Safe Haskell | None |
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Same general interface as Math.Polynomial, but using AdditiveGroup, VectorSpace, etc., instead of Num where sensible.
- data Endianness
- data Poly a
- poly :: (Eq a, AdditiveGroup a) => Endianness -> [a] -> Poly a
- polyDegree :: (Eq a, AdditiveGroup a) => Poly a -> Int
- vPolyCoeffs :: (Eq a, AdditiveGroup a) => Endianness -> Poly a -> [a]
- polyIsZero :: (Eq a, AdditiveGroup a) => Poly a -> Bool
- polyIsOne :: (Num a, Eq a) => Poly a -> Bool
- zero :: Poly a
- one :: (Num a, Eq a) => Poly a
- constPoly :: (Eq a, AdditiveGroup a) => a -> Poly a
- x :: (Num a, Eq a) => Poly a
- scalePoly :: (Eq a, VectorSpace a, AdditiveGroup (Scalar a), Eq (Scalar a)) => Scalar a -> Poly a -> Poly a
- negatePoly :: (AdditiveGroup a, Eq a) => Poly a -> Poly a
- composePolyWith :: (AdditiveGroup a, Eq a) => (a -> a -> a) -> Poly a -> Poly a -> Poly a
- addPoly :: (AdditiveGroup a, Eq a) => Poly a -> Poly a -> Poly a
- sumPolys :: (AdditiveGroup a, Eq a) => [Poly a] -> Poly a
- multPolyWith :: (AdditiveGroup a, Eq a) => (a -> a -> a) -> Poly a -> Poly a -> Poly a
- powPolyWith :: (AdditiveGroup a, Eq a, Integral b) => a -> (a -> a -> a) -> Poly a -> b -> Poly a
- quotRemPolyWith :: (AdditiveGroup a, Eq a) => (a -> a -> a) -> (a -> a -> a) -> Poly a -> Poly a -> (Poly a, Poly a)
- quotPolyWith :: (AdditiveGroup a, Eq a) => (a -> a -> a) -> (a -> a -> a) -> Poly a -> Poly a -> Poly a
- remPolyWith :: (AdditiveGroup a, Eq a) => (a -> a -> a) -> (a -> a -> a) -> Poly a -> Poly a -> Poly a
- evalPoly :: (VectorSpace a, Eq a, AdditiveGroup (Scalar a), Eq (Scalar a)) => Poly a -> Scalar a -> a
- evalPolyDeriv :: (VectorSpace a, Eq a) => Poly a -> Scalar a -> (a, a)
- evalPolyDerivs :: (VectorSpace a, Eq a, Num (Scalar a)) => Poly a -> Scalar a -> [a]
- contractPoly :: (VectorSpace a, Eq a) => Poly a -> Scalar a -> (Poly a, a)
- monicPolyWith :: (AdditiveGroup a, Eq a) => a -> (a -> a -> a) -> Poly a -> Poly a
- gcdPolyWith :: (AdditiveGroup a, Eq a) => a -> (a -> a -> a) -> (a -> a -> a) -> Poly a -> Poly a -> Poly a
- polyDeriv :: (VectorSpace a, Eq a, Num (Scalar a)) => Poly a -> Poly a
- polyDerivs :: (VectorSpace a, Eq a, Num (Scalar a)) => Poly a -> [Poly a]
- polyIntegral :: (VectorSpace a, Eq a, Fractional (Scalar a)) => Poly a -> Poly a
Documentation
data Endianness Source
Functor Poly | |
(AdditiveGroup a, Eq a) => Eq (Poly a) | |
(Num a, Eq a) => Num (Poly a) | |
Show a => Show (Poly a) | |
NFData a => NFData (Poly a) | |
(Pretty a, Num a, Ord a) => Pretty (Poly a) | |
(RealFloat a, Pretty (Complex a)) => Pretty (Poly (Complex a)) | |
(Eq a, VectorSpace a, AdditiveGroup (Scalar a), Eq (Scalar a)) => VectorSpace (Poly a) | |
AdditiveGroup a => AdditiveGroup (Poly a) |
poly :: (Eq a, AdditiveGroup a) => Endianness -> [a] -> Poly aSource
polyDegree :: (Eq a, AdditiveGroup a) => Poly a -> IntSource
vPolyCoeffs :: (Eq a, AdditiveGroup a) => Endianness -> Poly a -> [a]Source
Get the coefficients of a a Poly
in the specified order.
polyIsZero :: (Eq a, AdditiveGroup a) => Poly a -> BoolSource
constPoly :: (Eq a, AdditiveGroup a) => a -> Poly aSource
Given some constant k
, construct the polynomial whose value is
constantly k
.
