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MathGroup Archive 2003

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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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