-- Hoogle documentation, generated by Haddock
-- See Hoogle, http://www.haskell.org/hoogle/


-- | Factoring integers and polynomials
--   
--   This package contains a reference implementation library of factoring
--   algorithms for integers and univariate polynomials
@package factor
@version 1.5


module Factor.Gaussian
data Gaussian
Gaussian :: Integer -> Integer -> Gaussian
real :: Integer -> Gaussian
imaginary :: Integer -> Gaussian
zero :: Gaussian
one :: Gaussian
negate :: Gaussian -> Gaussian
add :: Gaussian -> Gaussian -> Gaussian
subtract :: Gaussian -> Gaussian -> Gaussian
multiply :: Gaussian -> Gaussian -> Gaussian
norm :: Gaussian -> Integer
division :: Gaussian -> Gaussian -> (Gaussian, Gaussian)
quotient :: Gaussian -> Gaussian -> Gaussian
remainder :: Gaussian -> Gaussian -> Gaussian
divides :: Gaussian -> Gaussian -> Bool
egcd :: Gaussian -> Gaussian -> (Gaussian, (Gaussian, Gaussian))
gcd :: Gaussian -> Gaussian -> Gaussian
instance GHC.Classes.Ord Factor.Gaussian.Gaussian
instance GHC.Classes.Eq Factor.Gaussian.Gaussian
instance GHC.Show.Show Factor.Gaussian.Gaussian


module Factor.Util
type Factor f a = Either f a
runFactor :: Show f => Factor f a -> a
data Verbose a
ResultVerbose :: a -> Verbose a
CommentVerbose :: String -> Verbose a -> Verbose a
timestampFormat :: String
comment :: String -> Verbose ()
runQuiet :: Verbose a -> a
runVerbose :: Verbose a -> IO a
runTimestampVerbose :: Verbose a -> IO a
isUnit :: Integer -> Bool
divides :: Integer -> Integer -> Bool
properDivisor :: Integer -> Integer -> Bool
division :: Integer -> Integer -> (Integer, Integer)
divisionClosest :: Integer -> Integer -> (Integer, Integer)
exactQuotient :: Integer -> Integer -> Maybe Integer
divPower :: Integer -> Integer -> (Integer, Integer)
factorial :: Integer -> Integer
egcd :: Integer -> Integer -> (Integer, (Integer, Integer))
coprime :: Integer -> Integer -> Bool
chineseRemainder :: Integer -> Integer -> Integer -> Integer -> Integer
nthRoot :: Integer -> Integer -> Integer
nthRootClosest :: Integer -> Integer -> Integer
destNthPower :: Integer -> Integer -> Maybe Integer
isNthPower :: Integer -> Integer -> Bool
destSquare :: Integer -> Maybe Integer
isSquare :: Integer -> Bool
type Width = Int
bitsInteger :: Integer -> [Bool]
widthInteger :: Integer -> Width
widthIntegerToString :: Integer -> String
uniformInteger :: RandomGen r => Width -> r -> (Integer, r)
uniformOddInteger :: RandomGen r => Width -> r -> (Integer, r)
type Log2Integer = Double
type Log2Probability = Double
log2 :: Double -> Double
log2e :: Double
log2Integer :: Integer -> Log2Integer
logInteger :: Integer -> Double
exp2Integer :: Log2Integer -> Integer
data Residue
Residue :: Residue
NonResidue :: Residue
ZeroResidue :: Residue
multiplyResidue :: Residue -> Residue -> Residue
jacobiSymbol :: Integer -> Integer -> Residue
singleton :: a -> [a]
doubleton :: a -> a -> [a]
