as from Title, I'm wondering why Mathematica does not automatically give a single, simple solution for the problem
Reduce[Sin[x] == 0, x]
for which I obtain the following result:
Element[C, Integers] && (x == 2*Pi*C || x == Pi + 2*Pi*C)
The answer is obviously correct, but it's equivalent to
Element[C, Integers] && x == Pi*C
Why doesn't Mathematica give this answer, and how can I possibly "simplify" the previous answer to this one?
In this case, the combined solution is immediately obvious; it becomes less obvious, though, when more parameters are introduced, like in the case of
Reduce[Sin[(Sqrt L Sqrt[m] Sqrt[ℰ])/ℏ] == 0 && L > 0 && m > 0 && ℏ > 0, ℰ]
which comes as a condition from the solution of the Schrödinger equation for a particle in a box, and which should solve to a much more elegant
Element[C, Integers] && C >= 1 && ℰ == (Pi^2*ℏ^2*C^2)/(2*L^2*m)
rather than the somehow ugly combination given by the Reduce function.
Funny enough: Wolfram Alpha DOES give the simpler solution!