Re: Solving a system of Inequalities

• To: mathgroup at smc.vnet.net
• Subject: [mg39863] Re: [mg39764] Solving a system of Inequalities
• From: "Christina Chan" <slash_jam at hotmail.com>
• Date: Sun, 9 Mar 2003 05:27:41 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

```The problem I am working on involves 28 variables in 192 inequalities.
I tried a simpler problem (one that involves 6 variables and 16 inequalities)
using InequalitySolve and it gave me a solution that was very difficult to
comprehend. The sample problem is solving {a,b,c,d,e,f,g}, from
c0,
b0,
a0,
a+b+c+4g2d+2e+2f,
2eb,
2ec
a+2eb+c,
a+4g2d+2f,
2fa,
b+2fa+c,
2fc,
b+4g2d+2e,
c+2da+b,
2da,
2db,
c+4g2e+ef

Solving the set of inequatlities by hand allows us to express all variables with dependence on g. Is there a way Mathematica can do that?

Christina

From: Andrzej Kozlowski <AKOZ at MIMUW.EDU.PL>
To: mathgroup at smc.vnet.net
Subject: [mg39863] Re: [mg39764] Solving a system of Inequalities

Mathematica has in fact a very rich collection of functions for
solving algebraic inequalities, but your message makes me doubt that
that the kind of solution you seem to expect to get for your system
is actually possible. You say that "InequalitySolve gives me a
solution that is more complicated than the problem itself". Actually
InequalitySolve represents the solution of a system in cylindrical
form, which is usually the most convenient for further processing.
In general there is nothing simpler available, although in special
cases humans rather than computer can find simpler representations.
To decide if your case is one of these one would have either to see
the full problem or at least a toy problem with the same sort of
structure.

Andrzej Kozlowski
Yokohama, Japan
http://www.mimuw.edu.pl/~akoz/
http://platon.c.u-tokyo.ac.jp/andrzej/

On Thursday, March 6, 2003, at 04:36 pm, Christina Chan wrote:

Hi,
I have 192 linear inequalities containing 28 variables and I want
to find the constraints for each of the variables. I am thinking
about solving the system by eiliminating the variables one by one
(similar to the Gaussian Elimination). Is there a way I can do it
with Mathematica? The function InequalitySolve gives me a solution
that is more complicated than the problem itself.Is there any other
functions that might help? Thank you!!

Christina

```

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