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 March 7, 1997 1 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) March 7, 1997 2