Man page of xref|hvref

Content-type: text/html; charset=UTF-8

# xref|hvref

Section: lrslib 7.3 (1)
Updated: 2023.1.4
Index Return to Main Contents

### Name

xref|hvref - produce a cross reference list between H- and V-representations.

### Synopsis

xref [input-file]
hvref [input-file]

### Description

  These programs are part of and must be compiled with lrslib which is a C library. All computations are done in exact arithmetic.

  xref and hvref produce a cross reference list between H- and V-representations.

  xref/hvref Cross reference listing between V- and H-representations

  In the example below we start from an H-representation of cube.ine but the same steps apply to the V-representation cube.ext. It is recommended to first remove any redundancies from the input file using redund.

  1. Add printcobasis and incidence options to cube.ine and run lrs.
  % cat cube.ine
  cube
  H-representation
  begin
  6 4 rational
  0 1 0 0
  0 0 1 0
  0 0 0 1
  1 -1 0 0
  1 0 -1 0
  1 0 0 -1
  end
  printcobasis
  incidence
  % lrs cube.ine cube.ext

  2. Run xref on the output file cube.ext getting cube.ext.ex

  % xref cube.ext
  % cat cube.ext.ex lg% cat cube.ext.x
  V-representation
  1 4 5 6 #
  2 1 5 6 #
  3 2 4 6 #
  4 1 2 6 #
  5 3 4 5 #
  6 1 3 5 #
  7 2 3 4 #
  8 1 2 3 #

  3. Edit the file cube.ext.x to insert a second line that contains two integers

  rows maxindex

  where rows >= # output lines in cube.ext.x
  maxindex >= # input lines in cube.ine

  or just use 0 0 and run hvref, the output will tell you which values to use.

  % hvref cube.ext.x % hvref cube.ext.x

  V-representation
  8 8
  1: 4 5 6
  2: 1 5 6
  3: 2 4 6
  4: 1 2 6
  5: 3 4 5
  6: 1 3 5
  7: 2 3 4
  8: 1 2 3
  H-representation
  6 8
  1: 2 4 6 8
  2: 3 4 7 8
  3: 5 6 7 8
  4: 1 3 5 7
  5: 1 2 5 6
  6: 1 2 3 4
  input rows=8 maxindex=6

  ### Notes

  1.
    FAQ page
      https://inf.ethz.ch/personal/fukudak/polyfaq/polyfaq.html
  2.
    User's guide for lrslib
      http://cgm.cs.mcgill.ca/~avis/C/lrslib/USERGUIDE.html

  ### Author

  David Avis <avis at cs dot mcgill dot ca >

  ### See also

  mplrs(1), lrslib(5), lrsnash(1)

  ## Index

  Name
  Synopsis
  Description
  Notes
  Author
  See also

  This document was created by man2html, using the manual pages.
  Time: 07:33:14 GMT, January 31, 2024