3 
x1*x2^2 + x1*x3^2 - 1.1*x1 + 1;
x2*x1^2 + x2*x3^2 - 1.1*x2 + 1;
x3*x1^2 + x3*x2^2 - 1.1*x3 + 1;

TITLE : A neural network modeled by an adaptive Lotka-Volterra system, n=3

ROOT COUNTS :

total degree : 27

generalized Bezout bound : 21
set structure:
  {x1} {x2 x3} {x2 x3}
  {x2} {x1 x3} {x1 x3}
  {x3} {x1 x2} {x1 x2}

mixed volume : 21

REFERENCES :

Karin Gatermann:
"Symbolic solution of polynomial equation systems with symmetry",
Proceedings of ISSAC-90, pp 112-119, ACM New York, 1990.

V. W. Noonburg:
"A neural network modeled by an adaptive Lotka-Volterra system",
SIAM J. Appl. Math., Vol. 49, No. 6, 1779-1792, 1989.

Jan Verschelde and Ann Haegemans:
`The GBQ-Algorithm for constructing start systems of homotopies for polynomial
systems, SIAM J. Numer. Anal., Vol. 30, No. 2, pp 583-594, 1993.

NOTE :

The coefficients have been chosen so that full permutation symmetry
was obtained.  The parameter c = 1.1.

The orbits of solutions :  3 4 1
  3*(a,a,a) 4*(a,a,b) and 1*(a,b,c) 

THE GENERATING SOLUTIONS :

8 3
===========================================================
solution 1 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
 x1 :  5.09959548065397E-01   4.79766841277292E-01
 x2 :  5.09959548065397E-01   4.79766841277292E-01
 x3 :  5.09959548065397E-01   4.79766841277292E-01
== err :  5.911E-16 = rco :  2.745E-01 = res :  2.493E-16 ==
solution 2 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
 x1 :  1.35560902253960E+00  -1.28703758201580E-17
 x2 : -6.77804511269800E-01  -5.27500584353303E-01
 x3 : -6.77804511269800E-01   5.27500584353303E-01
== err :  7.955E-16 = rco :  2.529E-01 = res :  4.003E-16 ==
solution 3 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
 x1 : -4.44383120980212E-01  -3.01427302521399E-61
 x2 : -1.29427788609688E+00   1.65298843318187E-61
 x3 : -1.29427788609688E+00   1.65298843318187E-61
== err :  2.849E-15 = rco :  2.583E-01 = res :  3.886E-16 ==
solution 4 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
 x1 :  8.98653694263692E-01   3.48820047576431E-01
 x2 : -1.65123467890611E-01   7.61734168646636E-01
 x3 :  8.98653694263692E-01   3.48820047576431E-01
== err :  3.699E-16 = rco :  2.949E-01 = res :  1.665E-16 ==
solution 5 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
 x1 :  5.09959548065397E-01  -4.79766841277292E-01
 x2 :  5.09959548065397E-01  -4.79766841277292E-01
 x3 :  5.09959548065397E-01  -4.79766841277292E-01
== err :  5.242E-16 = rco :  2.745E-01 = res :  5.662E-17 ==
solution 6 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
 x1 : -5.03029502430507E-01  -2.11770212163837E-55
 x2 : -5.03029502430507E-01   1.95759134039956E-54
 x3 :  1.68372096585234E+00  -1.95759134039956E-54
== err :  1.716E-15 = rco :  3.764E-01 = res :  3.331E-16 ==
solution 7 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
 x1 : -1.65123467890611E-01  -7.61734168646636E-01
 x2 :  8.98653694263692E-01  -3.48820047576431E-01
 x3 :  8.98653694263692E-01  -3.48820047576431E-01
== err :  3.702E-16 = rco :  2.761E-01 = res :  2.791E-16 ==
solution 8 :
t :  1.00000000000000E+00   0.00000000000000E+00
m : 1
the solution for t :
 x1 : -1.01991909613079E+00  -9.49556774575980E-66
 x2 : -1.01991909613079E+00  -7.59645419660784E-65
 x3 : -1.01991909613079E+00  -4.74778387287990E-65
== err :  3.234E-15 = rco :  2.070E-01 = res :  6.661E-16 ==
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