Q (Sqrt d) -> ExtensionField Q (Sqrt d) Source