Tableaux.hs

-- | Tableau diagrams

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

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

-- import Data.Monoid
import Data.VectorSpace
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 R2) b, Renderable Text b) => Tableau Int -> Diagram b R2
drawTableau = drawTableau' EnglishNotation black  


drawTableau' 
  :: (Renderable (Path R2) b, Renderable Text b)
  => PartitionConvention      -- ^ orientation
  -> Colour Double            -- ^ color
  -> Tableau Int
  -> Diagram b R2
drawTableau' convention color tableau = numbers <> boxes where

  part = shape 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 $ 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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