Format of FACETS

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falk

Format of FACETS

Postby falk » 03 Mar 2016, 10:29

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

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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:

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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?

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gawrilow
Main Author
Posts: 423
Joined: 25 Dec 2010, 17:40

Re: Format of FACETS

Postby gawrilow » 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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