Math.Polynomial

Documentation

data Endianness

Constructors

BE

Big-Endian (head is highest-order term)

LE

Little-Endian (head is const term)

Instances

Bounded Endianness

Enum Endianness

Eq Endianness

Ord Endianness

Show Endianness

data Poly a

Instances

Functor Poly

(Num a, Eq a) => Eq (Poly a)

Num a => Num (Poly a)

Num a => Show (Poly a)

(Pretty a, Num a, Ord a) => Pretty (Poly a)

(RealFloat a, Pretty (Complex a)) => Pretty (Poly (Complex a))

VectorSpace a => VectorSpace (Poly a)

AdditiveGroup a => AdditiveGroup (Poly a)

poly :: Num a => Endianness -> [a] -> Poly a

Make a Poly from a list of coefficients using the specified coefficient order.

polyCoeffs :: Num a => Endianness -> Poly a -> [a]

Get the coefficients of a a Poly in the specified order.

polyIsZero :: Num a => Poly a -> Bool

polyIsOne :: Num a => Poly a -> Bool

zero :: Num a => Poly a

one :: Num a => Poly a

x :: Num a => Poly a

scalePoly :: Num a => a -> Poly a -> Poly a

negatePoly :: Num a => Poly a -> Poly a

addPoly :: Num a => Poly a -> Poly a -> Poly a

sumPolys :: Num a => [Poly a] -> Poly a

multPoly :: Num a => Poly a -> Poly a -> Poly a

powPoly :: (Num a, Integral b) => Poly a -> b -> Poly a

quotRemPoly :: Fractional a => Poly a -> Poly a -> (Poly a, Poly a)

quotPoly :: Fractional a => Poly a -> Poly a -> Poly a

remPoly :: Fractional a => Poly a -> Poly a -> Poly a

evalPoly :: Num a => Poly a -> a -> a

evalPolyDeriv :: Num a => Poly a -> a -> (a, a)

evalPolyDerivs :: Num a => Poly a -> a -> [a]

contractPoly :: Num a => Poly a -> a -> (Poly a, a)

"Contract" a polynomial by attempting to divide out a root.

contractPoly p a returns (q,r) such that q*(x-a) + r == p

gcdPoly :: Fractional a => Poly a -> Poly a -> Poly a

separateRoots :: Fractional a => Poly a -> [Poly a]

Separate a polynomial into a set of factors none of which have multiple roots, and the product of which is the original polynomial. Note that if division is not exact, it may fail to separate roots. Rational coefficients is a good idea.

Useful when applicable as a way to simplify root-finding problems.

polyDeriv :: Num a => Poly a -> Poly a

polyIntegral :: Fractional a => Poly a -> Poly a