Tableaux.hs

-- | Tableau diagrams.
--
-- For example, the code
--
-- >  drawTableau $ 
-- >    [ [ 1 , 3 , 4 , 6 , 7 ]
-- >    , [ 2 , 5 , 8 ,10 ]
-- >    , [ 9 ]
-- >    ]
--
-- produces the diagram
--
-- <<svg/young_tableau.svg>>
-- 

{-# LANGUAGE FlexibleContexts, TypeFamilies #-}
module Math.Combinat.Diagrams.Tableaux where

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import Math.Combinat.Tableaux
import Math.Combinat.Partitions
import Math.Combinat.Diagrams.Partitions

import Linear.Vector

import Data.Colour

import Diagrams.Core
import Diagrams.Prelude
import Diagrams.TwoD.Text

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-- | Draws a Ferrers diagram with the default settings (English notation, black)
drawTableau :: (Renderable (Path V2 Double) b, Renderable (Text Double) b) => Tableau Int -> QDiagram b V2 Double Any
drawTableau = drawTableau' EnglishNotation black  


drawTableau' 
  :: (Renderable (Path V2 Double) b, Renderable (Text Double) b)
  => PartitionConvention      -- ^ orientation
  -> Colour Double            -- ^ color
  -> Tableau Int
  -> QDiagram b V2 Double Any
drawTableau' convention color tableau = numbers <> boxes where

  part = tableauShape tableau

  ps = fromPartition part :: [Int]
  n  = length ps 
    
  numbers = mconcat [ number j i a | i<-[(0::Int)..n-1], (j,a)<-zip [(0::Int)..] (tableau!!i) ]
          # lc color

  number  x y a = trafo x y $ scale (0.85 :: Double) $ text (show a) # lw none # lc color # fc color 

  v = 0.22 :: Double

  trafo   x y   = case convention of
    EnglishNotation    -> translate (r2 (0.5 + fromIntegral x , - 1 + v - fromIntegral y)) 
    EnglishNotationCCW -> translate (r2 (0.5 + fromIntegral y ,       v + fromIntegral x))
    FrenchNotation     -> translate (r2 (0.5 + fromIntegral x ,       v + fromIntegral y))                          

  -- numberSize = 0.35  :: Double
  -- linewidth  = 0.025 :: Double

  boxes = drawPartitionBoxes convention part

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