6 w1 + w2 + w3 + (-1.85584131425170E-01 + 9.82628378464191E-01*i); w1*x1 + w2*x2 + w3*x3 + (-9.91336064106736E-01 + 1.31349944809144E-01*i); w1*x1**2 + w2*x2**2 + w3*x3**2 + ( 3.99008911367837E-01 - 9.16947047898107E-01*i); w1*x1**3 + w2*x2**3 + w3*x3**3 + (-7.85981252767830E-01 + 6.18250329799760E-01*i); w1*x1**4 + w2*x2**4 + w3*x3**4 + ( 3.99008911367837E-01 - 9.16947047898107E-01*i); w1*x1**5 + w2*x2**5 + w3*x3**5 + ( 1.49480150971521E-01 + 9.88764726547995E-01*i); TITLE : Gaussian quadrature formula with 3 knots and 3 weights ROOT COUNTS : total degree : 720 2-homogeneous Bezout number : 225 with partition : {w1 w2 w3 }{x1 x2 x3 } generalized Bezout number : 225 based on the set structure : {w1 w2 w3 } {w1 w2 w3 }{x1 x2 x3 } {w1 w2 w3 }{x1 x2 x3 }{x1 x2 x3 } {w1 w2 w3 }{x1 x2 x3 }{x1 x2 x3 }{x1 x2 x3 } {w1 w2 w3 }{x1 x2 x3 }{x1 x2 x3 }{x1 x2 x3 }{x1 x2 x3 } {w1 w2 w3 }{x1 x2 x3 }{x1 x2 x3 }{x1 x2 x3 }{x1 x2 x3 }{x1 x2 x3 } mixed volume : 49 NOTE : The moments are chosen at random. By means of a particular symmetric subdivision, only one solution path needs to be traced. THE GENERATING SOLUTIONS : 1 6 =========================================================== solution 1 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 6 the solution for t : w1 : 8.82956381242511E-01 -4.97446186089554E-01 w2 : 1.74696857880646E-02 -4.37569014860605E-01 w3 : -7.14841935605406E-01 -4.76131775140323E-02 x1 : 4.67557036438764E-01 3.14543130902305E-01 x2 : -8.99531291584821E-02 -7.48528771335924E-01 x3 : -1.02732562627853E+00 3.52094231469549E-01 == err : 2.264E-15 = rco : 2.130E-02 = res : 2.945E-16 ==