This is maybe the worst type of question because it is super specific, but I am hoping that some Mathematica function or rule exists (built-in or custom) that can be helpful for simplifying a somewhat broad class of expressions involving square roots. Here is an example expression of the type I am trying to simplify:
2*s^2*(-1 + v^2) + 2*s*(-Sqrt[1 - v^2 + 2*s*(s - Sqrt[1 + s^2 - v^2])] + Sqrt[1 - v^2 + 2*s*(s + Sqrt[1 + s^2 - v^2])]) - (1 + v^2)*(-2 + 2*v^2 + Sqrt[(-1 - s^2 + v^2)*(-1 + v^2 + 2*s*(-s + Sqrt[1 + s^2 - v^2]))] + Sqrt[(1 + s^2 - v^2)*(1 - v^2 + 2*s*(s + Sqrt[1 + s^2 - v^2]))])
-v<s<v. Numerical evaluation suggests the above expression vanishes within those assumed ranges, but even with
Assuming in Mathematica I was unable to arrive at a satisfactory simplification. I tried
FullSimplify and many other related functions without success. Thoughts on possible simplification tools? I have a few cases like this to deal with where many do not vanish, and I am hoping that those non-vanishing expressions can be simplified extensively considering that the above example is similar and vanishes.