tripleton :: a -> a -> a -> [a]
unfoldlN :: (b -> (a, b)) -> Int -> b -> ([a], b)
unfoldrN :: (b -> (a, b)) -> Int -> b -> ([a], b)
unabbrevList :: [String] -> String
abbrevList :: String -> [String] -> String
underline :: String -> String
data Table
Table :: Bool -> Bool -> Int -> Table
[borderTable] :: Table -> Bool
[alignLeftTable] :: Table -> Bool
[paddingTable] :: Table -> Int
fmtTable :: Table -> [[String]] -> String
ppTable :: [[String]] -> String
instance GHC.Show.Show Factor.Util.Residue
instance GHC.Classes.Ord Factor.Util.Residue
instance GHC.Classes.Eq Factor.Util.Residue
instance GHC.Show.Show Factor.Util.Table
instance GHC.Base.Functor Factor.Util.Verbose
instance GHC.Base.Applicative Factor.Util.Verbose
instance GHC.Base.Monad Factor.Util.Verbose


module Factor.Prime
type Prime = Integer
primes :: [Prime]
type PrimePower = (Prime, Integer)
multiplyPrimePowers :: [PrimePower] -> [PrimePower] -> [PrimePower]
productPrimePowers :: [[PrimePower]] -> [PrimePower]
factor :: [Prime] -> Integer -> ([PrimePower], Integer)
factorProduct :: [Prime] -> [Integer] -> ([PrimePower], [Integer])
trialDivision :: Integer -> ([PrimePower], Integer)
primesUnder :: Integer -> Integer
primesUnderEstimate :: Log2Integer -> Log2Integer
nthPrime :: Integer -> Integer
nthPrimeEstimate :: Log2Integer -> Log2Integer
smoothUnderLowerBound :: Integer -> Log2Integer -> Log2Integer
smoothUnder :: Integer -> Log2Integer -> Log2Integer
smoothProb :: Integer -> Width -> Log2Probability
smoothProbTrials :: Integer -> Width -> Integer -> Log2Probability
type Gfp = Integer
valid :: Prime -> Gfp -> Bool
fromInt :: Prime -> Int -> Gfp
fromInteger :: Prime -> Integer -> Gfp
toSmallestInteger :: Prime -> Gfp -> Integer
negate :: Prime -> Gfp -> Gfp
add :: Prime -> Gfp -> Gfp -> Gfp
sum :: Prime -> [Gfp] -> Gfp
subtract :: Prime -> Gfp -> Gfp -> Gfp
multiply :: Prime -> Gfp -> Gfp -> Gfp
square :: Prime -> Gfp -> Gfp
cube :: Prime -> Gfp -> Gfp
product :: Prime -> [Gfp] -> Gfp
multiplyExp :: Prime -> Gfp -> Gfp -> Integer -> Gfp
exp :: Prime -> Gfp -> Integer -> Gfp
exp2 :: Prime -> Gfp -> Integer -> Gfp
invertF :: Prime -> Gfp -> Factor Integer Gfp
invert :: Prime -> Gfp -> Gfp
divideF :: Prime -> Gfp -> Gfp -> Factor Integer Gfp
divide :: Prime -> Gfp -> Gfp -> Gfp
elements :: Prime -> [Gfp]
uniform :: RandomGen r => Prime -> r -> (Gfp, r)
uniformNonZero :: RandomGen r => Prime -> r -> (Gfp, r)
millerRabinTrials :: Int
isPrime :: RandomGen r => Integer -> r -> (Bool, r)
nextPrime :: RandomGen r => Integer -> r -> (Prime, r)
previousPrime :: RandomGen r => Integer -> r -> (Prime, r)
uniformPrime :: RandomGen r => Int -> r -> (Prime, r)
uniformComposite :: RandomGen r => Int -> r -> (Integer, r)
isResidue :: Prime -> Integer -> Bool
nonResidue :: Prime -> Integer -> Bool
nextResidue :: Prime -> Integer -> Integer
nextNonResidue :: Prime -> Integer -> Integer
