       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

>

> Thanks a lot,

> Nilesh

>

>

```

• Prev by Date: Re: v.7.0 issues
• Next by Date: Re: v.7.0 issues
• Previous by thread: A query regarding polytope's faces and vertices
• Next by thread: ContourPlot and ColorFunction Opacity