################################ # Diagram information ################################ name = "A4" edges = [[1, 4], [1, 2], [2, 3], [3, 4]] nodes = [1, 2, 3, 4] internal_masses = [m2, m2, m2, m2] external_masses = [M[1], M[2], M[3], M[4]] U = x[1] + x[2] + x[3] + x[4] F = -m2*x[1]^2 + (M[1] - 2*m2)*x[1]*x[2] + (-2*m2 + s)*x[1]*x[3] + (M[4] - 2*m2)*x[1]*x[4] - m2*x[2]^2 + (M[2] - 2*m2)*x[2]*x[3] + (-2*m2 + t)*x[2]*x[4] - m2*x[3]^2 + (M[3] - 2*m2)*x[3]*x[4] - m2*x[4]^2 parameters = [M[1], M[2], M[3], M[4], m2, s, t] variables = [x[1], x[2], x[3], x[4]] χ_generic = 15 f_vector = [8, 16, 14, 6] ################################ # Component 1 ################################ D[1] = M[1] χ[1] = 13 weights[1] = [[-1, -1, 0, 0]] computed_with[1] = ["PLD_sym"] ################################ # Component 2 ################################ D[2] = M[1] - 4*m2 χ[2] = 14 weights[2] = [[-1, -1, 0, 0]] computed_with[2] = ["PLD_sym", "PLD_num", "HyperInt"] ################################ # Component 3 ################################ D[3] = M[1]^2 - 2*M[1]*M[2] - 2*M[1]*s + M[2]^2 - 2*M[2]*s + s^2 χ[3] = 14 weights[3] = [[0, 0, 0, 1]] computed_with[3] = ["PLD_sym", "PLD_num", "HyperInt"] ################################ # Component 4 ################################ D[4] = M[1]^2 - 2*M[1]*M[4] - 2*M[1]*t + M[4]^2 - 2*M[4]*t + t^2 χ[4] = 14 weights[4] = [[0, 0, 1, 0]] computed_with[4] = ["PLD_sym", "PLD_num", "HyperInt"] ################################ # Component 5 ################################ D[5] = M[1]^2*M[3] - M[1]*M[2]*M[3] - M[1]*M[2]*M[4] + M[1]*M[2]*s + M[1]*M[3]^2 - M[1]*M[3]*M[4] - M[1]*M[3]*s - M[1]*M[3]*t + M[1]*M[4]*t - M[1]*s*t + M[2]^2*M[4] - M[2]*M[3]*M[4] + M[2]*M[3]*t + M[2]*M[4]^2 - M[2]*M[4]*s - M[2]*M[4]*t - M[2]*s*t + M[3]*M[4]*s - M[3]*s*t - M[4]*s*t + s^2*t + s*t^2 χ[5] = 14 weights[5] = [[0, 0, 0, 0]] computed_with[5] = ["PLD_num", "HyperInt"] ################################ # Component 6 ################################ D[6] = M[1]^2*M[3]^2 - 4*M[1]^2*M[3]*m2 - 2*M[1]*M[2]*M[3]*M[4] + 4*M[1]*M[2]*M[3]*m2 + 4*M[1]*M[2]*M[4]*m2 - 4*M[1]*M[2]*m2*s - 4*M[1]*M[3]^2*m2 + 4*M[1]*M[3]*M[4]*m2 + 4*M[1]*M[3]*m2*s + 4*M[1]*M[3]*m2*t - 2*M[1]*M[3]*s*t - 4*M[1]*M[4]*m2*t + 4*M[1]*m2*s*t + M[2]^2*M[4]^2 - 4*M[2]^2*M[4]*m2 + 4*M[2]*M[3]*M[4]*m2 - 4*M[2]*M[3]*m2*t - 4*M[2]*M[4]^2*m2 + 4*M[2]*M[4]*m2*s + 4*M[2]*M[4]*m2*t - 2*M[2]*M[4]*s*t + 4*M[2]*m2*s*t - 4*M[3]*M[4]*m2*s + 4*M[3]*m2*s*t + 4*M[4]*m2*s*t - 4*m2*s^2*t - 4*m2*s*t^2 + s^2*t^2 χ[6] = 14 weights[6] = [[-1, -1, -1, -1]] computed_with[6] = ["PLD_sym", "PLD_num", "HyperInt"] ################################ # Component 7 ################################ D[7] = M[1]^2*m2 - 2*M[1]*M[2]*m2 + M[1]*M[2]*s - 2*M[1]*m2*s + M[2]^2*m2 - 2*M[2]*m2*s + m2*s^2 χ[7] = 14 weights[7] = [[-1, -1, -1, 0]] computed_with[7] = ["PLD_sym", "PLD_num", "HyperInt"] ################################ # Component 8 ################################ D[8] = M[1]^2*m2 - 2*M[1]*M[4]*m2 + M[1]*M[4]*t - 2*M[1]*m2*t + M[4]^2*m2 - 2*M[4]*m2*t + m2*t^2 χ[8] = 14 weights[8] = [[-1, -1, 0, -1]] computed_with[8] = ["PLD_sym", "PLD_num", "HyperInt"] ################################ # Component 9 ################################ D[9] = M[2] χ[9] = 13 weights[9] = [[0, -1, -1, 0]] computed_with[9] = ["PLD_sym", "PLD_num"] ################################ # Component 10 ################################ D[10] = M[2] - 4*m2 χ[10] = 14 weights[10] = [[0, -1, -1, 0]] computed_with[10] = ["PLD_sym", "PLD_num", "HyperInt"] ################################ # Component 11 ################################ D[11] = M[2]^2 - 2*M[2]*M[3] - 2*M[2]*t + M[3]^2 - 2*M[3]*t + t^2 χ[11] = 14 weights[11] = [[1, 0, 0, 0]] computed_with[11] = ["PLD_sym", "PLD_num", "HyperInt"] ################################ # Component 12 ################################ D[12] = M[2]^2*m2 - 2*M[2]*M[3]*m2 + M[2]*M[3]*t - 2*M[2]*m2*t + M[3]^2*m2 - 2*M[3]*m2*t + m2*t^2 χ[12] = 14 weights[12] = [[0, -1, -1, -1]] computed_with[12] = ["PLD_sym", "PLD_num", "HyperInt"] ################################ # Component 13 ################################ D[13] = M[3] χ[13] = 13 weights[13] = [[0, 0, -1, -1]] computed_with[13] = ["PLD_sym", "PLD_num"] ################################ # Component 14 ################################ D[14] = M[3] - 4*m2 χ[14] = 14 weights[14] = [[0, 0, -1, -1]] computed_with[14] = ["PLD_sym", "PLD_num", "HyperInt"] ################################ # Component 15 ################################ D[15] = M[3]^2 - 2*M[3]*M[4] - 2*M[3]*s + M[4]^2 - 2*M[4]*s + s^2 χ[15] = 14 weights[15] = [[0, 1, 0, 0]] computed_with[15] = ["PLD_sym", "PLD_num", "HyperInt"] ################################ # Component 16 ################################ D[16] = M[3]^2*m2 - 2*M[3]*M[4]*m2 + M[3]*M[4]*s - 2*M[3]*m2*s + M[4]^2*m2 - 2*M[4]*m2*s + m2*s^2 χ[16] = 14 weights[16] = [[-1, 0, -1, -1]] computed_with[16] = ["PLD_sym", "PLD_num", "HyperInt"] ################################ # Component 17 ################################ D[17] = M[4] χ[17] = 13 weights[17] = [[-1, 0, 0, -1]] computed_with[17] = ["PLD_sym", "PLD_num"] ################################ # Component 18 ################################ D[18] = M[4] - 4*m2 χ[18] = 14 weights[18] = [[-1, 0, 0, -1]] computed_with[18] = ["PLD_sym", "PLD_num", "HyperInt"] ################################ # Component 19 ################################ D[19] = m2 χ[19] = 11 weights[19] = [[-1, 0, 0, 0], [0, -1, 0, 0], [0, 0, -1, 0], [0, 0, 0, -1]] computed_with[19] = ["PLD_sym", "PLD_num"] ################################ # Component 20 ################################ D[20] = m2 - 1//4*s χ[20] = 14 weights[20] = [[-1, 0, -1, 0]] computed_with[20] = ["PLD_sym", "PLD_num", "HyperInt"] ################################ # Component 21 ################################ D[21] = m2 - 1//4*t χ[21] = 14 weights[21] = [[0, -1, 0, -1]] computed_with[21] = ["PLD_sym", "PLD_num", "HyperInt"] ################################ # Component 22 ################################ D[22] = s χ[22] = 13 weights[22] = [[-1, 0, -1, 0]] computed_with[22] = ["PLD_sym", "PLD_num"] ################################ # Component 23 ################################ D[23] = t χ[23] = 13 weights[23] = [[0, -1, 0, -1]] computed_with[23] = ["PLD_sym", "PLD_num"]