sqrt :: Prime -> Gfp -> Gfp


module Factor.Term
type Index = Int
type Var = String
data Term
IntegerTerm :: Integer -> Term
PrimeIndexTerm :: Index -> Term
NumberWidthTerm :: Width -> Term
PrimeWidthTerm :: Width -> Term
CompositeWidthTerm :: Width -> Term
NegateTerm :: Term -> Term
AddTerm :: Term -> Term -> Term
SubtractTerm :: Term -> Term -> Term
MultiplyTerm :: Term -> Term -> Term
ExpTerm :: Term -> Term -> Term
VarTerm :: Var -> Term
ModTerm :: Term -> Term -> Term
LetTerm :: Var -> Term -> Term -> Term
modulo :: Term -> Integer -> Term
fromGfp :: Prime -> Gfp -> Term
fromPrimePower :: PrimePower -> Term
fromPrimePowers :: [PrimePower] -> Term
mkSum :: [Term] -> Term
mkProduct :: [Term] -> Term
subterms :: Term -> [Term]
data Result
RewriteResult :: Term -> Result
UnchangedResult :: Result
ErrorResult :: Result
newtype Rewrite
Rewrite :: (Term -> Result) -> Rewrite
[unRewrite] :: Rewrite -> Term -> Result
applyRewrite :: Rewrite -> Term -> Maybe Term
applyRewriteUnsafe :: Rewrite -> Term -> Term
idRewrite :: Rewrite
errorRewrite :: Rewrite
tryRewrite :: Rewrite -> Rewrite
thenRewrite :: Rewrite -> Rewrite -> Rewrite
orelseRewrite :: Rewrite -> Rewrite -> Rewrite
firstRewrite :: [Rewrite] -> Rewrite
subtermRewrite :: Rewrite -> Rewrite
bottomUpRewrite :: Rewrite -> Rewrite
instVarRewrite :: Var -> Term -> Rewrite
expandLetRewrite :: Rewrite -> (Rewrite -> Rewrite) -> Rewrite
expandLetsRewrite :: Rewrite -> Rewrite
uniform :: RandomGen r => Term -> r -> (Term, r)
negativeIntegerRewrite :: Rewrite
negateNegateRewrite :: Rewrite
addNegate2Rewrite :: Rewrite
subtractNegate2Rewrite :: Rewrite
multiplyNegateRewrite :: Rewrite
nnfInteger :: Term -> Term
nnf :: Term -> Term
multiplyOneRewrite :: Rewrite
expOneRewrite :: Rewrite
expZeroRewrite :: Rewrite
simplify :: Term -> Term
isReservedWord :: String -> Bool
spaceParser :: Parsec String st ()
spacesParser :: Parsec String st ()
spaces1Parser :: Parsec String st ()
integerParser :: Parsec String st Integer
indexParser :: Parsec String st Index
widthParser :: Parsec String st Width
classIndexParser :: Char -> Parsec String st Index
primeIndexParser :: Parsec String st Index
classWidthParser :: Char -> Parsec String st Width
numberWidthParser :: Parsec String st Width
primeWidthParser :: Parsec String st Width
compositeWidthParser :: Parsec String st Width
varParser :: Parsec String st Var
termParser :: Parsec String st Term
parse :: String -> Either ParseError Term
fromString :: String -> Maybe Term
indexToDoc :: Index -> Doc
widthToDoc :: Width -> Doc
atomicToDoc :: Term -> Doc
expToDoc :: Term -> Doc
prodToDoc :: Term -> Doc
negateToDoc :: Term -> Doc
sumToDoc :: Term -> Doc
modToDoc :: Term -> Doc
toDoc :: Term -> Doc
toString :: Term -> String
instance GHC.Show.Show Factor.Term.Term
instance GHC.Classes.Ord Factor.Term.Term
instance GHC.Classes.Eq Factor.Term.Term
instance GHC.Show.Show Factor.Term.Result
