I'm using Reduce to verify some inequalities on vectors. I understand that the mathematical part of my computation is not important in this context, so I'll just show you the commands I want to execute in Mathematica.
I need to execute some Reduce commands concerning many variables. The following command
Reduce[{2 (1 + (-1 + a) s) (a^2 s u x - b^2 s x^2 + b (-1 + s) x (u +x)
+ c (-1 + s - c s) y^2 + a (-(-1 + s + b s) u x + (1 + (-1 + b) s) x^2
+ (1+ (-1 + c) s) y^2)) < 0 && a >= b && a >= c && a >= 0 && b >= 0 &&
c >= 0&& u > 0 && x > 0 && y > 0 && 0 < s < 1}, {a, b, c, u, x, y}]
gives the output "False" which is what I expect.
Unfortunately, adding one other variable $t$ and making an inequality more complicated, Mathematica isn't able anymore to compute the result of Reduce. In particular I'm referring to the following Reduce:
Reduce[{D[(1 + s (a - 1))^2, s]*(((1 + s (a - 1)) + x +
s ((-1 + b) x Cos[t]^2 + (b - c) y Cos[t] Sin[t] + (-1 + c) x
Sin[t]^2))^2 + (y + s ((-1 + c) y Cos[t]^2 + (b - c) x Cos[t] Sin[
t] + (-1 + b) y Sin[t]^2))^2) + (1 + s (a - 1))^2*D[((1 + s (a - 1)) +
x + s ((-1 + b) x Cos[t]^2 + (b - c) y Cos[t] Sin[t] + (-1 + c) x
Sin[t]^2))^2 + (y + s ((-1 + c) y Cos[t]^2 + (b - c) x Cos[t] Sin[t]
+ (-1 + b) y Sin[t]^2))^2, s] < 0 && a >= b && a >= c && b >= 0 &&
c >= 0 && x > 0 && y > 0 && 0 < t < 2*Pi && 0 < s < 1}, {a, b,c,t,x,y}]
I'm expecting (or hoping) the output "False", but Mathematica isn't able to finish computations within a reasonable time.
Do you know how can I make Mathematica solve my second Reduce? Maybe using another command instead of Reduce?
Thank you!