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 > >