GSoC 2020 - Week 8

Key highlights of this week’s work are:

• Fixed incorrect limit evaluation related to LambertW function

  • This was a minor bug fix. We added the _singularities feature to the LambertW function so that its limit gets evaluated using the meromorphic check already present in the limit codebase.
    
    

• Fixed errors in assumptions when rewriting RisingFactorial / FallingFactorial as gamma or factorial

  • This was a long pending issue. The rewrite to gamma or factorial methods of RisingFactorial and FallingFactorial did not handle all the possible cases, which caused errors in some evaluations. Thus, we decided to come up with a proper rewrite using Piecewise which accordingly returned the correct rewrite depending on the assumptions on the variables. Handling such rewrites using Piecewise is never easy, and thus there were a lot of failing testcases. After spending a lot of time debugging and fixing each failing testcase, we were finally able to merge this.

This marks the end of Phase-2 of the program. I learnt a lot during these two months and gained many important things from my mentors.

GSoC 2020 - Week 7

Key highlights of this week’s work are:

• Improved the limit evaluations of Power objects

  • This PR improves the limit evaluations of Power objects. We first check if the limit expression is a Power object and then accordingly evaluate the limit depending on different cases. First of all, we express b**e in the form of exp(e*log(b)). After this, we check if e*log(b) is meromorphic and accordingly evaluate the final result. This check helps us to handle the trivial cases in the beginning itself.

    Now, if e*log(b) is not meromorphic, then we separately evaluate the limit of the base and the exponent. This helps us to determine the indeterminant form of the limit expression if present. As we know, there are 3 indeterminate forms corresponding to power objects: 0**0, oo**0, and 1**oo, which need to be handled carefully. If there is no indeterminate form present, then no further evaluations are required. Otherwise, we handle all the three cases separately and correctly evaluate the final result.

    We also added some code to improve the evaluation of limits having Abs() expressions. For every Abs() term present in the limit expression, we replace it simply by its argument or the negative of its argument, depending on whether the value of the limit of the argument is greater than zero or less than zero for the given limit variable.

    Finally, we were able to merge this after resolving some failing testcases.
    
    

• Fixed limit evaluations involving error functions

  • The incorrect limit evaluations of error functions were mainly because the tractable rewrite was wrong and did not handle all the possible cases. For a proper rewrite, it was required that the limit variable be passed to the corresponding rewrite method. This is because, to define a correct rewrite we had to evaluate the limit of the argument of the error function, for the passed limit variable. Thus, we added a default argument limitvar to all the tractable rewrite methods and resolved this issue. While debugging, we also noticed that the _eval_as_leading_term method of error function was wrong, hence it was also fixed.

    Finally, we were able to merge this after resolving some failing testcases.

GSoC 2020 - Week 6

Key highlights of this week’s work are:

• Fixed RecursionError and Timeout in limit evaluations

  • The Recursion Errors in limit evaluations were mainly due to the fact that the indeterminant form of 1**oo was not handled accurately in the mrv() function of the Gruntz algorithm. So, some minor changes were required to fix those.

    The major issue was to handle those cases which were timing out. On deep digging, we identified that the cancel() function of polytools.py was the reason. Thus, we decided to completely transform the cancel() function to speed up its algorithm. Now after this major modification, many testcases were failing as the cancel() function plays an important role in simplifying evaluations and is thus used at many places across the codebase. Therefore, a lot of time was spent in debugging and rectifying these testcases.

    Finally we were able to merge this, enhancing the limit evaluation capabilities of SymPy.

GSoC 2020 - Week 5

Key highlights of this week’s work are:

• Adds cdir parameter to handle series expansions on branch cuts

  • Finally, after spending almost 2 weeks on this, we were able to merge the PR, adding a very important functionality of series expansions on the branch cuts to the codebase. Previously, either SymPy raised some error or the series expansion was computed incorrectly, when the value in the input was on the branch cut. But now, for most of the functions, the expansion produced is correct.

    Not only this, we added the cdir parameter to leadterm and as_leading_term functions as well. We even extended the functionality a bit to the limits module, so now, limits of values lying on the branch cuts of a function are also computed correctly in most cases.

    We are planning to extend this functionality to all the remaining special functions and wherever else possible to make the codebase even more robust.

GSoC 2020 - Week 4

Key highlights of this week’s work are:

• Fixed incorrect evaluation caused due to subfactorial in limit_seq expression

  • This was a minor bug fix. The functionality of rewriting the subfactorial term present in an expression into an equivalent term expressed in the form of factorial or gamma was added which helped resolve the issue.
    
    

• Adds cdir parameter to handle series expansions on branch cuts

  • Currently, many functions in the codebase are unable to produce correct series expansions on branch cuts. As a result, the limit evaluation takes place incorrectly for these functions when the limiting value lies on the branch cuts.

    Thus, we have decided to come up with a parameter named cdir which stands for complex direction and it indicates the direction from which the series expansion is required, thus helping us to produce the correct series expansion. Special care needs to be taken while handling series expansions on the branch points.

    Once we are finished with this work, it will be a major enhancement to the limit evaluation and series expansion capabilities of SymPy.

This marks the end of Phase-1 of the program. I learnt a lot during this one month and gained many important things from my mentors.