I would like to print/show all the possible solutions of a system of equations, more specifically:
sage:x,y,z = var(‚x,y,z‘)
sage:eqn = solve([(0.5*(1/(sqrt(x^4+y^4-2*x^3*y-2*x*y^3+3*x^2*y^2-5*x^2-5*y^2+6*x*y+9)))*(4*x^3-6*x^2*y-2*y^3+6*x*y^2-10*x+6*y))==0, (0.5*(1/(sqrt(x^4+y^4-2*x^3*y-2*x*y^3+3*x^2*y^2-5*x^2-5*y^2+6*x*y+9)))*(4*y^3-6*x*y^2-2*x^3+6*y*x^2-10*y+6*x))==0],x,y)
sage:stuck_out_tongue:rint(eqn)
results in only one of the possible solutions:
[
[x == 0, y == 0]
]
I would like to show/print all the possible solutions, which should be; x1= 0 y1= 0, x2=sqrt(2) y2=(sqrt(2), x3=-sqrt(2) y3=-sqrt(2),x4=-2/3*sqrt(2) y4=2/3*sqrt(2),
x5= 2/3 *sqrt(2) y5= -2/3*sqrt(2). These solutions were acquired with mathematica using a similar method
Thank you in advance,
Ben