# Coding Period Week 5

Organization : SymPy
Solvers: Completing Solveset

19 June 2016 - 25 June 2016

by Shekhar Prasad Rajak — Posted on June 21, 2016

Continue- nonlinsolve :

PR #11111

• I found the case where complex solution is missed. When `solve_poly_system` is solving polynomial equation and that result is used in solving non polynomial-equation to get other soln. May be `solve_poly_system` return only real solution( so complex solution is not being used for further steps) thats why further step is with this real solution.

• It seems `solve_poly_system` is doing it’s job since it is not designed for all solution. But we have `substitution` method using `solveset_real` and `solveset_complex` and retuning all solutionn. In new commits I improved the code and now `substitution` method can solve all kind of system independently.

• I come across these kind of situation many times :

``````In : x, y, z, r, t = symbols('x, y, z, r, t', real = True)

In : soln = solveset(sqrt(r)*Abs(tan(t))/sqrt(tan(t)**2 + 1) + x*tan(t),x,S.Reals)

In : soln
Out:
⎧      √r⋅│tan(t)│      ⎫
(-∞, ∞) ∩ ⎪───────────────────────⎪
⎨   _____________       ⎬
⎪  ╱    2               ⎪
⎩╲╱  tan (t) + 1 ⋅tan(t)⎭

In : soln = solveset(sqrt(r)*Abs(tan(t))/sqrt(tan(t)**2 + 1) + x*tan(t),x)

In : soln
Out:
⎧     -√r⋅│tan(t)│      ⎫
⎪───────────────────────⎪
⎨   _____________       ⎬
⎪  ╱    2               ⎪
⎩╲╱  tan (t) + 1 ⋅tan(t)⎭

``````

In other words :

``````In : Intersection(FiniteSet(-x), S.Reals)
Out: (-∞, ∞) ∩ {x}

In : Intersection(FiniteSet(x), S.Reals)
Out: ℝ ∩ {x}

``````

So I am not able to extract the `-x` here. Because of this `nonlinsolve` returning some extra soln. One case is in test file : `test_issue_5132`.

I opened a PR for this #11280

previous PRs update :

• #11188 - Simplified Solution for Trigonometric equation : I did some minor changes.Now I hope it is good to go.

• #11234 - Connecting Diophantine and solveset to get Integer solution: added some testcases. I have defined `solveset_integers` for this, it take take list of symbols(to get soln in that order).t But Currently solveset takes one symbol. I hope this PR is good to go.

• 11257 - solveset univariate trig inequality solvers : Actually to simplify the soln I need to use PR #11188, so if it got merged that code will help me in this PR.

Meanwhile :

• I worked on these previous PRs regarding issues I reported #11239, 11280.

continue..