| Copyright | (c) 2019 Andrew Lelechenko |
|---|---|
| License | BSD3 |
| Maintainer | Andrew Lelechenko <andrew.lelechenko@gmail.com> |
| Safe Haskell | None |
| Language | Haskell2010 |
Data.Poly.Semiring
Description
Dense polynomials and a Semiring-based interface.
Synopsis
- data Poly v a
- type VPoly = Poly Vector
- type UPoly = Poly Vector
- unPoly :: Poly v a -> v a
- leading :: Vector v a => Poly v a -> Maybe (Word, a)
- toPoly :: (Eq a, Semiring a, Vector v a) => v a -> Poly v a
- monomial :: (Eq a, Semiring a, Vector v a) => Word -> a -> Poly v a
- scale :: (Eq a, Semiring a, Vector v a) => Word -> a -> Poly v a -> Poly v a
- pattern X :: (Eq a, Semiring a, Vector v a, Eq (v a)) => Poly v a
- eval :: (Semiring a, Vector v a) => Poly v a -> a -> a
- deriv :: (Eq a, Semiring a, Vector v a) => Poly v a -> Poly v a
- newtype PolyOverFractional poly = PolyOverFractional {
- unPolyOverFractional :: poly
Documentation
Polynomials of one variable with coefficients from a,
backed by a Vector v (boxed, unboxed, storable, etc.).
Use pattern X for construction:
>>>(X + 1) + (X - 1) :: VPoly Integer2 * X + 0>>>(X + 1) * (X - 1) :: UPoly Int1 * X^2 + 0 * X + (-1)
Polynomials are stored normalized, without leading
zero coefficients, so 0 * X + 1 equals to 1.
Ord instance does not make much sense mathematically,
it is defined only for the sake of Set, Map, etc.
Instances
unPoly :: Poly v a -> v a Source #
Convert Poly to a vector of coefficients
(first element corresponds to a constant term).
leading :: Vector v a => Poly v a -> Maybe (Word, a) Source #
Return a leading power and coefficient of a non-zero polynomial.
>>>leading ((2 * X + 1) * (2 * X^2 - 1) :: UPoly Int)Just (3,4)>>>leading (0 :: UPoly Int)Nothing
Semiring interface
toPoly :: (Eq a, Semiring a, Vector v a) => v a -> Poly v a Source #
Make Poly from a vector of coefficients
(first element corresponds to a constant term).
>>>:set -XOverloadedLists>>>toPoly [1,2,3] :: VPoly Integer3 * X^2 + 2 * X + 1>>>toPoly [0,0,0] :: UPoly Int0
monomial :: (Eq a, Semiring a, Vector v a) => Word -> a -> Poly v a Source #
Create a monomial from a power and a coefficient.
scale :: (Eq a, Semiring a, Vector v a) => Word -> a -> Poly v a -> Poly v a Source #
Multiply a polynomial by a monomial, expressed as a power and a coefficient.
>>>scale 2 3 (X^2 + 1) :: UPoly Int3 * X^4 + 0 * X^3 + 3 * X^2 + 0 * X + 0
pattern X :: (Eq a, Semiring a, Vector v a, Eq (v a)) => Poly v a Source #
Create an identity polynomial.
eval :: (Semiring a, Vector v a) => Poly v a -> a -> a Source #
Evaluate at a given point.
>>>eval (X^2 + 1 :: UPoly Int) 310>>>eval (X^2 + 1 :: VPoly (UPoly Int)) (X + 1)1 * X^2 + 2 * X + 2
deriv :: (Eq a, Semiring a, Vector v a) => Poly v a -> Poly v a Source #
Take a derivative.
>>>deriv (X^3 + 3 * X) :: UPoly Int3 * X^2 + 0 * X + 3
Fractional coefficients
newtype PolyOverFractional poly Source #
Wrapper over polynomials,
providing a faster GcdDomain instance,
when coefficients are Fractional.
Constructors
| PolyOverFractional | |
Fields
| |