I tried to run the following get the region where (v,b,r) satisfies some complicated set of inequalities.
Resolve[Exists[{d}, (v + b (1 - r) (d)^0.5 -
d - ((v + b (1 - r) (d)^0.5 - d)^2 - v^2)^0.5) (v +
b (1 + r) (d)^0.5 -
d + ((v + b (1 - r) (d)^0.5 - d)^2 - v^2)^0.5) -
4 (v/2 + r^2 b^2/8)^2 == 0 && d > 0 && d < v&& ((3/4 b^2 r^2 < v < 3/4 b^2 &&
r < (8 v*b^2 + b^4)/(4 v + b^4)) || (v > 3/4 b^2 &&
r < ((1 + b^2) v + b^4/4)/(4 v + b^4))) && 0 < b < 1 && v > 0 &&
r > 0],Reals]
However, Mathematica always return the same set of existence conditions without numerical approximation. There is no sign of any evaluation.
Does anyone know why Resolve fails to work in this situation? What other commands can I try? Thanks!
