Factor.Prime

Documentation

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