diff --git a/LICENSE b/LICENSE
--- a/LICENSE
+++ b/LICENSE
@@ -1,674 +1,26 @@
-                    GNU GENERAL PUBLIC LICENSE
-                       Version 3, 29 June 2007
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-  To do so, attach the following notices to the program.  It is safest
-to attach them to the start of each source file to most effectively
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-    along with this program.  If not, see <http://www.gnu.org/licenses/>.
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-Also add information on how to contact you by electronic and paper mail.
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-notice like this when it starts in an interactive mode:
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-    <program>  Copyright (C) <year>  <name of author>
-    This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'.
-    This is free software, and you are welcome to redistribute it
-    under certain conditions; type `show c' for details.
-
-The hypothetical commands `show w' and `show c' should show the appropriate
-parts of the General Public License.  Of course, your program's commands
-might be different; for a GUI interface, you would use an "about box".
+Copyright (c) 2013 Henning Thielemann, Dylan Thurston, Mikael Johansson
+All rights reserved.
 
-  You should also get your employer (if you work as a programmer) or school,
-if any, to sign a "copyright disclaimer" for the program, if necessary.
-For more information on this, and how to apply and follow the GNU GPL, see
-<http://www.gnu.org/licenses/>.
+Redistribution and use in source and binary forms, with or without
+modification, are permitted provided that the following conditions
+are met:
+1. Redistributions of source code must retain the above copyright
+   notice, this list of conditions and the following disclaimer.
+2. Redistributions in binary form must reproduce the above copyright
+   notice, this list of conditions and the following disclaimer in the
+   documentation and/or other materials provided with the distribution.
+3. Neither the name of the University nor the names of its contributors
+   may be used to endorse or promote products derived from this software
+   without specific prior written permission.
 
