Numeric.Band.Rectangular

Documentation

data Rect i j

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

Constructors

Rect i j

Instances

Semigroupoid * Rect

Methods

o :: c j k1 -> c i j -> c i k1

(Eq j, Eq i) => Eq (Rect i j)

Methods

(==) :: Rect i j -> Rect i j -> Bool

(/=) :: Rect i j -> Rect i j -> Bool

(Ord j, Ord i) => Ord (Rect i j)

Methods

compare :: Rect i j -> Rect i j -> Ordering

(<) :: Rect i j -> Rect i j -> Bool

(<=) :: Rect i j -> Rect i j -> Bool

(>) :: Rect i j -> Rect i j -> Bool

(>=) :: Rect i j -> Rect i j -> Bool

max :: Rect i j -> Rect i j -> Rect i j

min :: Rect i j -> Rect i j -> Rect i j

(Read j, Read i) => Read (Rect i j)

Methods

readsPrec :: Int -> ReadS (Rect i j)

readList :: ReadS [Rect i j]

readPrec :: ReadPrec (Rect i j)

readListPrec :: ReadPrec [Rect i j]

(Show j, Show i) => Show (Rect i j)

Methods

showsPrec :: Int -> Rect i j -> ShowS

show :: Rect i j -> String

showList :: [Rect i j] -> ShowS

Multiplicative (Rect i j)

Methods

(*) :: Rect i j -> Rect i j -> Rect i j

pow1p :: Rect i j -> Natural -> Rect i j

productWith1 :: Foldable1 f => (a -> Rect i j) -> f a -> Rect i j

Band (Rect i j)