So, with 4.7 it doesn't work either. But if I do some transformation by hand, and square both sides (I'm not completely sure if that's allowed), then I get the solution.
f_2 = ((1/4*a^2*t^4 + a_x*t^3*v_x + a_x*t^2*x + t^2*v_x^2 + t^2*v_y^2 + 2*t*v_x*x + 2*t*v_y*y + x^2 + y^2 -m)/(t^3*v_y + t^2*y))**2 == (-sqrt(a^2 - a_x^2))**2 show(f_2) print(solve(f_2, a_x)) [ a_x == -1/4*(4*t^3*v_x^3 + 4*t^3*v_x*v_y^2 + 12*t*v_x*x^2 + 4*(t*v_x + x)*y^2 + 4*x^3 + 8*(t^2*v_x*v_y + t*v_y*x)*y + (a^2*t^5 - 4*m*t)*v_x + (a^2*t^4 + 12*t^2*v_x^2 + 4*t^2*v_y^2 - 4*m)*x + (t*v_y + y)*sqrt(-a^4*t^8 - 16*t^4*v_x^4 - 16*t^4*v_y^4 + 8*a^2*m*t^4 - 64*t*v_x*x^3 - 64*t*v_y*y^3 - 16*m^2 - 16*x^4 - 16*y^4 + 8*(a^2*t^6 + 4*m*t^2)*v_x^2 + 8*(a^2*t^6 - 4*t^4*v_x^2 + 4*m*t^2)*v_y^2 + 8*(a^2*t^4 - 12*t^2*v_x^2 - 4*t^2*v_y^2 + 4*m)*x^2 + 8*(a^2*t^4 - 4*t^2*v_x^2 - 12*t^2*v_y^2 - 8*t*v_x*x - 4*x^2 + 4*m)*y^2 - 16*(4*t^3*v_x^3 + 4*t^3*v_x*v_y^2 - (a^2*t^5 + 4*m*t)*v_x)*x - 16*(4*t^3*v_y^3 + 8*t^2*v_x*v_y*x + 4*t*v_y*x^2 - (a^2*t^5 - 4*t^3*v_x^2 + 4*m*t)*v_y)*y))/(t^4*v_x^2 + t^4*v_y^2 + 2*t^3*v_x*x + 2*t^3*v_y*y + t^2*x^2 + t^2*y^2), a_x == -1/4*(4*t^3*v_x^3 + 4*t^3*v_x*v_y^2 + 12*t*v_x*x^2 + 4*(t*v_x + x)*y^2 + 4*x^3 + 8*(t^2*v_x*v_y + t*v_y*x)*y + (a^2*t^5 - 4*m*t)*v_x + (a^2*t^4 + 12*t^2*v_x^2 + 4*t^2*v_y^2 - 4*m)*x - (t*v_y + y)*sqrt(-a^4*t^8 - 16*t^4*v_x^4 - 16*t^4*v_y^4 + 8*a^2*m*t^4 - 64*t*v_x*x^3 - 64*t*v_y*y^3 - 16*m^2 - 16*x^4 - 16*y^4 + 8*(a^2*t^6 + 4*m*t^2)*v_x^2 + 8*(a^2*t^6 - 4*t^4*v_x^2 + 4*m*t^2)*v_y^2 + 8*(a^2*t^4 - 12*t^2*v_x^2 - 4*t^2*v_y^2 + 4*m)*x^2 + 8*(a^2*t^4 - 4*t^2*v_x^2 - 12*t^2*v_y^2 - 8*t*v_x*x - 4*x^2 + 4*m)*y^2 - 16*(4*t^3*v_x^3 + 4*t^3*v_x*v_y^2 - (a^2*t^5 + 4*m*t)*v_x)*x - 16*(4*t^3*v_y^3 + 8*t^2*v_x*v_y*x + 4*t*v_y*x^2 - (a^2*t^5 - 4*t^3*v_x^2 + 4*m*t)*v_y)*y))/(t^4*v_x^2 + t^4*v_y^2 + 2*t^3*v_x*x + 2*t^3*v_y*y + t^2*x^2 + t^2*y^2) ] -- To post to this group, send email to [email protected] To unsubscribe from this group, send email to [email protected] For more options, visit this group at http://groups.google.com/group/sage-support URL: http://www.sagemath.org
