This post summarises the work that I have done during GSoC for SymPy. The links to the Pull Requests are in chronological order under each header. For following the progress made during GSoC, see my weekly posts.

This summer has been a great learning experience and has helped me get a good exposure of test-driven development. I plan to actively review the work that has went into this project and continue contributing to SymPy. I am grateful to my mentors, Kalevi and Aaron for reviewing my work, giving me valuable suggestions, and being readily available for discussions.

## Pull Requests

This is the list of merged Pull Requests.

• sympy/sympy#14725: Add discrete module, and transforms sub-module including Fast Fourier Transform, Number Theoretic Transform, and include docstring, doctests, unit-tests.
• sympy/sympy#14745: Add convolution sub-module including convolution_fft, convolution_ntt and a general method convolution for identifying the type of convolution and handling the cyclic convolution case, and include docstring, doctests, unit-tests.
• sympy/sympy#14765: Implement Walsh Hadamard Transform and include doctests, unit-tests, docstring for the same.
• sympy/sympy#14783: Implement convolution_fwht and add support for keyword dyadic in the general convolution method, and include docstring, doctests, unit-tests.
• sympy/sympy#14816: Add a method linrec which allows evaluation of linear recurrences without obtaining closed form expressions, and include tests for the same.
• sympy/sympy#14853: Implement Möbius Transform using Yate’s Dynamic Programming method while having subset keyword for flexibility of the implementation, and include docstring, doctests, unit-tests.
• sympy/sympy#14878: Implement subset convolution and include docstring, doctests, unit-tests.
• sympy/sympy#14928: Add covering product in convolutions sub-module and include docstring, doctests, unit-tests.
• sympy/sympy#14954: Add intersecting product in convolutions sub-module and include docstring, doctests, unit-tests.

#### Documentation and Code Refinements

• sympy/sympy#14969: Improve Sphinx docs for SymPy, use plural module names - convolutions and recurrences, refine the documentation for discrete module.
• sympy/sympy#14994: Add reStructuredText file for discrete module for inclusion in Sphinx docs, which can be referred here.
• sympy/sympy#15025: Refine discrete module to fix tests using floats instead of Rationals, adding warning about sequence size for fft and other improvements.

• sympy/sympy#14712: Add .rewrite(exp) capability for instances of Pow and fix bugs in solvers module.
• sympy/sympy#14907: Fix exception handling for factorial modulo and refine the signature for general convolution method.
• Adding a user-facing public method that internally calls discrete.recurrences.linrec and possibly extending it for different types of recurrences as well.
• Making methods fft and convolution_fft efficient for both symbolic and numeric variants, as some discussion and benchmarking has been done for it and there is some work done by Colin for implementing a ComplexFloat class in sympy/sympy#12192 which would be very helpful for the same.