```
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 ==
```