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
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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 ==