# Revision history [back]

This seems to be a bug, apparently due to the fact that Sage is not able to deal with what is returned by maxima (this might be related to the fat that the returned solution has conditions (if...)) . Thanks for reporting, this is now trac ticket 24800.

Note that sympy is not able to solve it either:

sage: solve([eq1,eq2,eq3],r2,si,co, algorithm='sympy')
NotImplementedError: could not solve 4*r22 - (si*(-sqrt(3 - 27*(-2*r32 - (12*r12 + 12*r32 - 4*sqrt(3)*sqrt(r12**2*si**2 - r12**2 + r12*r32*si**2 + 2*r12*r32 + r32**2*si**2 - r32**2))/(3*(si**2 - 4)))**2*(si**2 - 4)**2/(si**2*(12*r12 + 12*r32 - 4*sqrt(3)*sqrt(r12**2*si**2 - r12**2 + r12*r32*si**2 + 2*r12*r32 + r32**2*si**2 - r32**2))**2)) + 3*(-2*r32 - (12*r12 + 12*r32 - 4*sqrt(3)*sqrt(r12**2*si**2 - r12**2 + r12*r32*si**2 + 2*r12*r32 + r32**2*si**2 - r32**2))/(3*(si**2 - 4)))*(si**2 - 4)/(si*(12*r12 + 12*r32 - 4*sqrt(3)*sqrt(r12**2*si**2 - r12**2 + r12*r32*si**2 + 2*r12*r32 + r32**2*si**2 - r32**2)))) - 2)*(12*r12 + 12*r32 - 4*sqrt(3)*sqrt(r12**2*si**2 - r12**2 + r12*r32*si**2 + 2*r12*r32 + r32**2*si**2 - r32**2))/(3*(si**2 - 4))


That said, you can easily get rid of the square roots by hand, then solve the nex equations, and keep among the solutions the one for which what was under the square roots is non-negative.

This seems to be a bug, apparently due to the fact that Sage is not able to deal with what is returned by maxima (this might be related to the fat that the returned solution has conditions (if...)) . Thanks for reporting, this is now trac ticket 24800.

Note that sympy is not able to solve it either:

sage: solve([eq1,eq2,eq3],r2,si,co, algorithm='sympy')
NotImplementedError: could not solve 4*r22 - (si*(-sqrt(3 - 27*(-2*r32 - (12*r12 + 12*r32 - 4*sqrt(3)*sqrt(r12**2*si**2 - r12**2 + r12*r32*si**2 + 2*r12*r32 + r32**2*si**2 - r32**2))/(3*(si**2 - 4)))**2*(si**2 - 4)**2/(si**2*(12*r12 + 12*r32 - 4*sqrt(3)*sqrt(r12**2*si**2 - r12**2 + r12*r32*si**2 + 2*r12*r32 + r32**2*si**2 - r32**2))**2)) + 3*(-2*r32 - (12*r12 + 12*r32 - 4*sqrt(3)*sqrt(r12**2*si**2 - r12**2 + r12*r32*si**2 + 2*r12*r32 + r32**2*si**2 - r32**2))/(3*(si**2 - 4)))*(si**2 - 4)/(si*(12*r12 + 12*r32 - 4*sqrt(3)*sqrt(r12**2*si**2 - r12**2 + r12*r32*si**2 + 2*r12*r32 + r32**2*si**2 - r32**2)))) - 2)*(12*r12 + 12*r32 - 4*sqrt(3)*sqrt(r12**2*si**2 - r12**2 + r12*r32*si**2 + 2*r12*r32 + r32**2*si**2 - r32**2))/(3*(si**2 - 4))


That said, you can easily get rid of the square roots by hand, then solve the nex new equations, and keep among the solutions the one for which what was under the square roots is non-negative.