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Re: A query regarding polytope's faces and vertices

• To: mathgroup at smc.vnet.net
• Subject: [mg93836] Re: A query regarding polytope's faces and vertices
• From: dh <dh at metrohm.com>
• Date: Wed, 26 Nov 2008 07:23:25 -0500 (EST)
• References: <ggdr1i$mf$1@smc.vnet.net>

Hi Nilesh,

your question is not clear, what do you want to generalize?

Every linear equation defines a (hyper) surface. Every inequality a 

correponding half-space. Several inequalities define a polytop (this is 

a bit sloppy, because a polytope should be closed). Every inequality you 

add means an intersection of what you already have and the new 

half-space, giving either a smaller polytop, the same polytop, or an 

empty set.

Daniel



Nilesh Khude wrote:

> Hi,

> 

> I am a new mathematica user and I would like to know whether there is a

> standard mathematica command/ script to solve the following problem:

> 

> Any n- dimensional polytope is defined by the set of linear inequalities

> (faces of the polytope). It is also defined by the the set of vertices.

> for example:

> x <= a,

> y<=b;

> x+y <= c;

> x>=0;

> y>=0

> 

> Also with the condition that  0<= a,b <= c, this polytope is defined by the

> vertices (0,0), (a,0), (b,0), (a, c-a), (c-b, b).

> 

> How can this be generalized to any set of linear inequalities? Could you

> please help me solve this?

> 

> Thanks a lot,

> Nilesh

> 

>