################################ # Diagram information ################################ name = "env" edges = [[1, 4], [1, 2], [2, 3], [3, 4], [1, 3], [2, 4]] nodes = [1, 2, 3, 4] internal_masses = [0, 0, 0, 0, 0, 0] external_masses = [M[1], M[2], M[3], M[4]] U = x[1]*x[2]*x[3] + x[1]*x[2]*x[4] + x[1]*x[2]*x[6] + x[1]*x[3]*x[4] + x[1]*x[3]*x[5] + x[1]*x[3]*x[6] + x[1]*x[4]*x[5] + x[1]*x[5]*x[6] + x[2]*x[3]*x[4] + x[2]*x[3]*x[5] + x[2]*x[4]*x[5] + x[2]*x[4]*x[6] + x[2]*x[5]*x[6] + x[3]*x[4]*x[6] + x[3]*x[5]*x[6] + x[4]*x[5]*x[6] F = (M[1] + M[2] + M[3] + M[4] - s - t)*x[1]*x[2]*x[3]*x[4] + M[1]*x[1]*x[2]*x[3]*x[5] + M[2]*x[1]*x[2]*x[3]*x[6] + M[1]*x[1]*x[2]*x[4]*x[5] + M[4]*x[1]*x[2]*x[4]*x[6] + M[1]*x[1]*x[2]*x[5]*x[6] + M[3]*x[1]*x[3]*x[4]*x[5] + M[4]*x[1]*x[3]*x[4]*x[6] + s*x[1]*x[3]*x[5]*x[6] + M[4]*x[1]*x[4]*x[5]*x[6] + M[3]*x[2]*x[3]*x[4]*x[5] + M[2]*x[2]*x[3]*x[4]*x[6] + M[2]*x[2]*x[3]*x[5]*x[6] + t*x[2]*x[4]*x[5]*x[6] + M[3]*x[3]*x[4]*x[5]*x[6] parameters = [M[1], M[2], M[3], M[4], s, t] variables = [x[1], x[2], x[3], x[4], x[5], x[6]] χ_generic = 56 f_vector = [31, 162, 296, 247, 100, 18] ################################ # Component 1 ################################ D[1] = M[1] χ[1] = 38 weights[1] = [[-2, -2, -1, 1, -2, 1], [-2, -2, 1, -1, -2, 1], [-2, -2, 1, 1, -2, -1], [-2, -2, 0, 0, -2, 1], [-2, -2, 0, 1, -2, 0], [-2, -2, 1, 0, -2, 0], [-2, -2, 0, 0, -2, 0], [0, -1, -1, 1, 0, 0], [0, 0, -1, 0, -1, 1], [0, -1, 0, 1, 0, -1], [-1, 0, 1, -1, 0, 0], [0, 0, 0, -1, -1, 1], [-1, 0, 1, 0, 0, -1], [0, -1, 0, 1, 0, 0], [0, 0, 0, 0, -1, 1], [-1, 0, 1, 0, 0, 0]] computed_with[1] = ["PLD_sym", "PLD_num"] ################################ # Component 2 ################################ D[2] = M[1] + M[2] + M[3] + M[4] - s - t χ[2] = 50 weights[2] = [[-2, -2, -2, -2, 0, 0], [-1, -1, 0, 0, 0, 1], [0, -1, -1, 0, 1, 0], [-1, 0, 0, -1, 1, 0], [0, 0, -1, -1, 0, 1]] computed_with[2] = ["PLD_sym", "HyperInt"] ################################ # Component 3 ################################ D[3] = M[1]*M[3] - 1//4*M[2]^2 - 1//2*M[2]*M[4] + 1//2*M[2]*s + 1//2*M[2]*t - 1//4*M[4]^2 + 1//2*M[4]*s + 1//2*M[4]*t - 1//4*s^2 - 1//2*s*t - 1//4*t^2 χ[3] = 51 weights[3] = [[-1, -2, -2, -1, -1, -1], [-1, 0, -1, 0, 0, 1], [0, -1, -1, 0, 0, 1], [-2, -1, -1, -2, -1, -1], [-1, 0, 0, -1, 0, 1], [0, -1, 0, -1, 0, 1], [0, -1, -1, 0, 0, 0], [-1, 0, 0, 