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I am trying to reduce a bunch of inequalities using the Reduce command in Mathematica. But the output is very convoluted and I am wondering if there's a way to systematically organize it so that I can actually write it on a piece of paper, or at the very least, read it correctly.

For example,

Reduce[h1>=0 && h2>=0 && 2*x>=0 && -m+h1+y>=0 && m+x-y>=0 && h2-x+2y>=0, {x,y}]

produces output that looks like this

enter image description here

which, needless to say, looks horrendous.

Is there a way to clean this up?

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    $\begingroup$ The output is systematically organized in a Cylindrical algebraic decomposition -- if you learn what it means you'll find it easier to use. $\endgroup$ Commented May 25, 2018 at 0:22
  • $\begingroup$ Thanks, @MichaelE2. Knowing what it is doesn't help me read the output as cleanly as I would like, but thanks for enlightening me about CAD. $\endgroup$ Commented May 26, 2018 at 7:03

1 Answer 1

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If you are OK with turning the Ors into Columns, you can do something like:

result = Reduce[ h1 >= 0 && h2 >= 0 && 2*x >= 0 && -m + h1 + y >= 0 && m + x - y >= 0 && h2 - x + 2 y >= 0, {x, y}]; TraditionalForm[ result //. {Or -> (Column[#, Right, Background -> {{White, LightGray}}, Frame -> All] &)@*List}]

Mathematica graphics

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  • $\begingroup$ Your code does not work on MMA Version 8,0. What should @*List be? $\endgroup$ Commented May 25, 2018 at 5:09
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    $\begingroup$ @Akku14 See Composition $\endgroup$ Commented May 26, 2018 at 12:04
  • $\begingroup$ Thank you @chuy for the response. This is very nice. $\endgroup$ Commented May 26, 2018 at 14:36
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    $\begingroup$ @Michael E2, thanks for the hint. This is the only code, that works in version 8.0 TraditionalForm[ result //. Or -> Composition[(Column[#, Right, Background -> {{White, LightGray}}, Frame -> All] &), List]] $\endgroup$ Commented May 30, 2018 at 19:32

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