# 
# Birch, B: "Noncongruence Subgroups, Covers and Drawings",
# In "The Grothendieck Theory of Dessins d'Enfants", editor: Schneps, L.,
# London Mathematical Society Lecture Series 200,
# Cambridge University Press, pages 25-46, 1994. 
# 
# Solution 1 [4.85e-12]
# x1 = [3.78205552886..3.78205552887]
# x2 = [107.299037764..107.299037765]
# x3 = [-10.1252225843..-10.1252225842]
# x4 = [10.1363081259..10.136308126]
# x5 = [299.392733328..299.392733329]
# x6 = [-15.1879803755..-15.1879803754]
# x7 = [10.1465807766..10.1465807767]
# x8 = 1
# 
# Solution 2 [7.64e-13]
# x1 = [0.366215698318..0.366215698319]
# x2 = [30.2178218554..30.2178218555]
# x3 = [22.8143370261..22.8143370262]
# x4 = [13.3734293432..13.3734293433]
# x5 = [3.02814098281..3.02814098282]
# x6 = [-2.2073039086..-2.20730390859]
# x7 = [4.67670754966..4.67670754967]
# x8 = 1
# 
# Solution 3 [3.38e-14]
# x1 = [-0.0696812563417..-0.0696812563416]
# x2 = [1.46149368079..1.4614936808]
# x3 = [4.55178173702..4.55178173703]
# x4 = [6.21012535918..6.21012535919]
# x5 = [0.11430365049..0.114303650491]
# x6 = [-0.287638109547..-0.287638109546]
# x7 = [-0.350673915486..-0.350673915485]
# x8 = 1
# 
# Solution 4 [3.73e-13]
# x1 = [-1.43946955308..-1.43946955307]
# x2 = [-0.515200331459..-0.515200331458]
# x3 = [-2.11601605379..-2.11601605378]
# x4 = [3.2035775991..3.20357759911]
# x5 = [6.81756372345..6.81756372346]
# x6 = [-2.04515751034..-2.04515751033]
# x7 = [-5.00396184281..-5.0039618428]
# x8 = 1
# 




# Domains
var x1 >= -1000, <= 1000;
var x2 >= -1000, <= 1000;
var x3 >= -1000, <= 1000;
var x4 >= -1000, <= 1000;
var x5 >= -1000, <= 1000;
var x6 >= -1000, <= 1000;
var x7 >= -1000, <= 1000;

#  ,x8 in [-1000,1000] 


subject to
# x8 = 1,

cons1 : x2*(6*x1+ 14*x6) + x1*(10*x4*x6+ 48*x5) + x3*(8*x7*x1 - 162*x1^2 + 16*x5)  = 0;

cons2 : x3*(15*x1 + 27*x6) + x4*(30*x5 + 18*x1*x7 - 162*x1^2)+ x2*(24*x7 - 312*x1) + x1*(24*x5 + 84*x6) = 0;

cons3 : 240*x1 + 64*x4 = 420 + 112*x7;

cons4 : x1*(180 - 284*x4 - 162*x1) + 55*x3 + x7*(60*x4 + 50*x1) + 70*x5 + 260*x6 - 112*x2 = 0;

cons5 : -990*x1 + 336*x7 + 90*x6 + 78*x4 - 90*x3 = 0;


cons6 : x5*(4*x4*x1 + 6*x2) + x2*(2*x7*x1 - 162*x1^2) + 3*x6*x3*x1 = 0;

cons7 : x4*(28*x1 + 44*x6) + 36*x2*x6 + 192*x5 + 128*x7*x1 + x3*(40*x7-300*x1) - 648*x1^2  = 0;



# 
# 6*x8*x1*x2 + 10*x4*x1*x6 + 8*x7*x1*x3 - 162*x1^2*x3 + 16*x3*x5 + 14*x6*x2 + 48*x1*x5 = 0,
# 
# 15*x8*x1*x3 - 162*x1^2*x4 - 312*x1*x2 + 24*x1*x5 + 27*x6*x3 + 24*x7*x2 + 18*x4*x1*x7 + 30*x4*x5 + 84*x6*x1 = 0,
# 
# 240*x1 - 420*x8 + 64*x4 - 112*x7 = 0,
# 
# 180*x8*x1 - 284*x4*x1 - 162*x1^2 + 60*x4*x7 + 50*x7*x1 + 70*x5 + 55*x8*x3 + 260*x6 - 112*x2 = 0,
# 
# 66*x8*x1 + 336*x7 + 90*x6 + 78*x4*x8 - 1056*x1 - 90*x3 = 0,
# 
# 136*x8 - 136 = 0,
# 
# 4*x4*x1*x5 + 2*x7*x1*x2 + 6*x2*x5 - 162*x1^2*x2 + 3*x6*x3*x1 = 0,
# 
# 28*x4*x1*x8 + 192*x5 + 128*x7*x1 + 36*x6*x2 + 36*x8*x2 - 300*x1*x3 + 40*x7*x3 - 648*x1^2 + 44*x4*x6 = 0
# 
# 

solve;
display x1, x2, x3, x4, x5, x6, x7;