Opened 13 months ago

# Characteristic polynomial of central Hyperplane arrangement results wrong result? — at Version 1

Reported by: Owned by: jipilab major sage-9.5 geometry hyperplane arrangements, regions gh-kliem, gh-LaisRast, nailuj N/A

A central hyperplane arrangement must have an even number of regions by central symmetry... yet the one below gets 31 regions(!).

```R.<y> = QQ[]
v1 = AA.polynomial_root(AA.common_polynomial(y^2 - 3), RIF(RR(1.7320508075688772), RR(1.7320508075688774)))
v2 = QQbar.polynomial_root(AA.common_polynomial(y^4 - y^2 + 1), CIF(RIF(RR(0.8660254037844386), RR(0.86602540378443871)), RIF(-RR(0.50000000000000011), -RR(0.49999999999999994))))
my_vectors = (vector(AA, [-v1, -1, 1]), vector(AA, [0, 2, 1]), vector(AA,[v1, -1, 1]), vector(AA, [1, 0, 0]), vector(AA, [1/2, AA(-1/2*v2^3 + v2),0]), vector(AA, [-1/2, AA(-1/2*v2^3 + v2), 0]))

sage: H = HyperplaneArrangements(AA,names='xyz')
sage: x,y,z = H.gens()
sage: A = H(backend="normaliz")
sage: for v in my_vectors:
....:     a,b,c = v
....:     A = A.add_hyperplane(a*x + b*y + c*z)
sage: A
Arrangement of 6 hyperplanes of dimension 3 and rank 3
sage: A.n_regions()
31
sage: A.is_central()
True
```

### comment:1 Changed 13 months ago by chapoton

• Description modified (diff)
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