factor-1.5: Factoring integers and polynomials

Safe Haskell	Safe-Inferred
Language	Haskell2010

Factor.Zx

Description

Documentation

data Monomial Source #

Constructors

Monomial
Fields degreeMonomial :: Int coeffMonomial :: Integer

Instances

Instances details

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

isZeroMonomial :: Monomial -> Bool Source #

constantMonomial :: Integer -> Monomial Source #

negateMonomial :: Monomial -> Monomial Source #

toTermMonomial :: Var -> Monomial -> Term Source #

data Zx Source #

Constructors

Zx
Fields degree :: Int coeffMap :: IntMap Integer

Instances

Instances details

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

valid :: Zx -> Bool Source #

fromNormCoeffMap :: IntMap Integer -> Zx Source #

isZero :: Zx -> Bool Source #

isOne :: Zx -> Bool Source #

isConstant :: Zx -> Bool Source #

isLinear :: Zx -> Bool Source #

isMonic :: Zx -> Bool Source #

powerCoeff :: Zx -> Int -> Integer Source #

constantCoeff :: Zx -> Integer Source #

linearCoeff :: Zx -> Integer Source #

leadingCoeff :: Zx -> Integer Source #

trailingCoeff :: Zx -> (Int, Integer) Source #

monomials :: Zx -> [(Int, Integer)] Source #

lengthMonomials :: Zx -> Int Source #

filterMonomials :: (Int -> Integer -> Bool) -> Zx -> Zx Source #

constant :: Integer -> Zx Source #

variable :: Zx Source #

monomial :: Int -> Integer -> Zx Source #

simpleRoot :: Integer -> Zx Source #

evaluate :: Zx -> Integer -> Integer Source #

derivative :: Zx -> Zx Source #

fromMonomial :: Monomial -> Zx Source #

fromMonomials :: [Monomial] -> Zx Source #

toMonomials :: Zx -> [Monomial] Source #

fromCoeff :: [Integer] -> Zx Source #

toCoeff :: Zx -> [Integer] Source #

toTerm :: Var -> Zx -> Term Source #

zero :: Zx Source #

one :: Zx Source #

negate :: Zx -> Zx Source #

add :: Zx -> Zx -> Zx Source #

sum :: [Zx] -> Zx Source #

subtract :: Zx -> Zx -> Zx Source #

multiply :: Zx -> Zx -> Zx Source #

square :: Zx -> Zx Source #

product :: [Zx] -> Zx Source #

multiplyConstant :: Integer -> Zx -> Zx Source #

multiplyPower :: Int -> Zx -> Zx Source #

multiplyExp :: Zx -> Zx -> Integer -> Zx Source #

exp :: Zx -> Integer -> Zx Source #

compose :: Zx -> Zx -> Zx Source #

division :: Zx -> Zx -> (Zx, Zx) Source #

quotient :: Zx -> Zx -> Zx Source #

remainder :: Zx -> Zx -> Zx Source #

divides :: Zx -> Zx -> Bool Source #

exactQuotientConstant :: Integer -> Zx -> Zx Source #

content :: Zx -> Integer Source #

isPrimitive :: Zx -> Bool Source #

contentPrimitive :: Zx -> (Integer, Zx) Source #

primitive :: Zx -> Zx Source #

gcd :: Zx -> Zx -> Zx Source #

gcdPrimitive :: Zx -> Zx -> Zx Source #

squareFree :: Zx -> Bool Source #

squareFreeDecomposition :: Zx -> [Zx] Source #

squareFreeRecomposition :: [Zx] -> Zx Source #

composePlusMinusSqrt :: Zx -> Integer -> Zx Source #

swinnertonDyer :: [Zx] Source #