After checking old `solver` and finding ways to solve non linear system ,I 
found that one of the good way may 
be substitution method (for simple cases : 
http://www.purplemath.com/modules/syseqgen5.htm)and Using the Quadratic 
Formula(some complicated cases: 
http://www.purplemath.com/modules/syseqgen6.htm).

There are other ways also but to solve all types of Non linear system this 
method will be usefull and
I have checked that many times we get multiple solution in non linear 
system and sympy is able to solve
any type of equtaion that we get after the substitution.

Please give your valuable suggestion.

--
Shekhar Prasad Rajak

On Thursday, 4 February 2016 00:40:34 UTC+5:30, Shekhar Prasad Rajak wrote:
>
>
> Hello, 
> my name is Shekhar Prasad Rajak.I want to discuss about Solver and 
> Solveset module
> https://github.com/sympy/sympy/wiki/GSoC-2016-Ideas#solvers .I am going 
> to apply for GSoc'16, so trying to know
> what sympy community expecting.
> Solveset came to Replace all internal solve() calls 
> https://github.com/sympy/sympy/issues/8711
> So I should focus on Solveset,right?
> I have some questions :
> 1.What are the main problems/issues in Solver and Solveset right now?
> 2.Is Solveset module done?If not,what are the main features, that should 
> be added ?
> I have seen Harsh's PR : https://github.com/sympy/sympy/pull/7523
> It seems, these need some works :
> -functions solvable by LambertW
>   -functions that can be recast as polynomials with a change of variables 
> this, for example; this can be 
>   factored out of solve  where multiple generators are handled
>   -use something like this : 
> https://github.com/sympy/sympy/pull/7523#issuecomment-62198981
>   to handle the XFAILed test test_real_imag_splitting1, this will be 
> handled in the set module.
>
> 3.This is list of Issues/ Discussions I found. 
>
> https://github.com/sympy/sympy/wiki/GSoC-2014-Application-Harsh-Gupta:-Solvers#relevant-issues-discussions-and-references
>   
> <https://github.com/sympy/sympy/wiki/GSoC-2014-Application-Harsh-Gupta:-Solvers#relevant-issues-discussions-and-references>
> but I don't know, whether they are solved or not.
> Issues which are still open in github repo, need solutions.
> There are also links of pdf and research papers, I am not sure whether 
> they are implemented or not.
>
> 4.Can we use python library multiprocessing,Synchronization for the faster 
> execution?one issue was opened for the same,which is closed now.But it is 
> always better to take less time.
>
>
> --
> Shekhar Prasad Rajak
>
>

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