################################ # Diagram information ################################ name = "A4" edges = [[1, 4], [1, 2], [2, 3], [3, 4]] nodes = [1, 2, 3, 4] internal_masses = [m[1], m[2], m[3], m[4]] external_masses = [M[1], M[2], M[3], M[4]] U = x[1] + x[2] + x[3] + x[4] F = -m[1]*x[1]^2 + (M[1] - m[1] - m[2])*x[1]*x[2] + (-m[1] - m[3] + s)*x[1]*x[3] + (M[4] - m[1] - m[4])*x[1]*x[4] - m[2]*x[2]^2 + (M[2] - m[2] - m[3])*x[2]*x[3] + (-m[2] - m[4] + t)*x[2]*x[4] - m[3]*x[3]^2 + (M[3] - m[3] - m[4])*x[3]*x[4] - m[4]*x[4]^2 parameters = [M[1], M[2], M[3], M[4], m[1], m[2], m[3], m[4], 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] = 14 weights[1] = [[0, 0, 1, 1]] computed_with[1] = ["PLD_sym"] ################################ # Component 2 ################################ D[2] = M[1]^2 - 2*M[1]*M[2] - 2*M[1]*s + M[2]^2 - 2*M[2]*s + s^2 χ[2] = 14 weights[2] = [[0, 0, 0, 1]] computed_with[2] = ["PLD_sym", "HyperInt"] ################################ # Component 3 ################################ D[3] = M[1]^2 - 2*M[1]*M[4] - 2*M[1]*t + M[4]^2 - 2*M[4]*t + t^2 χ[3] = 14 weights[3] = [[0, 0, 1, 0]] computed_with[3] = ["PLD_sym", "HyperInt"] ################################ # Component 4 ################################ D[4] = M[1]^2 - 2*M[1]*m[1] - 2*M[1]*m[2] + m[1]^2 - 2*m[1]*m[2] + m[2]^2 χ[4] = 14 weights[4] = [[-1, -1, 0, 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 - 2*M[1]^2*M[3]*m[3] - 2*M[1]^2*M[3]*m[4] + M[1]^2*m[3]^2 - 2*M[1]^2*m[3]*m[4] + M[1]^2*m[4]^2 - 2*M[1]*M[2]*M[3]*M[4] + 2*M[1]*M[2]*M[3]*m[1] + 2*M[1]*M[2]*M[3]*m[4] + 2*M[1]*M[2]*M[4]*m[3] + 2*M[1]*M[2]*M[4]*m[4] - 2*M[1]*M[2]*m[1]*m[3] + 2*M[1]*M[2]*m[1]*m[4] + 2*M[1]*M[2]*m[3]*m[4] - 2*M[1]*M[2]*m[4]^2 - 4*M[1]*M[2]*m[4]*s - 2*M[1]*M[3]^2*m[1] - 2*M[1]*M[3]^2*m[2] + 2*M[1]*M[3]*M[4]*m[2] + 2*M[1]*M[3]*M[4]*m[3] - 4*M[1]*M[3]*m[1]*m[2] + 2*M[1]*M[3]*m[1]*m[3] + 2*M[1]*M[3]*m[1]*m[4] + 2*M[1]*M[3]*m[1]*t + 2*M[1]*M[3]*m[2]*m[3] + 2*M[1]*M[3]*m[2]*m[4] + 2*M[1]*M[3]*m[2]*s - 4*M[1]*M[3]*m[3]*m[4] + 2*M[1]*M[3]*m[3]*t + 2*M[1]*M[3]*m[4]*s - 2*M[1]*M[3]*s*t + 2*M[1]*M[4]*m[2]*m[3] - 2*M[1]*M[4]*m[2]*m[4] - 2*M[1]*M[4]*m[3]^2 + 2*M[1]*M[4]*m[3]*m[4] - 4*M[1]*M[4]*m[3]*t + 2*M[1]*m[1]*m[3]*t - 2*M[1]*m[1]*m[4]*t - 2*M[1]*m[2]*m[3]*s + 2*M[1]*m[2]*m[4]*s - 2*M[1]*m[3]^2*t + 2*M[1]*m[3]*m[4]*s + 2*M[1]*m[3]*m[4]*t + 2*M[1]*m[3]*s*t - 2*M[1]*m[4]^2*s + 2*M[1]*m[4]*s*t + M[2]^2*M[4]^2 - 2*M[2]^2*M[4]*m[1] - 2*M[2]^2*M[4]*m[4] + M[2]^2*m[1]^2 - 2*M[2]^2*m[1]*m[4] + M[2]^2*m[4]^2 + 2*M[2]*M[3]*M[4]*m[1] + 2*M[2]*M[3]*M[4]*m[2] - 2*M[2]*M[3]*m[1]^2 + 2*M[2]*M[3]*m[1]*m[2] + 2*M[2]*M[3]*m[1]*m[4] - 4*M[2]*M[3]*m[1]*t - 2*M[2]*M[3]*m[2]*m[4] - 2*M[2]*M[4]^2*m[2] - 2*M[2]*M[4]^2*m[3] + 2*M[2]*M[4]*m[1]*m[2] + 2*M[2]*M[4]*m[1]*m[3] - 4*M[2]*M[4]*m[1]*m[4] + 2*M[2]*M[4]*m[1]*t - 4*M[2]*M[4]*m[2]*m[3] + 2*M[2]*M[4]*m[2]*m[4] + 2*M[2]*M[4]*m[2]*s + 2*M[2]*M[4]*m[3]*m[4] + 2*M[2]*M[4]*m[3]*t + 2*M[2]*M[4]*m[4]*s - 2*M[2]*M[4]*s*t - 2*M[2]*m[1]^2*t - 2*M[2]*m[1]*m[2]*s + 2*M[2]*m[1]*m[3]*t + 2*M[2]*m[1]*m[4]*s + 2*M[2]*m[1]*m[4]*t + 2*M[2]*m[1]*s*t + 2*M[2]*m[2]*m[4]*s - 2*M[2]*m[3]*m[4]*t - 2*M[2]*m[4]^2*s + 2*M[2]*m[4]*s*t + M[3]^2*m[1]^2 - 2*M[3]^2*m[1]*m[2] + M[3]^2*m[2]^2 + 2*M[3]*M[4]*m[1]*m[2] - 2*M[3]*M[4]*m[1]*m[3] - 2*M[3]*M[4]*m[2]^2 + 2*M[3]*M[4]*m[2]*m[3] - 4*M[3]*M[4]*m[2]*s - 2*M[3]*m[1]^2*t + 2*M[3]*m[1]*m[2]*s + 2*M[3]*m[1]*m[2]*t + 2*M[3]*m[1]*m[3]*t - 2*M[3]*m[1]*m[4]*s + 2*M[3]*m[1]*s*t - 2*M[3]*m[2]^2*s - 2*M[3]*m[2]*m[3]*t + 2*M[3]*m[2]*m[4]*s + 2*M[3]*m[2]*s*t + M[4]^2*m[2]^2 - 2*M[4]^2*m[2]*m[3] + M[4]^2*m[3]^2 - 2*M[4]*m[1]*m[2]*t + 2*M[4]*m[1]*m[3]*t - 2*M[4]*m[2]^2*s + 2*M[4]*m[2]*m[3]*s + 2*M[4]*m[2]*m[3]*t + 2*M[4]*m[2]*m[4]*s + 2*M[4]*m[2]*s*t - 2*M[4]*m[3]^2*t - 2*M[4]*m[3]*m[4]*s + 2*M[4]*m[3]*s*t + m[1]^2*t^2 + 2*m[1]*m[2]*s*t - 4*m[1]*m[3]*s*t - 2*m[1]*m[3]*t^2 + 2*m[1]*m[4]*s*t - 2*m[1]*s*t^2 + m[2]^2*s^2 + 2*m[2]*m[3]*s*t - 2*m[2]*m[4]*s^2 - 4*m[2]*m[4]*s*t - 2*m[2]*s^2*t + m[3]^2*t^2 + 2*m[3]*m[4]*s*t - 2*m[3]*s*t^2 + m[4]^2*s^2 - 2*m[4]*s^2*t + s^2*t^2 χ[6] = 14 weights[6] = [[-1, -1, -1, -1]] computed_with[6] = ["PLD_num", "HyperInt"] ################################ # Component 7 ################################ D[7] = M[1]^2*m[3] - M[1]*M[2]*m[1] - M[1]*M[2]*m[3] + M[1]*M[2]*s + M[1]*m[1]*m[2] - M[1]*m[1]*m[3] - M[1]*m[2]*m[3] - M[1]*m[2]*s + M[1]*m[3]^2 - M[1]*m[3]*s + M[2]^2*m[1] + M[2]*m[1]^2 - M[2]*m[1]*m[2] - M[2]*m[1]*m[3] - M[2]*m[1]*s + M[2]*m[2]*m[3] - M[2]*m[2]*s - m[1]*m[2]*s + m[1]*m[3]*s + m[2]^2*s - m[2]*m[3]*s + m[2]*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*m[4] - M[1]*M[4]*m[2] - M[1]*M[4]*m[4] + M[1]*M[4]*t + M[1]*m[1]*m[2] - M[1]*m[1]*m[4] - M[1]*m[1]*t - M[1]*m[2]*m[4] + M[1]*m[4]^2 - M[1]*m[4]*t + M[4]^2*m[2] - M[4]*m[1]*m[2] + M[4]*m[1]*m[4] - M[4]*m[1]*t + M[4]*m[2]^2 - M[4]*m[2]*m[4] - M[4]*m[2]*t + m[1]^2*t - m[1]*m[2]*t - m[1]*m[4]*t + m[1]*t^2 + m[2]*m[4]*t 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] = 14 weights[9] = [[1, 0, 0, 1]] computed_with[9] = ["PLD_sym", "PLD_num"] ################################ # Component 10 ################################ D[10] = M[2]^2 - 2*M[2]*M[3] - 2*M[2]*t + M[3]^2 - 2*M[3]*t + t^2 χ[10] = 14 weights[10] = [[1, 0, 0, 0]] computed_with[10] = ["PLD_num", "HyperInt"] ################################ # Component 11 ################################ D[11] = M[2]^2 - 2*M[2]*m[2] - 2*M[2]*m[3] + m[2]^2 - 2*m[2]*m[3] + m[3]^2 χ[11] = 14 weights[11] = [[0, -1, -1, 0]] computed_with[11] = ["PLD_sym", "PLD_num", "HyperInt"] ################################ # Component 12 ################################ D[12] = M[2]^2*m[4] - M[2]*M[3]*m[2] - M[2]*M[3]*m[4] + M[2]*M[3]*t + M[2]*m[2]*m[3] - M[2]*m[2]*m[4] - M[2]*m[3]*m[4] - M[2]*m[3]*t + M[2]*m[4]^2 - M[2]*m[4]*t + M[3]^2*m[2] + M[3]*m[2]^2 - M[3]*m[2]*m[3] - M[3]*m[2]*m[4] - M[3]*m[2]*t + M[3]*m[3]*m[4] - M[3]*m[3]*t - m[2]*m[3]*t + m[2]*m[4]*t + m[3]^2*t - m[3]*m[4]*t + m[3]*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] = 14 weights[13] = [[1, 1, 0, 0]] computed_with[13] = ["PLD_sym", "PLD_num"] ################################ # Component 14 ################################ D[14] = M[3]^2 - 2*M[3]*M[4] - 2*M[3]*s + M[4]^2 - 2*M[4]*s + s^2 χ[14] = 14 weights[14] = [[0, 1, 0, 0]] computed_with[14] = ["PLD_sym", "PLD_num", "HyperInt"] ################################ # Component 15 ################################ D[15] = M[3]^2 - 2*M[3]*m[3] - 2*M[3]*m[4] + m[3]^2 - 2*m[3]*m[4] + m[4]^2 χ[15] = 14 weights[15] = [[0, 0, -1, -1]] computed_with[15] = ["PLD_sym", "PLD_num", "HyperInt"] ################################ # Component 16 ################################ D[16] = M[3]^2*m[1] - M[3]*M[4]*m[1] - M[3]*M[4]*m[3] + M[3]*M[4]*s + M[3]*m[1]^2 - M[3]*m[1]*m[3] - M[3]*m[1]*m[4] - M[3]*m[1]*s + M[3]*m[3]*m[4] - M[3]*m[4]*s + M[4]^2*m[3] - M[4]*m[1]*m[3] + M[4]*m[1]*m[4] + M[4]*m[3]^2 - M[4]*m[3]*m[4] - M[4]*m[3]*s - M[4]*m[4]*s + m[1]*m[3]*s - m[1]*m[4]*s - m[3]*m[4]*s + m[4]^2*s + m[4]*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] = 14 weights[17] = [[0, 1, 1, 0]] computed_with[17] = ["PLD_sym", "PLD_num"] ################################ # Component 18 ################################ D[18] = M[4]^2 - 2*M[4]*m[1] - 2*M[4]*m[4] + m[1]^2 - 2*m[1]*m[4] + m[4]^2 χ[18] = 14 weights[18] = [[-1, 0, 0, -1]] computed_with[18] = ["PLD_sym", "PLD_num", "HyperInt"] ################################ # Component 19 ################################ D[19] = m[1] χ[19] = 14 weights[19] = [[-1, 0, 0, 0]] computed_with[19] = ["PLD_sym", "PLD_num"] ################################ # Component 20 ################################ D[20] = m[1]^2 - 2*m[1]*m[3] - 2*m[1]*s + m[3]^2 - 2*m[3]*s + s^2 χ[20] = 14 weights[20] = [[-1, 0, -1, 0]] computed_with[20] = ["PLD_sym", "PLD_num", "HyperInt"] ################################ # Component 21 ################################ D[21] = m[2] χ[21] = 14 weights[21] = [[0, -1, 0, 0]] computed_with[21] = ["PLD_sym", "PLD_num"] ################################ # Component 22 ################################ D[22] = m[2]^2 - 2*m[2]*m[4] - 2*m[2]*t + m[4]^2 - 2*m[4]*t + t^2 χ[22] = 14 weights[22] = [[0, -1, 0, -1]] computed_with[22] = ["PLD_sym", "PLD_num", "HyperInt"] ################################ # Component 23 ################################ D[23] = m[3] χ[23] = 14 weights[23] = [[0, 0, -1, 0]] computed_with[23] = ["PLD_sym", "PLD_num"] ################################ # Component 24 ################################ D[24] = m[4] χ[24] = 14 weights[24] = [[0, 0, 0, -1]] computed_with[24] = ["PLD_sym", "PLD_num"] ################################ # Component 25 ################################ D[25] = s χ[25] = 14 weights[25] = [[0, 1, 0, 1]] computed_with[25] = ["PLD_sym", "PLD_num"] ################################ # Component 26 ################################ D[26] = t χ[26] = 1 weights[26] = [[1, 0, 1, 0]] computed_with[26] = ["PLD_sym", "PLD_num"]