GSoC 2021 Report: Improving Series Expansion (Sidharth Mundhra) - sympy/sympy GitHub Wiki

This report summarizes the work I have done as a part of GSoC 2021 for SymPy. The links to the PRs are in chronological order.

About Me

I am Sidharth Mundhra, a third-year undergraduate student pursuing a major in Mechanical Engineering and a minor in Computer Science from the Indian Institute of Technology (IIT) Bombay.

Project Synopsis

The primary goal of my project was to improve the series expansions capability of SymPy, by fixing the _eval_as_leading_term methods of various functions. These methods are used to give the leading (first) term of the series expansion and are used directly to calculate limits. When this method raises an error, the highly-recursive gruntz method is called, which is slower. Fixing the various issues allows more limits to be computed through the leading term method rather than gruntz, making overall limit computations faster. My weekly blogs can be found here.

Pull Requests

Merged

  • #21253: Fixes a few buggy _eval_as_leading_term methods: This PR changed leading term methods of Add and Pow to simplify irrational and imaginary expressions, and also those of tan and cot so that they can work for angles outside their principle domain. These changes also led to a few bug fixes which can be seen linked to the PR.

  • #21589: A few leading term methods changed: This PR fixes a long-standing issue of incorrect handling of leading term at singularities. Earlier, for compatibility reasons, the expression itself was returned, which is incorrect. exp(1/x) does not have any leading term as x->0, so an error must be raised. This PR changes Pow, exp, factorial and gamma _eval_as_leading_term to raise PoleError when the argument is unbounded. Apart from that, this PR also -

    • Added LambertW, SingularityFunction, fresnels, fresnelc, erfi _eval_as_leading_term` methods
    • Fixed besselj and bessely leading term methods
    • Added SingularityFunction power series expansion

  • #21731: Improvements to Limit.doit: This PR focused on removing and re-ordering heuristics of the Limit.doit method. In the process, leading term methods for many special functions were added.

  • #21775: Limit bug fixes: This PR focused on fixing a few new (not regressions) bugs that had popped up since the start of GSoC. The details can be found in the release notes section.

  • #21805: Fixes regression in limits: Due to a change in code path in a previous PR, a masked bug was revealed, leading to the failure of a limit that passed previously. This bug was identified and fix, and other similar places in the code were also patched.

Work in Progress

  • #21837: mrv_leadterm changes: This PR is focusing on removing the fragile calculate_series method. After the changes in the previous PRs, this method is no longer required, as we can simply calculate the leading term instead the series in most cases, and in other cases, we could call series. compute_leading_term is also being deprecated (see #21843 for more details).

  • Improving documentation of series related functions

Issues Opened

Future Work

  • A lot of special functions now have an _eval_as_leading_term method, but a few remain. It should also be added for them, along with _eval_nseries and _eval_aseries
  • Make Order substitution work better. This was mentioned in my proposal but was not implemented.
  • Implement the bound parameter of aseries. It was found during the summer that the bound parameter's intentions were not clear from the docstring, and it did not perform the presumed functions. Its purpose should be thought of and mentioned clearly, and then it should be implemented.
  • Extending ring_series module

Conclusion

The series module now attempts to find the limit by calculating the leading term of the series expansion, before jumping into the gruntz method. This is sufficient, and faster than gruntz in many cases, hence speeding up the limit calculations. Proper exception raising and handling have also been implemented, replacing make-shift solutions, making the module more robust, and fixing close to 20 issues. As the series module reaches a good extent of development, extending the faster ring_series module should be the next target for development.

This summer has been a great exposure to undertaking a large coding project, and working while documenting and writing tests I am grateful to my mentors, Kalevi Suominen and Sachin Agarwal for being readily available for discussions throughout the summer, which smoothened the development process. I plan to continue contributing to SymPy and will also try to help the new contributors.