added example

src/doc/en/reference/references/index.rst

@@ -3246,6 +3246,9 @@ REFERENCES:
 .. [KP2011] Manuel Kauers and Peter Paule. The Concrete Tetrahedron.
             Springer-Verlag, 2011.
 
+.. [KP2020] Lars Kastner and Marta Panizzut, *Hyperplane arrangements
+            in polymake*, arxiv:`2003.13548`.
+
 .. [KP2002b] James Kuzmanovich; Andrey Pavlichenkov, *Finite
              Groups of Matrices Whose Entries Are Integers*, The American
              Mathematical Monthly, Vol. 109, No. 2. (2002) pp. 173-186

src/sage/geometry/hyperplane_arrangement/arrangement.py

@@ -1601,6 +1601,31 @@ def regions(self):
             sage: chessboard = H(chessboard)
             sage: len(chessboard.bounded_regions())   # long time, 359 ms on a Core i7
             64
+
+        Example 6 of [KP2020]::
+
+            sage: from itertools import product
+            sage: def zero_one(d):
+            ....:     for x in product([0,1], repeat=d):
+            ....:         if any(y for y in x):
+            ....:             yield [0] + list(x)
+            ....:
+            sage: K.<x,y> = HyperplaneArrangements(QQ)
+            sage: A = K(*zero_one(2))
+            sage: len(A.regions())
+            6
+            sage: K.<x,y,z> = HyperplaneArrangements(QQ)
+            sage: A = K(*zero_one(3))
+            sage: len(A.regions())
+            32
+            sage: K.<x,y,z,w> = HyperplaneArrangements(QQ)
+            sage: A = K(*zero_one(4))
+            sage: len(A.regions())
+            370
+            sage: K.<x,y,z,w,r> = HyperplaneArrangements(QQ)
+            sage: A = K(*zero_one(5))
+            sage: len(A.regions())            # not tested (~25s)
+            11292
         """
         if self.base_ring().characteristic() != 0:
             raise ValueError('base field must have characteristic zero')