Dear Experts, I'm trying to solve the inequality:
fun2 = Compile[{x, y, a, b, c, d}, (2/3 a + 4/3 b x) (1 - y^2) + (1 - a) (2 c x^2 (1 - y^2)
+ 1/2 (1 - c) (1 - x^2) (1 + y^2) + 4/3 d (1 - x^2) y)]
Reduce[ForAll[{x, y}, -1 < x < 1 && -1 < y < 1 && 0 < a < 1 && -1 < b < 1 && 0 < c < 1 &&
-3/4 (1 - c) < d < 3/4 (1 - c), fun2[x, y, a, b, c, d] > 0] && 0 < a < 1 && -1 < b < 1 && 0 < c < 1 &&
-3/4 (1 - c) < d < 3/4 (1 - c), {a, b}, Reals]
Basically I would like to find the conditions on a and b that allow the expression to be always positive for every x and y (within their range, meaning -1 < x < 1 && -1 < y < 1)
(a) I'm not sure whether the Mathematica code that I wrote will do the job
(b) When I run this code it never ends, it's like it goes in an infinite loop
So my question is: is the Mathematica code correct ? If it is, is there a way to speed up the computation ?
Many thanks for your support.