Reduce Question

• To: mathgroup at smc.vnet.net
• Subject: [mg92898] Reduce Question
• From: Chris Metcalf <metcalcj at hotmail.com>
• Date: Fri, 17 Oct 2008 05:24:41 -0400 (EDT)

```Hi

My question concerns how mathematica arrives at the following result:

In:= Reduce[    Root[8 m - 16 m #1 - 8 x #1 + 2 m #1^2 + 16 m #1^3 +  8 x #1^3 - 7 m #1^4 - 8 m #1^5 - 4 x #1^5 +               3 m #1^6 + 2 m #1^7 + x #1^7 & 2] <         (1/2) (((-((m + x)/m)) + (8 + ((m + x))^2/m^2))) &&       m > 0 && x > 0]

Out:= m > 0 && x > 0

I think that the answer is the CylindricalDecomposition algorithm (since the same input into that function arrives at the same conclusion) but I am not sure what that algorithm is doing beyond the broadest terms.

Specifically my questions are:
(1) is there any way to replicate this conclusion by hand (that is to derive that the one expression is less than the other)?
(2) if not is there a satisfactory way to describe how the conclusion was reached?

Thanks
Chris Metcalf

_________________________________________________________________

```

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