0, 0, 1], [0, -1, 0, 0, 0, 1], [0, 0, -1, 0, 0, 1], [-1, 0, 0, -1, 0, 0], [0, 0, 0, -1, 0, 1], [0, 0, 0, 0, 0, 1]] computed_with[3] = ["PLD_sym", "PLD_num", "HyperInt"] ################################ # Component 4 ################################ D[4] = M[1]^2 + 2*M[1]*M[3] - 2*M[1]*s - 2*M[1]*t - 4*M[2]*M[4] + M[3]^2 - 2*M[3]*s - 2*M[3]*t + s^2 + 2*s*t + t^2 χ[4] = 51 weights[4] = [[-2, -2, -1, -1, -1, -1], [-1, -1, 0, 0, 1, 0], [-1, 0, -1, 0, 1, 0], [0, -1, 0, -1, 1, 0], [-1, -1, -2, -2, -1, -1], [0, 0, -1, -1, 1, 0], [-1, -1, 0, 0, 0, 0], [-1, 0, 0, 0, 1, 0], [0, -1, 0, 0, 1, 0], [0, 0, -1, 0, 1, 0], [0, 0, 0, -1, 1, 0], [0, 0, -1, -1, 0, 0], [0, 0, 0, 0, 1, 0]] computed_with[4] = ["PLD_sym", "PLD_num", "HyperInt"] ################################ # Component 5 ################################ D[5] = M[1]^2 - 2*M[1]*M[2] - 2*M[1]*s + M[2]^2 - 2*M[2]*s + s^2 χ[5] = 51 weights[5] = [[-1, 0, -1, 1, 0, 0], [-1, -1, -2, -1, -2, -1], [0, 0, -1, 1, -1, 0], [-2, -1, -1, -1, -1, -2], [-1, 0, 0, 1, 0, -1], [0, 0, 0, 1, -1, -1], [-1, 0, 0, 1, 0, 0], [0, 0, -1, 1, 0, 0], [0, 0, 0, 1, -1, 0], [0, 0, -1, 0, -1, 0], [-1, 0, 0, 0, 0, -1], [0, 0, 0, 1, 0, -1], [0, 0, 0, 1, 0, 0]] computed_with[5] = ["PLD_sym", "PLD_num", "HyperInt"] ################################ # Component 6 ################################ D[6] = M[1]^2 - 2*M[1]*M[4] - 2*M[1]*t + M[4]^2 - 2*M[4]*t + t^2 χ[6] = 51 weights[6] = [[-1, -2, -1, -1, -1, -2], [0, -1, 1, -1, 0, 0], [-1, -1, -1, -2, -2, -1], [0, 0, 1, -1, -1, 0], [0, -1, 1, 0, 0, -1], [0, 0, 1, 0, -1, -1], [0, -1, 0, 0, 0, -1], [0, -1, 1, 0, 0, 0], [0, 0, 1, -1, 0, 0], [0, 0, 1, 0, -1, 0], [0, 0, 0, -1, -1, 0], [0, 0, 1, 0, 0, -1], [0, 0, 1, 0, 0, 0]] computed_with[6] = ["PLD_sym", "PLD_num", "HyperInt"] ################################ # Component 7 ################################ D[7] = M[1]^2*M[2]^2 - 2*M[1]^2*M[2]*t + M[1]^2*t^2 - 2*M[1]*M[2]^2*t - 2*M[1]*M[2]*M[3]*M[4] - 2*M[1]*M[2]*M[3]*t - 2*M[1]*M[2]*M[4]*t + 2*M[1]*M[2]*s*t + 4*M[1]*M[2]*t^2 - 2*M[1]*M[3]*M[4]*t + 2*M[1]*M[3]*t^2 + 2*M[1]*M[4]*t^2 - 2*M[1]*s*t^2 - 2*M[1]*t^3 + M[2]^2*t^2 - 2*M[2]*M[3]*M[4]*t + 2*M[2]*M[3]*t^2 + 2*M[2]*M[4]*t^2 - 2*M[2]*s*t^2 - 2*M[2]*t^3 + M[3]^2*M[4]^2 - 2*M[3]^2*M[4]*t + M[3]^2*t^2 - 2*M[3]*M[4]^2*t + 2*M[3]*M[4]*s*t + 4*M[3]*M[4]*t^2 - 2*M[3]*s*t^2 - 2*M[3]*t^3 + M[4]^2*t^2 - 2*M[4]*s*t^2 - 2*M[4]*t^3 + s^2*t^2 + 2*s*t^3 + t^4 χ[7] = 55 weights[7] = [[-1, -2, -1, -2, -1, -1]] computed_with[7] = ["PLD_sym", "HyperInt"] ################################ # Component 8 ################################ D[8] = 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[8] = 46 weights[8] = [[-1, 0, -1, 0, 0, 0], [-2, -1, -1, -1, -1, -1], [-1, -2, -1, -1, -1, -1], [-1, -1, -2, -1, -1, -1], [0, -1, 0, -1, 0, 0], [-1, -1, -1, -2, -1, -1], [-1, -1, -1, -1, -2, -1], [-1, -1, -1, -1, -1, -2], [0, 0, 0, 0, -1, -1], [-1, 0, 0, 0, 0, 0], [0, -1, 0, 0, 0, 0], [0, 0, -1, 0, 0, 0], [-1, -1, -1, -1, -1, -1], [0, 0, 0, -1, 0, 0], [0, 0, 0, 0, -1, 0], [0, 0, 0, 0, 0, -1], [0, 0, 0, 0, 0, 0]] computed_with[8] = ["PLD_num", "HyperInt"] ################################ # Component 9 ################################ D[9] = M[1]^2*M[3]^2 - 2*M[1]*M[2]*M[3]*M[4] - 2*M[1]*M[3]*s*t + M[2]^2*M[4]^2 - 2*M[2]*M[4]*s*t + s^2*t^2 χ[9] = 55 weights[9] = [[-1, -1, -1, -1, -2, -2]] computed_with[9] = ["PLD_sym", "HyperInt"] ################################ # Component 10 ################################ D[10] = M[1]^2*M[4]^2 - 2*M[1]^2*M[4]*s + M[1]^2*s^2 - 2*M[1]*M[2]*M[3]*M[4] - 2*M[1]*M[2]*M[3]*s - 2*M[1]*M[2]*M[4]*s + 2*M[1]*M[2]*s^2 - 2*M[1]*M[3]*M[4]*s + 2*M[1]*M[3]*s^2 - 2*M[1]*M[4]^2*s + 4*M[1]*M[4]*s^2 + 2*M[1]*M[4]*s*t - 2*M[1]*s^3 - 2*M[1]*s^2*t + M[2]^2*M[3]^2 - 2*M[2]^2*M[3]*s + M[2]^2*s^2 - 2*M[2]*M[3]^2*s - 2*M[2]*M[3]*M[4]*s + 4*M[2]*M[3]*s^2 + 2*M[2]*M[3]*s*t + 2*M[2]*M[4]*s^2 - 2*M[2]*s^3 - 2*M[2]*s^2*t + M[3]^2*s^2 + 2*M[3]*M[4]*s^2 - 2*M[3]*s^3 - 2*M[3]*s^2*t + M[4]^2*s^2 - 2*M[4]*s^3 - 2*M[4]*s^2*t + s^4 + 2*s^3*t + s^2*t^2 χ[10] = 55 weights[10] = [[-2, -1, -2, -1, -1, -1]] computed_with[10] = ["PLD_sym", "HyperInt"] ################################ # Component 11 ################################ D[11] = M[2] χ[11] = 38 weights[11] = [[-1, -2, -2, 1, 1, -2], [1, -2, -2, -1, 1, -2], [1, -2, -2, 1, -1, -2], [0, -2, -2, 0, 1, -2], [0, -2, -2, 1, 0, -2], [1, -2, -2, 0, 0, -2], [0, -2, -2, 0, 0, -2], [-1, -1, 0, 1, 0, 0], [0, -1, 0, 1, -1, 0], [-1, 0, 0, 0, 1, -1], [0, 0, 0, -1, 1, -1], [1, 0, -1, -1, 0, 0], [1, 0, -1, 0, -1, 0], [0, -1, 0, 1, 0, 0], [0, 0, 0, 0, 1, -1], [1, 0, -1, 0, 0, 0]] computed_with[11] = ["PLD_sym", "PLD_num"] ################################ # Component 12 ################################ D[12] = M[2]^2 - 2*M[2]*M[3] - 