instance GHC.Classes.Ord Factor.Term.Result
instance GHC.Classes.Eq Factor.Term.Result


module Factor.Zx
data Monomial
Monomial :: Int -> Integer -> Monomial
[degreeMonomial] :: Monomial -> Int
[coeffMonomial] :: Monomial -> Integer
isZeroMonomial :: Monomial -> Bool
constantMonomial :: Integer -> Monomial
negateMonomial :: Monomial -> Monomial
toTermMonomial :: Var -> Monomial -> Term
data Zx
Zx :: Int -> IntMap Integer -> Zx
[degree] :: Zx -> Int
[coeffMap] :: Zx -> IntMap Integer
valid :: Zx -> Bool
fromNormCoeffMap :: IntMap Integer -> Zx
isZero :: Zx -> Bool
isOne :: Zx -> Bool
isConstant :: Zx -> Bool
isLinear :: Zx -> Bool
isMonic :: Zx -> Bool
powerCoeff :: Zx -> Int -> Integer
constantCoeff :: Zx -> Integer
linearCoeff :: Zx -> Integer
leadingCoeff :: Zx -> Integer
trailingCoeff :: Zx -> (Int, Integer)
monomials :: Zx -> [(Int, Integer)]
lengthMonomials :: Zx -> Int
filterMonomials :: (Int -> Integer -> Bool) -> Zx -> Zx
constant :: Integer -> Zx
variable :: Zx
monomial :: Int -> Integer -> Zx
simpleRoot :: Integer -> Zx
evaluate :: Zx -> Integer -> Integer
derivative :: Zx -> Zx
fromMonomial :: Monomial -> Zx
fromMonomials :: [Monomial] -> Zx
toMonomials :: Zx -> [Monomial]
fromCoeff :: [Integer] -> Zx
toCoeff :: Zx -> [Integer]
toTerm :: Var -> Zx -> Term
zero :: Zx
one :: Zx
negate :: Zx -> Zx
add :: Zx -> Zx -> Zx
sum :: [Zx] -> Zx
subtract :: Zx -> Zx -> Zx
multiply :: Zx -> Zx -> Zx
square :: Zx -> Zx
product :: [Zx] -> Zx
multiplyConstant :: Integer -> Zx -> Zx
multiplyPower :: Int -> Zx -> Zx
multiplyExp :: Zx -> Zx -> Integer -> Zx
exp :: Zx -> Integer -> Zx
compose :: Zx -> Zx -> Zx
division :: Zx -> Zx -> (Zx, Zx)
quotient :: Zx -> Zx -> Zx
remainder :: Zx -> Zx -> Zx
divides :: Zx -> Zx -> Bool
exactQuotientConstant :: Integer -> Zx -> Zx
content :: Zx -> Integer
isPrimitive :: Zx -> Bool
contentPrimitive :: Zx -> (Integer, Zx)
primitive :: Zx -> Zx
gcd :: Zx -> Zx -> Zx
gcdPrimitive :: Zx -> Zx -> Zx
squareFree :: Zx -> Bool
squareFreeDecomposition :: Zx -> [Zx]
squareFreeRecomposition :: [Zx] -> Zx
composePlusMinusSqrt :: Zx -> Integer -> Zx
swinnertonDyer :: [Zx]
instance GHC.Classes.Ord Factor.Zx.Monomial
instance GHC.Classes.Eq Factor.Zx.Monomial
instance GHC.Classes.Ord Factor.Zx.Zx
instance GHC.Classes.Eq Factor.Zx.Zx
instance GHC.Show.Show Factor.Zx.Zx
instance GHC.Show.Show Factor.Zx.Monomial


module Factor.Gfpx
data Gfpx
Gfpx :: Int -> IntMap Gfp -> Gfpx
[degree] :: Gfpx -> Int
[coeffMap] :: Gfpx -> IntMap Gfp
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)
instance GHC.Classes.Ord Factor.Gfpx.Gfpx
instance GHC.Classes.Eq Factor.Gfpx.Gfpx
instance GHC.Show.Show Factor.Gfpx.Gfpx


module Factor.Value
data Value
ZValue :: Integer -> Value
ZxValue :: Zx -> Var -> Value
GfpValue :: Prime -> Gfp -> Value
GfpxValue :: Prime -> Gfpx -> Var -> Value
free :: Value -> Set Var
normalize :: Value -> Value
negate :: Value -> Value
