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Let $Y = f(x_1, x_2, ... , x_n)$ be a continuous function of $n$ ($n$ is big, say $1000$) variables. I have an inequality, $a \leq Y \leq b$. The problem is to visualize $x_1, x_2,\dots, x_n$ satisfying the inequality. When $n \leq 3$, I can using RegionPlot or RegionPlot3D. Are there feasible solutions for higher dimensions? Many thanks.

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Maybe, I shall try FindInstance, and get a considerable amount of points. Then run a convex-hull algorithm to determine the shape, provided that the true shape is convex. –  Cheng Chou Apr 21 '13 at 23:40
You might be able to add colour, and potentially opacity, get you a couple of extra "dimensions", but interpretation will be a challenge. You could look at dimensionality reduction methods such as MDS or sammon mapping, but they are, of course, not perfect. –  image_doctor Apr 22 '13 at 0:16
Do you need a visualization or do you need to find the iso-surface (get the data, but not visualize)? I get the impression you want the latter. –  Szabolcs Apr 27 '13 at 17:42
What do you want to do with the points once you found them? Can you say more about the specific problem? Maybe someone can give you better advice by understanding the original problem. –  Thies Heidecke Apr 27 '13 at 20:49
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