-  The GNU General Public License does not permit incorporating your program
-into proprietary programs.  If your program is a subroutine library, you
-may consider it more useful to permit linking proprietary applications with
-the library.  If this is what you want to do, use the GNU Lesser General
-Public License instead of this License.  But first, please read
-<http://www.gnu.org/philosophy/why-not-lgpl.html>.
+THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS ``AS IS'' AND
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+SUCH DAMAGE.
diff --git a/gaussian/Gaussian.hs b/gaussian/Gaussian.hs
new file mode 100644
--- /dev/null
+++ b/gaussian/Gaussian.hs
@@ -0,0 +1,6 @@
+module Main where
+
+import qualified MathObj.Gaussian.Example as Example
+
+main :: IO ()
+main = Example.polyApprox
diff --git a/gaussian/MathObj/Gaussian/Bell.hs b/gaussian/MathObj/Gaussian/Bell.hs
new file mode 100644
--- /dev/null
+++ b/gaussian/MathObj/Gaussian/Bell.hs
@@ -0,0 +1,324 @@
+{-# LANGUAGE NoImplicitPrelude #-}
+{-
+Complex translated and modulated Gaussian bell curve.
+
+It could be extended to chirps
+using a complex valued quadratic term with (real c >= 0).
+This allows for a new test:
+Express the Fourier transform in terms of a convolution with a chirp.
+-}
+module MathObj.Gaussian.Bell where
+
+import qualified MathObj.Polynomial as Poly
+import qualified Number.Complex as Complex
+
+import qualified Algebra.Transcendental as Trans
+import qualified Algebra.Field          as Field
+import qualified Algebra.Absolute       as Absolute
+import qualified Algebra.Ring           as Ring
+import qualified Algebra.Additive       as Additive
+
+import Number.Complex ((+:), )
+
+import Test.QuickCheck (Arbitrary, arbitrary, )
+import Control.Monad (liftM4, )
+
+-- import Prelude (($))
+import NumericPrelude.Numeric
+import NumericPrelude.Base hiding (reverse, )
+
+
+data T a = Cons {amp :: a, c0, c1 :: Complex.T a, c2 :: a}
+   deriving (Eq, Show)
+
+instance (Absolute.C a, Arbitrary a) => Arbitrary (T a) where
+   arbitrary =
+      liftM4
+         (\k a b c -> Cons (abs k) a b (1 + abs c))
+         arbitrary arbitrary arbitrary arbitrary
+
+
+constant :: Ring.C a => T a
+constant = Cons one zero zero zero
+
+{- |
+eigenfunction of 'fourier'
+-}
+unit :: Ring.C a => T a
+unit = Cons one zero zero one
+
+{-# INLINE evaluate #-}
+evaluate :: (Trans.C a) =>
+   T a -> a -> Complex.T a
+evaluate f x =
+   Complex.scale
+     (sqrt (amp f))
+     (Complex.exp $ Complex.scale (-pi) $
+      c0 f + Complex.scale x (c1 f) + Complex.fromReal (c2 f * x^2))
+
+evaluateSqRt :: (Trans.C a) =>
+   T a -> a -> Complex.T a
+evaluateSqRt f x0 =
+   Complex.scale
+     (sqrt (amp f))
+     (let x = sqrt pi * x0
+      in  Complex.exp $ negate $
+          c0 f + Complex.scale x (c1 f) + Complex.fromReal (c2 f * x^2))
+
+exponentPolynomial :: (Additive.C a) =>
+   T a -> Poly.T (Complex.T a)
+exponentPolynomial f =
+   Poly.fromCoeffs [c0 f, c1 f, Complex.fromReal (c2 f)]
+
+
+{-
+norm functions depend on interpretation
+and would have to return both a rational and transcendental part
+expressed as @exp a@.
+-}
+
+variance :: (Trans.C a) =>
+   T a -> a
+variance f =
+   recip $ c2 f * 2*pi
+
+multiply :: (Ring.C a) =>
+   T a -> T a -> T a
+multiply f g =
+   Cons
+      (amp f * amp g)
+      (c0 f + c0 g) (c1 f + c1 g) (c2 f + c2 g)
+
+powerRing :: (Trans.C a) =>
+   Integer -> T a -> T a
+powerRing p f =
+   let pa = fromInteger p
+   in  Cons
+          (amp f ^ p)
+          (pa * c0 f) (pa * c1 f) (fromInteger p * c2 f)
+
+{-
+powerField does not makes sense,
+since the reciprocal of a Gaussian diverges.
+-}
+
+powerAlgebraic :: (Trans.C a) =>
+   Rational -> T a -> T a
+powerAlgebraic p f =
+   let pa = fromRational' p
+   in  Cons
+          (amp f ^/ p)
+          (pa * c0 f) (pa * c1 f) (fromRational' p * c2 f)
+
+powerTranscendental :: (Trans.C a) =>
+   a -> T a -> T a
+powerTranscendental p f =
+   Cons
+      (amp f ^? p)
+      (Complex.scale p $ c0 f) (Complex.scale p $ c1 f) (p * c2 f)
+
+
+{-
+let x=Cons 2 (1+:3) (4+:5) (7::Rational); y=Cons 7 (1+:4) (3+:2) (5::Rational)
+-}
+convolve :: (Field.C a) =>
+   T a -> T a -> T a
+convolve f g =
+   let s = c2 f + c2 g
+       {-
+       fd = f1/(2*f2)
+       gd = g1/(2*g2)
+       c = f2*g2/(f2+g2)
+
+       c*(fd+gd) = (f1*g2+f2*g1)/(2*(f2+g2)) = b/2
+
+       c*(fd+gd)^2 - fd^2*f2 - gd^2*g2
+         = f2*g2*(fd+gd)^2/(f2 + g2) - (fd^2*f2 + gd^2*g2)
+         = (f2*g2*(fd+gd)^2 - (f2+g2)*(fd^2*f2+gd^2*g2)) / (f2 + g2)
+         = (2*f2*g2*fd*gd - (fd^2*f2^2+gd^2*g2^2)) / (f2 + g2)
+         = (2*f1*g1 - (f1^2+g1^2)) / (4*(f2 + g2))
+         = -(f1 - g1)^2/(4*(f2 + g2))
+       -}
+   in  Cons
+          (amp f * amp g / s)
+          (c0 f + c0 g
+              - Complex.scale (recip (4*s)) ((c1 f - c1 g)^2))
+          (Complex.scale (c2 g / s) (c1 f) +
+           Complex.scale (c2 f / s) (c1 g))
+          (c2 f * c2 g / s)
+            -- recip $ recip (c2 f) + recip (c2 g)
+{-
+   Cons
+      (c0 f + c0 g) (c1 f + c1 g)
+      (recip $ recip (c2 f) + recip (c2 g))
+-}
+
+convolveByTranslation :: (Field.C a) =>
+   T a -> T a -> T a
+convolveByTranslation f0 g0 =
+   let fd = Complex.scale (recip (2 * c2 f0)) $ c1 f0
+       gd = Complex.scale (recip (2 * c2 g0)) $ c1 g0
+       f1 = translateComplex fd f0
+       g1 = translateComplex gd g0
+       s = c2 f1 + c2 g1
+   in  translateComplex (negate $ fd + gd) $
+       Cons
+          (amp f1 * amp g1 / s)
+          (c0 f1 + c0 g1) zero
+          (c2 f1 * c2 g1 / s)
+
+convolveByFourier :: (Field.C a) =>
+   T a -> T a -> T a
+convolveByFourier f g =
+   reverse $ fourier $ multiply (fourier f) (fourier g)
+
+fourier :: (Field.C a) =>
+   T a -> T a
+fourier f =
+   let a = c0 f
+       b = c1 f
+       rc = recip $ c2 f
+   in  Cons
+          (amp f * rc)
+          (Complex.scale (rc/4) (-b^2) + a)
+          (Complex.scale rc $ Complex.quarterRight b)
+          rc
+
+fourierByTranslation :: (Field.C a) =>
+   T a -> T a
+fourierByTranslation f =
+   translateComplex (Complex.scale (1/2) $ Complex.quarterLeft $ c1 f) $
+   Cons (amp f / c2 f) (c0 f) zero (recip $ c2 f)
+
+{-
+a + b*x + c*x^2
+ = c*(a/c + b/c*x + x^2)
+ = c*((x-b/(2*c))^2 + (4*a*c+b^2)/(4*c^2))
+ = c*(x-b/(2*c))^2 + (4*a*c+b^2)/(4*c)
+
+fourier ->
+   x^2/c - i*b/c*x + (4*a*c+b^2)/(4*c)
+
+fourier (x -> exp(-pi*c*(x-t)^2))
+ = fourier $ translate t $ shrink (sqrt c) $ x -> exp(-pi*x^2)
+ = modulate t $ dilate (sqrt c) $ fourier $ x -> exp(-pi*x^2)
+ = modulate t $ dilate (sqrt c) $ x -> exp(-pi*x^2)
+ = modulate t $ x -> exp(-pi*x^2/c)
+ = x -> exp(-pi*x^2/c) * exp(-2*pi*i*x*t)
+ = x -> exp(-pi*(x^2/c - 2*i*x*t))
+-}
+
+{-
+b*x + c*x^2
+ = c*(b/c*x + x^2)
+ = c*((x-br/(2*c))^2 + i*x*bi/c - br^2/(4*c^2))
+ = c*(x-br/(2*c))^2 + i*x*bi - br^2/(4*c)
+
+fourier ->
+   (x+bi/2)^2/c - i*br/c*(x+bi/2) - br^2/(4*c)
+ = (1/c) * ((x+bi/2)^2 - i*br*(x+bi/2) + (br/2)^2)
+ = (1/c) * (x^2 - i*b*x + -(br/2)^2 + (bi/2)^2 - i*br*bi/2)
+ = (1/c) * (x^2 - i*b*x - (br^2-bi^2+2*br*bi*i)^2 /4)
+ = (1/c) * (x^2 - i*b*x - b^2 / 4)
+ = (1/c) * (x^2 - i*b*x + (i*b/2)^2)
+ = (1/c) * (x - i*b/2)^2
+
+Example:
+  (x-b)^2 = b^2 - 2*b*x + x^2
+    ->  (- i*2*b*x + x^2)
+
+
+fourier (x -> exp(-pi*(c*(x-t)^2 + 2*i*m*x)))
+ = fourier $ modulate m $ translate t $ shrink (sqrt c) $ x -> exp(-pi*x^2)
+ = translate (-m) $ modulate t $ dilate (sqrt c) $ fourier $ x -> exp(-pi*x^2)
+ = translate (-m) $ modulate t $ dilate (sqrt c) $ x -> exp(-pi*x^2)
+ = translate (-m) $ modulate t $ x -> exp(-pi*x^2/c)
+ = translate (-m) $ x -> exp(-pi*x^2/c) * exp(-2*pi*i*x*t)
+ = x -> exp(-pi*(x+m)^2/c) * exp(-2*pi*i*(x+m)*t)
+ = x -> exp(-pi*((x+m)^2/c - 2*i*(x+m)*t))
+-}
+
+{-
+fourier (Cons a 0 0) =
+  Cons a 0 infinity
+
+fourier (Cons 0 0 c) =
+  Cons 0 0 (recip c)
+
+fourier (Cons 0 b 1) =
+  Cons 0 (i*b) 1
+-}
+
+translate :: Ring.C a => a -> T a -> T a
+translate d f =
+   let a = c0 f
+       b = c1 f
+       c = c2 f
+   in  Cons
+          (amp f)
+          (Complex.fromReal (c*d^2) - Complex.scale d b + a)
+          (Complex.fromReal (-2*c*d) + b)
+          c
+
+translateComplex :: Ring.C a => Complex.T a -> T a -> T a
+translateComplex d f =
+   let a = c0 f
+       b = c1 f
+       c = c2 f
+   in  Cons
+          (amp f)
+          (Complex.scale c (d^2) - b*d + a)
+          (Complex.scale (-2*c) d + b)
+          c
+
+modulate :: Ring.C a => a -> T a -> T a
+modulate d f =
+   Cons
+      (amp f)
+      (c0 f)
+      (c1 f + (zero +: 2*d))
+      (c2 f)
+
+turn :: Ring.C a => a -> T a -> T a
+turn d f =
+   Cons
+      (amp f)
+      (c0 f + (zero +: 2*d))
+      (c1 f)
+      (c2 f)
+
+reverse :: Additive.C a => T a -> T a
+reverse f =
+   f{c1 = negate $ c1 f}
+
+
+dilate :: Field.C a => a -> T a -> T a
+dilate k f =
+   Cons
+      (amp f)
+      (c0 f)
+      (Complex.scale (recip k) $ c1 f)
+      (c2 f / k^2)
+
+shrink :: Ring.C a => a -> T a -> T a
+shrink k f =
+   Cons
+      (amp f)
+      (c0 f)
+      (Complex.scale k $ c1 f)
+      (c2 f * k^2)
+
+amplify :: (Ring.C a) => a -> T a -> T a
+amplify k f =
+   Cons
+      (k^2 * amp f)
+      (c0 f)
+      (c1 f)
+      (c2 f)
+
+
+{- laws
+fourier (convolve f g) = fourier f * fourier g
+
+fourier (fourier f) = reverse f
+-}
diff --git a/gaussian/MathObj/Gaussian/Example.hs b/gaussian/MathObj/Gaussian/Example.hs
new file mode 100644
--- /dev/null
+++ b/gaussian/MathObj/Gaussian/Example.hs
@@ -0,0 +1,231 @@
+{-# LANGUAGE NoImplicitPrelude #-}
+{-
+Reciprocal of variance of a Gaussian bell curve.
+We describe the curve only in terms of its variance
+thus we represent a bell curve at the coordinate origin
+neglecting its amplitude.
+
+We could also define the amplitude as @root 4 c@,
+thus preserving L2 norm being one,
+but then @dilate@ and @shrink@ also include an amplification.
+
+We could do some projective geometry in the exponent
+in order to also have zero variance,
+which corresponds to the dirac impulse.
+-}
+module MathObj.Gaussian.Example where
+
+import qualified MathObj.Gaussian.Polynomial as PolyBell
+import qualified MathObj.Gaussian.Bell as Bell
+import qualified MathObj.Gaussian.Variance as Var
+
+import qualified MathObj.Polynomial as Poly
+
+import qualified Algebra.Transcendental as Trans
+import qualified Algebra.Algebraic      as Algebraic
+import qualified Algebra.Field          as Field
+-- import qualified Algebra.Absolute           as Absolute
+import qualified Algebra.Ring           as Ring
+-- import qualified Algebra.Additive       as Additive
+
+import qualified Number.Complex as Complex
+import qualified Number.Root as Root
+
+import Algebra.Transcendental (pi, )
+import Algebra.Algebraic (root, )
+import Algebra.Ring ((*), (^), )
+
+import Number.Complex ((+:), )
+
+import qualified Numerics.Function as Func
+import qualified Numerics.Fourier as Fourier
+import qualified Numerics.Integration as Integ
+import qualified Numerics.Differentiation as Diff
+
+import qualified Graphics.Gnuplot.Simple as GP
+
+import Control.Applicative (liftA2, )
+
+-- import System.Exit (ExitCode, )
+
+-- import Prelude (($))
+import NumericPrelude.Numeric
+import NumericPrelude.Base
+import qualified Prelude as P
+
+
+curve0 :: Var.T Double
+curve0 = curve0a
+
+curve0a :: Var.T Double
+curve0a = Var.Cons 1.4 3.3
+
+curve0b :: Var.T Double
+curve0b = Var.Cons 2.2 1.7
+
+variance0 :: (Double, Double)
+variance0 =
+   (Var.variance curve0,
+    (Integ.rectangular 1000 (-2,2) $ liftA2 (*) (^2) (Var.evaluate curve0)) /
+    (Integ.rectangular 1000 (-2,2) $ Var.evaluate curve0))
+
+norm10 :: (Double, Double, Double)
+norm10 =
+   (Integ.rectangular 1000 (-2,2) $ Var.evaluate curve0,
+    Var.norm1 curve0,
+    Root.toNumber (Var.norm1Root curve0))
+
+norm20 :: (Double, Double, Double)
+norm20 =
+   (sqrt $ Integ.rectangular 1000 (-2,2) $ (^2) . Var.evaluate curve0,
+    Var.norm2 curve0,
+    Root.toNumber (Var.norm2Root curve0))
+
+norm30 :: (Double, Double, Double)
+norm30 =
+   (root 3 $ Integ.rectangular 1000 (-2,2) $ (^3) . Var.evaluate curve0,
+    Var.normP 3 curve0,
+    Root.toNumber (Var.normPRoot 3 curve0))
+
+fourier0 :: IO ()
+fourier0 =
+   GP.plotFuncs []
+      (GP.linearScale 100 (-2,2))
+      [Var.evaluate $ Var.fourier curve0,
+       Fourier.analysisTransformOneReal 100 (-2,2) $ Var.evaluate curve0]
+
+multiply0 :: IO ()
+multiply0 =
+   GP.plotFuncs []
+      (GP.linearScale 100 (-1,1))
+      [Var.evaluate $ Var.multiply curve0a curve0b,
+       liftA2 (*) (Var.evaluate curve0a) (Var.evaluate curve0b)]
+
+convolve0 :: IO ()
+convolve0 =
+   GP.plotFuncs []
+      (GP.linearScale 100 (-2,2))
+      [Var.evaluate $ Var.convolve curve0a curve0b,
+       Integ.convolve 1000 (-3,3) (Var.evaluate curve0a) (Var.evaluate curve0b)]
+
+
+curve1 :: Bell.T Double
+curve1 = curve1a
+
+curve1a :: Bell.T Double
+curve1a = Bell.Cons 1.4 (0.1+:0.3) ((-0.2)+:1.4) 2.3
+
+curve1b :: Bell.T Double
+curve1b = Bell.Cons 2.2 ((-0.3)+:2.1) (0.2+:(-0.4)) 1.7
+
+variance1 :: (Double, Double)
+variance1 =
+   (Bell.variance curve1,
+    (Integ.rectangular 1000 (-2,2) $
+        liftA2 (*) (^2)
+           (Complex.magnitudeSqr .
+            Func.translateRight
+               (Complex.real (Bell.c1 curve1) / (2 * Bell.c2 curve1))
+               (Bell.evaluate curve1))) /
+    (Integ.rectangular 1000 (-2,2) $ Complex.magnitude . Bell.evaluate curve1))
+
+{- the norm depends on too much things
+norm0vs1 :: (Double, Double)
+norm0vs1 =
+   ((Integ.rectangular 1000 (-5,5) $ Var.evaluate curve0)
+         * exp (- Complex.real (Bell.c0 curve1)),
+    Integ.rectangular 1000 (-5,5) $ Complex.magnitude . Bell.evaluate curve1)
+-}
+
+fourier1 :: IO ()
+fourier1 =
+   GP.plotFuncs []
+      (GP.linearScale 100 (-5,5))
+      [Complex.real . (Bell.evaluate $ Bell.fourier curve1),
+       fourierAnalysisReal 100 (-2,2) $ Bell.evaluate curve1]
+
+
+curve2 :: PolyBell.T Double
+curve2 =
+   PolyBell.Cons
+--      Bell.unit
+--      (Bell.Cons 1.4 (0.1+:0.3) 0 1.2)
+--      (Bell.Cons 1.4 (0.1+:0.3) ((-0.2)+:1.4) 1)
+      curve1
+--      (Poly.fromCoeffs [one])
+--      (Poly.fromCoeffs [zero,one])
+--      (Poly.fromCoeffs [zero,zero,one])
+--      (Poly.fromCoeffs [0,Complex.imaginaryUnit])
+      (Poly.fromCoeffs [1.4+:(-0.1),0.8+:(0.1),(-1.1)+:0.3])
+
+differentiate2 :: IO ()
+differentiate2 =
+   GP.plotFuncs []
+      (GP.linearScale 100 (-2,2))
+      [Complex.real . (PolyBell.evaluateSqRt $ PolyBell.differentiate curve2),
+       ((/ sqrt pi) . ) $ Diff.diff (1e-5) $ Complex.real . PolyBell.evaluateSqRt curve2]
+
+fourier2 :: IO ()
+fourier2 =
+   GP.plotFuncs []
+      (GP.linearScale 100 (-5,5))
+      [Complex.real . (PolyBell.evaluateSqRt $ PolyBell.fourier curve2),
+       fourierAnalysisReal 100 (-2,2) $ PolyBell.evaluateSqRt curve2]
+
+
+
+fourierAnalysisReal ::
+   (P.Floating a) =>
+   Integer -> (a, a) -> (a -> Complex.T a) -> a -> a
+fourierAnalysisReal n rng f =
+   liftA2 (P.-)
+      (Fourier.analysisTransformOneReal n rng (Complex.real . f))
+      (Fourier.analysisTransformOneImag n rng (Complex.imag . f))
+
+
+{- |
+Try to approximate @\x -> exp (-x^2) * x@
+by a difference of translated Gaussian bells.
+
+exp(-x^2) * x
+  ==  exp(-(a+b*x+c*x^2)) - exp(-(a-b*x+c*x^2))
+  ==  exp(-(a+c*x^2)) * (exp(-b*x) - exp(b*x))
+  ==  exp(-(a+c*x^2)) * 2*sinh (b*x)
+
+It holds
+  lim (\b x -> sinh (b*x) / b)  =  id
+-}
+diffApprox :: IO ()
+diffApprox =
+   let amp = (2*b)^- (-2)
+       a = 0
+       {-
+       amp = 1
+       a = log (2 * abs b)
+       -}
+       b = -0.1
+       c = 1
+       ac = Complex.fromReal a
+       bc = Complex.fromReal b
+   in  GP.plotFuncs []
+          (GP.linearScale 100 (-2,2::Double))
+          [Complex.real .
+           (PolyBell.evaluateSqRt $
+              PolyBell.Cons Bell.unit (Poly.fromCoeffs [zero,one])),
+           Complex.real .
+           liftA2 (-)
+             (PolyBell.evaluateSqRt $
+                PolyBell.Cons (Bell.Cons amp ac bc c) (Poly.fromCoeffs [one]))
+             (PolyBell.evaluateSqRt $
+                PolyBell.Cons (Bell.Cons amp ac (-bc) c) (Poly.fromCoeffs [one]))]
+
+
+polyApprox :: IO ()
+polyApprox =
+   GP.plotFuncs []
+      (GP.linearScale 100 (-2,2::Double))
+      [Complex.real .
+         PolyBell.evaluateSqRt curve2,
+       Complex.real . sum .
+         mapM (\(amp,b) -> \x -> amp * Bell.evaluateSqRt b x)
+         (PolyBell.approximateByBells 0.1 curve2)]
diff --git a/gaussian/MathObj/Gaussian/Polynomial.hs b/gaussian/MathObj/Gaussian/Polynomial.hs
new file mode 100644
--- /dev/null
+++ b/gaussian/MathObj/Gaussian/Polynomial.hs
@@ -0,0 +1,480 @@
+{-# LANGUAGE NoImplicitPrelude #-}
+{-
+Complex Gaussian bell multiplied with a polynomial.
+
+In order to make this free of @pi@ factors,
+we have to choose @recip (sqrt pi)@
+as unit for translations and modulations,
+for linear factors and in the differentiation.
+-}
+{-
+ToDo:
+
+* In order to avoid the weird @sqrt pi@ factor,
+  use a polynomial expression in @pi@.
+
+* sum of multiple bells using Data.Map from exponent polynomial to coefficient polynomial
+  use of Algebra object.
+
+* Discrete Fourier Transform and its eigenvectors
+
+* Use projective geometry in order to support Dirac impulse.
+  There are many open questions:
+  1. What shall be the product of two Dirac impulses -
+     whether they are at the same location or not.
+  2. How to organize coefficients
+     such that the constant function can be modulated
+     and the Dirac impulse can be translated.
+-}
+module MathObj.Gaussian.Polynomial where
+
+import qualified MathObj.Gaussian.Bell as Bell
+
+import qualified MathObj.LaurentPolynomial as LPoly
+import qualified MathObj.Polynomial.Core   as PolyCore
+import qualified MathObj.Polynomial        as Poly
+import qualified Number.Complex     as Complex
+
+import qualified Algebra.ZeroTestable   as ZeroTestable
+import qualified Algebra.Differential   as Differential
+import qualified Algebra.Transcendental as Trans
+import qualified Algebra.Field          as Field
+import qualified Algebra.Absolute       as Absolute
+import qualified Algebra.Ring           as Ring
+import qualified Algebra.Additive       as Additive
+
+import qualified Data.Record.HT as Rec
+import qualified Data.List as List
+import Data.Function.HT (nest, )
+import Data.Eq.HT (equating, )
+import Data.List.HT (mapAdjacent, )
+import Data.Tuple.HT (forcePair, )
+
