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xref - Man Page

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)

Referenced By

lrs(1), lrslib(5).

The man page hvref(1) is an alias of xref(1).

2023.1.4 January 2024 lrslib 7.3