add :: Value -> Value -> Value
subtract :: Value -> Value -> Value
multiply :: Value -> Value -> Value
exp :: Value -> Value -> Value
fromTerm :: Term -> Value
toTerm :: Value -> Term
toString :: Value -> String
type Env = Map Var Value
emptyEnv :: Env
lookupEnv :: Env -> Var -> Value
extendEnv :: Env -> Var -> Value -> Env
data Context
ZContext :: Context
GfpContext :: Prime -> Context
combineContext :: Context -> Context -> Context
modContext :: Value -> Context
context :: Value -> Context
reduceInContext :: Context -> Value -> Value
importIntoContext :: Context -> Value -> Value
align :: Value -> Value -> (Value, Value)
interpret :: Env -> Context -> Term -> Value
instance GHC.Show.Show Factor.Value.Value
instance GHC.Classes.Ord Factor.Value.Value
instance GHC.Classes.Eq Factor.Value.Value
instance GHC.Show.Show Factor.Value.Context
instance GHC.Classes.Ord Factor.Value.Context
instance GHC.Classes.Eq Factor.Value.Context


module Factor.Nfzw
data Nfzw
Nfzw :: Integer -> Integer -> Nfzw
valid :: Nfzw -> Bool
filterValidLine :: (Nfzw -> Bool) -> Integer -> [Nfzw]
filterValid :: (Nfzw -> Bool) -> [Nfzw]
zero :: Nfzw
isZero :: Nfzw -> Bool
negate :: Nfzw -> Nfzw
toInteger :: Integer -> Nfzw -> Integer
norm :: Zx -> Nfzw -> Integer
type Ideal = (Gfp, Prime)
ideals :: Zx -> [Ideal]
inIdeal :: Nfzw -> Ideal -> Bool
factor :: Zx -> [Ideal] -> Nfzw -> ([(Ideal, Integer)], Integer)
instance GHC.Classes.Ord Factor.Nfzw.Nfzw
instance GHC.Classes.Eq Factor.Nfzw.Nfzw
instance GHC.Show.Show Factor.Nfzw.Nfzw


module Factor.Ec
data Curve
Curve :: Prime -> Gfp -> Gfp -> Curve
[kCurve] :: Curve -> Prime
[aCurve] :: Curve -> Gfp
[bCurve] :: Curve -> Gfp
data Point
Point :: Gfp -> Gfp -> Point
[xPoint] :: Point -> Gfp
[yPoint] :: Point -> Gfp
Infinity :: Point
rhs :: Curve -> Gfpx
rhsEvaluate :: Curve -> Gfp -> Gfp
onCurve :: Curve -> Point -> Bool
xPoints :: Curve -> Gfp -> [Point]
points :: Curve -> [Point]
discriminant :: Curve -> Gfp
singular :: Curve -> Bool
uniformCurve :: RandomGen r => Prime -> r -> ((Curve, Point), r)
uniformPoint :: RandomGen r => Curve -> r -> (Point, r)
negate :: Curve -> Point -> Point
addLambdaF :: Curve -> Gfp -> Gfp -> Gfp -> Gfp -> Gfp -> Factor Integer Point
doubleF :: Curve -> Point -> Factor Integer Point
double :: Curve -> Point -> Point
addF :: Curve -> Point -> Point -> Factor Integer Point
add :: Curve -> Point -> Point -> Point
addMultiplyF :: Curve -> Point -> Point -> Integer -> Factor Integer Point
addMultiply :: Curve -> Point -> Point -> Integer -> Point
multiplyF :: Curve -> Point -> Integer -> Factor Integer Point
multiply :: Curve -> Point -> Integer -> Point
data TargetConfig
CurvePointTargetConfig :: Int -> TargetConfig
PrimeTargetConfig :: Int -> TargetConfig
data Config
Config :: [TargetConfig] -> Config
[targetConfig] :: Config -> [TargetConfig]
defaultConfig :: Config
limitPrimesConfig :: Maybe Int -> Config -> Config