+import Test.QuickCheck (Arbitrary, arbitrary, )
+import Control.Monad (liftM2, )
+
+import NumericPrelude.Numeric
+import NumericPrelude.Base hiding (reverse, )
+-- import Prelude ()
+
+
+data T a = Cons {bell :: Bell.T a, polynomial :: Poly.T (Complex.T a)}
+   deriving (Show)
+
+instance (Absolute.C a, ZeroTestable.C a, Eq a) => Eq (T a) where
+   (==) = equal
+
+
+{-
+Helper data type for 'equal',
+that allows to call the (not quite trivial) polynomial equality check.
+@RootProduct r a@ represents @sqrt r * a@.
+The test using 'signum' works for real numbers,
+and I do not know, whether it is correct for other mathematical objects.
+However I cannot imagine other mathematical objects,
+that make sense at all, here.
+Maybe elements of a finite field.
+-}
+data RootProduct a = RootProduct a a
+
+instance (Absolute.C a, ZeroTestable.C a, Eq a) => Eq (RootProduct a) where
+   (RootProduct xr xa) == (RootProduct yr ya)  =
+      let xp = xr*xa^2
+          yp = yr*ya^2
+      in  xp==yp &&
+          (isZero xp || signum xa == signum ya)
+
+instance (ZeroTestable.C a) => ZeroTestable.C (RootProduct a) where
+   isZero (RootProduct r a) = isZero r || isZero a
+
+
+{-
+The derived Eq is not correct.
+We have to combine the amplitude of the bell with the polynomial,
+respecting signs and the square root of the bell amplitude.
+-}
+equal :: (Absolute.C a, ZeroTestable.C a, Eq a) => T a -> T a -> Bool
+equal x y =
+   let bx = bell x
+       by = bell y
+       scaleSqr b =
+          (\p ->
+              (fmap (RootProduct (Bell.amp b) . Complex.real) p,
+               fmap (RootProduct (Bell.amp b) . Complex.imag) p))
+           . polynomial
+   in  Rec.equal
+          (equating Bell.c0 :
+           equating Bell.c1 :
+           equating Bell.c2 :
+           [])
+          bx by
+       &&
+       scaleSqr bx x == scaleSqr by y
+
+
+instance (Absolute.C a, ZeroTestable.C a, Arbitrary a) => Arbitrary (T a) where
+   arbitrary =
+--      liftM2 Cons arbitrary arbitrary
+      liftM2 Cons
+         arbitrary
+         -- we have to restrict the number of polynomial coefficients,
+         -- since with the quadratic time algorithms like fourier and convolve,
+         -- in connection with Rational slow down tests too much.
+         (fmap (Poly.fromCoeffs . take 5 . Poly.coeffs) arbitrary)
+
+
+
+{-# INLINE evaluateSqRt #-}
+evaluateSqRt :: (Trans.C a) =>
+   T a -> a -> Complex.T a
+evaluateSqRt f x =
+   Bell.evaluateSqRt (bell f) x *
+   Poly.evaluate (polynomial f) (Complex.fromReal $ sqrt pi * x)
+{- ToDo: evaluating a complex polynomial for a real argument can be optimized -}
+
+
+constant :: (Ring.C a) => T a
+constant =
+   Cons Bell.constant (Poly.const one)
+
+scale :: (Ring.C a) => a -> T a -> T a
+scale x f =
+   f{polynomial = fmap (Complex.scale x) $ polynomial f}
+
+scaleComplex :: (Ring.C a) => Complex.T a -> T a -> T a
+scaleComplex x f =
+   f{polynomial = fmap (x*) $ polynomial f}
+
+
+unit :: (Ring.C a) => T a
+unit = eigenfunction0
+
+eigenfunction :: (Field.C a) => Int -> T a
+eigenfunction =
+   eigenfunctionDifferential
+
+eigenfunction0 :: (Ring.C a) => T a
+eigenfunction0 =
+   Cons Bell.unit (Poly.fromCoeffs [one])
+
+eigenfunction1 :: (Ring.C a) => T a
+eigenfunction1 =
+   Cons Bell.unit (Poly.fromCoeffs [zero, one])
+
+eigenfunction2 :: (Field.C a) => T a
+eigenfunction2 =
+   Cons Bell.unit (Poly.fromCoeffs [-(1/4), zero, one])
+
+eigenfunction3 :: (Field.C a) => T a
+eigenfunction3 =
+   Cons Bell.unit (Poly.fromCoeffs [zero, -(3/4), zero, one])
+
+
+eigenfunctionDifferential :: (Field.C a) => Int -> T a
+eigenfunctionDifferential n =
+   (\f -> f{bell = Bell.unit}) $
+   nest n (scale (-1/4) . differentiate) $
+   Cons (Bell.Cons one zero zero 2) one
+
+eigenfunctionIterative ::
+   (Field.C a, Absolute.C a, ZeroTestable.C a, Eq a) => Int -> T a
+eigenfunctionIterative n =
+   fst . head . dropWhile (uncurry (/=)) . mapAdjacent (,) $
+   eigenfunctionIteration $
+   Cons
+      Bell.unit
+      (Poly.fromCoeffs $ replicate n zero ++ [one])
+
+eigenfunctionIteration :: (Field.C a) => T a -> [T a]
+eigenfunctionIteration =
+   iterate (\x ->
+      let y = fourier x
+          px = polynomial x
+          py = polynomial y
+          c = last (Poly.coeffs px) / last (Poly.coeffs py)
+      in  y{polynomial = fmap (0.5*) (px + fmap (c*) py)})
+
+
+multiply :: (Ring.C a) =>
+   T a -> T a -> T a
+multiply f g =
+   Cons
+      (Bell.multiply (bell f) (bell g))
+      (polynomial f * polynomial g)
+
+convolve, {- convolveByDifferentiation, -} convolveByFourier :: (Field.C a) =>
+   T a -> T a -> T a
+convolve = convolveByFourier
+
+{-
+f <*> g =
+   let (foff,fint) = integrate f
+   in  fint <*> differentiate g + makeGaussPoly foff * g
+
+In principle this would work,
+but (makeGaussPoly foff * g) contains a lot of
+convolutions of Gaussian with Gaussian-polynomial-product,
+where the Gaussians have different parameters.
+
+convolveByDifferentiation f g =
+   case polynomial f of
+      fpoly ->
+         if null $ Poly.coeffs fpoly
+           then ...
+           else ...
+-}
+
+convolveByFourier f g =
+   reverse $ fourier $ multiply (fourier f) (fourier g)
+
+{-
+We use a Horner like scheme
+in order to translate multiplications with @id@
+to differentations on the Fourier side.
+Quadratic runtime.
+
+fourier (Cons bell (Poly.const a + Poly.shift f))
+  = fourier (Cons bell (Poly.const a)) + fourier (Cons bell (Poly.shift f))
+  = fourier (Cons bell (Poly.const a)) + differentiate (fourier (Cons bell f))
+
+We can certainly speed this up considerably
+by decomposing the polynomial into four polynomials,
+one for each of the four eigenvalues 1, i, -1, -i.
+-}
+fourier :: (Field.C a) =>
+   T a -> T a
+fourier f =
+   foldr
+      (\c p ->
+          let q = differentiate p
+          in  q{polynomial =
+                   Poly.const c +
+                   fmap (Complex.scale (1/2) . Complex.quarterLeft) (polynomial q)})
+      (Cons (Bell.fourier $ bell f) zero) $
+   Poly.coeffs $ polynomial f
+
+{- |
+Differentiate and divide by @sqrt pi@ in order to stay in a ring.
+This way, we do not need to fiddle with pi factors.
+-}
+differentiate :: (Ring.C a) => T a -> T a
+differentiate f =
+   f{polynomial =
+        Differential.differentiate (polynomial f)
+        - Differential.differentiate (Bell.exponentPolynomial (bell f))
+           * polynomial f}
+
+{-
+snd $ integrate $ differentiate (Cons Bell.unit (Poly.fromCoeffs [7,7,7,7]) :: T Double)
+
+g = (bell f * poly f)'
+  = bell f * ((poly f)' - (exppoly (bell f))' * poly f)
+poly g = (poly f)' - (exppoly (bell f))' * poly f
+
+Integration means we have g and ask for f.
+
+poly f = ((poly f)' - poly g) / (exppoly (bell f))'
+
+However must start with the highest term of 'poly f',
+and thus we need to perform the division on reversed polynomials.
+-}
+integrate ::
+   (Field.C a, ZeroTestable.C a) =>
+   T a -> (Complex.T a, T a)
+integrate f =
+   let fs = Poly.coeffs $ polynomial f
+       (ys,~[r]) =
+          PolyCore.divModRev
+             {-
+             We need the shortening convention of 'zipWith'
+             in order to limit the result list,
+             we cannot use list instance for (-).
+             -}
+             (zipWith (-)
+                (0 : 0 : diffRev ys)
+                (List.reverse fs))
+             (List.reverse $ Poly.coeffs $
+              Differential.differentiate $
+              Bell.exponentPolynomial $ bell f)
+   in  forcePair $
+       if null fs
+         then (zero, f)
+         else (r, f{polynomial = Poly.fromCoeffs $ List.reverse ys})
+
+diffRev :: Ring.C a => [a] -> [a]
+diffRev xs =
+   zipWith (*) xs
+      (drop 1 (iterate (subtract 1) (fromIntegral $ length xs)))
+
+{-
+integrateDefinite
+   (maybe rename integrate to antiderivative and call this one integrate)
+
+int(x^(2*n)*exp(-x^2),x=-infinity..infinity)
+ = 2 * int(x^(2*n)*exp(-x^2),x=0..infinity)
+     substitute t=x^2, dt = dx * 2 * sqrt t
+ = int(t^(n-1/2)*exp(-t),x=0..infinity)
+ = Gamma(n+1/2)
+ = (2n-1)!!/2^n * sqrt pi
+
+int(pi^n*x^(2*n)*exp(-pi*x^2),x=-infinity..infinity)
+ = (2n-1)!!/2^n
+
+
+The remainder value of 'integrate'
+is the coefficient of the error function
+and this is the only part that does not vanish when approaching the limit.
+
+
+In order to stay in a field,
+we have to return a rational number
+and a transcendental part written es @exp a@.
+
+It would be interesting to see how integral inequalities
+translate to scalar inequalities containing exponential functions.
+-}
+
+
+translate :: Ring.C a => a -> T a -> T a
+translate d =
+   translateComplex (Complex.fromReal d)
+
+translateComplex :: Ring.C a => Complex.T a -> T a -> T a
+translateComplex d f =
+   Cons
+      (Bell.translateComplex d $ bell f)
+      (Poly.translate d $ polynomial f)
+
+modulate :: Ring.C a => a -> T a -> T a
+modulate d f =
+   Cons
+      (Bell.modulate d $ bell f)
+      (polynomial f)
+
+turn :: Ring.C a => a -> T a -> T a
+turn d f =
+   Cons
+      (Bell.turn d $ bell f)
+      (polynomial f)
+
+reverse :: Additive.C a => T a -> T a
+reverse f =
+   Cons
+      (Bell.reverse $ bell f)
+      (Poly.reverse $ polynomial f)
+
+dilate :: Field.C a => a -> T a -> T a
+dilate k f =
+   Cons
+      (Bell.dilate k $ bell f)
+      (Poly.dilate (Complex.fromReal k) $ polynomial f)
+
+shrink :: Ring.C a => a -> T a -> T a
+shrink k f =
+   Cons
+      (Bell.shrink k $ bell f)
+      (Poly.shrink (Complex.fromReal k) $ polynomial f)
+
+{-
+We could also amplify the polynomial coefficients.
+-}
+amplify :: Ring.C a => a -> T a -> T a
+amplify k f =
+   Cons
+      (Bell.amplify k $ bell f)
+      (polynomial f)
+
+
+{- |
+Approximate a @T a@ using a linear combination of translated @Bell.T a@.
+The smaller the unit (e.g. 0.1, 0.01, 0.001)
+the better the approximation but the worse the numeric properties.
+
+We cannot put all information into @amp@ of @Bell@,
+since @amp@ must be real, but is complex here by construction.
+We really need at least signed amplitudes at this place,
+since we want to represent differences of Gaussians.
+-}
+approximateByBells ::
+   Field.C a =>
+   a -> T a -> [(Complex.T a, Bell.T a)]
+approximateByBells unit_ f =
+   let b = bell f
+       amps =
+          -- approximateByBellsByTranslation
+          approximateByBellsAtOnce
+             unit_
+             (Complex.scale (recip (2 * Bell.c2 b)) (Bell.c1 b))
+             (recip (2*unit_*Bell.c2 b))
+             (polynomial f)
+   in  zip (LPoly.coeffs amps) $
+       map
+          (\d -> Bell.translate d b)
+          (laurentAbscissas (unit_/2) amps)
+
+approximateByBellsAtOnce ::
+   Field.C a =>
+   a -> Complex.T a -> a -> Poly.T (Complex.T a) -> LPoly.T (Complex.T a)
+approximateByBellsAtOnce unit_ d s p =
+   foldr
+      (\x amps0 ->
+         {-
+         Decompose (bell t * (t-d)) = bell t * t - bell t * d
+         -}
+         let y = fmap (Complex.scale s) amps0
+         in  -- \t -> bell t * t
+             --    ~   (translate unit_ bell - translate (-unit_) bell) / unit_
+             LPoly.shift 1 y -
+             LPoly.shift (-1) y +
+             -- bell t * d
+             zipWithAbscissas
+                (\t z -> (Complex.fromReal t - d) * z)
+                (unit_/2) amps0 +
+             LPoly.const x)
+      (LPoly.fromCoeffs [])
+      (Poly.coeffs p)
+
+approximateByBellsByTranslation ::
+   Field.C a =>
+   a -> Complex.T a -> a -> Poly.T (Complex.T a) -> LPoly.T (Complex.T a)
+approximateByBellsByTranslation unit_ d s p =
+   foldr
+      (\x amps0 ->
+         {-
+         Decompose (bell t * (t-d)) = bell t * t - bell t * d
+         -}
+         let y = fmap (Complex.scale s) amps0
+         in  -- \t -> bell t * t
+             --    ~   (translate unit_ bell - translate (-unit_) bell) / unit_
+             LPoly.shift 1 y -
+             LPoly.shift (-1) y +
+             -- bell t * d
+             zipWithAbscissas Complex.scale (unit_/2) amps0 +
+             LPoly.const x)
+      (LPoly.fromCoeffs [])
+      (Poly.coeffs $ Poly.translate d p)
+
+zipWithAbscissas ::
+   (Ring.C a) =>
+   (a -> b -> c) -> a -> LPoly.T b -> LPoly.T c
+zipWithAbscissas h unit_ y =
+   LPoly.fromShiftCoeffs (LPoly.expon y) $
+   zipWith h
+      (laurentAbscissas unit_ y)
+      (LPoly.coeffs y)
+
+laurentAbscissas :: Ring.C a => a -> LPoly.T c -> [a]
+laurentAbscissas unit_ =
+   map (\d -> fromIntegral d * unit_) .
+   iterate (1+) . LPoly.expon
+
+
+{- No Ring instance for Gaussians
+instance (Ring.C a) => Differential.C (T a) where
+   differentiate = differentiate
+-}
+
+{- laws
+differentiate (f*g) =
+   (differentiate f) * g + f * (differentiate g)
+-}
diff --git a/gaussian/MathObj/Gaussian/Variance.hs b/gaussian/MathObj/Gaussian/Variance.hs
new file mode 100644
--- /dev/null
+++ b/gaussian/MathObj/Gaussian/Variance.hs
@@ -0,0 +1,206 @@
+{-# LANGUAGE NoImplicitPrelude #-}
+{-
+We represent a Gaussian bell curve in terms of the reciprocal of its variance
+and its value at the origin.
+
+We could do some projective geometry in the exponent
+in order to also have zero variance,
+which corresponds to the dirac impulse.
+
+The Gaussians form a nice multiplicative commutative monoid.
+Maybe we should have such a structure.
+It would also be useful for the Root data type
+and a new Exponential data type.
+-}
+module MathObj.Gaussian.Variance where
+
+import qualified MathObj.Polynomial as Poly
+import qualified Number.Root as Root
+
+import qualified Algebra.Transcendental as Trans
+import qualified Algebra.Algebraic      as Algebraic
+import qualified Algebra.Field          as Field
+import qualified Algebra.Absolute       as Absolute
+import qualified Algebra.Ring           as Ring
+import qualified Algebra.Additive       as Additive
+
+{-
+import Algebra.Transcendental (pi, )
+import Algebra.Ring ((*), (^), )
+import Algebra.Additive ((+))
+-}
+import Test.QuickCheck (Arbitrary, arbitrary, )
+import Control.Monad (liftM2, )
+
+-- import Prelude (($))
+import NumericPrelude.Numeric
+import NumericPrelude.Base
+
+
+{- |
+Since @amp@ is the square of the actual amplitude it must be non-negative.
+-}
+data T a = Cons {amp, c :: a}
+   deriving (Eq, Show)
+
+instance (Absolute.C a, Arbitrary a) => Arbitrary (T a) where
+   arbitrary =
+      liftM2 Cons
+         (fmap abs arbitrary)
+         (fmap ((1+) . abs) arbitrary)
+
+
+constant :: Ring.C a => T a
+constant = Cons one zero
+
+{- |
+eigenfunction of 'fourier'
+-}
+unit :: Ring.C a => T a
+unit = Cons one one
+
+{-# INLINE evaluate #-}
+evaluate :: (Trans.C a) =>
+   T a -> a -> a
+evaluate f x =
+   sqrt (amp f) * exp (-pi * c f * x^2)
+
+exponentPolynomial :: (Additive.C a) =>
+   T a -> Poly.T a
+exponentPolynomial f =
+   Poly.fromCoeffs [zero, zero, c 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 =
+   Root.sqrt $
+      Root.fromNumber (amp f)
+      `Root.div`
+      Root.sqrt (Root.fromNumber $ 2 * c f)
+
+normInfRoot :: (Field.C a) => T a -> Root.T a
+normInfRoot f =
+   Root.sqrt $ Root.fromNumber $ amp f
+
+normPRoot :: (Field.C a) => Rational -> T a -> Root.T a
+normPRoot p f =
+   Root.sqrt (Root.fromNumber (amp f))
+   `Root.div`
+   Root.rationalPower (recip (2*p)) (Root.fromNumber (fromRational' p * c f))
+
+
+-- ToDo: implement NormedSpace.Sum et.al.
+norm1 :: (Algebraic.C a) => T a -> a
+norm1 f =
+   sqrt $ amp f / c f
+
+norm2 :: (Algebraic.C a) => T a -> a
+norm2 f =
+   sqrt $ amp f / (sqrt $ 2 * c f)
+
+normInf :: (Algebraic.C a) => T a -> a
+normInf f =
+   sqrt (amp f)
+
+normP :: (Trans.C a) => a -> T a -> a
+normP p f =
+   sqrt (amp f) * (p * c f) ^? (- recip (2*p))
+
+
+variance :: (Trans.C a) =>
+   T a -> a
+variance f =
+   recip $ c f * 2*pi
+
+multiply :: (Ring.C a) =>
+   T a -> T a -> T a
+multiply f g =
+   Cons (amp f * amp g) (c f + c g)
+
+powerRing :: (Trans.C a) =>
+   Integer -> T a -> T a
+powerRing p f =
+   Cons (amp f ^ p) (fromInteger p * c f)
+
+{-
+powerField does not makes sense,
+since the reciprocal of a Gaussian diverges.
+-}
+
+powerAlgebraic :: (Trans.C a) =>
+   Rational -> T a -> T a
+powerAlgebraic p f =
+   Cons (amp f ^/ p) (fromRational' p * c f)
+
+powerTranscendental :: (Trans.C a) =>
+   a -> T a -> T a
+powerTranscendental p f =
+   Cons (amp f ^? p) (p * c f)
+
+{- |
+> convolve x y t =
+>    integrate $ \s -> x s * y(t-s)
+
+Convergence only for @c f + c g > 0@.
+-}
+convolve :: (Field.C a) =>
+   T a -> T a -> T a
+convolve f g =
+   let s = c f + c g
+   in  Cons
+          (amp f * amp g / s)
+          (c f * c g / s)
+
+{- |
+> fourier x f =
+>    integrate $ \t -> x t * cis (-2*pi*t*f)
+
+Convergence only for @c f > 0@.
+-}
+fourier :: (Field.C a) =>
+   T a -> T a
+fourier f =
+   Cons (amp f / c f) (recip $ c f)
+{-
+fourier (t -> exp(-(a*t)^2))
+-}
+
+dilate :: (Field.C a) => a -> T a -> T a
+dilate k f =
+   Cons (amp f) $ c f / k^2
+
+shrink :: (Ring.C a) => a -> T a -> T a
+shrink k f =
+   Cons (amp f) $ c f * k^2
+
+{- |
+@amplify k@ scales by @abs k@!
+-}
+amplify :: (Ring.C a) => a -> T a -> T a
+amplify k f =
+   Cons (k^2 * amp f) $ c f
+
+
+{- laws
+fourier (convolve f g) = multiply (fourier f) (fourier g)
+
+dilate k (dilate m f) = dilate (k*m) f
+
+dilate k (shrink k f) = f
+
+variance (dilate k f) = k^2 * variance f
+
+variance (convolve f g) = variance f + variance g
+-}
diff --git a/numeric-prelude.cabal b/numeric-prelude.cabal
--- a/numeric-prelude.cabal
+++ b/numeric-prelude.cabal
@@ -1,6 +1,6 @@
 Name:           numeric-prelude
-Version:        0.4.0.1
-License:        GPL
+Version:        0.4.0.2
+License:        BSD3
 License-File:   LICENSE
 Author:         Dylan Thurston <dpt@math.harvard.edu>, Henning Thielemann <numericprelude@henning-thielemann.de>, Mikael Johansson
 Maintainer:     Henning Thielemann <numericprelude@henning-thielemann.de>
@@ -9,7 +9,7 @@
 Stability:      Experimental
 Tested-With:    GHC==6.4.1, GHC==6.8.2, GHC==6.10.4, GHC==6.12.3
 Tested-With:    GHC==7.2.2, GHC==7.4.1, GHC==7.6.3
-Cabal-Version:  >=1.6
+Cabal-Version:  >=1.8
 Build-Type:     Simple
 Synopsis:       An experimental alternative hierarchy of numeric type classes
 Description:
@@ -79,7 +79,7 @@
   .
   Write modules in the following style:
   .
-  > [-# NoImplicitPrelude #-]
+  > [-# LANGUAGE NoImplicitPrelude #-]
   > module MyModule where
   >
   > ... various specific imports ...
@@ -146,15 +146,12 @@
   docs/README
   src/Algebra/GenerateRules.hs
 
