[Bodigrim#128] Add EuclideanDomain class

Math/NumberTheory/EuclideanDomain.hs

@@ -0,0 +1,38 @@
+-- |
+-- Module:      Math.NumberTheory.EuclideanDomain
+-- Copyright:   (c) 2018 Alexandre Rodrigues Baldé
+-- Licence:     MIT
+-- Maintainer:  Alexandre Rodrigues Baldé <[email protected]>
+-- Stability:   Provisional
+-- Portability: Non-portable (GHC extensions)
+--
+-- This module exports a class to represent Euclidean domains.
+--
+
+module Math.NumberTheory.EuclideanDomain
+  ( EuclideanDomain (..)
+  , divMod
+  , div
+  , mod
+  , quotRem
+  , quot
+  , rem
+  ) where
+
+import Prelude hiding (divMod, div, mod, quotRem, quot, rem)
+
+class EuclideanDomain a where
+  quotRem :: a -> a -> (a, a)
+  divMod  :: a -> a -> (a, a)
+
+quot :: EuclideanDomain a => a -> a -> a
+quot x y = fst (quotRem x y)
+
+rem :: EuclideanDomain a => a -> a -> a
+rem x y = snd (quotRem x y)
+
+div :: EuclideanDomain a => a -> a -> a
+div x y = fst (divMod x y)
+
+mod :: EuclideanDomain a => a -> a -> a
+mod x y = snd (divMod x y)

arithmoi.cabal

@@ -59,6 +59,7 @@ library
     Math.NumberTheory.ArithmeticFunctions.Standard
     Math.NumberTheory.Curves.Montgomery
     Math.NumberTheory.EisensteinIntegers
+    Math.NumberTheory.EuclideanDomain
     Math.NumberTheory.GaussianIntegers
     Math.NumberTheory.GCD
     Math.NumberTheory.GCD.LowLevel