Coding Period Week 5

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 [68]: x, y, z, r, t = symbols('x, y, z, r, t', real = True)

In [69]: soln = solveset(sqrt(r)*Abs(tan(t))/sqrt(tan(t)**2 + 1) + x*tan(t),x,S.Reals)

In [70]: soln
Out[70]:
          ⎧      √r⋅│tan(t)│      ⎫
(-∞, ∞) ∩ ⎪───────────────────────⎪
          ⎨   _____________       ⎬
          ⎪  ╱    2               ⎪
          ⎩╲╱  tan (t) + 1 ⋅tan(t)⎭

In [71]: soln = solveset(sqrt(r)*Abs(tan(t))/sqrt(tan(t)**2 + 1) + x*tan(t),x)

In [72]: soln
Out[72]:
⎧     -√r⋅│tan(t)│      ⎫
⎪───────────────────────⎪
⎨   _____________       ⎬
⎪  ╱    2               ⎪
⎩╲╱  tan (t) + 1 ⋅tan(t)⎭

In other words :

In [1]: Intersection(FiniteSet(-x), S.Reals)
Out[1]: (-∞, ∞) ∩ {x}

In [2]: Intersection(FiniteSet(x), S.Reals)
Out[2]: 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

• If someone wants to see the changes I did in nonlinsolve then check these gist nonlinsolve_till_24june_2016, nonlinsolve_till_21jun2016.py.

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..