-Flag splitBase
-  description: Choose the new smaller, split-up base package.
-
 Flag buildTests
   description: Build test executables
   default:     False
 
 Source-Repository this
-  Tag:         0.4.0.1
+  Tag:         0.4.0.2
   Type:        darcs
   Location:    http://code.haskell.org/numeric-prelude/
 
@@ -170,15 +167,14 @@
     non-negative >=0.0.5 && <0.2,
     utility-ht >=0.0.6 && <0.1,
     deepseq >=1.1 && <1.4
-  If flag(splitBase)
-    Build-Depends:
-      base >= 2 && <5,
-      array >=0.1 && <0.5,
-      containers >=0.1 && <0.6,
-      random >=1.0 && <1.1
-  Else
-    Build-Depends: base >= 1.0 && < 2
 
+  -- splitBase
+  Build-Depends:
+    array >=0.1 && <0.5,
+    containers >=0.1 && <0.6,
+    random >=1.0 && <1.1,
+    base >= 2 && <5
+
   If impl(ghc>=7.0)
     CPP-Options: -DNoImplicitPrelude=RebindableSyntax
     Extensions: CPP
@@ -282,29 +278,29 @@
     NumericPrelude.List
     Algebra.AffineSpace
     Algebra.RealRing98
-    MathObj.Gaussian.Variance
-    MathObj.Gaussian.Bell
-    MathObj.Gaussian.Polynomial
-    Number.ComplexSquareRoot
     -- I think I won't add them this way.
     -- It is certainly better to split the class into comparison and selection.
     Algebra.EqualityDecision
     Algebra.OrderDecision
 
 Executable test
-  Hs-Source-Dirs: src, test
+  Hs-Source-Dirs: test
   GHC-Options:    -Wall
   Main-Is: Test.hs
 
-  If !flag(buildTests)
-    Buildable:         False
+  If flag(buildTests)
+    Build-Depends:
+      numeric-prelude,
+      base
+  Else
+    Buildable: False
 
   If impl(ghc>=7.0)
     CPP-Options: -DNoImplicitPrelude=RebindableSyntax
     Extensions: CPP
 
 Executable testsuite
-  Hs-Source-Dirs: src, test
+  Hs-Source-Dirs: test, gaussian
   GHC-Options:    -Wall
   Other-modules:
     Test.NumericPrelude.Utility
@@ -321,10 +317,17 @@
     Test.MathObj.Gaussian.Variance
     Test.MathObj.Gaussian.Bell
     Test.MathObj.Gaussian.Polynomial
+    Number.ComplexSquareRoot
   Main-Is: Test/Run.hs
 
   If flag(buildTests)
-    Build-Depends: HUnit >=1 && <2
+    Build-Depends:
+      HUnit >=1 && <2,
+      numeric-prelude,
+      QuickCheck,
+      utility-ht,
+      random,
+      base
   Else
     Buildable: False
 
@@ -333,14 +336,22 @@
     Extensions: CPP
 
 Executable test-gaussian
-  Hs-Source-Dirs: src, test
+  Hs-Source-Dirs: gaussian
   Main-Is: Gaussian.hs
   Other-Modules:
     MathObj.Gaussian.Example
+    MathObj.Gaussian.Variance
+    MathObj.Gaussian.Bell
+    MathObj.Gaussian.Polynomial
+
   If flag(buildTests)
     Build-Depends:
       gnuplot >=0.5 && <0.6,
-      HTam >=0.0.2 && <0.1
+      HTam >=0.0.2 && <0.1,
+      numeric-prelude,
+      QuickCheck,
+      utility-ht,
+      base
   Else
     Buildable: False
 
diff --git a/src/Algebra/DimensionTerm.hs b/src/Algebra/DimensionTerm.hs
--- a/src/Algebra/DimensionTerm.hs
+++ b/src/Algebra/DimensionTerm.hs
@@ -1,12 +1,4 @@
 {- |
-Copyright   :  (c) Henning Thielemann 2008
-License     :  GPL
-
-Maintainer  :  numericprelude@henning-thielemann.de
-Stability   :  provisional
-Portability :  portable
-
-
 We already have the dynamically checked physical units
 provided by "Number.Physical"
 and the statically checked ones of the @dimensional@ package of Buckwalter,
diff --git a/src/Algebra/NormedSpace/Euclidean.hs b/src/Algebra/NormedSpace/Euclidean.hs
--- a/src/Algebra/NormedSpace/Euclidean.hs
+++ b/src/Algebra/NormedSpace/Euclidean.hs
@@ -3,13 +3,6 @@
 {-# LANGUAGE FlexibleInstances #-}
 
 {- |
-Copyright   :  (c) Henning Thielemann 2005-2010
-License     :  GPL
-
-Maintainer  :  numericprelude@henning-thielemann.de
-Stability   :  provisional
-Portability :  requires multi-parameter type classes
-
 Abstraction of normed vector spaces
 -}
 
diff --git a/src/Algebra/NormedSpace/Maximum.hs b/src/Algebra/NormedSpace/Maximum.hs
--- a/src/Algebra/NormedSpace/Maximum.hs
+++ b/src/Algebra/NormedSpace/Maximum.hs
@@ -3,13 +3,6 @@
 {-# LANGUAGE FlexibleInstances #-}
 
 {- |
-Copyright   :  (c) Henning Thielemann 2005-2010
-License     :  GPL
-
-Maintainer  :  numericprelude@henning-thielemann.de
-Stability   :  provisional
-Portability :  requires multi-parameter type classes
-
 Abstraction of normed vector spaces
 -}
 
diff --git a/src/Algebra/NormedSpace/Sum.hs b/src/Algebra/NormedSpace/Sum.hs
--- a/src/Algebra/NormedSpace/Sum.hs
+++ b/src/Algebra/NormedSpace/Sum.hs
@@ -3,13 +3,6 @@
 {-# LANGUAGE FlexibleInstances #-}
 
 {- |
-Copyright   :  (c) Henning Thielemann 2005-2010
-License     :  GPL
-
-Maintainer  :  numericprelude@henning-thielemann.de
-Stability   :  provisional
-Portability :  requires multi-parameter type classes
-
 Abstraction of normed vector spaces
 -}
 
