MATLAB: Easily solved equation isn’t being solved by ‘solve’

solvesyms

When using the function solve in matlab, I keep on having this returned:
minb =
Empty sym: 0-by-1
Yet when using a piece of paper to solve analytically for b, using the expression supplied by matlab, fmin == 0, I can very quickly find the value of b in terms of the other variables. Furthermore, when I solve for h2m, it solves it, and solves it correctly. Why is this happening?
Thank you very much.
syms x A alpha h2m
syms b positive rational
psi = A*exp(-(b*x^2));
V = alpha*x^4;
H = -h2m*diff(diff(psi)) + V*psi;
Hall = psi*H;
avgE=int(Hall,x,-inf,inf);
pretty(simplify(Hall))
pretty(simplify(avgE))
fmin = diff(avgE,b);
pretty(simplify(fmin));
eqn = (fmin == 0);
minb = solve(eqn,b)

Best Answer

There are 3 solutions, which you will find by setting the 'ReturnConditions' option to true:
syms x A alpha h2m
syms b positive rational
psi = A*exp(-(b*x^2));
V = alpha*x^4;
H = -h2m*diff(diff(psi)) + V*psi;
Hall = psi*H;
avgE=int(Hall,x,-inf,inf);
pretty(simplify(Hall))
pretty(simplify(avgE))
fmin = diff(avgE,b);
pretty(simplify(fmin));
eqn = (fmin == 0);
minb = solve(eqn,b ,'ReturnConditions',true);
minb.conditions
minb.b
results are:
ans =
 
