# GSoC 2018 Report Sidhant Nagpal: Discrete Transforms, Convolutions & Recurrences

This wiki page summarises the work I have done during GSoC 2018 for SymPy. The links to PRs are in chronological order under each header. For following the progress made during GSoC, see my blog for the weekly posts.

My name is Sidhant Nagpal and I have completed my third year of Bachelor's in Computer Science from University of Delhi at Netaji Subhas Institute of Technology.

## Project Synopsis

My project involved writing a new `discrete` module in SymPy to implement transforms & convolutions for finite sequences and add capabilities for recurrence evaluation. For further information, my proposal for the project can be referred.

I have implemented all that was planned plus a few additional things (discovering and fixing bugs). However, there is certainly room for improvement, and I will mention where the work could continue post GSoC.

## Pull Requests

1. sympy/sympy#14725: Add discrete module, and transforms sub-module including Fast Fourier Transform, Number Theoretic Transform, and include docstring, doctests, unit-tests.

2. 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.

3. sympy/sympy#14765: Implement Walsh Hadamard Transform and include doctests, unit-tests, docstring for the same.

4. sympy/sympy#14783: Implement `convolution_fwht` and add support for keyword `dyadic` in the general `convolution` method, and include docstring, doctests, unit-tests.

5. sympy/sympy#14816: Add a method `linrec` which allows evaluation of linear recurrences without obtaining closed form expressions, and include tests for the same.

6. 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.

7. sympy/sympy#14878: Implement subset convolution and include docstring, doctests, unit-tests.

8. sympy/sympy#14928: Add covering product in convolutions sub-module and include docstring, doctests, unit-tests.

9. sympy/sympy#14954: Add intersecting product in convolutions sub-module and include docstring, doctests, unit-tests.

#### Documentation and Code Refinements

1. sympy/sympy#14969: Improve Sphinx docs for SymPy, use plural module names - `convolutions` and `recurrences`, refine the documentation for `discrete` module.

2. sympy/sympy#14994: Add reStructuredText file for `discrete` module for inclusion in Sphinx docs, which can be referred here.

3. sympy/sympy#15025: Refine `discrete` module to fix tests using floats instead of Rationals, adding warning about sequence size for `fft` and other improvements.

1. sympy/sympy#14712: Add `.rewrite(exp)` capability for instances of `Pow` and fix bugs in `solvers` module.

2. sympy/sympy#14907: Fix exception handling for factorial modulo and refine the signature for general `convolution` method.

3. sympy/sympy-bot#18: Fix the issue of incorrect links being referred in wiki by explicitly specifying the links instead of using relative paths.

## Future Work

• 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.

## Conclusion

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.

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