Great that you are working on solvers.
> Multivariate functions with non point solution: (solvemv)
> ```python
> In [0] solveset((x - 1)*(y - 2), (x, y))
> Out[1] {{1, arbitrary}, {arbitrary, 2}}
> ```
> or we may return:
> `Out[1] {{1, (-oo, oo)}, {(-oo, oo), 2}}`
The output should rather be a set of ProductSets rather than a set of sets.
General FiniteSet is unordered so {(-oo, oo), 2} is same as {2, (-oo, oo)}.
This example shows how you can define and use a product set.
```
In [9]: s = FiniteSet(2)*Interval(-oo, oo)
In [10]: s
Out[10]: {2} x (-oo, oo)
In [11]: (2, 0) in s
Out[11]: True
```
> Solve System of Equation: (solvesys)
> (For system of Equation, we can have this):
> ```python
> In [0] solveset([x + y == 1, x - y == 0], (x,y))
> Out[1] {{1/2, 1/2}}
> ```
It has the same issue as I mentioned above {1/2, 1/2} is unordered. You can
use a FinteSet set of ordered tuple.
```
In [14]: FiniteSet((S(1)/2, S(1)/2))
Out[14]: {(1/2, 1/2)}
```
> we also need to extend singularities module (though useful in general)
+1
I suggest that you create a detailed plan of "how" you are going to solve
multivariate equations and how will you find a singular point. I did a
shallow
study of the current multivariate solver in `solve`. The writeup is here:
http://hargup.github.io/posts/week-7.html Try searching for some literature,
dig into other older CAS and probably you should ask professor Fateman for
help. He can be harsh but if you have a thick skin he can be a lot of help
too.
On Fri Feb 06 2015 at 2:28:21 AM AMiT Kumar <dtu.a...@gmail.com> wrote:
> Thanks, Jason
>
> I have pasted this in my Application Draft and moved to Sympy Wiki:
>
> https://github.com/sympy/sympy/wiki/GSoC-2015-Application-AMiT-Kumar--Solvers-:-Extending-Solveset
>
>
>
> Cheers!
> AMiT Kumar
> 3rd Year Undergrad
> Delhi Technological University
> www.iamit.in
>
> On Friday, February 6, 2015 at 2:10:49 AM UTC+5:30, Jason Moore wrote:
>
>> Amit,
>>
>> This sounds good. You should move this content to the SymPy wiki and use
>> it as a starting point for your application submission.
>>
>
>>
>> Jason
>> moorepants.info
>> +01 530-601-9791
>>
>> On Thu, Feb 5, 2015 at 10:38 AM, AMiT Kumar <dtu....@gmail.com> wrote:
>>
> Hi,
>>> I am AMiT Kumar, I would be GSoC Applicant to SymPy this year. I have
>>> been following the SymPy Community for quite sometime now and have also got
>>> around 11-12 patches Merged in the Code base. So, now, I have got a decent
>>> idea of `How things works`.
>>>
>>> I would like to work on Solvers as Mentioned on the Ideas Page. Last
>>> year Harsh Gupta did a very good job by Rewriting the Univariate solvers
>>> (solveset.py), I have gone through his work. After having conversation with
>>> him and digging into solveset, I got to know there is still a lot of work
>>> which needs to be done.
>>>
>>> I could see a couple of entry points on the Ideas page:
>>> https://github.com/sympy/sympy/issues/8725 (I have Merged a PR for
>>> this)
>>> https://github.com/sympy/sympy/issues/8711 (Replace all internal
>>> solve() calls with solveset() ): TODO
>>>
>>> Things, I would like to implement in solveset includes:
>>>
>>> Multivariate Equation solving:
>>>
>>> I think for solving multivariate equations, the order of variables
>>> should be given as input, so that we don't need to have a dict as output
>>> and we can return Set, as if we automatically detect variables, we need to
>>> output the dict of results.
>>>
>>> - Multivariate functions with non point solution: (solvemv)
>>> -
>>>
>>> In [0] solveset((x - 1)*(y - 2), (x, y))
>>> Out[1] {{1, arbitrary}, {arbitrary, 2}}
>>>
>>>
>>> or we may return:
>>>
>>> Out[1] {{1, (-oo, oo)}, {(-oo, oo), 2}}
>>>
>>>
>>>
>>> - Multivariate functions with point solutions: (solvemv)
>>>
>>>
>>>
>>> -
>>>
>>> In [0] solveset(x**2 + y**2, (x, y))
>>> Out[1] {0, 0}
>>>
>>>
>>> Solve System of Equation: (solvesys)
>>> (For system of Equation, we can have this):
>>>
>>>
>>> -
>>>
>>> In [0] solveset([x + y == 1, x - y == 0], (x,y))
>>> Out[1] {{1/2, 1/2}}
>>>
>>> - For inequality solver (or for solvers in general) we also need to
>>> extend singularities module (though useful in general), so as to prevent
>>> getting wrong results, caused due to incorrect simplification of
>>> expression, as we saw in this issue: https://github.com/symp
>>> y/sympy/issues/8715 , Example: x + 1/x > -2 + 1/x this inequality
>>> is written as expr = expr. lhs - expr.rhs , which cancels 1/x and gives
>>> wrong result, by including singular point in the solution.
>>> - inequality solver in solveset currently uses inequalities.py
>>> (dependent on solve) (some discussion here: https://groups.google.co
>>> m/forum/#!topic/sympy/Yp5NqrXmp2U
>>> <https://groups.google.com/forum/#!topic/sympy/Yp5NqrXmp2U>). It is
>>> related to the next point below.
>>> - All internal solve() calls needs to be replaced with solveset() , this
>>> is very important for bringing out the solveset from sandbox to
>>> eventually replace solve(). (we need to consider the output API
>>> (return type) also while replacing).
>>> - We also need to extend the set - boolean (relational) conversion
>>> methods to handle multivariate variables.
>>> - Complex set Infrastructure is also not there (though I see a WIP
>>> PR for that), and yes we also need to see what other set capabilities we
>>> need to implement to support various other kinds of solutions.
>>>
>>> And also other solvers as mentioned on ideas page like 'Equations
>>> solvable by LambertW function' also needs to work.
>>>
>>> I would love to get feedback from the community before presenting my
>>> proposal.
>>>
>>> Cheers!
>>> AMiT Kumar
>>> 3rd Year Undergrad
>>> Delhi Technological University
>>> www.iamit.in
>>>
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