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                      0 < (- 1 + 3^(1/2)*1i)^2*((15*alpha)/(16*h2m))^(1/3) & in(((3^(1/2)*1i)/2 - 1/2)^2*((15*alpha)/(16*h2m))^(1/3), 'rational') & A ~= 0 & ((~0 < (1 + 3^(1/2)*1i)^2*((15*alpha)/(16*h2m))^(1/3) & (signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1 | signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= 1 | signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 & signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= 1 & (signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 | signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1)) | signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= -1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= 1 & (signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 | signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1)) & ~0 < alpha/h2m | ~in(((15*alpha)/(16*h2m))^(1/3), 'rational') & (~0 < (1 + 3^(1/2)*1i)^2*((15*alpha)/(16*h2m))^(1/3) & (signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1 | signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= 1 | signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 & signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= 1 & (signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 | signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1)) | signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= -1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= 1 & (signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 | signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1)) & 0 < alpha/h2m | 0 < (1 + 3^(1/2)*1i)^2*((15*alpha)/(16*h2m))^(1/3) & ~in(((3^(1/2)*1i)/2 + 1/2)^2*((15*alpha)/(16*h2m))^(1/3), 'rational') & (~in(((15*alpha)/(16*h2m))^(1/3), 'rational') | ~0 < alpha/h2m) & (signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1 | signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= 1 | signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 & signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= 1 & (signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 | signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1))) | 0 < (- 1 + 3^(1/2)*1i)^2*((15*alpha)/(16*h2m))^(1/3) & in(((3^(1/2)*1i)/2 - 1/2)^2*((15*alpha)/(16*h2m))^(1/3), 'rational') & in(((15*alpha)/(16*h2m))^(1/3), 'rational') & A ~= 0 & 0 < alpha/h2m & (~0 < (1 + 3^(1/2)*1i)^2*((15*alpha)/(16*h2m))^(1/3) & (signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1 | signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= 1 | signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 & signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= 1 & (signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 | signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1)) | 0 < (1 + 3^(1/2)*1i)^2*((15*alpha)/(16*h2m))^(1/3) & ~in(((3^(1/2)*1i)/2 + 1/2)^2*((15*alpha)/(16*h2m))^(1/3), 'rational') & (signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1 | signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= 1 | signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 & signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= 1 & (signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 | signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1)) | signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= -1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= 1 & (signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 | signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1)) | 0 < (- 1 + 3^(1/2)*1i)^2*((15*alpha)/(16*h2m))^(1/3) & 0 < (1 + 3^(1/2)*1i)^2*((15*alpha)/(16*h2m))^(1/3) & in(((3^(1/2)*1i)/2 - 1/2)^2*((15*alpha)/(16*h2m))^(1/3), 'rational') & in(((3^(1/2)*1i)/2 + 1/2)^2*((15*alpha)/(16*h2m))^(1/3), 'rational') & (~in(((15*alpha)/(16*h2m))^(1/3), 'rational') | ~0 < alpha/h2m) & A ~= 0 & (signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1 | signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= 1 | signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 & signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= 1 & (signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 | signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1)) | 0 < (- 1 + 3^(1/2)*1i)^2*((15*alpha)/(16*h2m))^(1/3) & 0 < (1 + 3^(1/2)*1i)^2*((15*alpha)/(16*h2m))^(1/3) & in(((3^(1/2)*1i)/2 - 1/2)^2*((15*alpha)/(16*h2m))^(1/3), 'rational') & in(((3^(1/2)*1i)/2 + 1/2)^2*((15*alpha)/(16*h2m))^(1/3), 'rational') & in(((15*alpha)/(16*h2m))^(1/3), 'rational') & A ~= 0 & 0 < alpha/h2m & (signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1 | signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= 1 | signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 & signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= 1 & (signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 | signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1))
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                0 < (1 + 3^(1/2)*1i)^2*((15*alpha)/(16*h2m))^(1/3) & in(((3^(1/2)*1i)/2 + 1/2)^2*((15*alpha)/(16*h2m))^(1/3), 'rational') & A ~= 0 & ((~0 < (- 1 + 3^(1/2)*1i)^2*((15*alpha)/(16*h2m))^(1/3) & (signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1 | signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= 1 | signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 & signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= 1 & (signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 | signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1)) | signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= -1 & signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= 1 & (signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 | signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1)) & ~0 < alpha/h2m | ~in(((15*alpha)/(16*h2m))^(1/3), 'rational') & (~0 < (- 1 + 3^(1/2)*1i)^2*((15*alpha)/(16*h2m))^(1/3) & (signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1 | signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= 1 | signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 & signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= 1 & (signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 | signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1)) | signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= -1 & signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= 1 & (signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 | signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1)) & 0 < alpha/h2m | 0 < (- 1 + 3^(1/2)*1i)^2*((15*alpha)/(16*h2m))^(1/3) & ~in(((3^(1/2)*1i)/2 - 1/2)^2*((15*alpha)/(16*h2m))^(1/3), 'rational') & (~in(((15*alpha)/(16*h2m))^(1/3), 'rational') | ~0 < alpha/h2m) & (signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1 | signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= 1 | signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 & signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= 1 & (signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 | signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1))) | 0 < (1 + 3^(1/2)*1i)^2*((15*alpha)/(16*h2m))^(1/3) & in(((3^(1/2)*1i)/2 + 1/2)^2*((15*alpha)/(16*h2m))^(1/3), 'rational') & in(((15*alpha)/(16*h2m))^(1/3), 'rational') & A ~= 0 & 0 < alpha/h2m & (~0 < (- 1 + 3^(1/2)*1i)^2*((15*alpha)/(16*h2m))^(1/3) & (signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1 | signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= 1 | signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 & signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= 1 & (signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 | signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1)) | 0 < (- 1 + 3^(1/2)*1i)^2*((15*alpha)/(16*h2m))^(1/3) & ~in(((3^(1/2)*1i)/2 - 1/2)^2*((15*alpha)/(16*h2m))^(1/3), 'rational') & (signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1 | signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= 1 | signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 & signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= 1 & (signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 | signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1)) | signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= -1 & signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= 1 & (signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 | signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1)) | 0 < (- 1 + 