Math.Algebra.Field.Extension

Documentation

newtype UPoly a

Constructors

UP [a]

Instances

Eq a => Eq (UPoly a)

Defined in Math.Algebra.Field.Extension

Methods

(==) :: UPoly a -> UPoly a -> Bool

(/=) :: UPoly a -> UPoly a -> Bool

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

Defined in Math.Algebra.Field.Extension

Methods

(+) :: UPoly a -> UPoly a -> UPoly a

(-) :: UPoly a -> UPoly a -> UPoly a

(*) :: UPoly a -> UPoly a -> UPoly a

negate :: UPoly a -> UPoly a

abs :: UPoly a -> UPoly a

signum :: UPoly a -> UPoly a

fromInteger :: Integer -> UPoly a

Ord a => Ord (UPoly a)

Defined in Math.Algebra.Field.Extension

Methods

compare :: UPoly a -> UPoly a -> Ordering

(<) :: UPoly a -> UPoly a -> Bool

(<=) :: UPoly a -> UPoly a -> Bool

(>) :: UPoly a -> UPoly a -> Bool

(>=) :: UPoly a -> UPoly a -> Bool

max :: UPoly a -> UPoly a -> UPoly a

min :: UPoly a -> UPoly a -> UPoly a

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

Defined in Math.Algebra.Field.Extension

Methods

showsPrec :: Int -> UPoly a -> ShowS

show :: UPoly a -> String

showList :: [UPoly a] -> ShowS

x :: UPoly Integer

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

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

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

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

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

deg :: UPoly a -> Int

lt :: UPoly a -> a

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

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

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

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

class PolynomialAsType k poly where

Methods

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

Instances

PolynomialAsType F5 ConwayF25

Defined in Math.Algebra.Field.Extension

Methods

pvalue :: (F5, ConwayF25) -> UPoly F5

PolynomialAsType F3 ConwayF27

Defined in Math.Algebra.Field.Extension

Methods

pvalue :: (F3, ConwayF27) -> UPoly F3

PolynomialAsType F3 ConwayF9

Defined in Math.Algebra.Field.Extension

Methods

pvalue :: (F3, ConwayF9) -> UPoly F3

PolynomialAsType F2 ConwayF32

Defined in Math.Algebra.Field.Extension

Methods

pvalue :: (F2, ConwayF32) -> UPoly F2

PolynomialAsType F2 ConwayF16

Defined in Math.Algebra.Field.Extension

Methods

pvalue :: (F2, ConwayF16) -> UPoly F2

PolynomialAsType F2 ConwayF8

Defined in Math.Algebra.Field.Extension

Methods

pvalue :: (F2, ConwayF8) -> UPoly F2

PolynomialAsType F2 ConwayF4

Defined in Math.Algebra.Field.Extension

Methods

pvalue :: (F2, ConwayF4) -> UPoly F2

IntegerAsType n => PolynomialAsType Q (Sqrt n)

Defined in Math.Algebra.Field.Extension

Methods

pvalue :: (Q, Sqrt n) -> UPoly Q

data ExtensionField k poly

Constructors

Ext (UPoly k)

Instances

Eq k => Eq (ExtensionField k poly)

Defined in Math.Algebra.Field.Extension

Methods

(==) :: ExtensionField k poly -> ExtensionField k poly -> Bool

(/=) :: ExtensionField k poly -> ExtensionField k poly -> Bool

(Eq k, Fractional k, PolynomialAsType k poly) => Fractional (ExtensionField k poly)

Defined in Math.Algebra.Field.Extension

Methods

(/) :: ExtensionField k poly -> ExtensionField k poly -> ExtensionField k poly

recip :: ExtensionField k poly -> ExtensionField k poly

fromRational :: Rational -> ExtensionField k poly

(Eq k, Fractional k, PolynomialAsType k poly) => Num (ExtensionField k poly)

Defined in Math.Algebra.Field.Extension

Methods

(+) :: ExtensionField k poly -> ExtensionField k poly -> ExtensionField k poly

(-) :: ExtensionField k poly -> ExtensionField k poly -> ExtensionField k poly

(*) :: ExtensionField k poly -> ExtensionField k poly -> ExtensionField k poly

negate :: ExtensionField k poly -> ExtensionField k poly

abs :: ExtensionField k poly -> ExtensionField k poly

signum :: ExtensionField k poly -> ExtensionField k poly

fromInteger :: Integer -> ExtensionField k poly

Ord k => Ord (ExtensionField k poly)