scalePoly :: (Eq a, VectorSpace a, AdditiveGroup (Scalar a), Eq (Scalar a)) => Scalar a -> Poly a -> Poly aSource
Given some scalar s
and a polynomial f
, computes the polynomial g
such that:
evalPoly g x = s * evalPoly f x
negatePoly :: (AdditiveGroup a, Eq a) => Poly a -> Poly aSource
Given some polynomial f
, computes the polynomial g
such that:
evalPoly g x = negate (evalPoly f x)
composePolyWith :: (AdditiveGroup a, Eq a) => (a -> a -> a) -> Poly a -> Poly a -> Poly aSource
composePoly f g
constructs the polynomial h
such that:
evalPoly h = evalPoly f . evalPoly g
This is a very expensive operation and, in general, returns a polynomial
that is quite a bit more expensive to evaluate than f
and g
together
(because it is of a much higher order than either). Unless your
polynomials are quite small or you are quite certain you need the
coefficients of the composed polynomial, it is recommended that you
simply evaluate f
and g
and explicitly compose the resulting
functions. This will usually be much more efficient.
addPoly :: (AdditiveGroup a, Eq a) => Poly a -> Poly a -> Poly aSource
Given polynomials f
and g
, computes the polynomial h
such that:
evalPoly h x = evalPoly f x + evalPoly g x
multPolyWith :: (AdditiveGroup a, Eq a) => (a -> a -> a) -> Poly a -> Poly a -> Poly aSource
Given polynomials f
and g
, computes the polynomial h
such that:
evalPoly h x = evalPoly f x * evalPoly g x
powPolyWith :: (AdditiveGroup a, Eq a, Integral b) => a -> (a -> a -> a) -> Poly a -> b -> Poly aSource
Given a polynomial f
and exponent n
, computes the polynomial g
such that:
evalPoly g x = evalPoly f x ^ n
quotRemPolyWith :: (AdditiveGroup a, Eq a) => (a -> a -> a) -> (a -> a -> a) -> Poly a -> Poly a -> (Poly a, Poly a)Source
Given polynomials a
and b
, with b
not zero
, computes polynomials
q
and r
such that:
addPoly (multPoly q b) r == a
quotPolyWith :: (AdditiveGroup a, Eq a) => (a -> a -> a) -> (a -> a -> a) -> Poly a -> Poly a -> Poly aSource
remPolyWith :: (AdditiveGroup a, Eq a) => (a -> a -> a) -> (a -> a -> a) -> Poly a -> Poly a -> Poly aSource
evalPoly :: (VectorSpace a, Eq a, AdditiveGroup (Scalar a), Eq (Scalar a)) => Poly a -> Scalar a -> aSource
evalPolyDeriv :: (VectorSpace a, Eq a) => Poly a -> Scalar a -> (a, a)Source
Evaluate a polynomial and its derivative (respectively) at a point.
evalPolyDerivs :: (VectorSpace a, Eq a, Num (Scalar a)) => Poly a -> Scalar a -> [a]Source
Evaluate a polynomial and all of its nonzero derivatives at a point. This is roughly equivalent to:
evalPolyDerivs p x = map (`evalPoly` x) (takeWhile (not . polyIsZero) (iterate polyDeriv p))
contractPoly :: (VectorSpace a, Eq a) => Poly a -> Scalar a -> (Poly a, a)Source
"Contract" a polynomial by attempting to divide out a root.
contractPoly p a
returns (q,r)
such that q*(x-a) + r == p
monicPolyWith :: (AdditiveGroup a, Eq a) => a -> (a -> a -> a) -> Poly a -> Poly aSource
Normalize a polynomial so that its highest-order coefficient is 1
gcdPolyWith :: (AdditiveGroup a, Eq a) => a -> (a -> a -> a) -> (a -> a -> a) -> Poly a -> Poly a -> Poly aSource
gcdPoly a b
computes the highest order monic polynomial that is a
divisor of both a
and b
. If both a
and b
are zero
, the
result is undefined.
polyDeriv :: (VectorSpace a, Eq a, Num (Scalar a)) => Poly a -> Poly aSource
Compute the derivative of a polynomial.
polyDerivs :: (VectorSpace a, Eq a, Num (Scalar a)) => Poly a -> [Poly a]Source
Compute all nonzero derivatives of a polynomial, starting with its "zero'th derivative", the original polynomial itself.
polyIntegral :: (VectorSpace a, Eq a, Fractional (Scalar a)) => Poly a -> Poly aSource
Compute the definite integral (from 0 to x) of a polynomial.