porta(1)                                                 porta(1)


NAME porta
INTRODUCTION
       Porta  is a collection of routines for analyzing polytopes
       and polyhedra. The polyhedra are either given as the  con-
       vex  hull  of  a  set of points plus (possibly) the convex
       cone of a set of vectors, or as a system of  linear  equa-
       tions and inequalities.  The name porta is an abbreviation
       for POlyhedron Representation Transformation Algorithm and
       points  to  the basic function 'traf'.  This function per-
       forms a transformation from one  of  the  two  representa-
       tions  to the other representation.  For this, 'traf' uses
       a Fourier - Motzkin elimination  algorithm which  projects
       a  linear system on subspaces xi = 0. This projection of a
       given  system  of  linear   inequalities   can   be   done
       separately  by using the function 'fmel'.  Sometimes it is
       of interest to know all integral points  contained   in  a
       polyhedron   which   is  given by a system of linear equa-
       tions and inequalities. For this  one  has  the   function
       'vint'  which  enumerates  all  the  valid integral points
       within given bounds.  As a special function in  this  con-
       text  'fctp'  checks the facet inducing  property of a set
       of linear inequalities for a polyhedron given as a  convex
       hull  plus  a  convex  cone.   The  function 'fctp' uses a
       function 'dim', which computes the dimension of a  polyhe-
       dron  given  as a convex hull plus a convex cone.  Finally
       'portsort'  is  helpful   to   make  datafiles   readable.
       portsort  sorts  and formats given systems.  All functions
       read and write the data from  and  to  files.  Such  files
       can  be manipulated by the user with a default texteditor.
       porta guarantees correct numerical results,  because  only
       integer operations  are  performed. If an arithmetic over-
       flow occurs with the systems integer arithmetic  then  the
       computations   can  be restarted with a multiple precision
       integer arithmetic.

SEE ALSO
       dim(1), fmel(1), iespo(1), portsort(1), traf(1),  fctp(1),
       posie(1), vint(1)



















                        February 21, 1997                       1