diff --git a/ChangeLog b/ChangeLog
--- a/ChangeLog
+++ b/ChangeLog
@@ -1,5 +1,11 @@
 ChangeLog
 
+v0.4.0.0 2019/06/28
+	(2019/06/27) PS1 - fixed a compiler warning.
+	(2019/06/27) PS1 - use type class synonym to fix compiler warnings
+	about simplifiable class constraints. This changed the type class
+	assumptions of some API functions.
+
 v0.3.0.5 2019/02/23
 	(2019/02/23) PS1 - updated package dependencies to work with Stack.
 	(2019/02/22) PS1 - removed some unused LANGUAGE directives,
diff --git a/Quantum/Synthesis/Clifford.hs b/Quantum/Synthesis/Clifford.hs
--- a/Quantum/Synthesis/Clifford.hs
+++ b/Quantum/Synthesis/Clifford.hs
@@ -291,7 +291,7 @@
 cinv 2 1 2 = (1,1,0,2)
 cinv 2 1 3 = (2,0,1,6)
 
--- | 'tconj2' /a/ /b/ returns (/K/, /c/, /d/) such that
+-- | 'tconj' /a/ /b/ returns (/K/, /c/, /d/) such that
 -- 
 -- * /E/[sup /a/]/X/[sup /b/]/T/ = /K//T//X/[sup /b/]/S/[sup /c/]ω[sup /d/].
 tconj :: Int -> Int -> (Axis, Int, Int)
diff --git a/Quantum/Synthesis/CliffordT.hs b/Quantum/Synthesis/CliffordT.hs
--- a/Quantum/Synthesis/CliffordT.hs
+++ b/Quantum/Synthesis/CliffordT.hs
@@ -163,7 +163,7 @@
                  (0,     omega)
 
 -- | Convert a symbolic gate to the corresponding operator.
-u2_of_gate :: (RootHalfRing a, ComplexRing a) => Gate -> U2 a
+u2_of_gate :: (RootHalfRing a, ComplexRing a, OmegaRing a) => Gate -> U2 a
 u2_of_gate X = u2_X
 u2_of_gate Y = u2_Y
 u2_of_gate Z = u2_Z
@@ -173,7 +173,7 @@
 u2_of_gate E = u2_E
 u2_of_gate W = u2_W
 
-instance (RootHalfRing a, ComplexRing a) => FromGates (U2 a) where
+instance (RootHalfRing a, ComplexRing a, OmegaRing a) => FromGates (U2 a) where
   from_gates = product' . map u2_of_gate where
     product' = foldl' (*) 1
 
diff --git a/Quantum/Synthesis/GridSynth.hs b/Quantum/Synthesis/GridSynth.hs
--- a/Quantum/Synthesis/GridSynth.hs
+++ b/Quantum/Synthesis/GridSynth.hs
@@ -15,7 +15,7 @@
 module Quantum.Synthesis.GridSynth where
 
 import Quantum.Synthesis.Ring
-import Quantum.Synthesis.Ring.FixedPrec
+import Quantum.Synthesis.Ring.FixedPrec()
 import Quantum.Synthesis.Matrix
 import Quantum.Synthesis.CliffordT
 import Quantum.Synthesis.SymReal
diff --git a/Quantum/Synthesis/MultiQubitSynthesis.hs b/Quantum/Synthesis/MultiQubitSynthesis.hs
--- a/Quantum/Synthesis/MultiQubitSynthesis.hs
+++ b/Quantum/Synthesis/MultiQubitSynthesis.hs
@@ -118,7 +118,7 @@
     | otherwise = 0
 
 -- | Convert a symbolic one- or two-level operator into a matrix.
-matrix_of_twolevel :: (ComplexRing a, RootHalfRing a, Nat n) => TwoLevel -> Matrix n n a
+matrix_of_twolevel :: (OmegaRing a, RootHalfRing a, Nat n) => TwoLevel -> Matrix n n a
 matrix_of_twolevel (TL_X i j) = twolevel_matrix (0,1) (1,0) i j
 matrix_of_twolevel (TL_H i j) = twolevel_matrix (s,s) (s,-s) i j
   where s = roothalf
@@ -128,7 +128,7 @@
 -- | Convert a list of symbolic one- or two-level operators into a
 -- matrix. Note that the operators are to be applied right-to-left,
 -- exactly as in mathematical notation.
-matrix_of_twolevels :: (ComplexRing a, RootHalfRing a, Nat n) => [TwoLevel] -> Matrix n n a
+matrix_of_twolevels :: (OmegaRing a, RootHalfRing a, Nat n) => [TwoLevel] -> Matrix n n a
 matrix_of_twolevels gs = foldl' (*) 1 [ matrix_of_twolevel g | g <- gs ]
 
 -- ----------------------------------------------------------------------
diff --git a/Quantum/Synthesis/Ring.hs b/Quantum/Synthesis/Ring.hs
--- a/Quantum/Synthesis/Ring.hs
+++ b/Quantum/Synthesis/Ring.hs
@@ -6,6 +6,7 @@
 {-# LANGUAGE GeneralizedNewtypeDeriving #-}
 {-# LANGUAGE IncoherentInstances #-}
 {-# LANGUAGE BangPatterns #-}
+{-# LANGUAGE ConstraintKinds #-}
 
 -- | This module provides type classes for rings. It also provides
 -- several specific instances of rings, such as the ring ℤ₂ of
@@ -31,8 +32,7 @@
 -- don't make sense (or are inconvenient to define), we set 'abs' /x/
 -- = /x/ and 'signum' /x/ = 1.
 
