# hyperplane arrangements raises error on regions

Dear all,

When computing the regions of a hyperplane arrangements, it fails and raises the following:

```
ValueError: *Input Error: Input format is not correct.
*Format:
begin
m n NumberType(real, rational or integer)
b -A
end
```

Yet when running the command vertices, it computes it which is confusing!

The full code is:

```
P = [[-0.48, 0.83], [-5.33, 9.23]]
Q = [[0.43, 0. ], [9.04, 0. ]]
Z = [[-0.35, -0.60], [-1.44, -2.49]]
V = VoronoiDiagram(P)
R = [r for r in V.regions().items()]
s = R[0][1].hyperplane_arrangement()
V = VoronoiDiagram(Q)
R = [r for r in V.regions().items()]
s = s.add_hyperplane(R[0][1].hyperplane_arrangement())
V = VoronoiDiagram(Z)
R = [r for r in V.regions().items()]
s = s.add_hyperplane(R[0][1].hyperplane_arrangement())
s.regions()
```

How can I overcome this eerie bug?

This means that there is an intersection but the sage cant attain the regions which is weird as stated before!

P.s. The full traceback:

```
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
<ipython-input-6-4ba993d8025f> in <module>()
----> 1 s.regions()
/opt/sagemath-9.0/local/lib/python3.7/site-packages/sage/misc/cachefunc.pyx in sage.misc.cachefunc.CachedMethodCallerNoArgs.__call__ (build/cythonized/sage/misc/cachefunc.c:12712)()
2308 if self.cache is None:
2309 f = self.f
-> 2310 self.cache = f(self._instance)
2311 return self.cache
2312
/opt/sagemath-9.0/local/lib/python3.7/site-packages/sage/geometry/hyperplane_arrangement/arrangement.py in regions(self)
1608 R = self.base_ring()
1609 dim = self.dimension()
-> 1610 universe = Polyhedron(eqns=[[0] + [0] * dim], base_ring=R)
1611 regions = [universe]
1612 for hyperplane in self:
/opt/sagemath-9.0/local/lib/python3.7/site-packages/sage/geometry/polyhedron/constructor.py in Polyhedron(vertices, rays, lines, ieqs, eqns, ambient_dim, base_ring, minimize, verbose, backend)
660 if got_Vrep:
661 Vrep = [vertices, rays, lines]
--> 662 return parent(Vrep, Hrep, convert=convert, verbose=verbose)
/opt/sagemath-9.0/local/lib/python3.7/site-packages/sage/structure/parent.pyx in sage.structure.parent.Parent.__call__ (build/cythonized/sage/structure/parent.c:9245)()
900 return mor._call_(x)
901 else:
--> 902 return mor._call_with_args(x, args, kwds)
903
904 raise TypeError(_LazyString(_lazy_format, ("No conversion defined from %s to %s", R, self), {}))
/opt/sagemath-9.0/local/lib/python3.7/site-packages/sage/structure/coerce_maps.pyx in sage.structure.coerce_maps.DefaultConvertMap_unique._call_with_args (build/cythonized/sage/structure/coerce_maps.c:5081)()
178 print(type(C), C)
179 print(type(C._element_constructor), C._element_constructor)
--> 180 raise
181
182
/opt/sagemath-9.0/local/lib/python3.7/site-packages/sage/structure/coerce_maps.pyx in sage.structure.coerce_maps.DefaultConvertMap_unique._call_with_args (build/cythonized/sage/structure/coerce_maps.c:4969)()
173 return C._element_constructor(x, *args)
174 else:
--> 175 return C._element_constructor(x, *args, **kwds)
176 except Exception:
177 if print_warnings:
/opt/sagemath-9.0/local/lib/python3.7/site-packages/sage/geometry/polyhedron/parent.py in _element_constructor_(self, *args, **kwds)
523 if convert and Vrep:
524 Vrep = [convert_base_ring(_) for _ in Vrep]
--> 525 return self.element_class(self, Vrep, Hrep, **kwds)
526 if nargs == 1 and is_Polyhedron(args[0]):
527 polyhedron = args[0]
/opt/sagemath-9.0/local/lib/python3.7/site-packages/sage/geometry/polyhedron/backend_cdd.py in __init__(self, parent, Vrep, Hrep, **kwds)
459 sage: TestSuite(p).run()
460 """
--> 461 Polyhedron_cdd.__init__(self, parent, Vrep, Hrep, **kwds)
/opt/sagemath-9.0/local/lib/python3.7/site-packages/sage/geometry/polyhedron/base.py in __init__(self, parent, Vrep, Hrep, **kwds)
125 elif Hrep is not None:
126 ieqs, eqns = Hrep
--> 127 self._init_from_Hrepresentation(ieqs, eqns, **kwds)
128 else:
129 self._init_empty_polyhedron()
/opt/sagemath-9.0/local/lib/python3.7/site-packages/sage/geometry/polyhedron/backend_cdd.py in _init_from_Hrepresentation(self, ieqs, eqns, verbose)
114 s = cdd_Hrepresentation(self._cdd_type, ieqs, eqns)
115 s = self._run_cdd(s, '--redcheck', verbose=verbose)
--> 116 s = self._run_cdd(s, '--repall', verbose=verbose)
117 self._init_from_cdd_output(s)
118 if not self.base_ring().is_exact():
/opt/sagemath-9.0/local/lib/python3.7/site-packages/sage/geometry/polyhedron/backend_cdd.py in _run_cdd(self, cdd_input_string, cmdline_arg, verbose)
163 if 'Error:' in ans + err:
164 # cdd reports errors on stdout and misc information on stderr
--> 165 raise ValueError(ans.strip())
166 return ans
167
ValueError: *Input Error: Input format is not correct.
*Format:
begin
m n NumberType(real, rational or integer)
b -A
end
```

Trying the code on my system or SageMathCell does not reproduce the error. What operating system are you using, what version of SageMath, how did you install SageMath, and how are you interacting with SageMath (notebook, command line, script, etc.)?

I am using Windows and also my college used linux and on both systems it failed. We tried running it inside the sage shell, notebook and even from python itself (writing a script and running the command "sage -python script_name.py".

Note that it has been run on sagemath 9.0 (the newest version)

I added also the full traceback of running the piece of code from inside the sage shell

The bug can be seen more clearly as follows (it occurs sometimes, not always):

Apparently, the output of

`cddexec --redcheck`

is sometimes either incomplete, or not read correctly. The process communication is done in`Polyhedron_RDF_cdd._run_cdd`

.This SageMathCell does suggest that

`cddexec --redcheck`

sometimes segfaults.I would also try to use rational numbers instead of floats, this might facilitate the computations. You probably do not need floats, as the size of the input is reasonable.

say

`83/100`

instead of`0.83`

...