factorPrime :: [(Curve, Point)] -> Prime -> Factor Integer [(Curve, Point)]
factorPrimes :: [(Curve, Point)] -> [Prime] -> Factor Integer [(Curve, Point)]
factorTargets :: RandomGen r => Integer -> ([(Curve, Point)], Int) -> [TargetConfig] -> r -> Verbose (Maybe Integer, r)
factor :: RandomGen r => Config -> Integer -> r -> Verbose (Maybe Integer, r)
data DivisionPolynomial
DivisionPolynomial :: Gfpx -> Gfpx -> Gfpx -> DivisionPolynomial
[psiDivisionPolynomial] :: DivisionPolynomial -> Gfpx
[phiDivisionPolynomial] :: DivisionPolynomial -> Gfpx
[omegaDivisionPolynomial] :: DivisionPolynomial -> Gfpx
psiDivisionPolynomials :: Curve -> [Gfpx]
divisionPolynomials :: Curve -> [DivisionPolynomial]
data End
End :: Gfpx -> Gfpx -> End
evaluateEnd :: Curve -> End -> Point -> Point
identityEnd :: Curve -> Gfpx -> End
composeEnd :: Curve -> Gfpx -> End -> End -> End
negateEnd :: Curve -> End -> End
addLambdaEnd :: Curve -> Gfpx -> Gfpx -> Gfpx -> Gfpx -> Gfpx -> Gfpx -> Factor Gfpx End
doubleEnd :: Curve -> Gfpx -> End -> Factor Gfpx End
addEnd :: Curve -> Gfpx -> End -> End -> Factor Gfpx End
addMultiplyEnd :: Curve -> Gfpx -> End -> End -> Integer -> Factor Gfpx End
multiplyEnd :: Curve -> Gfpx -> End -> Integer -> Factor Gfpx End
frobeniusEnd :: Curve -> Gfpx -> End
traceOfFrobeniusMod2 :: Curve -> Integer
traceOfFrobeniusModOddPrime :: Curve -> Prime -> Gfpx -> Integer
traceOfFrobenius :: Curve -> Integer
supersingular :: Curve -> Bool
order :: Curve -> Integer
instance GHC.Classes.Ord Factor.Ec.Curve
instance GHC.Classes.Eq Factor.Ec.Curve
instance GHC.Classes.Ord Factor.Ec.Point
instance GHC.Classes.Eq Factor.Ec.Point
instance GHC.Show.Show Factor.Ec.TargetConfig
instance GHC.Classes.Ord Factor.Ec.TargetConfig
instance GHC.Classes.Eq Factor.Ec.TargetConfig
instance GHC.Show.Show Factor.Ec.Config
instance GHC.Classes.Ord Factor.Ec.Config
instance GHC.Classes.Eq Factor.Ec.Config
instance GHC.Show.Show Factor.Ec.DivisionPolynomial
instance GHC.Classes.Ord Factor.Ec.DivisionPolynomial
instance GHC.Classes.Eq Factor.Ec.DivisionPolynomial
instance GHC.Classes.Ord Factor.Ec.End
instance GHC.Classes.Eq Factor.Ec.End
instance GHC.Show.Show Factor.Ec.End
instance GHC.Show.Show Factor.Ec.Point
instance GHC.Show.Show Factor.Ec.Curve


module Factor.Bz
factorCoeffBound :: Zx -> Integer
monicGfpx :: Prime -> Zx -> Gfpx
suitablePrime :: Zx -> Prime
henselLiftQuadratic :: Zx -> (Integer, (Gfpx, Gfpx, Gfpx, Gfpx)) -> (Integer, (Gfpx, Gfpx, Gfpx, Gfpx))
henselLiftModulus :: Zx -> Prime -> (Int, Integer)
henselLiftFactors :: Zx -> Prime -> Int -> [Gfpx] -> [Gfpx]
recombineFactors :: Zx -> Integer -> [Gfpx] -> [Zx]
factorSquareFree :: Zx -> [Zx]
factorPrimitive :: Zx -> [(Zx, Integer)]
factor :: Zx -> (Integer, [(Zx, Integer)])
irreducible :: Zx -> Bool


module Factor.Nfs
data PolynomialDegree
FixedPolynomialDegree :: Int -> PolynomialDegree
