HaskellForMaths-0.4.9: Combinatorics, group theory, commutative algebra, non-commutative algebra
Safe HaskellNone
LanguageHaskell98

Math.Algebra.Field.Extension

Documentation

newtype UPoly a Source #

Constructors

UP [a] 

Instances

Instances details
Eq a => Eq (UPoly a) Source # 
Instance details

Defined in Math.Algebra.Field.Extension

Methods

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

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

(Eq a, Num a) => Num (UPoly a) Source # 
Instance details

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) Source # 
Instance details

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) Source # 
Instance details

Defined in Math.Algebra.Field.Extension

Methods

showsPrec :: Int -> UPoly a -> ShowS

show :: UPoly a -> String

showList :: [UPoly a] -> ShowS

x :: UPoly Integer Source #

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

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

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

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

convert :: (Eq a, Num 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 :: (Eq k, Fractional k) => UPoly k -> UPoly k -> UPoly k Source #

extendedEuclidUP :: (Eq k, Fractional 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 #

Instances

Instances details
PolynomialAsType F5 ConwayF25 Source # 
Instance details

Defined in Math.Algebra.Field.Extension

Methods

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

PolynomialAsType F3 ConwayF27 Source # 
Instance details

Defined in Math.Algebra.Field.Extension

Methods

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

PolynomialAsType F3 ConwayF9 Source # 
Instance details

Defined in Math.Algebra.Field.Extension

Methods

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

PolynomialAsType F2 ConwayF32 Source # 
Instance details

Defined in Math.Algebra.Field.Extension

Methods

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

PolynomialAsType F2 ConwayF16 Source # 
Instance details

Defined in Math.Algebra.Field.Extension

Methods

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

PolynomialAsType F2 ConwayF8 Source # 
Instance details

Defined in Math.Algebra.Field.Extension

Methods

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

PolynomialAsType F2 ConwayF4 Source # 
Instance details

Defined in Math.Algebra.Field.Extension

Methods

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

IntegerAsType n => PolynomialAsType Q (Sqrt n) Source # 
Instance details

Defined in Math.Algebra.Field.Extension

Methods

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

data ExtensionField k poly Source #

Constructors

Ext (UPoly k) 

Instances

Instances details
Eq k => Eq (ExtensionField k poly) Source # 
Instance details

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) Source # 
Instance details

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) Source # 
Instance details

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) Source # 
Instance details

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) Source # 
Instance details

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) Source # 
Instance details

Defined in Math.Algebra.Field.Extension

Methods

elts :: [ExtensionField fp poly] Source #

(FiniteField k, PolynomialAsType k poly) => FiniteField (ExtensionField k poly) Source # 
Instance details

Defined in Math.Algebra.Field.Extension

Methods

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

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

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

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

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

data ConwayF4 Source #

Instances

Instances details
PolynomialAsType F2 ConwayF4 Source # 
Instance details

Defined in Math.Algebra.Field.Extension

Methods

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

f4 :: [F4] Source #

data ConwayF8 Source #

Instances

Instances details
PolynomialAsType F2 ConwayF8 Source # 
Instance details

Defined in Math.Algebra.Field.Extension

Methods

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

f8 :: [F8] Source #

data ConwayF9 Source #

Instances

Instances details
PolynomialAsType F3 ConwayF9 Source # 
Instance details

Defined in Math.Algebra.Field.Extension

Methods

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

f9 :: [F9] Source #

data ConwayF16 Source #

Instances

Instances details
PolynomialAsType F2 ConwayF16 Source # 
Instance details

Defined in Math.Algebra.Field.Extension

Methods

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

data ConwayF25 Source #

Instances

Instances details
PolynomialAsType F5 ConwayF25 Source # 
Instance details

Defined in Math.Algebra.Field.Extension

Methods

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

data ConwayF27 Source #

Instances

Instances details
PolynomialAsType F3 ConwayF27 Source # 
Instance details

Defined in Math.Algebra.Field.Extension

Methods

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

data ConwayF32 Source #

Instances

Instances details
PolynomialAsType F2 ConwayF32 Source # 
Instance details

Defined in Math.Algebra.Field.Extension

Methods

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

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

data Sqrt a Source #

Constructors

Sqrt a 

Instances

Instances details
IntegerAsType n => PolynomialAsType Q (Sqrt n) Source # 
Instance details

Defined in Math.Algebra.Field.Extension

Methods

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