diff --git a/numeric-prelude.cabal b/numeric-prelude.cabal
--- a/numeric-prelude.cabal
+++ b/numeric-prelude.cabal
@@ -1,5 +1,5 @@
 Name:           numeric-prelude
-Version:        0.2.1
+Version:        0.2.2
 License:        GPL
 License-File:   LICENSE
 Author:         Dylan Thurston <dpt@math.harvard.edu>, Henning Thielemann <numericprelude@henning-thielemann.de>, Mikael Johansson
@@ -378,7 +378,7 @@
   default:     False
 
 Source-Repository this
-  Tag:         0.2.1
+  Tag:         0.2.2
   Type:        darcs
   Location:    http://code.haskell.org/numeric-prelude/
 
diff --git a/src-ghc-6.12/MathObj/Gaussian/Variance.hs b/src-ghc-6.12/MathObj/Gaussian/Variance.hs
--- a/src-ghc-6.12/MathObj/Gaussian/Variance.hs
+++ b/src-ghc-6.12/MathObj/Gaussian/Variance.hs
@@ -60,9 +60,17 @@
    Poly.fromCoeffs [zero, zero, c f]
 
 
-norm1Root :: (Field.C a) => T a -> Root.T a
-norm1Root f =
+integrateRoot :: (Field.C a) => T a -> Root.T a
+integrateRoot f =
    Root.sqrt $ Root.fromNumber $ amp f / c f
+
+scalarProductRoot :: (Field.C a) => T a -> T a -> Root.T a
+scalarProductRoot f g =
+   integrateRoot (multiply f g)
+
+
+norm1Root :: (Field.C a) => T a -> Root.T a
+norm1Root = integrateRoot
 
 norm2Root :: (Field.C a) => T a -> Root.T a
 norm2Root f =
diff --git a/src/MathObj/Gaussian/Variance.hs b/src/MathObj/Gaussian/Variance.hs
--- a/src/MathObj/Gaussian/Variance.hs
+++ b/src/MathObj/Gaussian/Variance.hs
@@ -60,9 +60,17 @@
    Poly.fromCoeffs [zero, zero, c f]
 
 
-norm1Root :: (Field.C a) => T a -> Root.T a
-norm1Root f =
+integrateRoot :: (Field.C a) => T a -> Root.T a
+integrateRoot f =
    Root.sqrt $ Root.fromNumber $ amp f / c f
+
+scalarProductRoot :: (Field.C a) => T a -> T a -> Root.T a
+scalarProductRoot f g =
+   integrateRoot (multiply f g)
+
+
+norm1Root :: (Field.C a) => T a -> Root.T a
+norm1Root = integrateRoot
 
 norm2Root :: (Field.C a) => T a -> Root.T a
 norm2Root f =
diff --git a/test-ghc-6.12/Test/MathObj/Gaussian/Variance.hs b/test-ghc-6.12/Test/MathObj/Gaussian/Variance.hs
--- a/test-ghc-6.12/Test/MathObj/Gaussian/Variance.hs
+++ b/test-ghc-6.12/Test/MathObj/Gaussian/Variance.hs
@@ -38,12 +38,20 @@
 data HoelderConjugates = HoelderConjugates Rational Rational
    deriving Show
 
+{-
 instance Arbitrary HoelderConjugates where
    arbitrary = liftM2
       (\(PositiveInteger p) (PositiveInteger q) ->
          let s  = 1%p + 1%q
          in  HoelderConjugates (fromInteger p * s) (fromInteger q * s))
       arbitrary arbitrary
+-}
+instance Arbitrary HoelderConjugates where
+   arbitrary = liftM2
+      (\(PositiveInteger p) (PositiveInteger q) ->
+         let s = p + q
+         in  HoelderConjugates (s % p) (s % q))
+      arbitrary arbitrary
 
