One problem with hooking functions into the Haskell numeric
classes is right at the beginning:
class (Eq a, Show a) => Num a
where (+) (-) (*) negate abs signum fromInteger
where functions are for good reason not members of Eq or Show.
Look at
http://www.haskell.org/haskellwiki/Numeric_Prelude
for a different set of numeric classes that should suit you
better.
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