4 w1 + w2 - 1; w1*x1 + w2*x2; w1*x1**2 + w2*x2**2 - 2/3; w1*x1**3 + w2*x2**3; TITLE : Gaussian quadrature formula with 2 knots and 2 weights over [-1,+1]. ROOT COUNTS : total degree : 24 2-homogeneous Bezout number : 11 with partition : {{w1 w2 }{x1 x2 }} mixed volume : 4 REFERENCE : Jan Verschelde and Karin Gatermann: `Symmetric Newton Polytopes for Solving Sparse Polynomial Systems', Adv. Appl. Math., 16(1): 95-127, 1995. THE GENERATING SOLUTIONS : 1 4 =========================================================== solution 1 : t : 1.00000000000000E+00 0.00000000000000E+00 m : 2 the solution for t : w1 : 5.00000000000000E-01 0.00000000000000E+00 w2 : 5.00000000000000E-01 0.00000000000000E+00 x1 : 8.16496580927726E-01 0.00000000000000E+00 x2 : -8.16496580927726E-01 0.00000000000000E+00 == err : 0.000E+00 = rco : 1.249E-01 = res : 0.000E+00 ==