diff --git a/src/MathObj/Gaussian/Bell.hs b/src/MathObj/Gaussian/Bell.hs
deleted file mode 100644
--- a/src/MathObj/Gaussian/Bell.hs
+++ /dev/null
@@ -1,324 +0,0 @@
-{-# LANGUAGE NoImplicitPrelude #-}
-{-
-Complex translated and modulated Gaussian bell curve.
-
-It could be extended to chirps
-using a complex valued quadratic term with (real c >= 0).
-This allows for a new test:
-Express the Fourier transform in terms of a convolution with a chirp.
--}
-module MathObj.Gaussian.Bell where
-
-import qualified MathObj.Polynomial as Poly
-import qualified Number.Complex as Complex
-
-import qualified Algebra.Transcendental as Trans
-import qualified Algebra.Field          as Field
-import qualified Algebra.Absolute       as Absolute
-import qualified Algebra.Ring           as Ring
-import qualified Algebra.Additive       as Additive
-
-import Number.Complex ((+:), )
-
-import Test.QuickCheck (Arbitrary, arbitrary, )
-import Control.Monad (liftM4, )
-
--- import Prelude (($))
-import NumericPrelude.Numeric
-import NumericPrelude.Base hiding (reverse, )
-
-
-data T a = Cons {amp :: a, c0, c1 :: Complex.T a, c2 :: a}
-   deriving (Eq, Show)
-
-instance (Absolute.C a, Arbitrary a) => Arbitrary (T a) where
-   arbitrary =
-      liftM4
-         (\k a b c -> Cons (abs k) a b (1 + abs c))
-         arbitrary arbitrary arbitrary arbitrary
-
-
-constant :: Ring.C a => T a
-constant = Cons one zero zero zero
-
-{- |
-eigenfunction of 'fourier'
--}
-unit :: Ring.C a => T a
-unit = Cons one zero zero one
-
-{-# INLINE evaluate #-}
-evaluate :: (Trans.C a) =>
-   T a -> a -> Complex.T a
-evaluate f x =
-   Complex.scale
-     (sqrt (amp f))
-     (Complex.exp $ Complex.scale (-pi) $
-      c0 f + Complex.scale x (c1 f) + Complex.fromReal (c2 f * x^2))
-
-evaluateSqRt :: (Trans.C a) =>
-   T a -> a -> Complex.T a
-evaluateSqRt f x0 =
-   Complex.scale
-     (sqrt (amp f))
-     (let x = sqrt pi * x0
-      in  Complex.exp $ negate $
-          c0 f + Complex.scale x (c1 f) + Complex.fromReal (c2 f * x^2))
-
-exponentPolynomial :: (Additive.C a) =>
-   T a -> Poly.T (Complex.T a)
-exponentPolynomial f =
-   Poly.fromCoeffs [c0 f, c1 f, Complex.fromReal (c2 f)]
-
-
-{-
-norm functions depend on interpretation
-and would have to return both a rational and transcendental part
-expressed as @exp a@.
--}
-
-variance :: (Trans.C a) =>
-   T a -> a
-variance f =
-   recip $ c2 f * 2*pi
-
-multiply :: (Ring.C a) =>
-   T a -> T a -> T a
-multiply f g =
-   Cons
-      (amp f * amp g)
-      (c0 f + c0 g) (c1 f + c1 g) (c2 f + c2 g)
-
-powerRing :: (Trans.C a) =>
-   Integer -> T a -> T a
-powerRing p f =
-   let pa = fromInteger p
-   in  Cons
-          (amp f ^ p)
-          (pa * c0 f) (pa * c1 f) (fromInteger p * c2 f)
-
-{-
-powerField does not makes sense,
-since the reciprocal of a Gaussian diverges.
--}
-
-powerAlgebraic :: (Trans.C a) =>
-   Rational -> T a -> T a
-powerAlgebraic p f =
-   let pa = fromRational' p
-   in  Cons
-          (amp f ^/ p)
-          (pa * c0 f) (pa * c1 f) (fromRational' p * c2 f)
-
-powerTranscendental :: (Trans.C a) =>
-   a -> T a -> T a
-powerTranscendental p f =
-   Cons
-      (amp f ^? p)
-      (Complex.scale p $ c0 f) (Complex.scale p $ c1 f) (p * c2 f)
-
-
-{-
-let x=Cons 2 (1+:3) (4+:5) (7::Rational); y=Cons 7 (1+:4) (3+:2) (5::Rational)
--}
-convolve :: (Field.C a) =>
-   T a -> T a -> T a
-convolve f g =
-   let s = c2 f + c2 g
-       {-
-       fd = f1/(2*f2)
-       gd = g1/(2*g2)
-       c = f2*g2/(f2+g2)
-
-       c*(fd+gd) = (f1*g2+f2*g1)/(2*(f2+g2)) = b/2
-
-       c*(fd+gd)^2 - fd^2*f2 - gd^2*g2
-         = f2*g2*(fd+gd)^2/(f2 + g2) - (fd^2*f2 + gd^2*g2)
-         = (f2*g2*(fd+gd)^2 - (f2+g2)*(fd^2*f2+gd^2*g2)) / (f2 + g2)
-         = (2*f2*g2*fd*gd - (fd^2*f2^2+gd^2*g2^2)) / (f2 + g2)
-         = (2*f1*g1 - (f1^2+g1^2)) / (4*(f2 + g2))
-         = -(f1 - g1)^2/(4*(f2 + g2))
-       -}
-   in  Cons
-          (amp f * amp g / s)
-          (c0 f + c0 g
-              - Complex.scale (recip (4*s)) ((c1 f - c1 g)^2))
-          (Complex.scale (c2 g / s) (c1 f) +
-           Complex.scale (c2 f / s) (c1 g))
-          (c2 f * c2 g / s)
-            -- recip $ recip (c2 f) + recip (c2 g)
-{-
-   Cons
-      (c0 f + c0 g) (c1 f + c1 g)
-      (recip $ recip (c2 f) + recip (c2 g))
--}
-
-convolveByTranslation :: (Field.C a) =>
-   T a -> T a -> T a
-convolveByTranslation f0 g0 =
-   let fd = Complex.scale (recip (2 * c2 f0)) $ c1 f0
-       gd = Complex.scale (recip (2 * c2 g0)) $ c1 g0
-       f1 = translateComplex fd f0
-       g1 = translateComplex gd g0
-       s = c2 f1 + c2 g1
-   in  translateComplex (negate $ fd + gd) $
-       Cons
-          (amp f1 * amp g1 / s)
-          (c0 f1 + c0 g1) zero
-          (c2 f1 * c2 g1 / s)
-
-convolveByFourier :: (Field.C a) =>
-   T a -> T a -> T a
-convolveByFourier f g =
-   reverse $ fourier $ multiply (fourier f) (fourier g)
-
-fourier :: (Field.C a) =>
-   T a -> T a
-fourier f =
-   let a = c0 f
-       b = c1 f
-       rc = recip $ c2 f
-   in  Cons
-          (amp f * rc)
-          (Complex.scale (rc/4) (-b^2) + a)
-          (Complex.scale rc $ Complex.quarterRight b)
-          rc
-
-fourierByTranslation :: (Field.C a) =>
-   T a -> T a
-fourierByTranslation f =
-   translateComplex (Complex.scale (1/2) $ Complex.quarterLeft $ c1 f) $
-   Cons (amp f / c2 f) (c0 f) zero (recip $ c2 f)
-
-{-
-a + b*x + c*x^2
- = c*(a/c + b/c*x + x^2)
- = c*((x-b/(2*c))^2 + (4*a*c+b^2)/(4*c^2))
- = c*(x-b/(2*c))^2 + (4*a*c+b^2)/(4*c)
-
-fourier ->
-   x^2/c - i*b/c*x + (4*a*c+b^2)/(4*c)
-
-fourier (x -> exp(-pi*c*(x-t)^2))
- = fourier $ translate t $ shrink (sqrt c) $ x -> exp(-pi*x^2)
- = modulate t $ dilate (sqrt c) $ fourier $ x -> exp(-pi*x^2)
- = modulate t $ dilate (sqrt c) $ x -> exp(-pi*x^2)
- = modulate t $ x -> exp(-pi*x^2/c)
- = x -> exp(-pi*x^2/c) * exp(-2*pi*i*x*t)
- = x -> exp(-pi*(x^2/c - 2*i*x*t))
--}
-
-{-
-b*x + c*x^2
- = c*(b/c*x + x^2)
- = c*((x-br/(2*c))^2 + i*x*bi/c - br^2/(4*c^2))
- = c*(x-br/(2*c))^2 + i*x*bi - br^2/(4*c)
-
-fourier ->
-   (x+bi/2)^2/c - i*br/c*(x+bi/2) - br^2/(4*c)
- = (1/c) * ((x+bi/2)^2 - i*br*(x+bi/2) + (br/2)^2)
- = (1/c) * (x^2 - i*b*x + -(br/2)^2 + (bi/2)^2 - i*br*bi/2)
- = (1/c) * (x^2 - i*b*x - (br^2-bi^2+2*br*bi*i)^2 /4)
- = (1/c) * (x^2 - i*b*x - b^2 / 4)
- = (1/c) * (x^2 - i*b*x + (i*b/2)^2)
- = (1/c) * (x - i*b/2)^2
-
-Example:
-  (x-b)^2 = b^2 - 2*b*x + x^2
-    ->  (- i*2*b*x + x^2)
-
-
-fourier (x -> exp(-pi*(c*(x-t)^2 + 2*i*m*x)))
- = fourier $ modulate m $ translate t $ shrink (sqrt c) $ x -> exp(-pi*x^2)
- = translate (-m) $ modulate t $ dilate (sqrt c) $ fourier $ x -> exp(-pi*x^2)
- = translate (-m) $ modulate t $ dilate (sqrt c) $ x -> exp(-pi*x^2)
- = translate (-m) $ modulate t $ x -> exp(-pi*x^2/c)
- = translate (-m) $ x -> exp(-pi*x^2/c) * exp(-2*pi*i*x*t)
- = x -> exp(-pi*(x+m)^2/c) * exp(-2*pi*i*(x+m)*t)
- = x -> exp(-pi*((x+m)^2/c - 2*i*(x+m)*t))
--}
-
-{-
-fourier (Cons a 0 0) =
-  Cons a 0 infinity
-
-fourier (Cons 0 0 c) =
-  Cons 0 0 (recip c)
-
-fourier (Cons 0 b 1) =
-  Cons 0 (i*b) 1
--}
-
-translate :: Ring.C a => a -> T a -> T a
-translate d f =
-   let a = c0 f
-       b = c1 f
-       c = c2 f
-   in  Cons
-          (amp f)
-          (Complex.fromReal (c*d^2) - Complex.scale d b + a)
-          (Complex.fromReal (-2*c*d) + b)
-          c
-
-translateComplex :: Ring.C a => Complex.T a -> T a -> T a
-translateComplex d f =
-   let a = c0 f
-       b = c1 f
-       c = c2 f
-   in  Cons
-          (amp f)
-          (Complex.scale c (d^2) - b*d + a)
-          (Complex.scale (-2*c) d + b)
-          c
-
-modulate :: Ring.C a => a -> T a -> T a
-modulate d f =
-   Cons
-      (amp f)
-      (c0 f)
-      (c1 f + (zero +: 2*d))
-      (c2 f)
-
-turn :: Ring.C a => a -> T a -> T a
-turn d f =
-   Cons
-      (amp f)
-      (c0 f + (zero +: 2*d))
-      (c1 f)
-      (c2 f)
-
-reverse :: Additive.C a => T a -> T a
-reverse f =
-   f{c1 = negate $ c1 f}
-
-
-dilate :: Field.C a => a -> T a -> T a
-dilate k f =
-   Cons
-      (amp f)
-      (c0 f)
-      (Complex.scale (recip k) $ c1 f)
-      (c2 f / k^2)
-
-shrink :: Ring.C a => a -> T a -> T a
-shrink k f =
-   Cons
-      (amp f)
-      (c0 f)
-      (Complex.scale k $ c1 f)
-      (c2 f * k^2)
-
-amplify :: (Ring.C a) => a -> T a -> T a
-amplify k f =
-   Cons
-      (k^2 * amp f)
-      (c0 f)
-      (c1 f)
-      (c2 f)
-
-
-{- laws
-fourier (convolve f g) = fourier f * fourier g
-
-fourier (fourier f) = reverse f
--}
diff --git a/src/MathObj/Gaussian/Example.hs b/src/MathObj/Gaussian/Example.hs
deleted file mode 100644
--- a/src/MathObj/Gaussian/Example.hs
+++ /dev/null
@@ -1,231 +0,0 @@
-{-# LANGUAGE NoImplicitPrelude #-}
-{-
-Reciprocal of variance of a Gaussian bell curve.
-We describe the curve only in terms of its variance
-thus we represent a bell curve at the coordinate origin
-neglecting its amplitude.
-
-We could also define the amplitude as @root 4 c@,
-thus preserving L2 norm being one,
-but then @dilate@ and @shrink@ also include an amplification.
-
-We could do some projective geometry in the exponent
-in order to also have zero variance,
-which corresponds to the dirac impulse.
--}
-module MathObj.Gaussian.Example where
-
-import qualified MathObj.Gaussian.Polynomial as PolyBell
-import qualified MathObj.Gaussian.Bell as Bell
-import qualified MathObj.Gaussian.Variance as Var
-
-import qualified MathObj.Polynomial as Poly
-
-import qualified Algebra.Transcendental as Trans
-import qualified Algebra.Algebraic      as Algebraic
-import qualified Algebra.Field          as Field
--- import qualified Algebra.Absolute           as Absolute
-import qualified Algebra.Ring           as Ring
--- import qualified Algebra.Additive       as Additive
-
-import qualified Number.Complex as Complex
-import qualified Number.Root as Root
-
-import Algebra.Transcendental (pi, )
-import Algebra.Algebraic (root, )
-import Algebra.Ring ((*), (^), )
-
-import Number.Complex ((+:), )
-
-import qualified Numerics.Function as Func
-import qualified Numerics.Fourier as Fourier
-import qualified Numerics.Integration as Integ
-import qualified Numerics.Differentiation as Diff
-
-import qualified Graphics.Gnuplot.Simple as GP
-
-import Control.Applicative (liftA2, )
-
--- import System.Exit (ExitCode, )
-
--- import Prelude (($))
-import NumericPrelude.Numeric
-import NumericPrelude.Base
-import qualified Prelude as P
-
-
-curve0 :: Var.T Double
-curve0 = curve0a
-
-curve0a :: Var.T Double
-curve0a = Var.Cons 1.4 3.3
-
-curve0b :: Var.T Double
-curve0b = Var.Cons 2.2 1.7
-
-variance0 :: (Double, Double)
-variance0 =
-   (Var.variance curve0,
-    (Integ.rectangular 1000 (-2,2) $ liftA2 (*) (^2) (Var.evaluate curve0)) /
-    (Integ.rectangular 1000 (-2,2) $ Var.evaluate curve0))
-
-norm10 :: (Double, Double, Double)
-norm10 =
-   (Integ.rectangular 1000 (-2,2) $ Var.evaluate curve0,
-    Var.norm1 curve0,
-    Root.toNumber (Var.norm1Root curve0))
-
-norm20 :: (Double, Double, Double)
-norm20 =
-   (sqrt $ Integ.rectangular 1000 (-2,2) $ (^2) . Var.evaluate curve0,
-    Var.norm2 curve0,
-    Root.toNumber (Var.norm2Root curve0))
-
-norm30 :: (Double, Double, Double)
-norm30 =
-   (root 3 $ Integ.rectangular 1000 (-2,2) $ (^3) . Var.evaluate curve0,
-    Var.normP 3 curve0,
-    Root.toNumber (Var.normPRoot 3 curve0))
-
-fourier0 :: IO ()
-fourier0 =
-   GP.plotFuncs []
-      (GP.linearScale 100 (-2,2))
-      [Var.evaluate $ Var.fourier curve0,
-       Fourier.analysisTransformOneReal 100 (-2,2) $ Var.evaluate curve0]
-
-multiply0 :: IO ()
-multiply0 =
-   GP.plotFuncs []
-      (GP.linearScale 100 (-1,1))
-      [Var.evaluate $ Var.multiply curve0a curve0b,
-       liftA2 (*) (Var.evaluate curve0a) (Var.evaluate curve0b)]
-
-convolve0 :: IO ()
-convolve0 =
-   GP.plotFuncs []
-      (GP.linearScale 100 (-2,2))
-      [Var.evaluate $ Var.convolve curve0a curve0b,
-       Integ.convolve 1000 (-3,3) (Var.evaluate curve0a) (Var.evaluate curve0b)]
-
-
-curve1 :: Bell.T Double
-curve1 = curve1a
-
-curve1a :: Bell.T Double
-curve1a = Bell.Cons 1.4 (0.1+:0.3) ((-0.2)+:1.4) 2.3
-
-curve1b :: Bell.T Double
-curve1b = Bell.Cons 2.2 ((-0.3)+:2.1) (0.2+:(-0.4)) 1.7
-
-variance1 :: (Double, Double)
-variance1 =
-   (Bell.variance curve1,
-    (Integ.rectangular 1000 (-2,2) $
-        liftA2 (*) (^2)
-           (Complex.magnitudeSqr .
-            Func.translateRight
-               (Complex.real (Bell.c1 curve1) / (2 * Bell.c2 curve1))
-               (Bell.evaluate curve1))) /
-    (Integ.rectangular 1000 (-2,2) $ Complex.magnitude . Bell.evaluate curve1))
-
-{- the norm depends on too much things
-norm0vs1 :: (Double, Double)
-norm0vs1 =
-   ((Integ.rectangular 1000 (-5,5) $ Var.evaluate curve0)
-         * exp (- Complex.real (Bell.c0 curve1)),
-    Integ.rectangular 1000 (-5,5) $ Complex.magnitude . Bell.evaluate curve1)
--}
-
-fourier1 :: IO ()
-fourier1 =
-   GP.plotFuncs []
-      (GP.linearScale 100 (-5,5))
-      [Complex.real . (Bell.evaluate $ Bell.fourier curve1),
-       fourierAnalysisReal 100 (-2,2) $ Bell.evaluate curve1]
-
-
-curve2 :: PolyBell.T Double
-curve2 =
-   PolyBell.Cons
---      Bell.unit
---      (Bell.Cons 1.4 (0.1+:0.3) 0 1.2)
---      (Bell.Cons 1.4 (0.1+:0.3) ((-0.2)+:1.4) 1)
-      curve1
---      (Poly.fromCoeffs [one])
---      (Poly.fromCoeffs [zero,one])
---      (Poly.fromCoeffs [zero,zero,one])
---      (Poly.fromCoeffs [0,Complex.imaginaryUnit])
-      (Poly.fromCoeffs [1.4+:(-0.1),0.8+:(0.1),(-1.1)+:0.3])
-
-differentiate2 :: IO ()
-differentiate2 =
-   GP.plotFuncs []
-      (GP.linearScale 100 (-2,2))
-      [Complex.real . (PolyBell.evaluateSqRt $ PolyBell.differentiate curve2),
-       ((/ sqrt pi) . ) $ Diff.diff (1e-5) $ Complex.real . PolyBell.evaluateSqRt curve2]
-
-fourier2 :: IO ()
-fourier2 =
-   GP.plotFuncs []
-      (GP.linearScale 100 (-5,5))
-      [Complex.real . (PolyBell.evaluateSqRt $ PolyBell.fourier curve2),
-       fourierAnalysisReal 100 (-2,2) $ PolyBell.evaluateSqRt curve2]
-
-
-
-fourierAnalysisReal ::
-   (P.Floating a) =>
-   Integer -> (a, a) -> (a -> Complex.T a) -> a -> a
-fourierAnalysisReal n rng f =
-   liftA2 (P.-)
-      (Fourier.analysisTransformOneReal n rng (Complex.real . f))
-      (Fourier.analysisTransformOneImag n rng (Complex.imag . f))
-
-
-{- |
-Try to approximate @\x -> exp (-x^2) * x@
-by a difference of translated Gaussian bells.
-
-exp(-x^2) * x
-  ==  exp(-(a+b*x+c*x^2)) - exp(-(a-b*x+c*x^2))
-  ==  exp(-(a+c*x^2)) * (exp(-b*x) - exp(b*x))
-  ==  exp(-(a+c*x^2)) * 2*sinh (b*x)
-
-It holds
-  lim (\b x -> sinh (b*x) / b)  =  id
--}
-diffApprox :: IO ()
-diffApprox =
-   let amp = (2*b)^- (-2)
-       a = 0
-       {-
-       amp = 1
-       a = log (2 * abs b)
-       -}
-       b = -0.1
-       c = 1
-       ac = Complex.fromReal a
-       bc = Complex.fromReal b
-   in  GP.plotFuncs []
-          (GP.linearScale 100 (-2,2::Double))
-          [Complex.real .
-           (PolyBell.evaluateSqRt $
-              PolyBell.Cons Bell.unit (Poly.fromCoeffs [zero,one])),
-           Complex.real .
-           liftA2 (-)
-             (PolyBell.evaluateSqRt $
-                PolyBell.Cons (Bell.Cons amp ac bc c) (Poly.fromCoeffs [one]))
-             (PolyBell.evaluateSqRt $
-                PolyBell.Cons (Bell.Cons amp ac (-bc) c) (Poly.fromCoeffs [one]))]
-
-
-polyApprox :: IO ()
-polyApprox =
-   GP.plotFuncs []
-      (GP.linearScale 100 (-2,2::Double))
-      [Complex.real .
-         PolyBell.evaluateSqRt curve2,
-       Complex.real . sum .
-         mapM (\(amp,b) -> \x -> amp * Bell.evaluateSqRt b x)
-         (PolyBell.approximateByBells 0.1 curve2)]
diff --git a/src/MathObj/Gaussian/Polynomial.hs b/src/MathObj/Gaussian/Polynomial.hs
deleted file mode 100644
--- a/src/MathObj/Gaussian/Polynomial.hs
+++ /dev/null
@@ -1,480 +0,0 @@
-{-# LANGUAGE NoImplicitPrelude #-}
-{-
-Complex Gaussian bell multiplied with a polynomial.
-
-In order to make this free of @pi@ factors,
-we have to choose @recip (sqrt pi)@
-as unit for translations and modulations,
-for linear factors and in the differentiation.
--}
-{-
-ToDo:
-
-* In order to avoid the weird @sqrt pi@ factor,
-  use a polynomial expression in @pi@.
-
-* sum of multiple bells using Data.Map from exponent polynomial to coefficient polynomial
-  use of Algebra object.
-
-* Discrete Fourier Transform and its eigenvectors
-
-* Use projective geometry in order to support Dirac impulse.
-  There are many open questions:
-  1. What shall be the product of two Dirac impulses -
-     whether they are at the same location or not.
-  2. How to organize coefficients
-     such that the constant function can be modulated
-     and the Dirac impulse can be translated.
--}
-module MathObj.Gaussian.Polynomial where
-
-import qualified MathObj.Gaussian.Bell as Bell
-
-import qualified MathObj.LaurentPolynomial as LPoly
-import qualified MathObj.Polynomial.Core   as PolyCore
-import qualified MathObj.Polynomial        as Poly
-import qualified Number.Complex     as Complex
-
-import qualified Algebra.ZeroTestable   as ZeroTestable
-import qualified Algebra.Differential   as Differential
-import qualified Algebra.Transcendental as Trans
-import qualified Algebra.Field          as Field
-import qualified Algebra.Absolute       as Absolute
-import qualified Algebra.Ring           as Ring
-import qualified Algebra.Additive       as Additive
-
-import qualified Data.Record.HT as Rec
-import qualified Data.List as List
-import Data.Function.HT (nest, )
-import Data.Eq.HT (equating, )
-import Data.List.HT (mapAdjacent, )
-import Data.Tuple.HT (forcePair, )
-
-import Test.QuickCheck (Arbitrary, arbitrary, )
-import Control.Monad (liftM2, )
-
-import NumericPrelude.Numeric
-import NumericPrelude.Base hiding (reverse, )
--- import Prelude ()
-
-
-data T a = Cons {bell :: Bell.T a, polynomial :: Poly.T (Complex.T a)}
-   deriving (Show)
-
-instance (Absolute.C a, ZeroTestable.C a, Eq a) => Eq (T a) where
-   (==) = equal
-
-
-{-
-Helper data type for 'equal',
-that allows to call the (not quite trivial) polynomial equality check.
-@RootProduct r a@ represents @sqrt r * a@.
-The test using 'signum' works for real numbers,
-and I do not know, whether it is correct for other mathematical objects.
-However I cannot imagine other mathematical objects,
-that make sense at all, here.
-Maybe elements of a finite field.
--}
-data RootProduct a = RootProduct a a
-
-instance (Absolute.C a, ZeroTestable.C a, Eq a) => Eq (RootProduct a) where
-   (RootProduct xr xa) == (RootProduct yr ya)  =
-      let xp = xr*xa^2
-          yp = yr*ya^2
-      in  xp==yp &&
-          (isZero xp || signum xa == signum ya)
-
-instance (ZeroTestable.C a) => ZeroTestable.C (RootProduct a) where
-   isZero (RootProduct r a) = isZero r || isZero a
-
-
-{-
-The derived Eq is not correct.
-We have to combine the amplitude of the bell with the polynomial,
-respecting signs and the square root of the bell amplitude.
--}
-equal :: (Absolute.C a, ZeroTestable.C a, Eq a) => T a -> T a -> Bool
-equal x y =
-   let bx = bell x
-       by = bell y
-       scaleSqr b =
-          (\p ->
-              (fmap (RootProduct (Bell.amp b) . Complex.real) p,
-               fmap (RootProduct (Bell.amp b) . Complex.imag) p))
-           . polynomial
-   in  Rec.equal
-          (equating Bell.c0 :
-           equating Bell.c1 :
-           equating Bell.c2 :
-           [])
-          bx by
-       &&
-       scaleSqr bx x == scaleSqr by y
-
-
