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


-- | A Haskell implementation for combining SU(n) multiplets.
--   
--   See README at <a>https://github.com/mdrslmr/MultipletCombiner</a>
@package MultipletCombiner
@version 0.0.2


-- | This module contains operators and functions for combining SU(n)
--   multiplets according to the algorithm presented by C.G. Wohl in the
--   PDG book 2021 section 48
--   <a>https://pdg.lbl.gov/2022/reviews/rpp2022-rev-young-diagrams.pdf</a>.
--   
--   It provides the operators <a>(&gt;&lt;)</a> and <a>(&gt;&gt;&lt;)</a>
--   for combining multiplets, and the function <a>multi</a> and
--   <a>multis</a> to calculate the multiplicities, e.g.:
--   
--   <pre>
--   [1,0] <a>&gt;&lt;</a> [0,1] = [[1,1],[0,0]]
--   
--   <a>multi</a> [1,0] = 3
--   
--   [1,0] <a>&gt;&lt;</a> [1,0] <a>&gt;&gt;&lt;</a> [1,0] = [[3,0],[1,1],[1,1],[0,0]]
--   
--   <a>multis</a> $ [1,0] <a>&gt;&lt;</a> [1,0] <a>&gt;&gt;&lt;</a> [1,0] = [10,8,8,1]
--   </pre>
--   
--   Example for combinaing two multiplets using Young-Diagrams:
--   
--   <pre>
--   (0,0)x(0,0) = (0,0)
--   #     a   # a  # a   # a
--   # (x) b = #  &gt; # b &gt; # b
--   #     c   #    #     # c
--   
--   (1,0)x(1,0) = (step -&gt;)   (2,0)      +   (step -&gt;) (0,1)
--   # #    a a    # # a a    # # a a           # # a    # # a
--   #   x  b    = #       &gt;  # b         +     # a    &gt; # a b
--   #      c      #          # c               #        # c
--   </pre>
module Physics.MultipletCombiner

-- | Produce multiplet structure from combining two SU(n) multiplets
(><) :: [Int] -> [Int] -> [[Int]]

-- | Produce multiplet structure from combining a list of multiplets with
--   another multiplet
(>><) :: [[Int]] -> [Int] -> [[Int]]

-- | Calculate the multiplicity of a multiplet
multi :: [Int] -> Int

-- | Calculate the multiplicities of a list of multiplets
multis :: [[Int]] -> [Int]

-- | Basic type used for a Tableau/Diagram
data Tableau

-- | Build a tableau bottom up from it's label.
ytSymbols :: [Int] -> Tableau

-- | Build multiple tableaux from multiple labels.
ytsSymbols :: [[Int]] -> [Tableau]

-- | Show like function to display a list of tableaux.
showt :: [Tableau] -> String

-- | Calculate the number representation from a tableau.
ytNums :: Tableau -> [Int]

-- | Calculate the list of labels fro a list of tableaux.
ytsNums :: [Tableau] -> [[Int]]

-- | Check for the string for being composed of admissible letters. |
--   Admissible and not admissible examples:
--   
--   <pre>
--   admis "aabacdaebbcbd"  = True
--   
--   last letter not admissable
--   admis "abacae"  = False
--   admis "abacdec"  = False
--   </pre>
admis :: String -> Bool

-- | Extract one strictly ordered chain from the given string, starting at
--   the given character.
unchain :: Char -> String -> Maybe String

-- | Convert a tableau of symbols into a tableau of letters
sym2letter :: Tableau -> Tableau

-- | Append a string to the i'th line of a tableau.
appendAt :: Int -> String -> Tableau -> Tableau

-- | Read a string of letters from a given tableau to be checked for
--   admissibility.
readTab :: Tableau -> String

-- | Produce a list of placing-coordinates of all combinations for a
--   tableau with t rows to place c character.
--   
--   E.g.: 3 rows, two characters -&gt; 3*3 possible placements:
--   
--   1:1, 1:2, 1:3, 2:1, 2:2, 2:3, 3:1, 3:2, 3:3
combis :: Int -> Int -> [[Int]]

-- | Create multiple new tableau using <a>newtab</a> given one tableau and
--   one line of a right side tableau.
--   
--   e.g.: tabs1 (ytSymbols [1,1,1]) "a a "
tabs1 :: Tableau -> String -> [Tableau]

-- | Create all tableaux from two given tableaux.
allTsFromSyms :: Tableau -> Tableau -> [Tableau]

-- | allTs [1,0] [1,1]
--   
--   Create all tableau from two tableaux identified by their labels.
--   
--   <pre>
--   putStrLn $ showt $ noDoubs.admisTabs $ allTs [1,1] [1,1]
--   ytsNums $ noDoubs.admisTabs $ allTs [1,1] [1,1]
--   [[2,2],[3,0],[0,3],[1,1],[1,1],[0,0]]
--   
--   </pre>
allTs :: [Int] -> [Int] -> [Tableau]
instance GHC.Classes.Eq Physics.MultipletCombiner.Tableau
instance GHC.Show.Show Physics.MultipletCombiner.Tableau