Safe Haskell	Safe-Inferred
Language	Haskell2010

Factor.Nfs

Description

Documentation

data PolynomialDegree Source #

Constructors

FixedPolynomialDegree Int
OptimalPolynomialDegree

Instances

Instances details

Eq PolynomialDegree Source #
Instance details Defined in Factor.Nfs Methods (==) :: PolynomialDegree -> PolynomialDegree -> Bool # (/=) :: PolynomialDegree -> PolynomialDegree -> Bool #
Ord PolynomialDegree Source #
Instance details Defined in Factor.Nfs Methods compare :: PolynomialDegree -> PolynomialDegree -> Ordering # (<) :: PolynomialDegree -> PolynomialDegree -> Bool # (<=) :: PolynomialDegree -> PolynomialDegree -> Bool # (>) :: PolynomialDegree -> PolynomialDegree -> Bool # (>=) :: PolynomialDegree -> PolynomialDegree -> Bool # max :: PolynomialDegree -> PolynomialDegree -> PolynomialDegree # min :: PolynomialDegree -> PolynomialDegree -> PolynomialDegree #
Show PolynomialDegree Source #
Instance details Defined in Factor.Nfs Methods showsPrec :: Int -> PolynomialDegree -> ShowS # show :: PolynomialDegree -> String # showList :: [PolynomialDegree] -> ShowS #

data PolynomialBase Source #

Constructors

FixedPolynomialBase Integer
ClosestPolynomialBase
FloorPolynomialBase

Instances

Instances details

Eq PolynomialBase Source #
Instance details Defined in Factor.Nfs Methods (==) :: PolynomialBase -> PolynomialBase -> Bool # (/=) :: PolynomialBase -> PolynomialBase -> Bool #
Ord PolynomialBase Source #
Instance details Defined in Factor.Nfs Methods compare :: PolynomialBase -> PolynomialBase -> Ordering # (<) :: PolynomialBase -> PolynomialBase -> Bool # (<=) :: PolynomialBase -> PolynomialBase -> Bool # (>) :: PolynomialBase -> PolynomialBase -> Bool # (>=) :: PolynomialBase -> PolynomialBase -> Bool # max :: PolynomialBase -> PolynomialBase -> PolynomialBase # min :: PolynomialBase -> PolynomialBase -> PolynomialBase #
Show PolynomialBase Source #
Instance details Defined in Factor.Nfs Methods showsPrec :: Int -> PolynomialBase -> ShowS # show :: PolynomialBase -> String # showList :: [PolynomialBase] -> ShowS #

data PolynomialCoeff Source #

Constructors

FixedPolynomialCoeff [Integer]
SmallestPolynomialCoeff
PositivePolynomialCoeff

Instances

Instances details

Eq PolynomialCoeff Source #
Instance details Defined in Factor.Nfs Methods (==) :: PolynomialCoeff -> PolynomialCoeff -> Bool # (/=) :: PolynomialCoeff -> PolynomialCoeff -> Bool #
Ord PolynomialCoeff Source #
Instance details Defined in Factor.Nfs Methods compare :: PolynomialCoeff -> PolynomialCoeff -> Ordering # (<) :: PolynomialCoeff -> PolynomialCoeff -> Bool # (<=) :: PolynomialCoeff -> PolynomialCoeff -> Bool # (>) :: PolynomialCoeff -> PolynomialCoeff -> Bool # (>=) :: PolynomialCoeff -> PolynomialCoeff -> Bool # max :: PolynomialCoeff -> PolynomialCoeff -> PolynomialCoeff # min :: PolynomialCoeff -> PolynomialCoeff -> PolynomialCoeff #
Show PolynomialCoeff Source #
Instance details Defined in Factor.Nfs Methods showsPrec :: Int -> PolynomialCoeff -> ShowS # show :: PolynomialCoeff -> String # showList :: [PolynomialCoeff] -> ShowS #

data PolynomialConfig Source #

Constructors

PolynomialConfig
Fields polynomialDegree :: PolynomialDegree polynomialBase :: PolynomialBase polynomialCoeff :: PolynomialCoeff

