Unexpected error with affine_hull()

[João Camarneiro]

Hi,

I stumbled upon a strange error with the affine_hull() function for polyhedra. A minimal example is:

pp = Polyhedron(vertices=[[-1, -1, 1, -1], [-1, -1, 5, 1], [-1, 5, -1, 1], [5, -1, -1, 1]])
pp.affine_hull()

This throws the following error:

TypeError: no conversion of this rational to integer

If I add "base_ring = QQ", i.e.

pp = Polyhedron(vertices=[[-1, -1, 1, -1], [-1, -1, 5, 1], [-1, 5, -1, 1], [5, -1, -1, 1]], base_ring=QQ)
pp.affine_hull()

then everything works fine.

Is this a bug?

I am using Ubuntu 24.04 through WSL, and running SageMath version 10.8 on a Jupyter Notebook.

See below for the full error output.

Thanks!

--------------------------------------------------------------------------- TypeError Traceback (most recent call last) Cell In[1], line 2 1 pp = Polyhedron(vertices=[[-Integer(1), -Integer(1), Integer(1), -Integer(1)], [-Integer(1), -Integer(1), Integer(5), Integer(1)], [-Integer(1), Integer(5), -Integer(1), Integer(1)], [Integer(5), -Integer(1), -Integer(1), Integer(1)]]) ----> 2 pp.affine_hull() File ~/miniforge3/envs/sage/lib/python3.12/site-packages/sage/geometry/polyhedron/base6.py:911, in Polyhedron_base6.affine_hull(self, *args, **kwds) 909 return self 910 self_as_face = self.faces(self.dimension())[0] --> 911 return self_as_face.affine_tangent_cone() File ~/miniforge3/envs/sage/lib/python3.12/site-packages/sage/misc/cachefunc.pyx:2353, in sage.misc.cachefunc.CachedMethodCallerNoArgs.__call__() 2351 if self.cache is None: 2352 f = self.f -> 2353 self.cache = f(self._instance) 2354 return self.cache 2355 File ~/miniforge3/envs/sage/lib/python3.12/site-packages/sage/geometry/polyhedron/face.py:941, in PolyhedronFace.affine_tangent_cone(self) 937 new_ieqs = [H for H in self.ambient_Hrepresentation() 938 if H.is_inequality()] 939 new_eqns = [H for H in self.ambient_Hrepresentation() 940 if H.is_equation()] --> 941 return parent.element_class(parent, None, [new_ieqs, new_eqns]) File ~/miniforge3/envs/sage/lib/python3.12/site-packages/sage/geometry/polyhedron/backend_ppl.py:70, in Polyhedron_ppl.__init__(self, parent, Vrep, Hrep, ppl_polyhedron, mutable, **kwds) 68 Polyhedron_mutable.__init__(self, parent, Vrep, Hrep, **kwds) 69 if not mutable: ---> 70 self.set_immutable() File ~/miniforge3/envs/sage/lib/python3.12/site-packages/sage/geometry/polyhedron/backend_ppl.py:193, in Polyhedron_ppl.set_immutable(self) 190 except TypeError as e: 191 # Apparently the polyhedron is (no longer) integral. 192 self._clear_cache() --> 193 raise e 194 if not hasattr(self, '_Hrepresentation'): 195 self._init_Hrepresentation_from_ppl(True) File ~/miniforge3/envs/sage/lib/python3.12/site-packages/sage/geometry/polyhedron/backend_ppl.py:189, in Polyhedron_ppl.set_immutable(self) 187 if not hasattr(self, '_Vrepresentation'): 188 try: --> 189 self._init_Vrepresentation_from_ppl(True) 190 except TypeError as e: 191 # Apparently the polyhedron is (no longer) integral. 192 self._clear_cache() File ~/miniforge3/envs/sage/lib/python3.12/site-packages/sage/geometry/polyhedron/backend_ppl.py:309, in Polyhedron_ppl._init_Vrepresentation_from_ppl(self, minimize) 307 parent._make_Vertex(self, coefficients) 308 else: --> 309 parent._make_Vertex(self, [x/d for x in coefficients]) 310 elif g.is_ray(): 311 parent._make_Ray(self, coefficients) File ~/miniforge3/envs/sage/lib/python3.12/site-packages/sage/geometry/polyhedron/parent.py:1096, in Polyhedra_base._make_Vertex(self, polyhedron, data) 1094 except IndexError: 1095 obj = Vertex(self) -> 1096 obj._set_data(polyhedron, data) 1097 return obj File ~/miniforge3/envs/sage/lib/python3.12/site-packages/sage/geometry/polyhedron/representation.py:1160, in Vrepresentation._set_data(self, polyhedron, data) 1157 if len(data) != self._vector.degree(): 1158 raise ValueError('V-representation data requires a list of length ambient_dim') -> 1160 self._vector[:] = data 1162 self._index = len(polyhedron._Vrepresentation) 1163 polyhedron._Vrepresentation.append(self) File ~/miniforge3/envs/sage/lib/python3.12/site-packages/sage/modules/free_module_element.pyx:1961, in sage.modules.free_module_element.FreeModuleElement.__setitem__() 1959 if isinstance(i, slice): 1960 PySlice_GetIndicesEx(i, d, &start, &stop, &step, &slicelength) -> 1961 values = [R(x) for x in value] 1962 if len(values) != slicelength: 1963 raise IndexError("slice assignment would change dimension") File ~/miniforge3/envs/sage/lib/python3.12/site-packages/sage/structure/parent.pyx:899, in sage.structure.parent.Parent.__call__() 897 if mor is not None: 898 if no_extra_args: --> 899 return mor._call_(x) 900 else: 901 return mor._call_with_args(x, args, kwds) File ~/miniforge3/envs/sage/lib/python3.12/site-packages/sage/rings/rational.pyx:4214, in sage.rings.rational.Q_to_Z._call_() 4212 """ 4213 if not mpz_cmp_si(mpq_denref((<Rational>x).value), 1) == 0: -> 4214 raise TypeError("no conversion of this rational to integer") 4215 cdef Integer n = Integer.__new__(Integer) 4216 n.set_from_mpz(mpq_numref((<Rational>x).value)) TypeError: no conversion of this rational to integer

