Automatic Differentiation
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Implementations of Functional differentiation:
- fad
- Vector-space
- http://comonad.com/haskell/monoids/dist/doc/html/monoids/Data-Ring-Module-AutomaticDifferentiation.html
Power Series
You may count arithmetic with power series also as Automatic Differentiation, since this means just working with all derivatives simultaneously.
Implementation with Haskell 98 type classes: http://darcs.haskell.org/htam/src/PowerSeries/Taylor.hs
With advanced type classes in Numeric Prelude: http://hackage.haskell.org/packages/archive/numeric-prelude/0.0.5/doc/html/MathObj-PowerSeri es.html