    module Numeric.Band.Rectangular
      ( Rect(..)
      ) where

    import Numeric.Algebra.Class
    import Numeric.Algebra.Idempotent
    import Data.Semigroupoid

    -- | a rectangular band is a nowhere commutative semigroup.
    -- That is to say, if ab = ba then a = b. From this it follows
    -- classically that aa = a and that such a band is isomorphic
    -- to the following structure
    data Rect i j = Rect i j deriving (Eq,Ord,Show,Read)

    instance Semigroupoid Rect where
      Rect _ i `o` Rect j _ = Rect j i

    instance Multiplicative (Rect i j) where
      Rect i _ * Rect _ j = Rect i j

    instance Band (Rect i j)