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
       --pp     Unbuffered redirection of  terminal  messages  into
              file filename_'.prt'

       --oo     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



                          March 7, 1997                         1





traf(1)                                                   traf(1)


              file as soon as they are identified.

       --cc     Fourier-Motzkin elimination without using the  rule
              of Chernikov

       --ss     Appends  a  statistical  part  to  each  line  with
              the number  of coefficients

       --vv     Printing a   table in the  output file which  indi-
              cates strong validity

       --ll     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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