traf(1) traf(1)
NAME traf
traf - transformation of polyhedral representations
SYNOPSIS
traf [-poscvl] filename_with_suffix_'.ieq'_or'.poi'
DESCRIPTION
traf transforms polyhedra between the following two rep-
resentations: - convex hull of points + convex cone of
vectors (poi-representation) - system of linear equations
and inequalities (ieq-representation) The direction of
transformation is determined by the input filename,
which ends either in '.poi' or in '.ieq'. All computa-
tions are carried out in rational arithmetic to have
guaranteed correct numerical results. Rational arith-
metic uses only integer operations. A possible arithmetic
overflow is recognized. In this case the computations can
be restarted with a special arithmetic allowing the inte-
gers to have arbitrary length. This arithmetic is not as
efficient as the system's integer arithmetic with respect
to time and storage requirements. The computation of the
ieq-representation is performed using Gaussian and
Fourier-Motzkin elimination. In the output file the right
hand sides are 0, or determined by the smallest inte-
ger value for which the coefficients of the inequality
are integral. If this is not possible with system integer
arithmetic or if multiple precision integer arithmetic is
set, the right hand sides are 0 or 1 or -1 and the values
are reduced as far as possible. If PORTA terminates suc-
cessfully then the resulting inequalities are all facet-
defining for your polyhedron and give together with equa-
tions a minimal linear description of your polyhedron. If
an 'ieq'-representation is given as input and if 0 is
not valid for the linear system, 'traf' needs a valid
points. To give such a valid point use the function spe-
cific keyword VALID. The line after VALID contains
exactly dim rational values, where dim is the dimension of
the space considered. 'traf' transforms the ieq repre-
sentation to the poi-representation, after elimination of
equations and 0-centering, by applying the 'poi'-to-'ieq'
direction to the polar polyhedron. Hint: If you give a
valid point or if 0 is valid, then this vector may appear
again in the resulting system, even if this vector might
be redundant in a minimal description. (All other vectors
are non-redundant.)
OPTIONS
-p Unbuffered redirection of terminal messages into
file filename_'.prt'
-o Use a heuristic to eliminate that variable next,
for which the number of new inequalities is minimal
(local criterion). If this option is set, inequal-
ities which are recognized to be facet-inducing
for the finite linear system are printed into a
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traf(1) traf(1)
file as soon as they are identified.
-c Fourier-Motzkin elimination without using the rule
of Chernikov
-s Appends a statistical part to each line with
the number of coefficients
-v Printing a table in the output file which indi-
cates strong validity
-l Use a special integer arithmetic allowing the inte-
gers to have arbitrary lengths. This arithmetic is
not as efficient as the system's integer arithmetic
with respect to time and storage requirements.
Note: Output values which exceed the 32-bit integer
storage size are written in hexadecimal format
(hex). Such hexadecimal format can not be reread as
input.
SEE ALSO
porta(1), dim(1), fmel(1), iespo(1), portsort(1), fctp(1),
posie(1), vint(1) ort(1), fctp(1), posie(1), vint(1)
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