 {- |
 For @(YoungConjugates p q r)@ it holds
@@ -135,6 +143,10 @@
       ("fourier dilate",
           simple $ \x a -> a>0 ==>
              G.fourier (G.dilate a x) == G.amplify a (G.shrink a (G.fourier x))) :
+      ("fourier, unitary",
+          simple $ \x y ->
+             G.scalarProductRoot x y
+              == G.scalarProductRoot (G.fourier x) (G.fourier y)) :
       ("norm1 vs. normP 1",
           simple $ \x -> G.norm1Root x == G.normPRoot 1 x) :
       ("norm2 vs. normP 2",
@@ -167,18 +179,18 @@
 -}
       ("Cauchy-Schwarz inequality",
           simple $ \x y ->
-             G.norm1Root (G.multiply x y)
+             G.scalarProductRoot x y
                 <= G.norm2Root x `Root.mul` G.norm2Root y) :
       ("Hoelder conjugates",
           quickCheck $ \(HoelderConjugates p q) ->
              p>=1 && q>=1 && 1/p + 1/q == 1) :
       ("Hoelder inequality with infinity norm",
           simple $ \x y ->
-             G.norm1Root (G.multiply x y)
+             G.scalarProductRoot x y
                 <= G.norm1Root x `Root.mul` G.normInfRoot y) :
       ("Hoelder inequality",
           simple $ \x y (HoelderConjugates p q) ->
-             G.norm1Root (G.multiply x y)
+             G.scalarProductRoot x y
                 <= G.normPRoot p x `Root.mul` G.normPRoot q y) :
       ("Young inequality with two infinity norms",
           simple $ \x y ->
diff --git a/test/Test/MathObj/Gaussian/Variance.hs b/test/Test/MathObj/Gaussian/Variance.hs
--- a/test/Test/MathObj/Gaussian/Variance.hs
+++ b/test/Test/MathObj/Gaussian/Variance.hs
@@ -38,12 +38,20 @@
 data HoelderConjugates = HoelderConjugates Rational Rational
    deriving Show
 
+{-
 instance Arbitrary HoelderConjugates where
    arbitrary = liftM2
       (\(PositiveInteger p) (PositiveInteger q) ->
          let s  = 1%p + 1%q
          in  HoelderConjugates (fromInteger p * s) (fromInteger q * s))
       arbitrary arbitrary
+-}
+instance Arbitrary HoelderConjugates where
+   arbitrary = liftM2
+      (\(PositiveInteger p) (PositiveInteger q) ->
+         let s = p + q
+         in  HoelderConjugates (s % p) (s % q))
+      arbitrary arbitrary
 
 {- |
 For @(YoungConjugates p q r)@ it holds
@@ -135,6 +143,10 @@
       ("fourier dilate",
           simple $ \x a -> a>0 ==>
              G.fourier (G.dilate a x) == G.amplify a (G.shrink a (G.fourier x))) :
+      ("fourier, unitary",
+          simple $ \x y ->
+             G.scalarProductRoot x y
+              == G.scalarProductRoot (G.fourier x) (G.fourier y)) :
       ("norm1 vs. normP 1",
           simple $ \x -> G.norm1Root x == G.normPRoot 1 x) :
       ("norm2 vs. normP 2",
@@ -167,18 +179,18 @@
 -}
       ("Cauchy-Schwarz inequality",
           simple $ \x y ->
-             G.norm1Root (G.multiply x y)
+             G.scalarProductRoot x y
                 <= G.norm2Root x `Root.mul` G.norm2Root y) :
       ("Hoelder conjugates",
           quickCheck $ \(HoelderConjugates p q) ->
              p>=1 && q>=1 && 1/p + 1/q == 1) :
       ("Hoelder inequality with infinity norm",
           simple $ \x y ->
-             G.norm1Root (G.multiply x y)
+             G.scalarProductRoot x y
                 <= G.norm1Root x `Root.mul` G.normInfRoot y) :
       ("Hoelder inequality",
           simple $ \x y (HoelderConjugates p q) ->
-             G.norm1Root (G.multiply x y)
+             G.scalarProductRoot x y
                 <= G.normPRoot p x `Root.mul` G.normPRoot q y) :
       ("Young inequality with two infinity norms",
           simple $ \x y ->