-- Hoogle documentation, generated by Haddock
-- See Hoogle, http://www.haskell.org/hoogle/


-- | Polynomials
--   
--   A type to represent polynomials with Num and Semiring instances.
@package poly
@version 0.1.0.0


-- | Polynomials.
module Data.Poly

-- | Polynomials of one variable.
--   
--   <pre>
--   &gt;&gt;&gt; :set -XOverloadedLists
--   
--   &gt;&gt;&gt; -- (1 + x) * (-1 + x) = (-1 + x^2)
--   
--   &gt;&gt;&gt; toPoly [1,1] * toPoly [-1,1]
--   Poly {unPoly = [-1,0,1]}
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; :set -XOverloadedLists
--   
--   &gt;&gt;&gt; -- (1 + x) + (1 - x) = 2
--   
--   &gt;&gt;&gt; toPoly [1,1] + toPoly [1,-1]
--   Poly {unPoly = [2]}
--   </pre>
data Poly a

-- | Convert <a>Poly</a> to a vector of coefficients (first element
--   corresponds to a constant term).
unPoly :: Poly a -> Vector a

-- | Make <a>Poly</a> from a list of coefficients (first element
--   corresponds to a constant term).
--   
--   <pre>
--   &gt;&gt;&gt; :set -XOverloadedLists
--   
--   &gt;&gt;&gt; toPoly [1,2,3]
--   Poly {unPoly = [1,2,3]}
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; :set -XOverloadedLists
--   
--   &gt;&gt;&gt; toPoly [0,0,0]
--   Poly {unPoly = []}
--   </pre>
toPoly :: (Eq a, Num a) => Vector a -> Poly a

-- | Make <a>Poly</a> from a vector of coefficients (first element
--   corresponds to a constant term).
--   
--   <pre>
--   &gt;&gt;&gt; :set -XOverloadedLists
--   
--   &gt;&gt;&gt; toPoly' [1,2,3]
--   Poly {unPoly = [1,2,3]}
--   </pre>
--   
--   <pre>
--   &gt;&gt;&gt; :set -XOverloadedLists
--   
--   &gt;&gt;&gt; toPoly' [0,0,0]
--   Poly {unPoly = []}
--   </pre>
toPoly' :: (Eq a, Semiring a) => Vector a -> Poly a