5
 x1**2*x2**2*x3**2*x4**2*x5**2 
    + 3*x1**2 + x2**2 + x3**2 + x4**2 + x5**2 + x1*x2*x3*x4*x5 + 5;
 x1**2*x2**2*x3**2*x4**2*x5**2 
    + x1**2 + 3*x2**2 + x3**2 + x4**2 + x5**2 + x1*x2*x3*x4*x5 + 5;
 x1**2*x2**2*x3**2*x4**2*x5**2 
    + x1**2 + x2**2 + 3*x3**2 + x4**2 + x5**2 + x1*x2*x3*x4*x5 + 5;
 x1**2*x2**2*x3**2*x4**2*x5**2 
    + x1**2 + x2**2 + x3**2 + 3*x4**2 + x5**2 + x1*x2*x3*x4*x5 + 5;
 x1**2*x2**2*x3**2*x4**2*x5**2 
    + x1**2 + x2**2 + x3**2 + x4**2 + 3*x5**2 + x1*x2*x3*x4*x5 + 5;

TITLE : a 5-dimensional sparse symmetric polynomial system

ROOT COUNTS :

Total degree : 10000
5-homogeneous Bezout number : 3840
mixed volume : 160

REFERENCES :

Jan Verschelde and Karin Gatermann:
`Symmetric Newton Polytopes for Solving Sparse Polynomial Systems',
Adv. Appl. Math., 16(1): 95-127, 1995.

SYMMETRY GROUP :

invariant under all permutations
+ sign symmetry, generated by

-x1 -x2 x3 x4 x5
-x1 x2 -x3 x4 x5
-x1 x2 x3 -x4 x5
-x1 x2 x3 x4 -x5

THE GENERATING SOLUTIONS :

10 5
===========================================================
solution 1 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 16
the solution for t :
 x1 :  5.23681844701480E-01  -1.16679253451397E+00
 x2 :  5.23681844701480E-01  -1.16679253451397E+00
 x3 : -5.23681844701480E-01   1.16679253451397E+00
 x4 :  5.23681844701480E-01  -1.16679253451397E+00
 x5 :  5.23681844701480E-01  -1.16679253451397E+00
== err :  3.555E-15 = rco :  6.219E-02 = res :  3.722E-15 ==
solution 2 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 16
the solution for t :
 x1 :  5.62945437488535E-01  -1.06731054777957E+00
 x2 :  5.62945437488535E-01  -1.06731054777957E+00
 x3 : -5.62945437488535E-01   1.06731054777957E+00
 x4 :  5.62945437488535E-01  -1.06731054777957E+00
 x5 : -5.62945437488535E-01   1.06731054777957E+00
== err :  2.585E-15 = rco :  7.123E-02 = res :  3.286E-15 ==
solution 3 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 16
the solution for t :
 x1 : -2.86768329351213E-02   8.27714843748319E-01
 x2 : -2.86768329351213E-02   8.27714843748319E-01
 x3 :  2.86768329351213E-02  -8.27714843748319E-01
 x4 :  2.86768329351213E-02  -8.27714843748319E-01
 x5 : -2.86768329351213E-02   8.27714843748319E-01
== err :  3.373E-16 = rco :  2.222E-01 = res :  4.450E-16 ==
solution 4 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 16
the solution for t :
 x1 :  2.86768329351213E-02   8.27714843748319E-01
 x2 :  2.86768329351213E-02   8.27714843748319E-01
 x3 : -2.86768329351213E-02  -8.27714843748319E-01
 x4 : -2.86768329351213E-02  -8.27714843748319E-01
 x5 : -2.86768329351213E-02  -8.27714843748319E-01
== err :  3.406E-16 = rco :  2.222E-01 = res :  4.441E-16 ==
solution 5 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 16
the solution for t :
 x1 :  5.23681844701480E-01   1.16679253451397E+00
 x2 : -5.23681844701480E-01  -1.16679253451397E+00
 x3 :  5.23681844701480E-01   1.16679253451397E+00
 x4 :  5.23681844701480E-01   1.16679253451397E+00
 x5 :  5.23681844701480E-01   1.16679253451397E+00
== err :  3.555E-15 = rco :  6.219E-02 = res :  3.722E-15 ==
solution 6 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 16
the solution for t :
 x1 :  1.23947841569073E+00   4.36197964162307E-01
 x2 : -1.23947841569073E+00  -4.36197964162307E-01
 x3 :  1.23947841569073E+00   4.36197964162307E-01
 x4 :  1.23947841569073E+00   4.36197964162307E-01
 x5 :  1.23947841569073E+00   4.36197964162307E-01
== err :  3.568E-15 = rco :  5.702E-02 = res :  1.601E-14 ==
solution 7 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 16
the solution for t :
 x1 :  1.22889165583880E+00   5.12364025922987E-01
 x2 : -1.22889165583880E+00  -5.12364025922987E-01
 x3 : -1.22889165583880E+00  -5.12364025922987E-01
 x4 : -1.22889165583880E+00  -5.12364025922987E-01
 x5 : -1.22889165583880E+00  -5.12364025922987E-01
== err :  5.297E-16 = rco :  4.594E-02 = res :  3.972E-15 ==
solution 8 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 16
the solution for t :
 x1 :  1.22889165583880E+00  -5.12364025922987E-01
 x2 : -1.22889165583880E+00   5.12364025922987E-01
 x3 : -1.22889165583880E+00   5.12364025922987E-01
 x4 : -1.22889165583880E+00   5.12364025922987E-01
 x5 : -1.22889165583880E+00   5.12364025922987E-01
== err :  5.297E-16 = rco :  4.594E-02 = res :  3.972E-15 ==
solution 9 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 16
the solution for t :
 x1 : -1.23947841569073E+00   4.36197964162307E-01
 x2 : -1.23947841569073E+00   4.36197964162307E-01
 x3 : -1.23947841569073E+00   4.36197964162307E-01
 x4 : -1.23947841569073E+00   4.36197964162307E-01
 x5 : -1.23947841569073E+00   4.36197964162307E-01
== err :  3.568E-15 = rco :  5.702E-02 = res :  1.601E-14 ==
solution 10 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 16
the solution for t :
 x1 : -5.62945437488535E-01  -1.06731054777957E+00
 x2 : -5.62945437488535E-01  -1.06731054777957E+00
 x3 : -5.62945437488535E-01  -1.06731054777957E+00
 x4 : -5.62945437488535E-01  -1.06731054777957E+00
 x5 :  5.62945437488535E-01   1.06731054777957E+00
== err :  2.585E-15 = rco :  7.123E-02 = res :  3.286E-15 ==