Some comments on your wiki entry,
https://github.com/sympy/sympy/wiki/Solveset-and-Solver-Discussion
* As you noticed there exists a diophantine equation solver written by
Thilina, that work was done before solveset was developed and imageset
weren't well developed at that time either. It will be totally a
worthwhile project to interface the diophantine solver with solveset.
I think you should think more on this direction.
* I like the direction of your idea on simplifying unions but I need
to think more on it. One of the issue I feel is, how do determine the
points between which you are talking the difference? Also can you
provide a link to the original Quora discussion.
* You can also try to implement the collapsing constants paper [1]
mentioned in the professor Fateman's paper on solvers. Though it is
not immediately useful it will help us simplfiy imagesets like {n + k,
n \in Integers, k \in Integers} and also be useful in solutions of
PDEs.
* You need not worry about "Handling large expression and nested
operation", at least for now. It will be premature optimization.
* The method to solve system of polynomial equations above looks good,
the book also mentions that they have discussed an alternate technique
in Chapter 4 using Grober Basis. Have a look at it and let us know.
* The checksol for inequalities is not required as, we can substitute
a number in the inequalities to see if it satisfies it or not, for
example you can do (2*(x-5) <= 4*x).subs(x, 0)
[1]: http://www.cs.berkeley.edu/~fateman/papers/CollapsingConstants-Soiffer.pdf
On 8 March 2016 at 15:20, Shekhar Prasad Rajak
<[email protected]> wrote:
> Right now solveset can't solve multivariate polynomial equation system .
> For example :
>
> >>> solve([x*y -1 , 4*x**2 + y**2 -5],(x,y))
> [(1/2, 2), (1, 1)]
>
> Even solve also don't give two more solutions
> `(-1/2 , -2) and (-1,-1) `
>
> I found a good way to solve these types of equations, after reading some
> good books on this topic.
> Link is : (page 9 example 2.2)
> http://people.math.gatech.edu/~aleykin3/math4803spr13/BOOK/chapter1.pdf
>
> So here we need to construct a `Res(f1,f2 )` matrix.I hope this method will
> work for most of the equation.
>
> Please share your view on this approach.
>
> I also updated the Solveset and solver wiki, please have a look :
> https://github.com/sympy/sympy/wiki/Solveset-and-Solver-Discussion
>
>
> --
> 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
>> 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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