Factor.Gfpx

Documentation

data Gfpx

Constructors

Gfpx

Fields

• degree :: Int
• coeffMap :: IntMap Gfp

Instances

Eq Gfpx

Defined in Factor.Gfpx

Methods

(==) :: Gfpx -> Gfpx -> Bool

(/=) :: Gfpx -> Gfpx -> Bool

Ord Gfpx

Defined in Factor.Gfpx

Methods

compare :: Gfpx -> Gfpx -> Ordering

(<) :: Gfpx -> Gfpx -> Bool

(<=) :: Gfpx -> Gfpx -> Bool

(>) :: Gfpx -> Gfpx -> Bool

(>=) :: Gfpx -> Gfpx -> Bool

max :: Gfpx -> Gfpx -> Gfpx

min :: Gfpx -> Gfpx -> Gfpx

Show Gfpx

Defined in Factor.Gfpx

Methods

showsPrec :: Int -> Gfpx -> ShowS

show :: Gfpx -> String

showList :: [Gfpx] -> ShowS

valid :: Prime -> Gfpx -> Bool

fromNormCoeffMap :: IntMap Gfp -> Gfpx

fromCoeffMap :: IntMap Gfp -> Gfpx

isZero :: Gfpx -> Bool

isOne :: Gfpx -> Bool

isConstant :: Gfpx -> Bool

isLinear :: Gfpx -> Bool

isMonic :: Gfpx -> Bool

constMonic :: Prime -> Gfpx -> (Gfp, Gfpx)

powerCoeff :: Gfpx -> Int -> Gfp

constantCoeff :: Gfpx -> Gfp

linearCoeff :: Gfpx -> Gfp

leadingCoeff :: Gfpx -> Gfp

monomials :: Gfpx -> [(Int, Gfp)]

lengthMonomials :: Gfpx -> Int

filterMonomials :: (Int -> Gfp -> Bool) -> Gfpx -> Gfpx

constant :: Gfp -> Gfpx

variable :: Gfpx

monomial :: Int -> Gfp -> Gfpx

simpleRoot :: Prime -> Gfp -> Gfpx

evaluate :: Prime -> Gfpx -> Gfp -> Gfp

derivative :: Prime -> Gfpx -> Gfpx

fromCoeff :: [Gfp] -> Gfpx

fromZx :: Prime -> Zx -> Gfpx

toZx :: Gfpx -> Zx

toSmallestZx :: Prime -> Gfpx -> Zx

uniform :: RandomGen r => Prime -> Int -> r -> (Gfpx, r)

polyToTerm :: Prime -> Var -> Gfpx -> Term

toTerm :: Prime -> Var -> Gfpx -> Term

zero :: Gfpx

one :: Gfpx

negate :: Prime -> Gfpx -> Gfpx

add :: Prime -> Gfpx -> Gfpx -> Gfpx

sum :: Prime -> [Gfpx] -> Gfpx

subtract :: Prime -> Gfpx -> Gfpx -> Gfpx

multiply :: Prime -> Gfpx -> Gfpx -> Gfpx

square :: Prime -> Gfpx -> Gfpx

cube :: Prime -> Gfpx -> Gfpx

product :: Prime -> [Gfpx] -> Gfpx

multiplyConstant :: Prime -> Gfp -> Gfpx -> Gfpx

multiplyPower :: Int -> Gfpx -> Gfpx

multiplyExp :: Prime -> Gfpx -> Gfpx -> Integer -> Gfpx

exp :: Prime -> Gfpx -> Integer -> Gfpx

compose :: Prime -> Gfpx -> Gfpx -> Gfpx

division :: Prime -> Gfpx -> Gfpx -> (Gfpx, Gfpx)

quotient :: Prime -> Gfpx -> Gfpx -> Gfpx

remainder :: Prime -> Gfpx -> Gfpx -> Gfpx

divides :: Prime -> Gfpx -> Gfpx -> Bool

properDivisor :: Prime -> Gfpx -> Gfpx -> Bool

egcd :: Prime -> Gfpx -> Gfpx -> (Gfpx, (Gfpx, Gfpx))

gcd :: Prime -> Gfpx -> Gfpx -> Gfpx

chineseRemainder :: Prime -> Gfpx -> Gfpx -> Gfpx -> Gfpx -> Gfpx

multiplyRemainder :: Prime -> Gfpx -> Gfpx -> Gfpx -> Gfpx

squareRemainder :: Prime -> Gfpx -> Gfpx -> Gfpx

multiplyExpRemainder :: Prime -> Gfpx -> Gfpx -> Gfpx -> Integer -> Gfpx

expRemainder :: Prime -> Gfpx -> Gfpx -> Integer -> Gfpx

composeRemainder :: Prime -> Gfpx -> Gfpx -> Gfpx -> Gfpx

invertRemainderF :: Prime -> Gfpx -> Gfpx -> Factor Gfpx Gfpx

invertRemainder :: Prime -> Gfpx -> Gfpx -> Gfpx

divideRemainderF :: Prime -> Gfpx -> Gfpx -> Gfpx -> Factor Gfpx Gfpx

divideRemainder :: Prime -> Gfpx -> Gfpx -> Gfpx -> Gfpx

roots :: Prime -> Gfpx -> [Gfp]

totallySplits :: Zx -> Prime -> Maybe [Gfp]

irreducible :: Prime -> Gfpx -> Bool

liftRoot :: Zx -> Prime -> Gfp -> [(Integer, Integer)]

frobenius :: Prime -> Gfpx -> Gfpx

frobeniusRange :: Prime -> Gfpx -> Bool

frobeniusInverse :: Prime -> Gfpx -> Gfpx

squareFree :: Prime -> Gfpx -> Bool

squareFreeDecomposition :: Prime -> Gfpx -> [Gfpx]

squareFreeRecomposition :: Prime -> [Gfpx] -> Gfpx

matrixBerlekamp :: Prime -> Gfpx -> [[Gfp]]

nullBerlekamp :: Prime -> [[Gfp]] -> Maybe [Gfp]

splitBerlekamp :: Prime -> Gfpx -> Maybe (Gfpx, Gfpx)

factorDistinctDegree :: Prime -> Gfpx -> [(Gfpx, Int)]

factorEqualDegreeBerlekamp :: Prime -> Gfpx -> Int -> [Gfpx]

factorEqualDegree :: RandomGen r => Prime -> Gfpx -> Int -> r -> ([Gfpx], r)

factorSquareFreeBerlekamp :: Prime -> Gfpx -> [Gfpx]

factorSquareFree :: RandomGen r => Prime -> Gfpx -> r -> ([Gfpx], r)

factorMonicBerlekamp :: Prime -> Gfpx -> [(Gfpx, Integer)]

factorMonic :: RandomGen r => Prime -> Gfpx -> r -> ([(Gfpx, Integer)], r)