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

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