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