2*M[2]*t + M[3]^2 - 2*M[3]*t + t^2 χ[12] = 51 weights[12] = [[-1, -2, -1, -1, -2, -1], [-1, -1, -1, -2, -1, -2], [1, -1, 0, -1, 0, 0], [1, -1, 0, 0, -1, 0], [1, 0, 0, -1, 0, -1], [1, 0, 0, 0, -1, -1], [0, -1, 0, 0, -1, 0], [0, 0, 0, -1, 0, -1], [1, -1, 0, 0, 0, 0], [1, 0, 0, -1, 0, 0], [1, 0, 0, 0, -1, 0], [1, 0, 0, 0, 0, -1], [1, 0, 0, 0, 0, 0]] computed_with[12] = ["PLD_sym", "PLD_num", "HyperInt"] ################################ # Component 13 ################################ D[13] = M[3] χ[13] = 38 weights[13] = [[-1, 1, -2, -2, -2, 1], [1, -1, -2, -2, -2, 1], [1, 1, -2, -2, -2, -1], [0, 0, -2, -2, -2, 1], [0, 1, -2, -2, -2, 0], [1, 0, -2, -2, -2, 0], [0, 0, -2, -2, -2, 0], [-1, 0, 0, 0, -1, 1], [0, -1, 0, 0, -1, 1], [-1, 1, 0, -1, 0, 0], [0, 1, 0, -1, 0, -1], [1, -1, -1, 0, 0, 0], [1, 0, -1, 0, 0, -1], [0, 0, 0, 0, -1, 1], [0, 1, 0, -1, 0, 0], [1, 0, -1, 0, 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] = 51 weights[14] = [[-2, -1, -1, -1, -2, -1], [-1, -1, -2, -1, -1, -2], [-1, 1, -1, 0, 0, 0], [-1, 1, 0, 0, -1, 0], [0, 1, -1, 0, 0, -1], [0, 1, 0, 0, -1, -1], [-1, 0, 0, 0, -1, 0], [0, 0, -1, 0, 0, -1], [-1, 1, 0, 0, 0, 0], [0, 1, -1, 0, 0, 0], [0, 1, 0, 0, -1, 0], [0, 1, 0, 0, 0, -1], [0, 1, 0, 0, 0, 0]] computed_with[14] = ["PLD_sym", "PLD_num", "HyperInt"] ################################ # Component 15 ################################ D[15] = M[4] χ[15] = 38 weights[15] = [[-2, -1, 1, -2, 1, -2], [-2, 1, -1, -2, 1, -2], [-2, 1, 1, -2, -1, -2], [-2, 0, 0, -2, 1, -2], [-2, 0, 1, -2, 0, -2], [-2, 1, 0, -2, 0, -2], [-2, 0, 0, -2, 0, -2], [0, -1, 0, 0, 1, -1], [0, 0, -1, 0, 1, -1], [-1, -1, 1, 0, 0, 0], [-1, 0, 1, 0, -1, 0], [0, 1, -1, -1, 0, 0], [0, 1, 0, -1, -1, 0], [0, 0, 0, 0, 1, -1], [-1, 0, 1, 0, 0, 0], [0, 1, 0, -1, 0, 0]] computed_with[15] = ["PLD_sym", "PLD_num"] ################################ # Component 16 ################################ D[16] = s χ[16] = 50 weights[16] = [[-2, 0, -2, 0, -2, -2], [-1, 0, 0, 1, -1, 0], [0, 0, -1, 1, 0, -1], [0, 1, -1, 0, -1, 0], [-1, 1, 0, 0, 0, -1]] computed_with[16] = ["PLD_sym", "PLD_num"] ################################ # Component 17 ################################ D[17] = t χ[17] = 50 weights[17] = [[0, -2, 0, -2, -2, -2], [0, -1, 1, 0, -1, 0], [0, 0, 1, -1, 0, -1], [1, 0, 0, -1, -1, 0], [1, -1, 0, 0, 0, -1]] computed_with[17] = ["PLD_sym", "PLD_num"]