Hello all,

I have implemented a module giving steps for most derivatives and some 
integrals for SymPy Gamma. However, it was suggested that at least some of 
this functionality should be added to SymPy itself. If so, what 
functionality should be added and how should it be integrated into SymPy?

The pull request is at https://github.com/sympy/sympy_gamma/pull/8. There 
is still some work left to do, which is listed in the pull request. In 
particular, integral forms involving the application of trigonometric 
identities need to be implemented.

Examples:

   - Integral involving arctangent and exponentiation: 
   
http://sympy-gamma-li.appspot.com/input/?i=integrate%28exp%28x%29%20/%20%281%20%2B%20exp%282x%29%29%29
   - Trig integral involving u-substitution: 
   http://sympy-gamma-li.appspot.com/input/?i=integrate%28sin%28sin+x%29cos+x%29
   - Trig derivative: 
   http://sympy-gamma-li.appspot.com/input/?i=diff%28cot+sin+x%29

Implementation:

The module builds a tree of rules to apply, with the first rule on the top 
of the tree. Examples of rules would be AddRule, ChainRule, RewriteRule, 
AlternativeRule (in case multiple methods exist), and so on. Separate 
functions apply the rules and return the resulting derivative or integral 
(currently derivatives and integrals are separate functions). A set of 
classes walks the tree and generates steps for the rules; there is no 
translation support but multiple output formats should work (currently only 
plaintext and HTML+LaTeX are implemented).

The code makes use of context managers, which would need to be replaced in 
order to maintain Python 2.5 compatibility. 

Thank you,
David Li

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