Instances

Instances details

Eq PolynomialConfig Source #
Instance details Defined in Factor.Nfs Methods (==) :: PolynomialConfig -> PolynomialConfig -> Bool # (/=) :: PolynomialConfig -> PolynomialConfig -> Bool #
Ord PolynomialConfig Source #
Instance details Defined in Factor.Nfs Methods compare :: PolynomialConfig -> PolynomialConfig -> Ordering # (<) :: PolynomialConfig -> PolynomialConfig -> Bool # (<=) :: PolynomialConfig -> PolynomialConfig -> Bool # (>) :: PolynomialConfig -> PolynomialConfig -> Bool # (>=) :: PolynomialConfig -> PolynomialConfig -> Bool # max :: PolynomialConfig -> PolynomialConfig -> PolynomialConfig # min :: PolynomialConfig -> PolynomialConfig -> PolynomialConfig #
Show PolynomialConfig Source #
Instance details Defined in Factor.Nfs Methods showsPrec :: Int -> PolynomialConfig -> ShowS # show :: PolynomialConfig -> String # showList :: [PolynomialConfig] -> ShowS #

defaultPolynomialConfig :: PolynomialConfig Source #

fixedPolynomialConfig :: Zx -> Integer -> PolynomialConfig Source #

selectPolynomialDegree :: PolynomialDegree -> Integer -> Int Source #

selectPolynomialBase :: PolynomialBase -> Integer -> Int -> Integer Source #

selectPolynomialCoeff :: PolynomialCoeff -> Integer -> Int -> Integer -> [Integer] Source #

selectPolynomial :: PolynomialConfig -> Integer -> (Zx, Integer) Source #

type FactorBase = [Prime] Source #

data FactorBaseConfig Source #

Constructors

FixedFactorBase Integer
OptimalFactorBase Double

Instances

Instances details

Eq FactorBaseConfig Source #
Instance details Defined in Factor.Nfs Methods (==) :: FactorBaseConfig -> FactorBaseConfig -> Bool # (/=) :: FactorBaseConfig -> FactorBaseConfig -> Bool #
Ord FactorBaseConfig Source #
Instance details Defined in Factor.Nfs Methods compare :: FactorBaseConfig -> FactorBaseConfig -> Ordering # (<) :: FactorBaseConfig -> FactorBaseConfig -> Bool # (<=) :: FactorBaseConfig -> FactorBaseConfig -> Bool # (>) :: FactorBaseConfig -> FactorBaseConfig -> Bool # (>=) :: FactorBaseConfig -> FactorBaseConfig -> Bool # max :: FactorBaseConfig -> FactorBaseConfig -> FactorBaseConfig # min :: FactorBaseConfig -> FactorBaseConfig -> FactorBaseConfig #
Show FactorBaseConfig Source #
Instance details Defined in Factor.Nfs Methods showsPrec :: Int -> FactorBaseConfig -> ShowS # show :: FactorBaseConfig -> String # showList :: [FactorBaseConfig] -> ShowS #

defaultFactorBaseConfig :: FactorBaseConfig Source #

maxFactorBase :: FactorBaseConfig -> Integer -> Integer Source #

destSmoothInteger :: FactorBase -> Integer -> Maybe Integer Source #

isSmoothInteger :: FactorBase -> Integer -> Bool Source #

notSmoothInteger :: FactorBase -> Integer -> Bool Source #

rationalNorm :: Integer -> Nfzw -> Integer Source #

algebraicNorm :: Zx -> Nfzw -> Integer Source #

isSmoothNfzw :: Zx -> Integer -> FactorBase -> FactorBase -> Nfzw -> Bool Source #

