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plonkathon's Issues

Make `k_1 = 2`, `k_2 = 3` top-level constants

k_1, k_2 are quadratic non-residues used to create distinct cosets in the permutation argument. This implementation hard-codes them to k_1 = 2, k_2 = 3; these should be declared as top-level constants.

Screenshot 2023-01-28 at 3 18 24 PM

Basis.MONOMIAL should be Basis.LAGRANGE

plonkathon/poly.py

Lines 161 to 163 in cea88fd

return Polynomial(
[v * inv_offset**i for (i, v) in enumerate(shifted_coeffs)],
Basis.LAGRANGE,

Basis.LAGRANGE should be replaced for Basis.MONOMIAL here, as well as including FFT. All-in-all,

return Polynomial(
            [v * inv_offset**i for (i, v) in enumerate(shifted_coeffs)],
            Basis.LAGRANGE,
 )

should be replaced by

return Polynomial(
            [v * inv_offset**i for (i, v) in enumerate(shifted_coeffs)],
            Basis.MONOMIAL,
 ).fft()

Root of unity

Hello,

Screenshot 2024-01-02 at 12 30 12
I don't understand where the number 5 comes from in the root_of_unity function, could you please explain it?

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