[Dima Pasechnik]

On Wed, May 6, 2026 at 9:28 PM João Camarneiro <joao.ca...@ed.ac.uk> wrote:
>
> Hi,
>
> I stumbled upon a strange error with the affine_hull() function for polyhedra. A minimal example is:
>
> pp = Polyhedron(vertices=[[-1, -1, 1, -1], [-1, -1, 5, 1], [-1, 5, -1, 1], [5, -1, -1, 1]])
> pp.affine_hull()
>
> This throws the following error:
> TypeError: no conversion of this rational to integer
>
> If I add "base_ring = QQ", i.e.
> pp = Polyhedron(vertices=[[-1, -1, 1, -1], [-1, -1, 5, 1], [-1, 5, -1, 1], [5, -1, -1, 1]], base_ring=QQ)
> pp.affine_hull()
>
> then everything works fine.

Yes, sure, and you have a vertex with non-integer coordinate.

sage: pp.affine_hull().lines()
(A line in the direction (0, 0, 2, 1),
A line in the direction (2, 0, 0, 1),
A line in the direction (0, 2, 0, 1))
sage: pp.affine_hull().vertices()
(A vertex at (0, 0, 0, -1/2),)

It's because affine_hill() is given by Minkowski sum of a vertex and a
linear hyperplane.
(the latter given by 3 lines)

The hull is an affine hyperplane {x | <x,(1, 1, 1, -2)>=1}
sage: pp.affine_hull().Hrepresentation()
(An equation (1, 1, 1, -2) x - 1 == 0,)
No wonder this breaks for the default base_ring=ZZ.
>
> Is this a bug?

it's a documentation bug, as it's not clear from the docs on
affine_hull that you have such an
unusual representation of the result.

HTH
Dima

> --
> You received this message because you are subscribed to the Google Groups "sage-support" group.
> To unsubscribe from this group and stop receiving emails from it, send an email to sage-support...@googlegroups.com.
> To view this discussion visit https://groups.google.com/d/msgid/sage-support/700916ed-e068-4ef0-82da-6bb743b0dbb4n%40googlegroups.com.

[João Camarneiro]

Thank you for the clarification!

So the problem is that a non-integer point is picked as a base vertex of this hyperplane. However this hyperplane does contain integer points which could be used instead, wouldn't that be the expected behaviour when calling affine_hull() from a polytope with base ring ZZ?

Best,

João

[Dima Pasechnik]

yes, it's a bug, I opened https://github.com/sagemath/sage/issues/42142

On Thu, May 7, 2026 at 12:31 PM João Camarneiro

> To view this discussion visit https://groups.google.com/d/msgid/sage-support/de19e5e2-0699-4a88-9217-98111b1f3f8bn%40googlegroups.com.