Coding Period Week 3

Organization : SymPy
Solvers: Completing Solveset

5 June 2016 - 11 June 2016

by Shekhar Prasad Rajak — Posted on June 8, 2016

Back to Main Blog Home page

Continue: Simplified solution for Trigonometric Equation:

PR #11188

New Problems :

  • When I tried more testcases having sqrt and other types I found new issues on reduce_imageset method. Some of the Simplified solutions contains undesired n values.

Changes in solveset/_solve_radical

  • Sometimes _solve_radical may get exp(I*x) terms and solving them we give Imageset, I added the
if isinstance(result, ImageSet) or any(isinstance(r, ImageSet) for r in result.args):
        return result

in the method.

Using factor_list in solve_trig :

  • There are many cases we can do factor of expression and solve each factor may give us more simplified solution.

  • I added the factor_list and solving each factors and union the solution.

  • When I analyzed how exp form is solved and found correct order to use factor or factor_list ,the summery is in this gist

  • I implemented the above order and shifted the reduce_imageset method in _union for ImageSet. I created _union_simiplify a helper method for _union .

_union_simplify better than my previous implementation :

  • Previous implementation was returning solution in simplified ImageSet, although it passed the all test-case except 2-3 cases. But these 2-3 test-cases taught me you are doing over simplification. So now I understood that we should not simplify the ImageSet(s) of the one factor solution, it may get simplified with other factor solution ImageSet(s).

  • Simplify them if there is difference of pi, that means club [(2n + 1) and (2n) => (npi)] or [(2n* + 1) and (2npi + 2) => (n*pi)].

So now _solve_trig uses factor_list for trig eq and then solve each factor F_i. To solve each factor F_i first do F_i.rewrite(exp) and get this exp form factors F_ij so now the unnecessary exp will come out that dont contribute in final solution. That’s why we get simplified ImageSet that will be Union with previous solution. Inside the Union => _union => _union_simplify checks for simplification with already present ImageSet. This is the process till last factor F_i.

Meanwhile :

  • After working on blog for 1 week created my own blog template powered by Jekyll. and shifted the old blog into github. PR for the blog link update in planet: pull/42

  • I edited my old template(already hosted on s-hacker.info) to make it mobile responsive. Now it works perfectly for mobile. shekharrajak.github.io

  • Found a issue in factor_list. issues/11198 , When I passed f = sqrt(2)*sin(x) -1 into solveset I got this problem.

  • To solve factor_list issue I opened a PR pull/11201.


Follow @shekharrajak