smoothNfzw :: Zx -> Integer -> FactorBase -> FactorBase -> [Nfzw] Source #

data QuadraticCharacterConfig Source #

Constructors

FixedQuadraticCharacterConfig Int
LinearQuadraticCharacterConfig Int Double

Instances

Instances details

Eq QuadraticCharacterConfig Source #
Instance details Defined in Factor.Nfs Methods (==) :: QuadraticCharacterConfig -> QuadraticCharacterConfig -> Bool # (/=) :: QuadraticCharacterConfig -> QuadraticCharacterConfig -> Bool #
Ord QuadraticCharacterConfig Source #
Instance details Defined in Factor.Nfs Methods compare :: QuadraticCharacterConfig -> QuadraticCharacterConfig -> Ordering # (<) :: QuadraticCharacterConfig -> QuadraticCharacterConfig -> Bool # (<=) :: QuadraticCharacterConfig -> QuadraticCharacterConfig -> Bool # (>) :: QuadraticCharacterConfig -> QuadraticCharacterConfig -> Bool # (>=) :: QuadraticCharacterConfig -> QuadraticCharacterConfig -> Bool # max :: QuadraticCharacterConfig -> QuadraticCharacterConfig -> QuadraticCharacterConfig # min :: QuadraticCharacterConfig -> QuadraticCharacterConfig -> QuadraticCharacterConfig #
Show QuadraticCharacterConfig Source #
Instance details Defined in Factor.Nfs Methods showsPrec :: Int -> QuadraticCharacterConfig -> ShowS # show :: QuadraticCharacterConfig -> String # showList :: [QuadraticCharacterConfig] -> ShowS #

defaultQuadraticCharacterConfig :: QuadraticCharacterConfig Source #

quadraticCharacters :: QuadraticCharacterConfig -> Integer -> Int Source #

isQuadraticCharacter :: Zx -> [Nfzw] -> Ideal -> Bool Source #

nextQuadraticCharacter :: Zx -> [Nfzw] -> [Ideal] -> (Ideal, [Ideal]) Source #

takeQuadraticCharacters :: Zx -> [Nfzw] -> Int -> [Ideal] -> ([Ideal], [Ideal]) Source #

isQuadraticResidue :: Ideal -> Nfzw -> Bool Source #

notQuadraticResidue :: Ideal -> Nfzw -> Bool Source #

productIsQuadraticResidue :: Ideal -> [Nfzw] -> Bool Source #

type Row = [Bool] Source #

formRow :: Zx -> Integer -> [Prime] -> [Ideal] -> [Ideal] -> Nfzw -> Row Source #

rationalRow :: [Prime] -> Integer -> Row Source #

algebraicRow :: Zx -> [Ideal] -> [Ideal] -> Nfzw -> Row Source #

oddPower :: Eq a => [(a, Integer)] -> a -> ([(a, Integer)], Bool) Source #

gaussianElimination :: [Row] -> [[Int]] Source #

rationalSquareRoot :: Integer -> Integer -> Zx -> [Prime] -> [Nfzw] -> Integer Source #

algebraicSquareRoot :: Integer -> Zx -> Integer -> Zx -> [Ideal] -> [Nfzw] -> (Integer -> Bool) -> Verbose (Maybe Integer) Source #

data Config Source #

Constructors

Config
Fields polynomialConfig :: PolynomialConfig rationalFactorBaseConfig :: FactorBaseConfig algebraicFactorBaseConfig :: FactorBaseConfig quadraticCharacterConfig :: QuadraticCharacterConfig extraRankConfig :: Int verboseConfig :: Bool

Instances

Instances details

Eq Config Source #
Instance details Defined in Factor.Nfs Methods (==) :: Config -> Config -> Bool # (/=) :: Config -> Config -> Bool #
Ord Config Source #
Instance details Defined in Factor.Nfs Methods compare :: Config -> Config -> Ordering # (<) :: Config -> Config -> Bool # (<=) :: Config -> Config -> Bool # (>) :: Config -> Config -> Bool # (>=) :: Config -> Config -> Bool # max :: Config -> Config -> Config # min :: Config -> Config -> Config #
Show Config Source #
Instance details Defined in Factor.Nfs Methods showsPrec :: Int -> Config -> ShowS # show :: Config -> String # showList :: [Config] -> ShowS #

defaultConfig :: Config Source #

setVerboseConfig :: Bool -> Config -> Config Source #

setQuadraticCharacterConfig :: Maybe Int -> Config -> Config Source #

verboseList :: Config -> String -> [String] -> String Source #

factorSquareRoots :: Config -> Integer -> Zx -> Integer -> FactorBase -> Zx -> [Ideal] -> [[Nfzw]] -> Verbose (Maybe Integer) Source #

factorWithPolynomial :: Config -> Integer -> Zx -> Integer -> Verbose (Maybe Integer) Source #

factor :: Config -> Integer -> Verbose (Maybe Integer) Source #