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script/research: plonk_kate copy constraints.

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parazyd
2021-11-25 12:38:24 +01:00
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script/research/halo/plonk_kate.sage
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@@ -162,3 +162,26 @@ q_R_coeffs = inverse_matrix(H) * q_R
q_O_coeffs = inverse_matrix(H) * q_O
q_M_coeffs = inverse_matrix(H) * q_M
q_C_coeffs = inverse_matrix(H) * q_C
# The copy constraints involving left, right, output values are encoded as
# polynomials S_sigma_1, S_sigma_2, S_sigma_3 using the cosets we found
# earlier. The roots of unity H are used to label entries in vector a,
# the elements of k1H are used to label entries in vector b, and vector c is
# labeled by the elements of k2H.
print("Copy constraints:")
print(f"a: {a}")
print(f"b: {b}")
print(f"c: {c}")
# a1 = b1, a2 = b2, a3 = b3, a4 = c1
sigma_1 = vector([k1H[0], k1H[1], k1H[2], k2H[0]])
print(f"sigma_1: {sigma_1}")
# b1 = a1, b2 = a2, b3 = a3, b4 = c2
sigma_2 = vector([H[0], H[1], H[2], k2H[1]])
print(f"sigma_2: {sigma_2}")
# c1 = a4, c2 = b4, c3 = c4, c4 = c3
sigma_3 = vector([H[3], k1H[3], k2H[3], k2H[2]])
print(f"sigma_3: {sigma_3}")
S_sigma_1_coeffs = inverse_matrix(H) * sigma_1
S_sigma_2_coeffs = inverse_matrix(H) * sigma_2
S_sigma_3_coeffs = inverse_matrix(H) * sigma_3