Regarding Solver

[Mugdha Joshi]

I have gone through the sets module that include many functions https://docs.sympy.org/latest/modules/sets.html

So at this time what other functions are to be implemented?

Some of the things that I not found in the docs of sets module are:

1. Set builder form to roaster form or vice versa

2. Cardinality of a set

3. Fuzzy Set 

Do these need to be implemented?

To solve trigonometric and transcendental equation we can use Newton Raphson method, I have also gone through other methods like Bisection method and Regular Falsi method etc and I think Newton Raphson is best as it converges to solution much faster.

To solve transcendental equations in complex domain we can use modified Newton Raphson method as described in this paper.

https://www.iasj.net/iasj?func=fulltext&aId=41098

And for handling modular equation I think that part is completed as the issue has been closed, is there anything remaining that should be worked on?

And for linear equations in more than three variables and also non- linear equations has also been implemented,right?

The remaining is trigonometric equation in which if we apply newton raphson method then it would work like in this issue https://github.com/sympy/sympy/issues/12340

I think Newton Raphson will work

[Mugdha Joshi]

Hey Aaron Meurer, I want to know if I am going in the right direction. I want your review in this(Regarding Solver) so that I can confidently proceed further with my proposal.
Thanks in advanced.

[Jogi Miglani]

Hi Mugdha Joshi,

Its very good to know that you are interested in solvers and you know what is pending. I am not able to understand how you will be going to apply Newton Raphson method for Trigonometric equations and what will be its pros and cons. And for rest I will suggest to keep contributing and try to start contribute on one of the above topic you mentioned.

Cheers!!

On Sat, Feb 29, 2020 at 8:50 AM Mugdha Joshi <mugdha15...@gmail.com> wrote:

Hey Aaron Meurer, I want to know if I am going in the right direction. I want your review in this(Regarding Solver) so that I can confidently proceed further with my proposal.
Thanks in advanced.

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[Mugdha Joshi]

Hey Jogi Miglani, 

Thank you so much for your reply. 

I also want to know if Set buider form to roaster form, cardinality of a set, fuzzy set etc are to be implemented? 

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[Aaron Meurer]

Can you clarify what you mean by set builder form to roaster form?

Cardinality is already implemented as the size attribute, although
don't support infinite cardinals beyond just "infinity".

Fuzzy sets could be implemented, but I don't think they belong in the
set module, which deals only with classical set theory.

If the goal here is to support the solvers, I don't think these things
will be of much use. What is needed for the solvers is to improve the
existing methods of sets, so they are able to simplify in more cases.
For example, we currently have

>>> solveset(sin(x), x)
Union(ImageSet(Lambda(_n, 2*_n*pi + pi), Integers),
ImageSet(Lambda(_n, 2*_n*pi), Integers))

the union code should be able to simplify this to just
ImageSet(Lambda(n, n*pi), Integers), which is the more classical
solution to sin(x) = 0. ImageSet in particular is something that
should be improved a lot so that the solveset answers can be
simplified better.

Aaron Meurer

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[Oscar Benjamin]

There has been some work in simplifying unions of imagesets:
https://github.com/sympy/sympy/pull/18489

I think that work could be continued by someone else (better to ask
first on that pull request before working on it though).

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