Math.Polynomial.Type

Low-level interface for the Poly type.

Documentation

data Endianness

Constructors

BE

Big-Endian (head is highest-order term)

LE

Little-Endian (head is const term)

Instances

Bounded Endianness

Methods

minBound :: Endianness

maxBound :: Endianness

Enum Endianness

Methods

succ :: Endianness -> Endianness

pred :: Endianness -> Endianness

toEnum :: Int -> Endianness

fromEnum :: Endianness -> Int

enumFrom :: Endianness -> [Endianness]

enumFromThen :: Endianness -> Endianness -> [Endianness]

enumFromTo :: Endianness -> Endianness -> [Endianness]

enumFromThenTo :: Endianness -> Endianness -> Endianness -> [Endianness]

Eq Endianness

Methods

(==) :: Endianness -> Endianness -> Bool

(/=) :: Endianness -> Endianness -> Bool

Ord Endianness

Methods

compare :: Endianness -> Endianness -> Ordering

(<) :: Endianness -> Endianness -> Bool

(<=) :: Endianness -> Endianness -> Bool

(>) :: Endianness -> Endianness -> Bool

(>=) :: Endianness -> Endianness -> Bool

max :: Endianness -> Endianness -> Endianness

min :: Endianness -> Endianness -> Endianness

Show Endianness

Methods

showsPrec :: Int -> Endianness -> ShowS

show :: Endianness -> String

showList :: [Endianness] -> ShowS

NFData Endianness

Methods

rnf :: Endianness -> ()

data Poly a

Instances

Functor Poly

Methods

fmap :: (a -> b) -> Poly a -> Poly b

(<$) :: a -> Poly b -> Poly a

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

Methods

(==) :: Poly a -> Poly a -> Bool

(/=) :: Poly a -> Poly a -> Bool

Show a => Show (Poly a)

Methods

showsPrec :: Int -> Poly a -> ShowS

show :: Poly a -> String

showList :: [Poly a] -> ShowS

NFData a => NFData (Poly a)

Methods

rnf :: Poly a -> ()

(Eq a, VectorSpace a, AdditiveGroup (Scalar a), Eq (Scalar a)) => VectorSpace (Poly a)

Associated Types

type Scalar (Poly a) :: *

Methods

(*^) :: Scalar (Poly a) -> Poly a -> Poly a

AdditiveGroup a => AdditiveGroup (Poly a)

Methods

zeroV :: Poly a

(^+^) :: Poly a -> Poly a -> Poly a

negateV :: Poly a -> Poly a

(^-^) :: Poly a -> Poly a -> Poly a

type Scalar (Poly a)

type Scalar (Poly a) = Scalar a

zero :: Poly a

The polynomial "0"

poly :: (Num a, Eq a) => Endianness -> [a] -> Poly a

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

polyN :: (Num a, Eq a) => Int -> Endianness -> [a] -> Poly a

Make a Poly from a list of coefficients, at most n of which are significant.

unboxedPoly :: (Unbox a, Num a, Eq a) => Endianness -> [a] -> Poly a

unboxedPolyN :: (Unbox a, Num a, Eq a) => Int -> Endianness -> [a] -> Poly a

mapPoly :: (Num a, Eq a) => (a -> a) -> Poly a -> Poly a

Like fmap, but able to preserve unboxedness

rawMapPoly :: (a -> a) -> Poly a -> Poly a

wrapPoly :: Poly a -> Poly (WrappedNum a)

like fmap WrapNum but using unsafeCoerce to avoid a pointless traversal

unwrapPoly :: Poly (WrappedNum a) -> Poly a

like fmap unwrapNum but using unsafeCoerce to avoid a pointless traversal

unboxPoly :: Unbox a => Poly a -> Poly a

rawListPoly :: Endianness -> [a] -> Poly a

Make a Poly from a list of coefficients using the specified coefficient order, without the Num context (and therefore without trimming zeroes from the coefficient list)

rawListPolyN :: Int -> Endianness -> [a] -> Poly a

rawVectorPoly :: Endianness -> Vector a -> Poly a

rawUVectorPoly :: Unbox a => Endianness -> Vector a -> Poly a

trim :: (a -> Bool) -> Poly a -> Poly a

Trim zeroes from a polynomial (given a predicate for identifying zero). In particular, drops zeroes from the highest-order coefficients, so that 0x^n + 0x^(n-1) + 0x^(n-2) + ... + ax^k + ..., a /= 0 is normalized to ax^k + ....

The Eq instance for Poly and all the standard constructors / destructors are defined using trim (0==).

vTrim :: (Eq a, AdditiveGroup a) => Poly a -> Poly a

polyIsZero :: (Num a, Eq a) => Poly a -> Bool

polyIsOne :: (Num a, Eq a) => Poly a -> Bool

polyCoeffs :: (Num a, Eq a) => Endianness -> Poly a -> [a]

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

vPolyCoeffs :: (Eq a, AdditiveGroup a) => Endianness -> Poly a -> [a]

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

rawCoeffsOrder :: Poly a -> Endianness

rawPolyCoeffs :: Poly a -> [a]

untrimmedPolyCoeffs :: Endianness -> Poly a -> [a]

polyDegree :: (Num a, Eq a) => Poly a -> Int

Get the degree of a a Poly (the highest exponent with nonzero coefficient)

rawPolyDegree :: Poly a -> Int

rawPolyLength :: Poly a -> Int