modular square root UI

app/Main.hs

@@ -2,19 +2,20 @@ module Main where
 
 import Utils (askChoice)
 import qualified FactorizationUI
+import qualified ModularSquareRootUI
 import qualified PrimesUI
 
 main :: IO ()
 main = do
     putStrLn "Haskell Math Toolkit"
     putStrLn "1) Factorization"
-    putStrLn "2) Modular square root (not yet implemented)"
+    putStrLn "2) Modular square root"
     putStrLn "3) Primality tests"
 
     choice <- askChoice 3
 
     case choice of
         1 -> FactorizationUI.run
-        2 -> putStrLn "Modular square root: not implemented yet."
+        2 -> ModularSquareRootUI.run
         3 -> PrimesUI.run
         _ -> error "Impossible"

app/ModularSquareRootUI.hs

@@ -0,0 +1,20 @@
+module ModularSquareRootUI (run) where
+
+import Utils (askNumber)
+import ModularSquareRoot (tonelliShanks)
+
+run :: IO ()
+run = do
+    putStrLn "Modular square root (Tonelli–Shanks)"
+    putStrLn "Solve x^2 = n (mod p), with p an odd prime."
+
+    n <- askNumber "Enter n:"
+    p <- askNumber "Enter prime modulus p:"
+
+    case tonelliShanks n p of
+        Just x -> do
+            putStrLn "Solution found:"
+            putStrLn ("x = " ++ show x ++ " (mod " ++ show p ++ ")")
+            putStrLn ("Other root: " ++ show ((p - x) `mod` p))
+        Nothing ->
+            putStrLn "No square root exists modulo p."