# Domains
var x >= -1.0e8, <= 1.0e8;
var y >= -1.0e8, <= 1.0e8;
var z >= -1.0e8, <= 1.0e8;

subject to
cons1 : x^2 - y^2 + z^2  = 0.5;
cons2 : x^3 - y^3 + z^3  = 0.5;
cons3 : x^4 - y^4 + z^4  = 0.5;

cons4 : 2*x*y+6*y^2+2*y*z-2*x-4*y-2*z+1 = 0;
# 
# 2*x^2-2*y^2+2*z^2-1 = 0,
# 8*y^2*z-4*x*z^2+4*y*z^2+4*z^3-8*y^2-8*y*z-4*z^2+3*x+4*y+3*z-2 = 0,
# 32*y^3+12*x*z^2-4*y*z^2-12*z^3+16*y^2+8*y*z+4*z^2-15*x-16*y-11*z+10= 0,
# 24*y*z^3+40*z^4-16*x*z^2-24*y*z^2-8*z^3-8*y^2+6*x*z-12*y*z-18*z^2+6*x+12*y+6*z-7= 0,
# 16*x*z^3+8*y*z^3-8*z^4-8*y*z^2-8*z^3-4*x*y-4*y^2-6*x*z+2*z^2-2*x+4*y+6*z+3= 0,
# 192*z^5+32*z^4+10*x*z^2-60*y*z^2-118*z^3-16*y^2+12*x*z-60*z^2-24*x+33*y+6*z+13= 0;
# 

# 
# {z = -.1874232831, x = .8768642569, y = .5513786467}
# {y = .6353521306, x = .8992525249, z = .3082486435}
# {y = .5513786467, z = .8768642569, x = -.1874232831}
# {y = .6353521306, z = .8992525249, x = .3082486435}
# 

solve;
display x, y, z;