# **************************************************************************
# Reference :
# 
# @unpublished{             bini-mourrain-poly,
# author          = "D. Bini and B. Mourrain",
# title           = "{Handbook} of {Polynomial} {Systems}",
# month           = "November",
# year            = 1996
# }
# 
# System generated by F. Rouiller as a deformation of a system found in
# Innocenti.
# 
# 24 real roots
# ***************************************************************************



# Domains
var x1 >= -1.0e8, <= 1.0e8;
var x2 >= -1.0e8, <= 1.0e8;
var x3 >= -1.0e8, <= 1.0e8;
var y1 >= -1.0e8, <= 1.0e8;
var y2 >= -1.0e8, <= 1.0e8;
var y3 >= -1.0e8, <= 1.0e8;
var z1 >= -1.0e8, <= 1.0e8;
var z2 >= -1.0e8, <= 1.0e8;
var z3 >= -1.0e8, <= 1.0e8;



subject to


#  FACTORISATION A LA MAIN : 
# x2 = -1271/3200,
# x1^2 + y1^2 + z1^2 = 74529/62500,
# (x2-1)^2 + y2^2 + z2^2 = 2624/625 + 1,
# (x3+0.1)^2 + (y3-(44975/25000))^2 + z3^2 = 10982/12500 + 0.01 + (44975/25000)^2,
# x2*(x1-1) + y1*y2 + z1*z2 = -178837/400000,
# x3*(x1+0.1) + y3*(y1- 1.799) + z1*z3   = 0.805427,
# x2*(x3-1) + y3*(y2-(3598000/2000000)) + z2*z3 + 0.1*x3  = 1403/2000000,
# x1*(y3*(z2 - (20688.84/11380)) +
#     y2*((20688.84/11380) - z3) +
#     (201.426/11380)*(z2-z3) - (36296.07168/11380)) +
# x2*(y1*(z3 - (20688.84/11380)) +
#     y3*((20688.84/11380) - z1) -
#     (201.426/11380)*(z1-z3) + (3802.52016/11380)) +
# x3*(y1*((20688.84/11380) - z2) +
#     y2*(z1 - (20688.84/11380)) +
#     (201.426/11380)*(z1-z2)+ (29254.88496/11380)) +
# y1*((6190.72/11380)*(z2-z3) + (1180.956744/11380)) +
# y2*((6190.72/11380)*(z3-z1) + (147.597822/11380)) +
# y3*((6190.72/11380)*(z1-z2) - (82526.940228/11380)) -
# (121298.26896/11380)*z1 - (15160.04748/11380)*z2 + (82585.99512/11380)*z3
# = (1929.5432410527/11380),
# 
# x1*(y2*(z3 + (140.90112/77.76)) -
#     y3*(z2 + (140.90112/77.76)) +
#     (106.5312/77.76)*(z2-z3) + (23.56850272/77.76)) +
# x2*(y3*(z1 + (140.90112/77.76)) -
#     y1*(z3 + (140.90112/77.76)) -
#     (106.5312/77.76)*(z1-z3) + (39.84175104/77.76)) +
# x3*(y1*(z2 + (140.90112/77.76)) -
#     y2*(z1 + (140.90112/77.76)) +
#     (106.5312/77.76)*(z1-z2) + (15.86269152/77.76)) +
# y1*((80.55936/77.76)*(z2-z3) - (31.1668424/77.76)) +
# y2*((80.55936/77.76)*(z3-z1) - (26.8090368/77.76)) +
# y3*((80.55936/77.76)*(z1-z2) + (7.27040028/77.76)) +
# (41.22213024/77.76)*z1 + (35.45837568/77.76)*z2 + (30.70854384/77.76)*z3
# = -(28.2499646407/77.76)
# 


# 
# x1*(y3*(113800000000000*z2 - 206888400000000) +
#     y2*(206888400000000 - 113800000000000*z3) +
#     2014260000000*(z2-z3) - 362960716800000) +
# x2*(y1*(113800000000000*z3 - 206888400000000) +
#     y3*(206888400000000 - 113800000000000*z1) -
#     2014260000000*(z1-z3) + 38025201600000) +
# x3*(y1*(206888400000000 - 113800000000000*z2) +
#     y2*(113800000000000*z1 - 206888400000000) +
#     2014260000000*(z1-z2)+ 292548849600000) +
# y1*(61907200000000*(z2-z3) + 11809567440000) +
# y2*(61907200000000*(z3-z1) + 1475978220000) +
# y3*(61907200000000*(z1-z2) - 825269402280000) -
# 1212982689600000*z1 - 151600474800000*z2 + 825859951200000*z3 = 19295432410527,
# 
# x1*(y2*(777600000000*z3 + 1409011200000) -
#     y3*(777600000000*z2 + 1409011200000) +
#     1065312000000*(z2-z3) + 235685027200) +
# x2*(y3*(777600000000*z1 + 1409011200000) -
#     y1*(777600000000*z3 + 1409011200000) -
#     1065312000000*(z1-z3) + 398417510400) +
# x3*(y1*(777600000000*z2 + 1409011200000) -
#     y2*(777600000000*z1 + 1409011200000) +
#     1065312000000*(z1-z2) + 158626915200) +
# y1*(805593600000*(z2-z3) - 311668424000) +
# y2*(805593600000*(z3-z1) - 268090368000) +
# y3*(805593600000*(z1-z2) + 72704002800) +
# 412221302400*z1 + 354583756800*z2 + 307085438400*z3 = -282499646407
# 
# 



cons1 : 62500*x1^2 + 62500*y1^2 + 62500*z1^2 - 74529 = 0;

cons2 : 625*x2^2 -1250*x2 + 625*y2^2 + 625*z2^2 - 2624 = 0;

cons3 : 12500*x3^2 + 12500*y3^2 + 12500*z3^2 + 2500*x3 - 44975*y3 - 10982 = 0;

cons4 : 400000*x1*x2 + 400000*y1*y2 + 400000*z1*z2 - 400000*x2 + 178837 = 0;

cons5 : 1000000*x1*x3 + 1000000*y1*y3 + 1000000*z1*z3 + 100000*x3 - 1799000*y3 - 805427 = 0;

cons6 : 2000000*x2*x3 + 2000000*y2*y3 + 2000000*z2*z3 -2000000*x2 + 200000*x3 -3598000*y3 - 1403 = 0;

cons7 : 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;

cons8 : -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;

cons9 : 3200*x2 + 1271 = 0;



solve;
display x1, x2, x3, y1, y2, y3, z1, z2, z3;