From 4575ca91adfabd81ecab5e83790ff3c5289daf6d Mon Sep 17 00:00:00 2001
From: Junaid Rasheed <jrasheed178@gmail.com>
Date: Fri, 2 Oct 2026 11:23:10 +0100
Subject: [PATCH 1/2] fix(prettify): render fractions and separators correctly

---
 src/Linear/Simplex/Prettify.hs             | 19 ++++++++++---------
 test/Linear/Simplex/Solver/TwoPhaseSpec.hs | 20 ++++++++++++--------
 2 files changed, 22 insertions(+), 17 deletions(-)

diff --git a/src/Linear/Simplex/Prettify.hs b/src/Linear/Simplex/Prettify.hs
index adb62ec..ea3e6f6 100644
--- a/src/Linear/Simplex/Prettify.hs
+++ b/src/Linear/Simplex/Prettify.hs
@@ -13,23 +13,24 @@
 module Linear.Simplex.Prettify where
 
 import Data.Generics.Labels ()
+import Data.List (intercalate)
 import Data.Map qualified as M
 import Data.Ratio (denominator, numerator)
 import Linear.Simplex.Types (ObjectiveFunction (..), PolyConstraint (..), VarLitMapSum)
 
 -- | Convert a 'VarLitMapSum' into a human-readable 'String'
 prettyShowVarLitMapSum :: VarLitMapSum -> String
-prettyShowVarLitMapSum = aux . M.toList
+prettyShowVarLitMapSum = intercalate " + " . map prettyShowTerm . M.toList
   where
-    aux [] = ""
-    aux ((vName, vCoeff) : vs) = prettyShowRational vCoeff ++ " * " ++ show vName ++ " + " ++ aux vs
+    prettyShowTerm (vName, vCoeff) = prettyShowRational vCoeff ++ " * " ++ show vName
+
+    prettyShowRational r =
+      if r < 0 then "(" ++ rendered ++ ")" else rendered
       where
-        prettyShowRational r =
-          if r < 0
-            then "(" ++ r' ++ ")"
-            else r'
-          where
-            r' = if denominator r == 1 then show (numerator r) else show (numerator r) ++ " / " ++ show (numerator r)
+        rendered =
+          if denominator r == 1
+            then show (numerator r)
+            else show (numerator r) ++ " / " ++ show (denominator r)
 
 -- | Convert a 'PolyConstraint' into a human-readable 'String'
 prettyShowPolyConstraint :: PolyConstraint -> String
diff --git a/test/Linear/Simplex/Solver/TwoPhaseSpec.hs b/test/Linear/Simplex/Solver/TwoPhaseSpec.hs
index 9ca2246..f6c5673 100644
--- a/test/Linear/Simplex/Solver/TwoPhaseSpec.hs
+++ b/test/Linear/Simplex/Solver/TwoPhaseSpec.hs
@@ -3058,31 +3058,35 @@ spec = do
       prettyShowVarLitMapSum M.empty `shouldBe` ""
 
     it "shows single positive coefficient" $ do
-      prettyShowVarLitMapSum (M.fromList [(1, 3)]) `shouldBe` "3 * 1 + "
+      prettyShowVarLitMapSum (M.fromList [(1, 3)]) `shouldBe` "3 * 1"
 
     it "shows single negative coefficient with parentheses" $ do
-      prettyShowVarLitMapSum (M.fromList [(1, -2)]) `shouldBe` "(-2) * 1 + "
+      prettyShowVarLitMapSum (M.fromList [(1, -2)]) `shouldBe` "(-2) * 1"
+
+    it "shows positive and negative fractional coefficients exactly" $ do
+      prettyShowVarLitMapSum (M.fromList [(1, 1 % 2), (2, (-3) % 4)])
+        `shouldBe` "1 / 2 * 1 + (-3 / 4) * 2"
 
     it "shows multiple coefficients" $ do
       let result = prettyShowVarLitMapSum (M.fromList [(1, 2), (2, 3)])
-      result `shouldBe` "2 * 1 + 3 * 2 + "
+      result `shouldBe` "2 * 1 + 3 * 2"
 
   describe "prettyShowPolyConstraint" $ do
     it "shows LEQ constraint" $ do
-      prettyShowPolyConstraint (LEQ (M.fromList [(1, 2)]) 10) `shouldBe` "2 * 1 + " ++ " <= " ++ show (10 :: Rational)
+      prettyShowPolyConstraint (LEQ (M.fromList [(1, 2)]) 10) `shouldBe` "2 * 1" ++ " <= " ++ show (10 :: Rational)
 
     it "shows GEQ constraint" $ do
-      prettyShowPolyConstraint (GEQ (M.fromList [(1, 1)]) 5) `shouldBe` "1 * 1 + " ++ " >= " ++ show (5 :: Rational)
+      prettyShowPolyConstraint (GEQ (M.fromList [(1, 1)]) 5) `shouldBe` "1 * 1" ++ " >= " ++ show (5 :: Rational)
 
     it "shows EQ constraint" $ do
-      prettyShowPolyConstraint (EQ (M.fromList [(1, 1)]) 3) `shouldBe` "1 * 1 + " ++ " == " ++ show (3 :: Rational)
+      prettyShowPolyConstraint (EQ (M.fromList [(1, 1)]) 3) `shouldBe` "1 * 1" ++ " == " ++ show (3 :: Rational)
 
   describe "prettyShowObjectiveFunction" $ do
     it "shows Max objective" $ do
-      prettyShowObjectiveFunction (Max (M.fromList [(1, 2)])) `shouldBe` "max: 2 * 1 + "
+      prettyShowObjectiveFunction (Max (M.fromList [(1, 2)])) `shouldBe` "max: 2 * 1"
 
     it "shows Min objective" $ do
-      prettyShowObjectiveFunction (Min (M.fromList [(1, 5)])) `shouldBe` "min: 5 * 1 + "
+      prettyShowObjectiveFunction (Min (M.fromList [(1, 5)])) `shouldBe` "min: 5 * 1"
 
   describe "twoPhaseSimplex with multiple objectives" $ do
     it "optimizes two objectives over the same feasible region" $ do

From 0819de4c7a6c46a4b304b1a8da984a2ab5f67061 Mon Sep 17 00:00:00 2001
From: Junaid Rasheed <jrasheed178@gmail.com>
Date: Fri, 2 Oct 2026 11:46:20 +0100
Subject: [PATCH 2/2] docs(changelog): document changes in PR #19

---
 ChangeLog.md | 1 +
 1 file changed, 1 insertion(+)

diff --git a/ChangeLog.md b/ChangeLog.md
index d47e0a4..4b52eb0 100644
--- a/ChangeLog.md
+++ b/ChangeLog.md
@@ -2,6 +2,7 @@
 
 ## Unreleased changes
 
+- Correct fractional coefficients in pretty-printed expressions and remove trailing plus separators. ([#19](https://github.com/rasheedja/simplex-method/pull/19))
 - `twoPhaseSimplex` now takes a `VarDomainMap` as its first argument
   - Specify each variable's domain using smart constructors: `nonNegative`, `unbounded`, `lowerBoundOnly`, `upperBoundOnly`, or `boundedRange`
   - Variables not in the `VarDomainMap` are assumed to be `unbounded`