Hyperplane arrangement D52

[vladimir.i]

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.

Skripta_D0n.txt

(2.38 KiB) Downloaded 20963 times

. 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).

D52Rays.txt

(930 Bytes) Downloaded 20517 times

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.

D52SIGNATURE_full.txt

m is number od x_i+x_j and n numer of x_i+x_j+x_k hyperplanes.

(9.39 KiB) Downloaded 21196 times

[lkastner]

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.