-class (Num a) => Ring a
-instance (Num a) => Ring a
+type Ring a = (Num a)
 
 -- ----------------------------------------------------------------------
 -- * Rings with particular elements
@@ -143,6 +143,9 @@
 instance (Ring a, RealFloat a) => ComplexRing (Complex a) where
   i = 0 :+ 1
 
+instance (RealFloat a, RootHalfRing a) => OmegaRing (Complex a) where
+  omega = roothalf * (1 + i)
+
 -- ----------------------------------------------------------------------
 -- ** Rings with ω
 
@@ -152,8 +155,8 @@
   -- | The square root of /i/.
   omega :: a
   
-instance (ComplexRing a, RootHalfRing a) => OmegaRing a where
-  omega = roothalf * (1 + i)
+-- instance (Ring a, ComplexRing a, RootHalfRing a) => OmegaRing a where
+--   omega = roothalf * (1 + i)
 
 -- ----------------------------------------------------------------------
 -- * Rings with particular automorphisms
@@ -455,6 +458,9 @@
 instance (Eq a, ComplexRing a) => ComplexRing (RootTwo a) where
   i = RootTwo i 0
 
+instance (Eq a, ComplexRing a, HalfRing a) => OmegaRing (RootTwo a) where
+  omega = roothalf * (1 + i)
+
 instance (Adjoint a) => Adjoint (RootTwo a) where  
   adj (RootTwo a b) = RootTwo (adj a) (adj b)
 
@@ -566,6 +572,9 @@
 instance (Ring a) => ComplexRing (Cplx a) where
   i = Cplx 0 1
 
+instance (Ring a, RootHalfRing a) => OmegaRing (Cplx a) where        
+  omega = roothalf * (1 + i)
+
 instance (HalfRing a) => HalfRing (Cplx a) where
   half = Cplx half 0
   fromDyadic x = Cplx (fromDyadic x) 0
@@ -733,12 +742,7 @@
       c = norm z
       d = norm w
 
--- This is an undecidable instance, but is not overlapping. Note: we
--- do not declare OmegaRing (Omega a), because this usually follows
--- from (ComplexRing a, RootHalfRing a). But there are some
--- exceptions, such as OmegaRing (Omega Z2) and OmegaRing (Omega
--- Integer).
-instance OmegaRing (Omega Z2) where
+instance (Ring a) => OmegaRing (Omega a) where
   omega = Omega 0 0 1 0
 
 -- ----------------------------------------------------------------------
@@ -761,10 +765,6 @@
 fromZOmega :: (OmegaRing a) => ZOmega -> a
 fromZOmega (Omega a b c d) = fromInteger a * omega^3 + fromInteger b * omega^2 + fromInteger c * omega + fromInteger d
 
--- This is an undecidable instance, but is not overlapping.
-instance OmegaRing ZOmega where
-  omega = Omega 0 0 1 0
-
 -- | Inverse of the embedding ℤ[√2] → ℤ[ω]. Note that ℤ[√2] = ℤ[ω] ∩
 -- ℝ. This function takes an element of ℤ[ω] that is real, and
 -- converts it to an element of ℤ[√2]. It throws an error if the input
@@ -783,8 +783,8 @@
 type DOmega = Omega Dyadic
 
 -- | The unique ring homomorphism from [bold D][ω] to any ring containing
--- 1\/√2 and /i/. This exists because [bold D][ω] is the free such ring.
-fromDOmega :: (RootHalfRing a, ComplexRing a) => DOmega -> a
+-- ω and 1\/2. This exists because [bold D][ω] is the free such ring.
+fromDOmega :: (OmegaRing a, HalfRing a) => DOmega -> a
 fromDOmega (Omega a b c d) = fromDyadic a * omega^3 + fromDyadic b * omega^2 + fromDyadic c * omega + fromDyadic d
 
 -- This is an overlapping instance. It is nicer to show an element of
@@ -805,9 +805,9 @@
 type QOmega = Omega Rationals
 
 -- | The unique ring homomorphism from ℚ[ω] to any ring containing the
--- rational numbers, √2, and /i/. This exists because ℚ[ω] is the free
+-- rational numbers and ω. This exists because ℚ[ω] is the free
 -- such ring.
-fromQOmega :: (RootHalfRing a, ComplexRing a, Fractional a) => QOmega -> a
+fromQOmega :: (OmegaRing a, Fractional a) => QOmega -> a
 fromQOmega (Omega a b c d) = fromRationals a * omega^3 + fromRationals b * omega^2 + fromRationals c * omega + fromRationals d
 
 -- ----------------------------------------------------------------------
diff --git a/newsynth.cabal b/newsynth.cabal
--- a/newsynth.cabal
+++ b/newsynth.cabal
@@ -7,7 +7,7 @@
 -- PVP summary:      +-+------- breaking API changes
 --                   | | +----- non-breaking API additions
 --                   | | | +--- code changes with no API change
-version:             0.3.0.5
+version:             0.4.0.0
 
 -- A short (one-line) description of the package.
 synopsis:            Exact and approximate synthesis of quantum circuits
@@ -91,7 +91,7 @@
   -- profiling enabled.
   ghc-prof-options:
 
-  ghc-options:  -fno-warn-simplifiable-class-constraints
+  ghc-options:
   
 executable gridsynth
   -- .hs or .lhs file containing the Main module.