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


-- | Vertex enumeration
--   
--   Vertex enumeration of convex polytopes given by linear inequalities.
@package vertexenum
@version 1.0.0.0


-- | Enumeration of the vertices of a convex polytope given by linear
--   inequalities. See README for an example.
module Geometry.VertexEnum
data Constraint a
Constraint :: LinearCombination a -> Sense -> LinearCombination a -> Constraint a
type Var a = LinearCombination a
data Sense
Gt :: Sense
Lt :: Sense
newtype LinearCombination a
LinearCombination :: IntMap a -> LinearCombination a
type VarIndex = Int

-- | new variable
newVar :: Num a => VarIndex -> Var a
(.>=.) :: LinearCombination a -> LinearCombination a -> Constraint a
infix 4 .>=.
(.<=.) :: LinearCombination a -> LinearCombination a -> Constraint a
infix 4 .<=.
(.>=) :: LinearCombination a -> a -> Constraint a
infix 4 .>=
(.<=) :: LinearCombination a -> a -> Constraint a
infix 4 .<=

-- | linear combination from list of terms
linearCombination :: Num a => [(a, Var a)] -> LinearCombination a

-- | constant linear combination
constant :: a -> LinearCombination a

-- | alias for <a>constant</a>
cst :: a -> LinearCombination a

-- | Vertex enumeration
vertexenum :: Real a => [Constraint a] -> Maybe [Double] -> IO [[Double]]

-- | Checks whether a point fulfills some inequalities; returns the
--   difference between the upper member and the lower member for each
--   inequality, which is positive in case if the inequality is fulfilled.
checkConstraints :: Real a => [Constraint a] -> [Double] -> [(Double, Bool)]

-- | Returns a point fulfilling a list of inequalities
interiorPoint :: Real a => [Constraint a] -> IO [Double]