-instance (Absolute.C a, ZeroTestable.C a, Arbitrary a) => Arbitrary (T a) where
-   arbitrary =
---      liftM2 Cons arbitrary arbitrary
-      liftM2 Cons
-         arbitrary
-         -- we have to restrict the number of polynomial coefficients,
-         -- since with the quadratic time algorithms like fourier and convolve,
-         -- in connection with Rational slow down tests too much.
-         (fmap (Poly.fromCoeffs . take 5 . Poly.coeffs) arbitrary)
-
-
-
-{-# INLINE evaluateSqRt #-}
-evaluateSqRt :: (Trans.C a) =>
-   T a -> a -> Complex.T a
-evaluateSqRt f x =
-   Bell.evaluateSqRt (bell f) x *
-   Poly.evaluate (polynomial f) (Complex.fromReal $ sqrt pi * x)
-{- ToDo: evaluating a complex polynomial for a real argument can be optimized -}
-
-
-constant :: (Ring.C a) => T a
-constant =
-   Cons Bell.constant (Poly.const one)
-
-scale :: (Ring.C a) => a -> T a -> T a
-scale x f =
-   f{polynomial = fmap (Complex.scale x) $ polynomial f}
-
-scaleComplex :: (Ring.C a) => Complex.T a -> T a -> T a
-scaleComplex x f =
-   f{polynomial = fmap (x*) $ polynomial f}
-
-
-unit :: (Ring.C a) => T a
-unit = eigenfunction0
-
-eigenfunction :: (Field.C a) => Int -> T a
-eigenfunction =
-   eigenfunctionDifferential
-
-eigenfunction0 :: (Ring.C a) => T a
-eigenfunction0 =
-   Cons Bell.unit (Poly.fromCoeffs [one])
-
-eigenfunction1 :: (Ring.C a) => T a
-eigenfunction1 =
-   Cons Bell.unit (Poly.fromCoeffs [zero, one])
-
-eigenfunction2 :: (Field.C a) => T a
-eigenfunction2 =
-   Cons Bell.unit (Poly.fromCoeffs [-(1/4), zero, one])
-
-eigenfunction3 :: (Field.C a) => T a
-eigenfunction3 =
-   Cons Bell.unit (Poly.fromCoeffs [zero, -(3/4), zero, one])
-
-
-eigenfunctionDifferential :: (Field.C a) => Int -> T a
-eigenfunctionDifferential n =
-   (\f -> f{bell = Bell.unit}) $
-   nest n (scale (-1/4) . differentiate) $
-   Cons (Bell.Cons one zero zero 2) one
-
-eigenfunctionIterative ::
-   (Field.C a, Absolute.C a, ZeroTestable.C a, Eq a) => Int -> T a
-eigenfunctionIterative n =
-   fst . head . dropWhile (uncurry (/=)) . mapAdjacent (,) $
-   eigenfunctionIteration $
-   Cons
-      Bell.unit
-      (Poly.fromCoeffs $ replicate n zero ++ [one])
-
-eigenfunctionIteration :: (Field.C a) => T a -> [T a]
-eigenfunctionIteration =
-   iterate (\x ->
-      let y = fourier x
-          px = polynomial x
-          py = polynomial y
-          c = last (Poly.coeffs px) / last (Poly.coeffs py)
-      in  y{polynomial = fmap (0.5*) (px + fmap (c*) py)})
-
-
-multiply :: (Ring.C a) =>
-   T a -> T a -> T a
-multiply f g =
-   Cons
-      (Bell.multiply (bell f) (bell g))
-      (polynomial f * polynomial g)
-
-convolve, {- convolveByDifferentiation, -} convolveByFourier :: (Field.C a) =>
-   T a -> T a -> T a
-convolve = convolveByFourier
-
-{-
-f <*> g =
-   let (foff,fint) = integrate f
-   in  fint <*> differentiate g + makeGaussPoly foff * g
-
-In principle this would work,
-but (makeGaussPoly foff * g) contains a lot of
-convolutions of Gaussian with Gaussian-polynomial-product,
-where the Gaussians have different parameters.
-
-convolveByDifferentiation f g =
-   case polynomial f of
-      fpoly ->
-         if null $ Poly.coeffs fpoly
-           then ...
-           else ...
--}
-
-convolveByFourier f g =
-   reverse $ fourier $ multiply (fourier f) (fourier g)
-
-{-
-We use a Horner like scheme
-in order to translate multiplications with @id@
-to differentations on the Fourier side.
-Quadratic runtime.
-
-fourier (Cons bell (Poly.const a + Poly.shift f))
-  = fourier (Cons bell (Poly.const a)) + fourier (Cons bell (Poly.shift f))
-  = fourier (Cons bell (Poly.const a)) + differentiate (fourier (Cons bell f))
-
-We can certainly speed this up considerably
-by decomposing the polynomial into four polynomials,
-one for each of the four eigenvalues 1, i, -1, -i.
--}
-fourier :: (Field.C a) =>
-   T a -> T a
-fourier f =
-   foldr
-      (\c p ->
-          let q = differentiate p
-          in  q{polynomial =
-                   Poly.const c +
-                   fmap (Complex.scale (1/2) . Complex.quarterLeft) (polynomial q)})
-      (Cons (Bell.fourier $ bell f) zero) $
-   Poly.coeffs $ polynomial f
-
-{- |
-Differentiate and divide by @sqrt pi@ in order to stay in a ring.
-This way, we do not need to fiddle with pi factors.
--}
-differentiate :: (Ring.C a) => T a -> T a
-differentiate f =
-   f{polynomial =
-        Differential.differentiate (polynomial f)
-        - Differential.differentiate (Bell.exponentPolynomial (bell f))
-           * polynomial f}
-
-{-
-snd $ integrate $ differentiate (Cons Bell.unit (Poly.fromCoeffs [7,7,7,7]) :: T Double)
-
-g = (bell f * poly f)'
-  = bell f * ((poly f)' - (exppoly (bell f))' * poly f)
-poly g = (poly f)' - (exppoly (bell f))' * poly f
-
-Integration means we have g and ask for f.
-
-poly f = ((poly f)' - poly g) / (exppoly (bell f))'
-
-However must start with the highest term of 'poly f',
-and thus we need to perform the division on reversed polynomials.
--}
-integrate ::
-   (Field.C a, ZeroTestable.C a) =>
-   T a -> (Complex.T a, T a)
-integrate f =
-   let fs = Poly.coeffs $ polynomial f
-       (ys,~[r]) =
-          PolyCore.divModRev
-             {-
-             We need the shortening convention of 'zipWith'
-             in order to limit the result list,
-             we cannot use list instance for (-).
-             -}
-             (zipWith (-)
-                (0 : 0 : diffRev ys)
-                (List.reverse fs))
-             (List.reverse $ Poly.coeffs $
-              Differential.differentiate $
-              Bell.exponentPolynomial $ bell f)
-   in  forcePair $
-       if null fs
-         then (zero, f)
-         else (r, f{polynomial = Poly.fromCoeffs $ List.reverse ys})
-
-diffRev :: Ring.C a => [a] -> [a]
-diffRev xs =
-   zipWith (*) xs
-      (drop 1 (iterate (subtract 1) (fromIntegral $ length xs)))
-
-{-
-integrateDefinite
-   (maybe rename integrate to antiderivative and call this one integrate)
-
-int(x^(2*n)*exp(-x^2),x=-infinity..infinity)
- = 2 * int(x^(2*n)*exp(-x^2),x=0..infinity)
-     substitute t=x^2, dt = dx * 2 * sqrt t
- = int(t^(n-1/2)*exp(-t),x=0..infinity)
- = Gamma(n+1/2)
- = (2n-1)!!/2^n * sqrt pi
-
-int(pi^n*x^(2*n)*exp(-pi*x^2),x=-infinity..infinity)
- = (2n-1)!!/2^n
-
-
-The remainder value of 'integrate'
-is the coefficient of the error function
-and this is the only part that does not vanish when approaching the limit.
-
-
-In order to stay in a field,
-we have to return a rational number
-and a transcendental part written es @exp a@.
-
-It would be interesting to see how integral inequalities
-translate to scalar inequalities containing exponential functions.
--}
-
-
-translate :: Ring.C a => a -> T a -> T a
-translate d =
-   translateComplex (Complex.fromReal d)
-
-translateComplex :: Ring.C a => Complex.T a -> T a -> T a
-translateComplex d f =
-   Cons
-      (Bell.translateComplex d $ bell f)
-      (Poly.translate d $ polynomial f)
-
-modulate :: Ring.C a => a -> T a -> T a
-modulate d f =
-   Cons
-      (Bell.modulate d $ bell f)
-      (polynomial f)
-
-turn :: Ring.C a => a -> T a -> T a
-turn d f =
-   Cons
-      (Bell.turn d $ bell f)
-      (polynomial f)
-
-reverse :: Additive.C a => T a -> T a
-reverse f =
-   Cons
-      (Bell.reverse $ bell f)
-      (Poly.reverse $ polynomial f)
-
-dilate :: Field.C a => a -> T a -> T a
-dilate k f =
-   Cons
-      (Bell.dilate k $ bell f)
-      (Poly.dilate (Complex.fromReal k) $ polynomial f)
-
-shrink :: Ring.C a => a -> T a -> T a
-shrink k f =
-   Cons
-      (Bell.shrink k $ bell f)
-      (Poly.shrink (Complex.fromReal k) $ polynomial f)
-
-{-
-We could also amplify the polynomial coefficients.
--}
-amplify :: Ring.C a => a -> T a -> T a
-amplify k f =
-   Cons
-      (Bell.amplify k $ bell f)
-      (polynomial f)
-
-
-{- |
-Approximate a @T a@ using a linear combination of translated @Bell.T a@.
-The smaller the unit (e.g. 0.1, 0.01, 0.001)
-the better the approximation but the worse the numeric properties.
-
-We cannot put all information into @amp@ of @Bell@,
-since @amp@ must be real, but is complex here by construction.
-We really need at least signed amplitudes at this place,
-since we want to represent differences of Gaussians.
--}
-approximateByBells ::
-   Field.C a =>
-   a -> T a -> [(Complex.T a, Bell.T a)]
-approximateByBells unit_ f =
-   let b = bell f
-       amps =
-          -- approximateByBellsByTranslation
-          approximateByBellsAtOnce
-             unit_
-             (Complex.scale (recip (2 * Bell.c2 b)) (Bell.c1 b))
-             (recip (2*unit_*Bell.c2 b))
-             (polynomial f)
-   in  zip (LPoly.coeffs amps) $
-       map
-          (\d -> Bell.translate d b)
-          (laurentAbscissas (unit_/2) amps)
-
-approximateByBellsAtOnce ::
-   Field.C a =>
-   a -> Complex.T a -> a -> Poly.T (Complex.T a) -> LPoly.T (Complex.T a)
-approximateByBellsAtOnce unit_ d s p =
-   foldr
-      (\x amps0 ->
-         {-
-         Decompose (bell t * (t-d)) = bell t * t - bell t * d
-         -}
-         let y = fmap (Complex.scale s) amps0
-         in  -- \t -> bell t * t
-             --    ~   (translate unit_ bell - translate (-unit_) bell) / unit_
-             LPoly.shift 1 y -
-             LPoly.shift (-1) y +
-             -- bell t * d
-             zipWithAbscissas
-                (\t z -> (Complex.fromReal t - d) * z)
-                (unit_/2) amps0 +
-             LPoly.const x)
-      (LPoly.fromCoeffs [])
-      (Poly.coeffs p)
-
-approximateByBellsByTranslation ::
-   Field.C a =>
-   a -> Complex.T a -> a -> Poly.T (Complex.T a) -> LPoly.T (Complex.T a)
-approximateByBellsByTranslation unit_ d s p =
-   foldr
-      (\x amps0 ->
-         {-
-         Decompose (bell t * (t-d)) = bell t * t - bell t * d
-         -}
-         let y = fmap (Complex.scale s) amps0
-         in  -- \t -> bell t * t
-             --    ~   (translate unit_ bell - translate (-unit_) bell) / unit_
-             LPoly.shift 1 y -
-             LPoly.shift (-1) y +
-             -- bell t * d
-             zipWithAbscissas Complex.scale (unit_/2) amps0 +
-             LPoly.const x)
-      (LPoly.fromCoeffs [])
-      (Poly.coeffs $ Poly.translate d p)
-
-zipWithAbscissas ::
-   (Ring.C a) =>
-   (a -> b -> c) -> a -> LPoly.T b -> LPoly.T c
-zipWithAbscissas h unit_ y =
-   LPoly.fromShiftCoeffs (LPoly.expon y) $
-   zipWith h
-      (laurentAbscissas unit_ y)
-      (LPoly.coeffs y)
-
-laurentAbscissas :: Ring.C a => a -> LPoly.T c -> [a]
-laurentAbscissas unit_ =
-   map (\d -> fromIntegral d * unit_) .
-   iterate (1+) . LPoly.expon
-
-
-{- No Ring instance for Gaussians
-instance (Ring.C a) => Differential.C (T a) where
-   differentiate = differentiate
--}
-
-{- laws
-differentiate (f*g) =
-   (differentiate f) * g + f * (differentiate g)
--}
diff --git a/src/MathObj/Gaussian/Variance.hs b/src/MathObj/Gaussian/Variance.hs
deleted file mode 100644
--- a/src/MathObj/Gaussian/Variance.hs
+++ /dev/null
@@ -1,206 +0,0 @@
-{-# LANGUAGE NoImplicitPrelude #-}
-{-
-We represent a Gaussian bell curve in terms of the reciprocal of its variance
-and its value at the origin.
-
-We could do some projective geometry in the exponent
-in order to also have zero variance,
-which corresponds to the dirac impulse.
-
-The Gaussians form a nice multiplicative commutative monoid.
-Maybe we should have such a structure.
-It would also be useful for the Root data type
-and a new Exponential data type.
--}
-module MathObj.Gaussian.Variance where
-
-import qualified MathObj.Polynomial as Poly
-import qualified Number.Root as Root
-
-import qualified Algebra.Transcendental as Trans
-import qualified Algebra.Algebraic      as Algebraic
-import qualified Algebra.Field          as Field
-import qualified Algebra.Absolute       as Absolute
-import qualified Algebra.Ring           as Ring
-import qualified Algebra.Additive       as Additive
-
-{-
-import Algebra.Transcendental (pi, )
-import Algebra.Ring ((*), (^), )
-import Algebra.Additive ((+))
--}
-import Test.QuickCheck (Arbitrary, arbitrary, )
-import Control.Monad (liftM2, )
-
--- import Prelude (($))
-import NumericPrelude.Numeric
-import NumericPrelude.Base
-
-
-{- |
-Since @amp@ is the square of the actual amplitude it must be non-negative.
--}
-data T a = Cons {amp, c :: a}
-   deriving (Eq, Show)
-
-instance (Absolute.C a, Arbitrary a) => Arbitrary (T a) where
-   arbitrary =
-      liftM2 Cons
-         (fmap abs arbitrary)
-         (fmap ((1+) . abs) arbitrary)
-
-
-constant :: Ring.C a => T a
-constant = Cons one zero
-
-{- |
-eigenfunction of 'fourier'
--}
-unit :: Ring.C a => T a
-unit = Cons one one
-
-{-# INLINE evaluate #-}
-evaluate :: (Trans.C a) =>
-   T a -> a -> a
-evaluate f x =
-   sqrt (amp f) * exp (-pi * c f * x^2)
-
-exponentPolynomial :: (Additive.C a) =>
-   T a -> Poly.T a
-exponentPolynomial f =
-   Poly.fromCoeffs [zero, zero, c 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 =
-   Root.sqrt $
-      Root.fromNumber (amp f)
-      `Root.div`
-      Root.sqrt (Root.fromNumber $ 2 * c f)
-
-normInfRoot :: (Field.C a) => T a -> Root.T a
-normInfRoot f =
-   Root.sqrt $ Root.fromNumber $ amp f
-
-normPRoot :: (Field.C a) => Rational -> T a -> Root.T a
-normPRoot p f =
-   Root.sqrt (Root.fromNumber (amp f))
-   `Root.div`
-   Root.rationalPower (recip (2*p)) (Root.fromNumber (fromRational' p * c f))
-
-
--- ToDo: implement NormedSpace.Sum et.al.
-norm1 :: (Algebraic.C a) => T a -> a
-norm1 f =
-   sqrt $ amp f / c f
-
-norm2 :: (Algebraic.C a) => T a -> a
-norm2 f =
-   sqrt $ amp f / (sqrt $ 2 * c f)
-
-normInf :: (Algebraic.C a) => T a -> a
-normInf f =
-   sqrt (amp f)
-
-normP :: (Trans.C a) => a -> T a -> a
-normP p f =
-   sqrt (amp f) * (p * c f) ^? (- recip (2*p))
-
-
-variance :: (Trans.C a) =>
-   T a -> a
-variance f =
-   recip $ c f * 2*pi
-
-multiply :: (Ring.C a) =>
-   T a -> T a -> T a
-multiply f g =
-   Cons (amp f * amp g) (c f + c g)
-
-powerRing :: (Trans.C a) =>
-   Integer -> T a -> T a
-powerRing p f =
-   Cons (amp f ^ p) (fromInteger p * c f)
-
-{-
-powerField does not makes sense,
-since the reciprocal of a Gaussian diverges.
--}
-
-powerAlgebraic :: (Trans.C a) =>
-   Rational -> T a -> T a
-powerAlgebraic p f =
-   Cons (amp f ^/ p) (fromRational' p * c f)
-
-powerTranscendental :: (Trans.C a) =>
-   a -> T a -> T a
-powerTranscendental p f =
-   Cons (amp f ^? p) (p * c f)
-
-{- |
-> convolve x y t =
->    integrate $ \s -> x s * y(t-s)
-
-Convergence only for @c f + c g > 0@.
--}
-convolve :: (Field.C a) =>
-   T a -> T a -> T a
-convolve f g =
-   let s = c f + c g
-   in  Cons
-          (amp f * amp g / s)
-          (c f * c g / s)
-
-{- |
-> fourier x f =
->    integrate $ \t -> x t * cis (-2*pi*t*f)
-
-Convergence only for @c f > 0@.
--}
-fourier :: (Field.C a) =>
-   T a -> T a
-fourier f =
-   Cons (amp f / c f) (recip $ c f)
-{-
-fourier (t -> exp(-(a*t)^2))
--}
-
-dilate :: (Field.C a) => a -> T a -> T a
-dilate k f =
-   Cons (amp f) $ c f / k^2
-
-shrink :: (Ring.C a) => a -> T a -> T a
-shrink k f =
-   Cons (amp f) $ c f * k^2
-
-{- |
-@amplify k@ scales by @abs k@!
--}
-amplify :: (Ring.C a) => a -> T a -> T a
-amplify k f =
-   Cons (k^2 * amp f) $ c f
-
-
-{- laws
-fourier (convolve f g) = multiply (fourier f) (fourier g)
-
-dilate k (dilate m f) = dilate (k*m) f
-
-dilate k (shrink k f) = f
-
-variance (dilate k f) = k^2 * variance f
-
-variance (convolve f g) = variance f + variance g
--}
diff --git a/src/Number/ComplexSquareRoot.hs b/src/Number/ComplexSquareRoot.hs
deleted file mode 100644
--- a/src/Number/ComplexSquareRoot.hs
+++ /dev/null
@@ -1,117 +0,0 @@
-module Number.ComplexSquareRoot where
-
--- import qualified Algebra.Algebraic as Algebraic
-import qualified Algebra.RealField as RealField
-import qualified Algebra.RealRing as RealRing
--- import qualified Algebra.Field as Field
-import qualified Algebra.Ring as Ring
-import qualified Algebra.Additive as Additive
-import qualified Algebra.ZeroTestable as ZeroTestable
-
-import qualified Number.Complex as Complex
-
-import Test.QuickCheck (Arbitrary, arbitrary, )
-
-import Control.Monad (liftM2, )
-
-import qualified NumericPrelude.Numeric as NP
-import NumericPrelude.Numeric hiding (recip, )
-import NumericPrelude.Base
-import Prelude ()
-
-{- |
-Represent the square root of a complex number
-without actually having to compute a square root.
-If the Bool is False,
-then the square root is represented with positive real part
-or zero real part and positive imaginary part.
-If the Bool is True the square root is negated.
--}
-data T a = Cons Bool (Complex.T a)
-   deriving (Show)
-
-{- |
-You must use @fmap@ only for number type conversion.
--}
-instance Functor T where
-   fmap f (Cons n x) = Cons n (fmap f x)
-
-instance (ZeroTestable.C a) => ZeroTestable.C (T a) where
-   isZero (Cons _b s) = isZero s
-
-instance (ZeroTestable.C a, Eq a) => Eq (T a) where
-   (Cons xb xs) == (Cons yb ys) =
-      isZero xs && isZero ys  ||
-      xb==yb && xs==ys
-
-instance (Arbitrary a) => Arbitrary (T a) where
-   arbitrary = liftM2 Cons arbitrary arbitrary
-
-
-fromNumber :: (RealRing.C a) => Complex.T a -> T a
-fromNumber x =
-   Cons
-      (case compare zero (Complex.real x) of
-         LT -> False
-         GT -> True
-         EQ -> Complex.imag x < zero)
-      (x^2)
-
--- htam:Wavelet.DyadicResultant.parityFlip
-toNumber :: (RealRing.C a, Complex.Power a) => T a -> Complex.T a
-toNumber (Cons n x) =
-   case sqrt x of y -> if n then NP.negate y else y
-
-
-one :: (Ring.C a) => T a
-one = Cons False NP.one
-
-inUpperHalfplane :: (Additive.C a, Ord a) => Complex.T a -> Bool
-inUpperHalfplane x =
-   case compare (Complex.imag x) zero of
-      GT -> True
-      LT -> False
-      EQ -> Complex.real x < zero
-
-mul, mulAlt, mulAlt2 :: (RealRing.C a) => T a -> T a -> T a
-mul (Cons xb xs) (Cons yb ys) =
-   let zs = xs*ys
-   in  Cons
-          ((xb /= yb) /=
-             case (inUpperHalfplane xs,
-                   inUpperHalfplane ys,
-                   inUpperHalfplane zs) of
-                (True,True,False) -> True
-                (False,False,True) -> True
-                _ -> False)
-          zs
-
-mulAlt (Cons xb xs) (Cons yb ys) =
-   let zs = xs*ys
-   in  Cons
-          ((xb /= yb) /=
-             let xi = Complex.imag xs
-                 yi = Complex.imag ys
-                 zi = Complex.imag zs
-             in  (xi>=zero) /= (yi>=zero) &&
-                 (xi>=zero) /= (zi>=zero))
-          zs
-
-mulAlt2 (Cons xb xs) (Cons yb ys) =
-   let zs = xs*ys
-   in  Cons
-          ((xb /= yb) /=
-             let xi = Complex.imag xs
-                 yi = Complex.imag ys
-                 zi = Complex.imag zs
-             in  xi*yi<zero && xi*zi<zero)
-          zs
-
-div :: (RealField.C a) => T a -> T a -> T a
-div x y = mul x (recip y)
-
-recip :: (RealField.C a) => T a -> T a
-recip (Cons b s) =
-   Cons
-      (b /= (Complex.imag s == zero && Complex.real s < zero))
-      (NP.recip s)
diff --git a/src/Number/DimensionTerm.hs b/src/Number/DimensionTerm.hs
--- a/src/Number/DimensionTerm.hs
+++ b/src/Number/DimensionTerm.hs
@@ -1,14 +1,6 @@
 {-# LANGUAGE MultiParamTypeClasses #-}
 {-# LANGUAGE FlexibleInstances #-}
 {- |
-Copyright   :  (c) Henning Thielemann 2008
-License     :  GPL
-
-Maintainer  :  numericprelude@henning-thielemann.de
-Stability   :  provisional
-Portability :  portable
-
-
 See "Algebra.DimensionTerm".
 -}
 
