diff --git a/lagrangian.cabal b/lagrangian.cabal
--- a/lagrangian.cabal
+++ b/lagrangian.cabal
@@ -10,7 +10,7 @@
 -- PVP summary:      +-+------- breaking API changes
 --                   | | +----- non-breaking API additions
 --                   | | | +--- code changes with no API change
-version:             0.3.0.0
+version:             0.3.0.1
 
 -- A short (one-line) description of the package.
 synopsis:            Solve lagrange multiplier problems
@@ -24,7 +24,7 @@
  .
  @
    \> solve 0.00001 (negate . sum . map (\x -> x * log x)) [sum \<=\> 1] 3
-   ([0.33, 0.33, 0.33], [-0.09])
+   Right ([0.33, 0.33, 0.33], [-0.09])
  @
  .
  The first elements of the result pair are the arguments for the 
diff --git a/src/Numeric/AD/Lagrangian.hs b/src/Numeric/AD/Lagrangian.hs
--- a/src/Numeric/AD/Lagrangian.hs
+++ b/src/Numeric/AD/Lagrangian.hs
@@ -1,11 +1,10 @@
 -- |Numerically solve convex lagrange multiplier problems with conjugate gradient descent. 
 --  
---  For example, find the maximum entropy with the constraint that the probabilities add
---  up to one. 
---  
+--  Here is an example from the Wikipedia page on Lagrange multipliers.
+--  Maximize f(x, y) = x + y, subject to the constraint x^2 + y^2 = 1 
 --  
---  >>> solve 0.00001 (negate . sum . map (\x -> x * log x)) [sum <=> 1] 3
---  ([0.33, 0.33, 0.33], [-0.09])
+--  >>> solve 0.00001 (\[x, y] -> x + y) [\[x, y] -> x^2 + y^2 <=> 1] 2
+--  Right ([0.707,0.707], [-0.707])
 --  
 --  The first elements of the result pair are the arguments for the objective function at the minimum. 
 --  The second elements are the lagrange multipliers.
diff --git a/src/Numeric/AD/Lagrangian/Internal.hs b/src/Numeric/AD/Lagrangian/Internal.hs
--- a/src/Numeric/AD/Lagrangian/Internal.hs
+++ b/src/Numeric/AD/Lagrangian/Internal.hs
@@ -37,7 +37,7 @@
       -- ^ The arity of the objective function which should equal the arity of 
       --   the constraints.
       -> Either (Result, Statistics) (S.Vector Double, S.Vector Double) 
-      -- ^ Either an explaination of why the gradient descent failed or a pair 
+      -- ^ Either an explanation of why the gradient descent failed or a pair 
       --   containing the arguments at the minimum and the lagrange multipliers
 solve tolerance toMin constraints argCount = result where
     -- The function to minimize for the langrangian is the squared gradient
@@ -85,7 +85,7 @@
 
 -- | WARNING. Experimental.
 --   This is not a true feasibility test for the function. I am not sure 
---   exactly how to implement that. This just checks the feasiblility at point.
+--   exactly how to implement that. This just checks the feasiblility at a point.
 --   If this ever returns false, 'solve' can fail.
 feasible :: (forall s r. (Mode s, Mode r) => [AD2 s r Double] -> AD2 s r Double)
          -> (forall s r. (Mode s, Mode r) => [Constraint (AD2 s r Double)] )