Guidance on implementing the non-linear multivariate system in the solveset

[Jogi Miglani]

Hello Everyone

I went through the solvers project in the ideas list of GSOC 18. Enhancing capabilities of solveset seems interesting to me. I went through the task list in #10006 in which the following tasks are unmarked and the completed work in Gsoc 2018 by @Yathartha22

* Non-linear multivariate system

* Equations solvable by LambertW (Transcendental equation solver)

* nested (trig) expression e.g. issue #10217

The Transcedental equation solver is in progress by @aktech . I also went through the things got implemmented in previous year by @Yathartha22 .

I am very interested towards implementing the non-linear multivariate system in the solvers. Previously I had added support for solving some special exponential equations in #15735 with the help of @smichr and @oscarbenjamin.

Mentors please guide me further on how to plan for implementing non linear multivariate system .

[Yathartha Joshi]

Hey Jogi,

It's good to see you are interested.

Non-linear multivariate system was implemented as `nonlinsolve`, you can have a look at it. Though some work needs to be done towards handling transcendental and trigonometric equations in it.

Regarding trigonometric equations, as there is no general specified way to present such equations there are issues with some variants of equations, #12340 have some discussions and useful PR's link to give you a headstart.

Also as of now `transolve` lags evaluating Lambert type equations, I had a PR #14972 which has been quiet for a while now (I actually didn't get much time post GSoC, though I will try to wrap it up soon.) If you feel to work along you are free to give suggestions.

• Handling modular equations (#13178)
• Support for transcendental equations in complex domain; will be nice additions in `transolve` .

I would also recommend you to go through `solve` module to get more idea of how things work. 

Cheers!

Yathartha Joshi