/* Problem: System generated by F. Rouiller as a deformation of
   a system found in Innocenti.

@unpublished{BiniMourrain1996,
author    = {D. Bini and B. Mourrain},
title     = {{Handbook} of {Polynomial} {Systems}},
month     = {November},
year      = {1996}
}

24 real roots
*/


Variables
  x1 in [-1.0e8,1.0e8],
  x2 in [-1.0e8,1.0e8],
  x3 in [-1.0e8,1.0e8],
  y1 in [-1.0e8,1.0e8],
  y2 in [-1.0e8,1.0e8],
  y3 in [-1.0e8,1.0e8],
  z1 in [-1.0e8,1.0e8],
  z2 in [-1.0e8,1.0e8],
  z3 in [-1.0e8,1.0e8]
;



Constraints
  62500*x1^2 + 62500*y1^2 + 62500*z1^2 - 74529 = 0,

  625*x2^2 -1250*x2 + 625*y2^2 + 625*z2^2 - 2624 = 0,

  12500*x3^2 + 12500*y3^2 + 12500*z3^2 + 2500*x3 - 44975*y3 - 10982 = 0,

  400000*x1*x2 + 400000*y1*y2 + 400000*z1*z2 - 400000*x2 + 178837 = 0,

  1000000*x1*x3 + 1000000*y1*y3 + 1000000*z1*z3 + 100000*x3 - 1799000*y3 - 805427 = 0,

  2000000*x2*x3 + 2000000*y2*y3 + 2000000*z2*z3 -2000000*x2 + 200000*x3 -3598000*y3 - 1403 = 0,

  113800000000000*x3*y2*z1 -113800000000000*x2*y3*z1 -113800000000000*x3*y1*z2 +
  113800000000000*x1*y3*z2 + 113800000000000*x2*y1*z3 -113800000000000*x1*y2*z3 -
  206888400000000*x2*y1 + 206888400000000*x3*y1 + 206888400000000*x1*y2 -
  206888400000000*x3*y2 -206888400000000*x1*y3 + 206888400000000*x2*y3 -
  2014260000000*x2*z1 + 2014260000000*x3*z1 -61907200000000*y2*z1 +
  61907200000000*y3*z1 + 2014260000000*x1*z2 -2014260000000*x3*z2 +
  61907200000000*y1*z2 -61907200000000*y3*z2 -2014260000000*x1*z3 +
  2014260000000*x2*z3 -61907200000000*y1*z3 + 61907200000000*y2*z3 -
  362960716800000*x1 + 38025201600000*x2 + 292548849600000*x3 +
  11809567440000*y1 + 1475978220000*y2 -825269402280000*y3 -
  1212982689600000*z1 -151600474800000*z2 + 825859951200000*z3 -
  19295432410527 = 0,

  -777600000000*x3*y2*z1 + 777600000000*x2*y3*z1 + 777600000000*x3*y1*z2 -
  777600000000*x1*y3*z2 -777600000000*x2*y1*z3 + 777600000000*x1*y2*z3 -
  1409011200000*x2*y1 + 1409011200000*x3*y1 + 1409011200000*x1*y2 -
  1409011200000*x3*y2 -1409011200000*x1*y3 + 1409011200000*x2*y3 -
  1065312000000*x2*z1 + 1065312000000*x3*z1 -805593600000*y2*z1 +
  805593600000*y3*z1 + 1065312000000*x1*z2 -1065312000000*x3*z2 +
  805593600000*y1*z2 -805593600000*y3*z2 -1065312000000*x1*z3 +
  1065312000000*x2*z3 -805593600000*y1*z3 + 805593600000*y2*z3 +
  235685027200*x1 + 398417510400*x2 + 158626915200*x3 -311668424000*y1 -
  268090368000*y2 + 72704002800*y3 + 412221302400*z1 + 354583756800*z2 +
  307085438400*z3 + 282499646407 = 0,

  3200*x2 + 1271 = 0
;
