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 ==