Defined in Math.Algebra.Field.Extension

Methods

compare :: ExtensionField k poly -> ExtensionField k poly -> Ordering

(<) :: ExtensionField k poly -> ExtensionField k poly -> Bool

(<=) :: ExtensionField k poly -> ExtensionField k poly -> Bool

(>) :: ExtensionField k poly -> ExtensionField k poly -> Bool

(>=) :: ExtensionField k poly -> ExtensionField k poly -> Bool

max :: ExtensionField k poly -> ExtensionField k poly -> ExtensionField k poly

min :: ExtensionField k poly -> ExtensionField k poly -> ExtensionField k poly

(Eq k, Show k, Num k) => Show (ExtensionField k poly)

Defined in Math.Algebra.Field.Extension

Methods

showsPrec :: Int -> ExtensionField k poly -> ShowS

show :: ExtensionField k poly -> String

showList :: [ExtensionField k poly] -> ShowS

(FinSet fp, Eq fp, Num fp, PolynomialAsType fp poly) => FinSet (ExtensionField fp poly)

Defined in Math.Algebra.Field.Extension

Methods

elts :: [ExtensionField fp poly]

(FiniteField k, PolynomialAsType k poly) => FiniteField (ExtensionField k poly)

Defined in Math.Algebra.Field.Extension

Methods

eltsFq :: ExtensionField k poly -> [ExtensionField k poly]

basisFq :: ExtensionField k poly -> [ExtensionField k poly]

(/>) :: (Eq a, Fractional a) => a -> UPoly a -> UPoly a

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

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

data ConwayF4

Instances

PolynomialAsType F2 ConwayF4

Defined in Math.Algebra.Field.Extension

Methods

pvalue :: (F2, ConwayF4) -> UPoly F2

type F4 = ExtensionField F2 ConwayF4

f4 :: [F4]

a4 :: F4

data ConwayF8

Instances

PolynomialAsType F2 ConwayF8

Defined in Math.Algebra.Field.Extension

Methods

pvalue :: (F2, ConwayF8) -> UPoly F2

type F8 = ExtensionField F2 ConwayF8

f8 :: [F8]

a8 :: F8

data ConwayF9

Instances

PolynomialAsType F3 ConwayF9

Defined in Math.Algebra.Field.Extension

Methods

pvalue :: (F3, ConwayF9) -> UPoly F3

type F9 = ExtensionField F3 ConwayF9

f9 :: [F9]

a9 :: F9

data ConwayF16

Instances

PolynomialAsType F2 ConwayF16

Defined in Math.Algebra.Field.Extension

Methods

pvalue :: (F2, ConwayF16) -> UPoly F2

type F16 = ExtensionField F2 ConwayF16

f16 :: [F16]

a16 :: F16

data ConwayF25

Instances

PolynomialAsType F5 ConwayF25

Defined in Math.Algebra.Field.Extension

Methods

pvalue :: (F5, ConwayF25) -> UPoly F5

type F25 = ExtensionField F5 ConwayF25

f25 :: [F25]

a25 :: F25

data ConwayF27

Instances

PolynomialAsType F3 ConwayF27

Defined in Math.Algebra.Field.Extension

Methods

pvalue :: (F3, ConwayF27) -> UPoly F3

type F27 = ExtensionField F3 ConwayF27

f27 :: [F27]

a27 :: F27

data ConwayF32

Instances

PolynomialAsType F2 ConwayF32

Defined in Math.Algebra.Field.Extension

Methods

pvalue :: (F2, ConwayF32) -> UPoly F2

type F32 = ExtensionField F2 ConwayF32

f32 :: [F32]

a32 :: F32

frobeniusAut :: FiniteField a => a -> a

degree :: Foldable t => t a -> Int

data Sqrt a

Constructors

Sqrt a

Instances

IntegerAsType n => PolynomialAsType Q (Sqrt n)

Defined in Math.Algebra.Field.Extension

Methods

pvalue :: (Q, Sqrt n) -> UPoly Q

type QSqrt2 = ExtensionField Q (Sqrt T2)

sqrt2 :: QSqrt2

type QSqrt3 = ExtensionField Q (Sqrt T3)

sqrt3 :: QSqrt3

type QSqrt5 = ExtensionField Q (Sqrt T5)

sqrt5 :: QSqrt5

type QSqrt7 = ExtensionField Q (Sqrt T7)

sqrt7 :: QSqrt7

type QSqrtMinus1 = ExtensionField Q (Sqrt TMinus1)

i :: QSqrtMinus1

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

sqrtminus2 :: QSqrtMinus2

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

sqrtminus3 :: QSqrtMinus3

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

sqrtminus5 :: QSqrtMinus5

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