Equivalence between a PORTA output and Polymake output for same input
Posted: 04 Mar 2022, 16:47
Hello,
In PORTA, I process the test.poi file with content reproduced below (the online message system does not allow me to attach a .poi file):
On running this through PORTA, to generate the facets, I obtain the file test.poi.ieq, contents of which are reproduced below:
I am attempting to reproduce the same output via Polymake by creating attached file points.txt reproduced below:
Essentially, I have mapped the points in the porta input in CONV_SECTION contents to the first 8 rows of the polymake input file by prepending a 1 to denote that it is a point. The 6 rays of CONE_SECTION, I have mapped as the last 6 rows of the polymake input file by preprending a 0 to denote that it should be interpreted as a ray. I have done so based on the discussion in this thread in the forum: viewtopic.php?f=8&t=24
When I have polymake read this input file and print the facets, I obtain the following:
I am having a tough time interpreting Facet # 3 which says 0 >= -1. Why does polymake provide this as a facet? I have been able to confirm that all of the other facets generated by polymake indeed match the facets given by PORTA.
Can one safely disregard a facet generated by polymake which does not have any variable in it?
Thanks.
In PORTA, I process the test.poi file with content reproduced below (the online message system does not allow me to attach a .poi file):
Code: Select all
DIM = 6
CONV_SECTION
0 1 1 0 0 1
1 0 0 1 1 0
0 0 1 1 0 1
1 0 0 1 1 0
0 1 1 0 0 1
1 0 0 1 1 0
0 1 1 0 0 1
0 0 0 1 1 1
CONE_SECTION
1 0 0 0 0 0
0 1 0 0 0 0
0 0 1 0 0 0
0 0 0 1 0 0
0 0 0 0 1 0
0 0 0 0 0 1
END
Code: Select all
DIM = 6
VALID
0 0 0 1 1 1
INEQUALITIES_SECTION
( 1) -x1 -x6 <= -1
( 2) -x2 -x4 <= -1
( 3) -x3-x4 <= -1
( 4) -x3 -x5 <= -1
( 5) -x4 -x6 <= -1
( 6) -x5-x6 <= -1
( 7) -x1 <= 0
( 8) -x2 <= 0
( 9) -x3 <= 0
( 10) -x4 <= 0
( 11) -x5 <= 0
( 12) -x6 <= 0
END
Code: Select all
1 0 1 1 0 0 1
1 1 0 0 1 1 0
1 0 0 1 1 0 1
1 1 0 0 1 1 0
1 0 1 1 0 0 1
1 1 0 0 1 1 0
1 0 1 1 0 0 1
1 0 0 0 1 1 1
0 1 0 0 0 0 0
0 0 1 0 0 0 0
0 0 0 1 0 0 0
0 0 0 0 1 0 0
0 0 0 0 0 1 0
0 0 0 0 0 0 1
When I have polymake read this input file and print the facets, I obtain the following:
Code: Select all
Facets:
0: x1 >= 0
1: x5 >= 0
2: x4 >= 0
3: 0 >= -1
4: x6 >= 0
5: x4 + x6 >= 1
6: x5 + x6 >= 1
7: x1 + x6 >= 1
8: x2 >= 0
9: x3 >= 0
10: x3 + x4 >= 1
11: x2 + x4 >= 1
12: x3 + x5 >= 1
Can one safely disregard a facet generated by polymake which does not have any variable in it?
Thanks.