3^(1/2)*1i)^2*((15*alpha)/(16*h2m))^(1/3) & 0 < (1 + 3^(1/2)*1i)^2*((15*alpha)/(16*h2m))^(1/3) & in(((3^(1/2)*1i)/2 - 1/2)^2*((15*alpha)/(16*h2m))^(1/3), 'rational') & in(((3^(1/2)*1i)/2 + 1/2)^2*((15*alpha)/(16*h2m))^(1/3), 'rational') & (~in(((15*alpha)/(16*h2m))^(1/3), 'rational') | ~0 < alpha/h2m) & A ~= 0 & (signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1 | signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= 1 | signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 & signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= 1 & (signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 | signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1)) | 0 < (- 1 + 3^(1/2)*1i)^2*((15*alpha)/(16*h2m))^(1/3) & 0 < (1 + 3^(1/2)*1i)^2*((15*alpha)/(16*h2m))^(1/3) & in(((3^(1/2)*1i)/2 - 1/2)^2*((15*alpha)/(16*h2m))^(1/3), 'rational') & in(((3^(1/2)*1i)/2 + 1/2)^2*((15*alpha)/(16*h2m))^(1/3), 'rational') & in(((15*alpha)/(16*h2m))^(1/3), 'rational') & A ~= 0 & 0 < alpha/h2m & (signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1 | signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= 1 | signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 & signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= 1 & (signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 | signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1))
 in(((15*alpha)/(16*h2m))^(1/3), 'rational') & A ~= 0 & 0 < alpha/h2m & (0 < (- 1 + 3^(1/2)*1i)^2*((15*alpha)/(16*h2m))^(1/3) & ~in(((3^(1/2)*1i)/2 - 1/2)^2*((15*alpha)/(16*h2m))^(1/3), 'rational') & (~0 < (1 + 3^(1/2)*1i)^2*((15*alpha)/(16*h2m))^(1/3) & (signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1 | signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= 1 | signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 & signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= 1 & (signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 | signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1)) | 0 < (1 + 3^(1/2)*1i)^2*((15*alpha)/(16*h2m))^(1/3) & ~in(((3^(1/2)*1i)/2 + 1/2)^2*((15*alpha)/(16*h2m))^(1/3), 'rational') & (signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1 | signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= 1 | signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 & signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= 1 & (signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 | signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1)) | signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= -1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= 1 & (signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 | signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1)) | ~0 < (- 1 + 3^(1/2)*1i)^2*((15*alpha)/(16*h2m))^(1/3) & ~0 < (1 + 3^(1/2)*1i)^2*((15*alpha)/(16*h2m))^(1/3) & (signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1 | signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= 1 | signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 & signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= 1 & (signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 | signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1)) | 0 < (1 + 3^(1/2)*1i)^2*((15*alpha)/(16*h2m))^(1/3) & ~in(((3^(1/2)*1i)/2 + 1/2)^2*((15*alpha)/(16*h2m))^(1/3), 'rational') & (~0 < (- 1 + 3^(1/2)*1i)^2*((15*alpha)/(16*h2m))^(1/3) & (signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1 | signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= 1 | signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 & signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= 1 & (signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 | signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1)) | signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= -1 & signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= 1 & (signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 | signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1)) | ~0 < (- 1 + 3^(1/2)*1i)^2*((15*alpha)/(16*h2m))^(1/3) & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= -1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= 1 & (signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 | signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1) | ~0 < (1 + 3^(1/2)*1i)^2*((15*alpha)/(16*h2m))^(1/3) & signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= -1 & signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= 1 & (signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 | signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1) | signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= -1 & signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= 1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= -1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= 1) | 0 < (- 1 + 3^(1/2)*1i)^2*((15*alpha)/(16*h2m))^(1/3) & in(((3^(1/2)*1i)/2 - 1/2)^2*((15*alpha)/(16*h2m))^(1/3), 'rational') & in(((15*alpha)/(16*h2m))^(1/3), 'rational') & A ~= 0 & 0 < alpha/h2m & (~0 < (1 + 3^(1/2)*1i)^2*((15*alpha)/(16*h2m))^(1/3) & (signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1 | signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= 1 | signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 & signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= 1 & (signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 | signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1)) | 0 < (1 + 3^(1/2)*1i)^2*((15*alpha)/(16*h2m))^(1/3) & ~in(((3^(1/2)*1i)/2 + 1/2)^2*((15*alpha)/(16*h2m))^(1/3), 'rational') & (signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1 | signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= 1 | signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 & signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= 1 & (signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 | signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1)) | signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= -1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= 1 & (signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 | signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1)) | 0 < (1 + 3^(1/2)*1i)^2*((15*alpha)/(16*h2m))^(1/3) & in(((3^(1/2)*1i)/2 + 1/2)^2*((15*alpha)/(16*h2m))^(1/3), 'rational') & in(((15*alpha)/(16*h2m))^(1/3), 'rational') & A ~= 0 & 0 < alpha/h2m & (~0 < (- 1 + 3^(1/2)*1i)^2*((15*alpha)/(16*h2m))^(1/3) & (signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1 | signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= 1 | signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 & signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= 1 & (signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 | signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1)) | 0 < (- 1 + 3^(1/2)*1i)^2*((15*alpha)/(16*h2m))^(1/3) & ~in(((3^(1/2)*1i)/2 - 1/2)^2*((15*alpha)/(16*h2m))^(1/3), 'rational') & (signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1 | signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= 1 | signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 & signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= 1 & (signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 | signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1)) | signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= -1 & signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= 1 & (signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 | signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1)) | 0 < (- 1 + 3^(1/2)*1i)^2*((15*alpha)/(16*h2m))^(1/3) & 0 < (1 + 3^(1/2)*1i)^2*((15*alpha)/(16*h2m))^(1/3) & in(((3^(1/2)*1i)/2 - 1/2)^2*((15*alpha)/(16*h2m))^(1/3), 'rational') & in(((3^(1/2)*1i)/2 + 1/2)^2*((15*alpha)/(16*h2m))^(1/3), 'rational') & in(((15*alpha)/(16*h2m))^(1/3), 'rational') & A ~= 0 & 0 < alpha/h2m & (signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1 | signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 & signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= 1 | signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 & signIm(((3^(1/2)*1i)/2 - 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) ~= 1 & (signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == -1 | signIm(((3^(1/2)*1i)/2 + 1/2)*((15*alpha)/(16*h2m))^(1/6)*1i) == 1))
 
 
ans =
 
 ((3^(1/2)*1i)/2 - 1/2)^2*((15*alpha)/(16*h2m))^(1/3)
 ((3^(1/2)*1i)/2 + 1/2)^2*((15*alpha)/(16*h2m))^(1/3)
                          ((15*alpha)/(16*h2m))^(1/3)
Related Question