GSoC'19 Project in Galois Fields and related plan of action.

[shrivast...@gmail.com]

Hello,

I plan to implement almost all of the functions in Galois Fields (taking reference from MATLAB) that are currently lacking in SymPy. Here's my plan of action - the function which I plan to implement (subject to modification upon consultation with mentors):-

1. Create Galois field array

2. Add, subtract, multiply, divide polynomials over Galois field (are present in galoistools.py)

3. Add, subtract, multiply, divide elements of Galois field (are present in galoistools.py)

4. Provide default primitive polynomials for Galois field

5. Simplify or convert Galois field element formatting

6. Produce cyclotomic cosets for Galois field

7. Convolution matrix of Galois field vector

8. Find minimal polynomial of Galois field element

9. Logarithm in Galois field

10. Find roots of polynomial over prime Galois field

11. Check whether polynomial over Galois field is primitive

12. Find primitive polynomials for Galois field

13. Compute rank of matrix over Galois field

14. Find minimal polynomial of Galois field element

15. Find particular solution of Ax = b over prime Galois field

16. Inverse discrete Fourier transform of the Galois field vector

17. Discrete Fourier transform of the Galois field vector

18. Convert one binary polynomial representation to another

I'd highly appreciate any suggestions or remarks on this plan of action. If any mentor is willing to take this up as a project during the GSoC'19 summer please let me know. I'd love to receive any reviews on this plan (whether it's about addition of a few topics/algorithms or modification) so that I can start working on my proposal.

Thank You,

Regards,

Avi Shrivastava