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