#3276 regression in to_poly_solve

[Dima Pasechnik]

the following used to output 2 different solutions, not just one (as is now in 5.39.0):

(%i5) to_poly_solve(Q*sqrt(Q^2 + 2)=1,Q);
(%o5) %union([Q = - sqrt((- sqrt(2)) - 1)])

[David Scherfgen]

Odd that it finds only the imaginary solution, not the real one.

[David Scherfgen]

In Maxima 5.50post (SBCL 2.6.7) to_poly_solve returns both solutions again, so the regression is gone. The second one is the real root that was missing, (sqrt(2)-1)*sqrt(sqrt(2)+1) = 0.6435942529055828 = sqrt(sqrt(2)-1), and substituting either root into Q*sqrt(Q^2+2) gives 1.0000000000000002.

(%i2) load(to_poly_solve)$
(%i3) to_poly_solve(Q*sqrt(Q^2 + 2)=1,Q);
(%o3) %union([Q = -sqrt(-sqrt(2)-1)],[Q = (sqrt(2)-1)*sqrt(sqrt(2)+1)])

Verified by Claude.