Arithmetic.Polynomial

Documentation

data Polynomial a

Constructors

Polynomial

Fields

• carrier :: Ring a
• coefficients :: [a]

Instances

(Eq a, Show a) => Show (Polynomial a)

Defined in Arithmetic.Polynomial

Methods

showsPrec :: Int -> Polynomial a -> ShowS

show :: Polynomial a -> String

showList :: [Polynomial a] -> ShowS

fromCoefficients :: Eq a => Ring a -> [a] -> Polynomial a

zero :: Ring a -> Polynomial a

isZero :: Polynomial a -> Bool

constant :: Eq a => Ring a -> a -> Polynomial a

destConstant :: Polynomial a -> Maybe a

isConstant :: Polynomial a -> Bool

fromNatural :: Eq a => Ring a -> Natural -> Polynomial a

one :: Eq a => Ring a -> Polynomial a

multiplyByPower :: Polynomial a -> Natural -> Polynomial a

monomial :: Eq a => Ring a -> a -> Natural -> Polynomial a

variablePower :: Eq a => Ring a -> Natural -> Polynomial a

variable :: Eq a => Ring a -> Polynomial a

degree :: Polynomial a -> Natural

leadingCoefficient :: Polynomial a -> Maybe a

nthCoefficient :: Polynomial a -> Natural -> a

isMonic :: Eq a => Polynomial a -> Bool

evaluate :: Polynomial a -> a -> a

addCoefficients :: Ring a -> [a] -> [a] -> [a]

add :: Eq a => Polynomial a -> Polynomial a -> Polynomial a

negate :: Polynomial a -> Polynomial a

multiply :: Eq a => Polynomial a -> Polynomial a -> Polynomial a

multiplyByScalar :: Eq a => Polynomial a -> a -> Polynomial a

invert :: Polynomial a -> Maybe (Polynomial a)

subtract :: Eq a => Polynomial a -> Polynomial a -> Polynomial a

quotientRemainder :: Eq a => Polynomial a -> Polynomial a -> Maybe (Polynomial a, Polynomial a)

divide :: Eq a => Polynomial a -> Polynomial a -> Maybe (Polynomial a)

ring :: Eq a => Ring a -> Ring (Polynomial a)