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@@ -36,7 +36,7 @@ assert omega^n == 1
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# sxy + (s - 1)(x + y) - z = 0
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# s(s - 1) = 0
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-# F1(A1 - 1) + F2 A1 + F3(1 - A1)(A2 + A3) + F4(A1 A2 A3 - A4) - I = 0
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+# F1(A1 - 1) + F2 (A1 - I) + F3((1 - A1)(A2 + A3) - A4) + F4(A1 A2 A3 - A4) = 0
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A = []
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F = []
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@@ -65,7 +65,7 @@ F_1_2, F_2_2, F_3_2, F_4_2 = 0, 1, 0, 0
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I_2 = 0
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# Row 3
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-A_1_3, A_2_3, A_3_3, A_4_3 = var_s, var_s, var_zero, 0
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+A_1_3, A_2_3, A_3_3, A_4_3 = var_s, var_s, var_zero, var_zero
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F_1_3, F_2_3, F_3_3, F_4_3 = 0, 0, 1, 0
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I_3 = 0
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@@ -80,15 +80,15 @@ F_1_5, F_2_5, F_3_5, F_4_5 = 0, 0, 1, 0
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I_5 = 0
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# Row 6
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-A_1_6, A_2_6, A_3_6, A_4_6 = var_zero, var_sxy, var_1s_xy, 0
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+A_1_6, A_2_6, A_3_6, A_4_6 = var_zero, var_sxy, var_1s_xy, var_z
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F_1_6, F_2_6, F_3_6, F_4_6 = 0, 0, 1, 0
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-I_6 = var_z
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+I_6 = 0
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# Row 7
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# Empty row
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-A_1_7, A_2_7, A_3_7, A_4_7 = 0, 0, 0, 0
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-F_1_7, F_2_7, F_3_7, F_4_7 = 0, 0, 0, 0
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-I_7 = 0
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+A_1_7, A_2_7, A_3_7, A_4_7 = var_z, 0, 0, 0
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+F_1_7, F_2_7, F_3_7, F_4_7 = 0, 1, 0, 0
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+I_7 = var_z
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# Row 8
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# Empty row
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@@ -109,9 +109,9 @@ I = [I_1, I_2, I_3, I_4, I_5, I_6, I_7, I_8]
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for A_1_i, A_2_i, A_3_i, A_4_i, F_1_i, F_2_i, F_3_i, F_4_i, I_i in zip(
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A1, A2, A3, A4, F1, F2, F3, F4, I):
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assert (F_1_i * (A_1_i - 1)
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- + F_2_i * A_1_i
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- + F_3_i * (1 - A_1_i) * (A_2_i + A_3_i)
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- + F_4_i * (A_1_i * A_2_i * A_3_i - A_4_i) - I_i) == 0
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+ + F_2_i * (A_1_i - I_i)
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+ + F_3_i * ((1 - A_1_i) * (A_2_i + A_3_i) - A_4_i)
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+ + F_4_i * (A_1_i * A_2_i * A_3_i - A_4_i)) == 0
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a_1_X = P.lagrange_polynomial((omega^i, A_1_i) for i, A_1_i in enumerate(A1))
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a_2_X = P.lagrange_polynomial((omega^i, A_2_i) for i, A_2_i in enumerate(A2))
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@@ -136,3 +136,17 @@ for i, (A_1_i, A_2_i, A_3_i, A_4_i, F_1_i, F_2_i, F_3_i, F_4_i, I_i) in \
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assert f_3_X(omega^i) == F_3_i
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assert f_4_X(omega^i) == F_4_i
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+# beta, gamma
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+
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+y = K.random_element()
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+
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+gate_0 = f_1_X * (a_1_X - 1)
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+gate_1 = f_2_X * (a_1_X - a_5_X)
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+gate_2 = f_3_X * ((1 - a_1_X) * (a_2_X + a_3_X) - a_4_X)
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+gate_3 = f_4_X * (a_1_X * a_2_X * a_3_X - a_4_X)
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+
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+h = gate_0 + y * gate_1 + y^2 * gate_2 + y^3 * gate_3
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+t = X^n - 1
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+for i in range(n):
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+ assert h(omega^i) == 0
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+
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narodnik