# How to Reduce a system of algebraic inequalities in two variables?

Posted 3 months ago
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 I want to prove that expression1[u,v] <= 0 for all real u, v satisfying 0<=u<=2 and v^2<=u^3 where the formula for expression1 is algebraic but very large and messy. Based on numerical experiments, I strongly believe this statement is true.In other words, I want to compute Reduce[expression1[u,v]<=0 && 0<=u<=2 && v^2<=u^3, {u,v}] However, I am unable to compute this on my laptop (not enough computational resources I suppose, Reduce keeps running even after several hours). So I have two questions:(1) Is there a way to monitor the progress of Reduce[]?(2) I have access to powerful computing clusters as well as AWS. Is there a way to use these resources to solve this problem in a reasonable amount of time?I have attached the explicit formula for expression1. Attachments:
 Your conjecture appears to be true. Here's a visual approach: Show[Plot[{-Sqrt[u^3], Sqrt[u^3]}, {u, 0, 2}, PlotStyle -> Red, Filling -> {1 -> {{2}, {LightRed, Transparent}}}, Frame -> True], ContourPlot[expression1[u, v], {u, 0, 2}, {v, -Sqrt[8], Sqrt[8]}, PlotRange -> All, Contours -> 20, ContourLabels -> True, ContourShading -> None] ]