Hi Aaron and Sudhanshu,

Since I last posted on this thread I have tackled some issues related to 
assumptions. I also read Aaron's post on the mailing list explaining the 
need for new assumptions and I went through Sudhanshu's work last summer. 
After some discussion on SymPy Gitter, I have a much more clear picture of 
the state of assumptions right now.

Aaron, you said that there's still a lot of work need to be done on 
assumptions. I have listed down a list of tasks that I think are still 
pending in assumptions. Please add to it if you think I'm still missing 
something. It will help me to include the list of tasks in my proposal.

1. Inconsistencies between old assumptions and new assumptions: I think 
this is one of the biggest roadblocks for assumptions. (extended_real/real)

In [5]: ask(Q.real(oo))
Out[5]: False


In [6]: oo.is_real
Out[6]: True


2. Improve refine: Currently, refine is very slow. Issue 9714 
<https://github.com/sympy/sympy/issues/9714>

3. Old assumptions should call new assumptions internally.
Currently, old assumptions (for eg. `x.is_real`) are evaluated using 
`_eval_is_real` method. Instead, we need to use new assumptions. This is 
not done yet, I think. So, I think this can be included under GSOC 2016.

4. New assumptions
    - for matrices/matrix symbol: Issue 8803 
<https://github.com/sympy/sympy/issues/8803>, Issue 10265 
<https://github.com/sympy/sympy/issues/10265>
    - for functions: Issue 8760 <https://github.com/sympy/sympy/issues/8760>

Please let me know yours thoughts on this. Thank you.
Anish Shah

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