# 
# 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 [1.03e-13]
# x1  = [2.65776274396..2.65776274397]
# x2  = [6.91718100964..6.91718100965]
# x3  = [9.99414484462..9.99414484463]
# x4  = [9.63176834344..9.63176834345]
# x5  = [1.18854045347..1.18854045348]
# x6  = [-1.60177246299..-1.60177246298]
# x7  = [-0.469214069581..-0.46921406958]
# x8  = [-0.399584919922..-0.399584919921]
# x9  = [1.10030360314..1.10030360315]
# x10 = 1
# 
# Solution 2 [2.38e-12]
# x1  = [0.779008417263..0.779008417265]
# x2  = [4.33907947158..4.33907947159]
# x3  = [9.34873086416..9.34873086418]
# x4  = [9.78828230464..9.78828230465]
# x5  = [0.0120632369858..0.012063236986]
# x6  = [-0.047163914433..-0.0471639144329]
# x7  = [-0.399652309049..-0.399652309048]
# x8  = [-0.00189503161014..-0.00189503161013]
# x9  = [0.146701234205..0.146701234206]
# x10 = 1
# 
# Solution 3 [3.56e-14]
# x1  = [-2.16580787517..-2.16580787516]
# x2  = [-3.12784134069..-3.12784134068]
# x3  = [3.18261760274..3.18261760275]
# x4  = [8.12238892404..8.12238892405]
# x5  = [0.16452523838..0.164525238381]
# x6  = [-0.450407537406..-0.450407537405]
# x7  = [-1.1400493671..-1.14004936709]
# x8  = [-0.0996817823765..-0.0996817823764]
# x9  = [0.519796429923..0.519796429924]
# x10 = 1
# 



# Domains
var x1 >= -10, <= 10;
var x2 >= -10, <= 10;
var x3 >= -10, <= 10;
var x4 >= -10, <= 10;
var x5 >= -10, <= 10;
var x6 >= -10, <= 10;
var x7 >= -10, <= 10;
var x8 >= -10, <= 10;
var x9 >= -10, <= 10;
var x10 >= -10, <= 10;


subject to
cons1 : 16*x1*x6 + 18*x2*x5 + 20*x3*x8 = 0;
cons2 : 7*x1*x5 + 8*x2*x8 = 0;
cons3 : 210*x10 - 210 = 0;
cons4 : 78*x2*x10 + 84*x3*x7 + 90*x4*x9 - 170*x1 + 102*x5 + 480*x6 = 0;
cons5 : 136*x4*x10 - 114*x3 + 152*x9 + 720*x7 = 0;
cons6 : 105*x3*x10 + 112*x4*x7 - 144*x2 + 126*x6  + 595*x9 = 0;
cons7 : 180*x7 -80*x4 + 855*x10 = 0;
cons8 : 40*x1*x7 + 44*x2*x9 + 48*x3*x6 + 52*x4*x5 + 280*x8 = 0;
cons9 : 27*x1*x9 + 30*x2*x6 + 33*x3*x5 + 36*x4*x8 = 0;
cons10 : 55*x1*x10 + 60*x2*x7 + 65*x3*x9 + 70*x4*x6 + 80*x8 + 375*x5 = 0;
cons11 : x9 - (114/152)*x3 + (1026/152)*x7 + (1453.5/152) = 0;
cons12 : x9 - (114/152)*x3 + (456/152)*x4 - (3420/152) = 0;

#  The original system has been scaled into: (but less fast)
#   x1*x6 + (18/16)*x2*x5 + (20/16)*x3*x8 = 0 ,
#   x1*x5 + (8/7)*x2*x8 = 0 ,
#   x10 = 1,
#   x2*x10 + (84/78)*x3*x7 + (90/78)*x4*x9 - (170/78)*x1 + (102/78)*x5 + (480/78)*x6 = 0 ,
#   x4*x10 - (114/136)*x3 + (152/136)*x9 + (720/136)*x7 = 0 ,
#   x3*x10 + (112/105)*x4*x7 - (144/105)*x2 + (126/105)*x6 + (595/105)*x9 = 0 ,
#   x7 - (80/180)*x4 + (855/180)*x10 = 0,
#   x1*x7 + (44/40)*x2*x9 + (48/40)*x3*x6 + (52/40)*x4*x5 + (280/40)*x8 = 0 ,
#   x1*x9 + (30/27)*x2*x6 + (33/27)*x3*x5 + (36/27)*x4*x8 = 0 ,
#   x1*x10 + (60/55)*x2*x7 + (65/55)*x3*x9 + (70/55)*x4*x6 + (80/55)*x8 + (375/55)*x5 = 0 ,
#   x9 - (114/152)*x3 + (1026/152)*x7 + (1453.5/152) = 0,
#   x9 - (114/152)*x3 + (456/152)*x4 - (3420/152) = 0
# 



solve;
display x1, x10, x2, x3, x4, x5, x6, x7, x8, x9;