This question is a continuation to one answered by kglr here.

In the following situation, I find that given my assumptions, it is indeed possible for $g$ to be negative.

g = f - (-1 + f) P + (-2 f + 2 f P) w
Assuming[0 <= w <= 1 && 0 <= P <= 1 && 0 <= f <= 1 , FullSimplify@Reduce[g < 0]]
P + f (-1 + P) (-1 + 2 w) < 0

Given this finding, can Mathematica output combinations of regions of P, f, and w, that give the specified result $P + f (-1 + P) (-1 + 2 w) < 0$ ?

  • 1
    Thanks for accepting my answer, but I think you were too hasty doing that. While accepting is one of the things to do after your question is answered, we recommend that users should test answers before voting and wait 24 hours before accepting the best one. That allows people in all timezones to answer your question and an opportunity for other users to point alternatives, caveats or limitations of the available answers. – rhermans Aug 10 at 13:29
  • @rhermans Thank you. I will keep that in mind. – user120911 Aug 10 at 13:32
FullSimplify @ Reduce[{P + f (-1 + P) (-1 + 2 w) < 0, 
   0 <= w <= 1 && 0 <= P <= 1 && 0 <= f <= 1}, { P, f, w}]

0 <= P < 1/2 &&
-(P/(-1 + P)) < f <= 1 &&
(f + P - f P)/( 2 f - 2 f P) < w <= 1

region = ImplicitRegion[
 P + f (-1 + P) (-1 + 2 w) < 0
 , {P, f, w}
 ]

RegionPlot3D[
 P + f (-1 + P) (-1 + 2 w) < 0
 , {P, -3, 3}
 , {f, -3, 3}
 , {w, -3, 3}
 ]

Mathematica graphics

Your Answer

By clicking "Post Your Answer", you acknowledge that you have read our updated terms of service, privacy policy and cookie policy, and that your continued use of the website is subject to these policies.

Not the answer you're looking for? Browse other questions tagged or ask your own question.