OptimalPolynomialDegree :: PolynomialDegree
data PolynomialBase
FixedPolynomialBase :: Integer -> PolynomialBase
ClosestPolynomialBase :: PolynomialBase
FloorPolynomialBase :: PolynomialBase
data PolynomialCoeff
FixedPolynomialCoeff :: [Integer] -> PolynomialCoeff
SmallestPolynomialCoeff :: PolynomialCoeff
PositivePolynomialCoeff :: PolynomialCoeff
data PolynomialConfig
PolynomialConfig :: PolynomialDegree -> PolynomialBase -> PolynomialCoeff -> PolynomialConfig
[polynomialDegree] :: PolynomialConfig -> PolynomialDegree
[polynomialBase] :: PolynomialConfig -> PolynomialBase
[polynomialCoeff] :: PolynomialConfig -> PolynomialCoeff
defaultPolynomialConfig :: PolynomialConfig
fixedPolynomialConfig :: Zx -> Integer -> PolynomialConfig
selectPolynomialDegree :: PolynomialDegree -> Integer -> Int
selectPolynomialBase :: PolynomialBase -> Integer -> Int -> Integer
selectPolynomialCoeff :: PolynomialCoeff -> Integer -> Int -> Integer -> [Integer]
selectPolynomial :: PolynomialConfig -> Integer -> (Zx, Integer)
type FactorBase = [Prime]
data FactorBaseConfig
FixedFactorBase :: Integer -> FactorBaseConfig
OptimalFactorBase :: Double -> FactorBaseConfig
defaultFactorBaseConfig :: FactorBaseConfig
maxFactorBase :: FactorBaseConfig -> Integer -> Integer
destSmoothInteger :: FactorBase -> Integer -> Maybe Integer
isSmoothInteger :: FactorBase -> Integer -> Bool
notSmoothInteger :: FactorBase -> Integer -> Bool
rationalNorm :: Integer -> Nfzw -> Integer
algebraicNorm :: Zx -> Nfzw -> Integer
isSmoothNfzw :: Zx -> Integer -> FactorBase -> FactorBase -> Nfzw -> Bool
smoothNfzw :: Zx -> Integer -> FactorBase -> FactorBase -> [Nfzw]
data QuadraticCharacterConfig
FixedQuadraticCharacterConfig :: Int -> QuadraticCharacterConfig
LinearQuadraticCharacterConfig :: Int -> Double -> QuadraticCharacterConfig
defaultQuadraticCharacterConfig :: QuadraticCharacterConfig
quadraticCharacters :: QuadraticCharacterConfig -> Integer -> Int
isQuadraticCharacter :: Zx -> [Nfzw] -> Ideal -> Bool
nextQuadraticCharacter :: Zx -> [Nfzw] -> [Ideal] -> (Ideal, [Ideal])
takeQuadraticCharacters :: Zx -> [Nfzw] -> Int -> [Ideal] -> ([Ideal], [Ideal])
isQuadraticResidue :: Ideal -> Nfzw -> Bool
notQuadraticResidue :: Ideal -> Nfzw -> Bool
productIsQuadraticResidue :: Ideal -> [Nfzw] -> Bool
type Row = [Bool]
formRow :: Zx -> Integer -> [Prime] -> [Ideal] -> [Ideal] -> Nfzw -> Row
rationalRow :: [Prime] -> Integer -> Row
algebraicRow :: Zx -> [Ideal] -> [Ideal] -> Nfzw -> Row
oddPower :: Eq a => [(a, Integer)] -> a -> ([(a, Integer)], Bool)
gaussianElimination :: [Row] -> [[Int]]
rationalSquareRoot :: Integer -> Integer -> Zx -> [Prime] -> [Nfzw] -> Integer
algebraicSquareRoot :: Integer -> Zx -> Integer -> Zx -> [Ideal] -> [Nfzw] -> (Integer -> Bool) -> Verbose (Maybe Integer)
data Config
Config :: PolynomialConfig -> FactorBaseConfig -> FactorBaseConfig -> QuadraticCharacterConfig -> Int -> Bool -> Config
