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Finding constraints using Mathematica

Posted 1 month ago
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I have a fraction frac1 as below

frac1 = (-2 a + 2 b - 2 d + 4 a gamma - 4 b gamma + 4 d gamma) / (-3 a + 2 b - 3 d + 6 a gamma - 6 b gamma + 6 d gamma)

All the 4 variables in the fraction, a, b, d, and gamma, can only take values from 0 through 1 (inclusive). I want to find what relationship should a, b and d satisfy (for example, a + 3d < 6b, etc) such that the fraction frac1 always assumes values less than or equal to 0.6 for every value of gamma (from 0 through 1). In other words, how should a, b, and d be related so that there exists no value of gamma from 0 through 1 that makes the value of frac1 exceed 0.6?

I have been trying hard to find the correct command for this in Mathematica, but I'm really stuck. Any help is appreciated!!

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Posted 1 month ago

Try

Reduce[{0<=a<=1,0<=b<=1,0<=d<=1,0<=gamma<=1,(-2a+2b-2d+4a gamma-4b gamma+4d gamma)/
  (-3a+2b-3d+6a gamma-6b gamma+6d gamma)<6/10},{a,b,d,gamma}]

Please check all this very carefully to understand how it works and see if I have made any mistakes.

The values the 4 variables can take are not just 0 or 1. They can take any value between 0 and 1, like 0.001, 0.002,,..... 0.999 etc. So there are actually a large number of alternatives here.

The Reduce code from @BillNelson explicitly allows for variables to take on all values between 0 and 1 inclusive.

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