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

Safe HaskellNone
LanguageHaskell98

Math.Algebra.Field.Extension

Documentation

newtype UPoly a Source #

Constructors

UP [a] 

Instances

Eq a => Eq (UPoly a) Source # 

Methods

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

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

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

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 # 

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 # 

Methods

showsPrec :: Int -> UPoly a -> ShowS #

show :: UPoly a -> String #

showList :: [UPoly a] -> ShowS #

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 #

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

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

data ExtensionField k poly Source #

Constructors

Ext (UPoly k) 

Instances

Eq k => Eq (ExtensionField k poly) Source # 

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 # 

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 # 

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 # 

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 # 

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 # 

Methods

elts :: [ExtensionField fp poly] Source #

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

Methods

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

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

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

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

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

f4 :: [F4] Source #

f8 :: [F8] Source #

f9 :: [F9] Source #

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

data Sqrt a Source #

Constructors

Sqrt a 

Instances