forum.polymake.org

Hyperplane arrangement is defined by:

\( x_i+x_j=1 \) and \( x_i+x_j+x_k=1 \) for all \( i,j,k \in \{1,\dots,5\} \).

Supporting inequalities are \( 0\leq x_i\leq 1 \) and \( x_1+x_2+x_3+x_4+x_5\geq 2 \).
Hyperplane matrix:
-1 1 1 0 0 0
-1 1 0 1 0 0
-1 1 0 0 1 0
-1 1 0 0 0 1
-1 0 1 1 0 0
-1 0 1 0 1 0
-1 0 1 0 0 1
-1 0 0 1 1 0
-1 0 0 1 0 1
-1 0 0 0 1 1

-1 1 1 1 0 0
-1 1 1 0 1 0
-1 1 1 0 0 1
-1 1 0 1 1 0
-1 1 0 1 0 1
-1 1 0 0 1 1
-1 0 1 1 1 0
-1 0 1 1 0 1
-1 0 1 0 1 1
-1 0 0 1 1 1
Sp matrix:
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
1 -1 0 0 0 0
1 0 -1 0 0 0
1 0 0 -1 0 0
1 0 0 0 -1 0
1 0 0 0 0 -1
-2 1 1 1 1 1

My pl script is in the attachment. . The result CHAMBER_DECOMPOSITION is not of the correct form.

Firstly, rays are not "symmetric". There are just 3 points of type with two 1 and rest 0 ex.(1,1,0,0,0) (should be 10) and 7 points of type with three 1 and rest 0 ex.(1,1,1,0,0) (should be 10). Secondly, for example point (2/5+1/100,2/5+1/100,2/5+1/100,2/5+1/100,2/5+1/100) belongs to the interior of chamber with the signature [10,11,..,19] but such chamber does not exist in the result.

You are correct, there was an error with the ordering of nodes in the search tree that wasn't triggered in our previous settings. There will be a fix in the upcoming release.