[polynomialConfig] :: Config -> PolynomialConfig
[rationalFactorBaseConfig] :: Config -> FactorBaseConfig
[algebraicFactorBaseConfig] :: Config -> FactorBaseConfig
[quadraticCharacterConfig] :: Config -> QuadraticCharacterConfig
[extraRankConfig] :: Config -> Int
[verboseConfig] :: Config -> Bool
defaultConfig :: Config
setVerboseConfig :: Bool -> Config -> Config
setQuadraticCharacterConfig :: Maybe Int -> Config -> Config
verboseList :: Config -> String -> [String] -> String
factorSquareRoots :: Config -> Integer -> Zx -> Integer -> FactorBase -> Zx -> [Ideal] -> [[Nfzw]] -> Verbose (Maybe Integer)
factorWithPolynomial :: Config -> Integer -> Zx -> Integer -> Verbose (Maybe Integer)
factor :: Config -> Integer -> Verbose (Maybe Integer)
instance GHC.Show.Show Factor.Nfs.PolynomialDegree
instance GHC.Classes.Ord Factor.Nfs.PolynomialDegree
instance GHC.Classes.Eq Factor.Nfs.PolynomialDegree
instance GHC.Show.Show Factor.Nfs.PolynomialBase
instance GHC.Classes.Ord Factor.Nfs.PolynomialBase
instance GHC.Classes.Eq Factor.Nfs.PolynomialBase
instance GHC.Show.Show Factor.Nfs.PolynomialCoeff
instance GHC.Classes.Ord Factor.Nfs.PolynomialCoeff
instance GHC.Classes.Eq Factor.Nfs.PolynomialCoeff
instance GHC.Show.Show Factor.Nfs.PolynomialConfig
instance GHC.Classes.Ord Factor.Nfs.PolynomialConfig
instance GHC.Classes.Eq Factor.Nfs.PolynomialConfig
instance GHC.Show.Show Factor.Nfs.FactorBaseConfig
instance GHC.Classes.Ord Factor.Nfs.FactorBaseConfig
instance GHC.Classes.Eq Factor.Nfs.FactorBaseConfig
instance GHC.Show.Show Factor.Nfs.QuadraticCharacterConfig
instance GHC.Classes.Ord Factor.Nfs.QuadraticCharacterConfig
instance GHC.Classes.Eq Factor.Nfs.QuadraticCharacterConfig
instance GHC.Show.Show Factor.Nfs.Config
instance GHC.Classes.Ord Factor.Nfs.Config
instance GHC.Classes.Eq Factor.Nfs.Config


module Factor
type IntegerFactorer r = Config -> Integer -> r -> Verbose ([PrimePower], r)
data Config
Config :: Integer -> Config -> Config -> Config
[trialDivisionConfig] :: Config -> Integer
[ecmConfig] :: Config -> Config
[nfsConfig] :: Config -> Config
defaultConfig :: Config
powerInteger :: Integer -> Integer -> Maybe (Integer, Integer)
nfsFactorInteger :: RandomGen r => IntegerFactorer r
ecmFactorInteger :: RandomGen r => IntegerFactorer r
primeFactorInteger :: RandomGen r => IntegerFactorer r -> IntegerFactorer r
powerFactorInteger :: RandomGen r => IntegerFactorer r -> IntegerFactorer r
mergeFactorInteger :: RandomGen r => IntegerFactorer r -> Config -> Integer -> Integer -> r -> Verbose ([PrimePower], r)
factorInteger :: RandomGen r => IntegerFactorer r
factorZx :: Zx -> [(Zx, Integer)]
factorGfpx :: RandomGen r => Prime -> Gfpx -> r -> ([(Gfpx, Integer)], r)
factorValue :: RandomGen r => Config -> Value -> r -> Verbose (Term, r)
instance GHC.Show.Show Factor.Config
instance GHC.Classes.Ord Factor.Config
instance GHC.Classes.Eq Factor.Config