diff --git a/src/Number/DimensionTerm/SI.hs b/src/Number/DimensionTerm/SI.hs
--- a/src/Number/DimensionTerm/SI.hs
+++ b/src/Number/DimensionTerm/SI.hs
@@ -1,12 +1,5 @@
 {-# LANGUAGE NoImplicitPrelude #-}
 {- |
-Copyright   :  (c) Henning Thielemann 2003
-License     :  GPL
-
-Maintainer  :  numericprelude@henning-thielemann.de
-Stability   :  provisional
-Portability :  portable
-
 Special physical units: SI unit system
 -}
 
diff --git a/src/Number/OccasionallyScalarExpression.hs b/src/Number/OccasionallyScalarExpression.hs
--- a/src/Number/OccasionallyScalarExpression.hs
+++ b/src/Number/OccasionallyScalarExpression.hs
@@ -2,13 +2,6 @@
 {-# LANGUAGE MultiParamTypeClasses #-}
 {-# LANGUAGE FlexibleInstances #-}
 {- |
-Copyright   :  (c) Henning Thielemann 2004
-License     :  GPL
-
-Maintainer  :  numericprelude@henning-thielemann.de
-Stability   :  provisional
-Portability :  multi-type parameter classes (vector space)
-
 Physical expressions track the operations made on physical values
 so we are able to give detailed information on how to resolve
 unit violations.
diff --git a/src/Number/Physical.hs b/src/Number/Physical.hs
--- a/src/Number/Physical.hs
+++ b/src/Number/Physical.hs
@@ -2,13 +2,6 @@
 {-# LANGUAGE MultiParamTypeClasses #-}
 {-# LANGUAGE FlexibleInstances #-}
 {- |
-Copyright   :  (c) Henning Thielemann 2003-2006
-License     :  GPL
-
-Maintainer  :  numericprelude@henning-thielemann.de
-Stability   :  provisional
-Portability :  generic instances
-
 Numeric values combined with abstract Physical Units
 -}
 
