forum.polymake.org

Posted: **03 Mar 2016, 10:29**

In https://polymake.org/doku.php/tutorial/coordinates, there is the following example:

polytope > $p=new Polytope(POINTS=>[[1,0,0,0],[0,1,0,0],[0,0,1,0],[0,0,0,1]]);
polytope > print $p->FACETS;
1 0 0 0
0 1 0 0
0 0 1 0
0 0 0 1

It is claimed that

Each line describes one linear inequality. The encoding is as follows: (a_0,a_1,…,a_d) is the inequality a_0 + a_1 x_1 + … + a_d x_d >= 0. [...] Use the command print_constraints($m) to display the inequalities of the matrix $m in a nice way.

However, there are only 4 entries per line. print_constraints seems to be as confused as me, since it prints:

Code: Select all

polytope > print_constraints $p->FACETS;
0: 0 >= -1
1: x1 >= 0
2: x2 >= 0
3: x3 >= 0

So how do I have to interpret the output of FACETS?

Posted: **03 Mar 2016, 12:44**

The first line of the output is the so called "far hyperplane" encompassing all your rays. You have specified an unbounded polyhedron, more precisely, the positive orthant of Q^3, it has three rays and their common facet is x_0==0. Please recall that polymake works with homogeneous coordinates. Indeed, the printed text might deserve an improvement. Lines 2 to 4 are correct, they describe the hyperplanes confining your orthant.

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Format of FACETS

Format of FACETS

Re: Format of FACETS