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 On Thursday, 7 May 2026 at 05:52:36 UTC+1 [email protected] wrote: > On Wed, May 6, 2026 at 9:28 PM João Camarneiro <[email protected]> > 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 > > > > > > 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 > > > > -- > > 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 [email protected]. > > To view this discussion visit > https://groups.google.com/d/msgid/sage-support/700916ed-e068-4ef0-82da-6bb743b0dbb4n%40googlegroups.com > . > -- You received this message because you are subscribed to the Google Groups "sage-support" group. 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