diff --git a/src/Number/Physical/Read.hs b/src/Number/Physical/Read.hs
--- a/src/Number/Physical/Read.hs
+++ b/src/Number/Physical/Read.hs
@@ -1,12 +1,5 @@
 {-# LANGUAGE NoImplicitPrelude #-}
 {- |
-Copyright   :  (c) Henning Thielemann 2004
-License     :  GPL
-
-Maintainer  :  numericprelude@henning-thielemann.de
-Stability   :  provisional
-Portability :  multi-parameter type classes (VectorSpace.hs)
-
 Convert a human readable string to a physical value.
 -}
 
diff --git a/src/Number/Physical/Show.hs b/src/Number/Physical/Show.hs
--- a/src/Number/Physical/Show.hs
+++ b/src/Number/Physical/Show.hs
@@ -1,12 +1,5 @@
 {-# LANGUAGE NoImplicitPrelude #-}
 {- |
-Copyright   :  (c) Henning Thielemann 2004
-License     :  GPL
-
-Maintainer  :  numericprelude@henning-thielemann.de
-Stability   :  provisional
-Portability :  multi-parameter type classes (VectorSpace.hs, Normalization.hs)
-
 Convert a physical value to a human readable string.
 -}
 
diff --git a/src/Number/Physical/Unit.hs b/src/Number/Physical/Unit.hs
--- a/src/Number/Physical/Unit.hs
+++ b/src/Number/Physical/Unit.hs
@@ -1,12 +1,5 @@
 {-# LANGUAGE NoImplicitPrelude #-}
 {- |
-Copyright   :  (c) Henning Thielemann 2003-2006
-License     :  GPL
-
-Maintainer  :  numericprelude@henning-thielemann.de
-Stability   :  provisional
-Portability :  portable
-
 Abstract Physical Units
 -}
 
@@ -30,8 +23,8 @@
 
    Example: Let the quantity of length (meter, m) be the zeroth dimension
    and let the quantity of time (second, s) be the first dimension,
-   then the composed unit "m_s²" corresponds to the Map
-   [(0,1),(1,-2)]
+   then the composed unit @m/s^2@ corresponds to the Map
+   @[(0,1),(1,-2)]@.
 
    In future I want to have more abstraction here,
    e.g. a type class from the Edison project
diff --git a/src/Number/Physical/UnitDatabase.hs b/src/Number/Physical/UnitDatabase.hs
--- a/src/Number/Physical/UnitDatabase.hs
+++ b/src/Number/Physical/UnitDatabase.hs
@@ -1,12 +1,5 @@
 {-# LANGUAGE NoImplicitPrelude #-}
 {- |
-Copyright   :  (c) Henning Thielemann 2003
-License     :  GPL
-
-Maintainer  :  numericprelude@henning-thielemann.de
-Stability   :  provisional
-Portability :  portable
-
 Tools for creating a data base of physical units
 and for extracting data from it
 -}
diff --git a/src/Number/Positional.hs b/src/Number/Positional.hs
--- a/src/Number/Positional.hs
+++ b/src/Number/Positional.hs
@@ -1,12 +1,5 @@
 {-# LANGUAGE NoImplicitPrelude #-}
 {- |
-Copyright   :  (c) Henning Thielemann 2006
-License     :  GPL
-
-Maintainer  :  numericprelude@henning-thielemann.de
-Stability   :  provisional
-
-
 Exact Real Arithmetic - Computable reals.
 Inspired by ''The most unreliable technique for computing pi.''
 See also <http://www.haskell.org/haskellwiki/Exact_real_arithmetic> .
diff --git a/src/Number/Positional/Check.hs b/src/Number/Positional/Check.hs
--- a/src/Number/Positional/Check.hs
+++ b/src/Number/Positional/Check.hs
@@ -1,12 +1,5 @@
 {-# LANGUAGE NoImplicitPrelude #-}
 {- |
-Copyright   :  (c) Henning Thielemann 2006
-License     :  GPL
-
-Maintainer  :  numericprelude@henning-thielemann.de
-Stability   :  provisional
-
-
 Interface to "Number.Positional" which dynamically checks for equal bases.
 -}
 module Number.Positional.Check where
diff --git a/src/Number/SI.hs b/src/Number/SI.hs
--- a/src/Number/SI.hs
+++ b/src/Number/SI.hs
@@ -3,13 +3,6 @@
 {-# LANGUAGE FlexibleInstances #-}
 {-# LANGUAGE GeneralizedNewtypeDeriving #-}
 {- |
-Copyright   :  (c) Henning Thielemann 2003-2012
-License     :  GPL
-
-Maintainer  :  numericprelude@henning-thielemann.de
-Stability   :  provisional
-Portability :  portable
-
 Numerical values equipped with SI units.
 This is considered as the user front-end.
 -}
diff --git a/src/Number/SI/Unit.hs b/src/Number/SI/Unit.hs
--- a/src/Number/SI/Unit.hs
+++ b/src/Number/SI/Unit.hs
@@ -1,12 +1,5 @@
 {-# LANGUAGE NoImplicitPrelude #-}
 {- |
-Copyright   :  (c) Henning Thielemann 2003
-License     :  GPL
-
-Maintainer  :  numericprelude@henning-thielemann.de
-Stability   :  provisional
-Portability :  portable
-
 Special physical units: SI unit system
 -}
 
diff --git a/test/Gaussian.hs b/test/Gaussian.hs
deleted file mode 100644
--- a/test/Gaussian.hs
+++ /dev/null
@@ -1,6 +0,0 @@
-module Main where
-
-import qualified MathObj.Gaussian.Example as Example
-
-main :: IO ()
-main = Example.polyApprox
diff --git a/test/Number/ComplexSquareRoot.hs b/test/Number/ComplexSquareRoot.hs
new file mode 100644
--- /dev/null
+++ b/test/Number/ComplexSquareRoot.hs
@@ -0,0 +1,117 @@
+module Number.ComplexSquareRoot where
+
+-- import qualified Algebra.Algebraic as Algebraic
+import qualified Algebra.RealField as RealField
+import qualified Algebra.RealRing as RealRing
+-- import qualified Algebra.Field as Field
+import qualified Algebra.Ring as Ring
+import qualified Algebra.Additive as Additive
+import qualified Algebra.ZeroTestable as ZeroTestable
+
+import qualified Number.Complex as Complex
+
+import Test.QuickCheck (Arbitrary, arbitrary, )
+
+import Control.Monad (liftM2, )
+
+import qualified NumericPrelude.Numeric as NP
+import NumericPrelude.Numeric hiding (recip, )
+import NumericPrelude.Base
+import Prelude ()
+
+{- |
+Represent the square root of a complex number
+without actually having to compute a square root.
+If the Bool is False,
+then the square root is represented with positive real part
+or zero real part and positive imaginary part.
+If the Bool is True the square root is negated.
+-}
+data T a = Cons Bool (Complex.T a)
+   deriving (Show)
+
+{- |
+You must use @fmap@ only for number type conversion.
+-}
+instance Functor T where
+   fmap f (Cons n x) = Cons n (fmap f x)
+
+instance (ZeroTestable.C a) => ZeroTestable.C (T a) where
+   isZero (Cons _b s) = isZero s
+
+instance (ZeroTestable.C a, Eq a) => Eq (T a) where
+   (Cons xb xs) == (Cons yb ys) =
+      isZero xs && isZero ys  ||
+      xb==yb && xs==ys
+
+instance (Arbitrary a) => Arbitrary (T a) where
+   arbitrary = liftM2 Cons arbitrary arbitrary
+
+
+fromNumber :: (RealRing.C a) => Complex.T a -> T a
+fromNumber x =
+   Cons
+      (case compare zero (Complex.real x) of
+         LT -> False
+         GT -> True
+         EQ -> Complex.imag x < zero)
+      (x^2)
+
+-- htam:Wavelet.DyadicResultant.parityFlip
+toNumber :: (RealRing.C a, Complex.Power a) => T a -> Complex.T a
+toNumber (Cons n x) =
+   case sqrt x of y -> if n then NP.negate y else y
+
+
+one :: (Ring.C a) => T a
+one = Cons False NP.one
+
+inUpperHalfplane :: (Additive.C a, Ord a) => Complex.T a -> Bool
+inUpperHalfplane x =
+   case compare (Complex.imag x) zero of
+      GT -> True
+      LT -> False
+      EQ -> Complex.real x < zero
+
+mul, mulAlt, mulAlt2 :: (RealRing.C a) => T a -> T a -> T a
+mul (Cons xb xs) (Cons yb ys) =
+   let zs = xs*ys
+   in  Cons
+          ((xb /= yb) /=
+             case (inUpperHalfplane xs,
+                   inUpperHalfplane ys,
+                   inUpperHalfplane zs) of
+                (True,True,False) -> True
+                (False,False,True) -> True
+                _ -> False)
+          zs
+
+mulAlt (Cons xb xs) (Cons yb ys) =
+   let zs = xs*ys
+   in  Cons
+          ((xb /= yb) /=
+             let xi = Complex.imag xs
+                 yi = Complex.imag ys
+                 zi = Complex.imag zs
+             in  (xi>=zero) /= (yi>=zero) &&
+                 (xi>=zero) /= (zi>=zero))
+          zs
+
+mulAlt2 (Cons xb xs) (Cons yb ys) =
+   let zs = xs*ys
+   in  Cons
+          ((xb /= yb) /=
+             let xi = Complex.imag xs
+                 yi = Complex.imag ys
+                 zi = Complex.imag zs
+             in  xi*yi<zero && xi*zi<zero)
+          zs
+
+div :: (RealField.C a) => T a -> T a -> T a
+div x y = mul x (recip y)
+
+recip :: (RealField.C a) => T a -> T a
+recip (Cons b s) =
+   Cons
+      (b /= (Complex.imag s == zero && Complex.real s < zero))
+      (NP.recip s)
diff --git a/test/Test.hs b/test/Test.hs
--- a/test/Test.hs
+++ b/test/Test.hs
@@ -12,7 +12,7 @@
 
 import qualified Number.NonNegativeChunky as Chunky
 import qualified Number.NonNegative       as NonNegW
-import qualified Number.Positional.Check  as Absolute
+import qualified Number.Positional.Check  as Real
 import qualified Number.FixedPoint.Check  as FixedPoint
 import qualified Number.ResidueClass.Func as ResidueClass
 import qualified Number.Peano             as Peano
@@ -79,13 +79,13 @@
 {- * Reals -}
 
 testReal :: String
-testReal = Absolute.defltShow (sqrt 2 + log 2 * pi)
+testReal = Real.defltShow (sqrt 2 + log 2 * pi)
 
-testComplexReal :: Complex.T Absolute.T
+testComplexReal :: Complex.T Real.T
 testComplexReal = exp (0 +: pi) + exp (0 -: pi)
 
-showReal :: Absolute.T -> String
-showReal = Absolute.defltShow
+showReal :: Real.T -> String
+showReal = Real.defltShow
 
 
 {- * Fixed point numbers -}
diff --git a/test/Test/MathObj/PartialFraction.hs b/test/Test/MathObj/PartialFraction.hs
--- a/test/Test/MathObj/PartialFraction.hs
+++ b/test/Test/MathObj/PartialFraction.hs
@@ -16,11 +16,12 @@
 import qualified Algebra.Laws as Laws
 import qualified Test.QuickCheck as QC
 
-import Control.Monad.HT as M
 import Test.NumericPrelude.Utility (testUnit)
 import Test.QuickCheck (quickCheck)
 import qualified Test.HUnit as HUnit
 
+
+import qualified Control.Monad.HT as M
 
 import NumericPrelude.Base as P
 import NumericPrelude.Numeric as NP