10 
 5*x1*x2+ 5*x1+ 3*x2+ 55;
 7*x2*x3+ 9*x2+ 9*x3+ 19;
 3*x3*x4+ 6*x3+ 5*x4-4;
 6*x4*x5+ 6*x4+ 7*x5+ 118;
x5*x6+ 3*x5+ 9*x6+ 27;
 6*x6*x7+ 7*x6+x7+ 72;
 9*x7*x8+ 7*x7+x8+ 35;
 4*x8*x9+ 4*x8+ 6*x9+ 16;
 8*x9*x10+ 4*x9+ 3*x10-51;
 3*x1*x10-6*x1+x10+ 5;

TITLE : 10-dimensional system of Ku

ROOT COUNTS :

total degree : 1024
10-homogeneous Bezout number : 2
  with partition : {x1 }{x2 }{x3 }{x4 }{x5 }{x6 }{x7 }{x8 }{x9 }{x10 }
generalized Bezout number : 2
  based on the set structure :
     {x1 }{x2 }
     {x2 }{x3 }
     {x3 }{x4 }
     {x4 }{x5 }
     {x5 }{x6 }
     {x6 }{x7 }
     {x7 }{x8 }
     {x8 }{x9 }
     {x9 }{x10 }
     {x1 }{x10 }
mixed volume : 2

REFERENCES :

M.C. Steenkamp :
`Die numeriese oplos van stelsels polinoomvergelykings'.
Technical report, Nasionale Navorsingsinstituut vir Wiskundige Wetenskappe,
Pretoria, 1982.

NOTE :

This system was known as an easy system for elimination, but difficult 
for homotopy continuation.  With multi-homogenization, this is also an 
easy system for homotopy continuation methods.

THE SOLUTIONS :

2 10
===========================================================
solution 1 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
 x1 :  2.00000000000000E+00  -2.67276471009220E-51
 x2 : -5.00000000000000E+00  -5.34552942018439E-51
 x3 : -1.00000000000000E+00  -4.17619485951906E-52
 x4 :  5.00000000000000E+00   4.00914706513829E-51
 x5 : -4.00000000000000E+00   2.00457353256915E-51
 x6 : -3.00000000000000E+00   4.17619485951906E-53
 x7 :  3.00000000000000E+00   8.35238971903811E-53
 x8 : -2.00000000000000E+00   2.08809742975953E-53
 x9 :  4.00000000000000E+00   3.34095588761525E-52
 x10 :  1.00000000000000E+00  -1.67047794380762E-52
== err :  3.762E-35 = rco :  6.097E-03 = res :  1.604E-50 ==
solution 2 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
 x1 :  7.73143904674611E+00  -6.81046792009123E-57
 x2 : -2.24828375286041E+00  -9.75768795568627E-58
 x3 : -1.83222958057395E-01  -1.11516433779272E-57
 x4 :  1.14583333333333E+00   2.34981056892037E-57
 x5 : -9.00000000000000E+00   7.16891360009604E-57
 x6 : -3.32551987064446E+00  -1.54330778890956E-58
 x7 :  2.57062493671946E+00  -1.24460305557223E-58
 x8 : -2.19569105036795E+00  -1.19481893334934E-58
 x9 :  2.59354917484962E+00  -1.99136488891557E-59
 x10 :  1.71067585997878E+00  -9.95682444457783E-59
== err :  4.749E-15 = rco :  3.440E-03 = res :  1.421E-14 ==