Two bugs with dilation

[kliem]

The new dilation with #29200 discovered two bugs:

sage: 2*Polyhedron([[]], backend='cdd')
...
TypeError ...

and

sage: K.<sqrt2> = QuadraticField(2)
sage: sqrt2*Polyhedron(backend='normaliz')
...
AttributeError

The underlying errors are the following:

sage: from sage.geometry.polyhedron.backend_cdd import Polyhedron_QQ_cdd
sage: from sage.geometry.polyhedron.parent import Polyhedra_QQ_cdd
sage: parent = Polyhedra_QQ_cdd(QQ, 0, 'cdd')
sage: p = Polyhedron_QQ_cdd(parent, [iter([]), iter([]), iter([])], None)
Traceback (most recent call last):
...
TypeError: can't multiply sequence by non-int of type 'NoneType'

sage: Polyhedron(ieqs=[], ambient_dim=5, backend='cdd')
Traceback (most recent call last):
...
TypeError: unsupported operand type(s) for -=: 'NoneType' and 'int'

sage: from sage.geometry.polyhedron.parent import Polyhedra_RDF_cdd
sage: from sage.geometry.polyhedron.backend_cdd import Polyhedron_RDF_cdd
sage: parent = Polyhedra_RDF_cdd(RDF, 1, 'cdd')
sage: Vrep = [[], [], [[1.0]]]
sage: Hrep = [[], []]
sage: p = Polyhedron_RDF_cdd(parent, Vrep, Hrep,
....:                        Vrep_minimal=True, Hrep_minimal=True) 
Traceback (most recent call last):
...
TypeError: unsupported operand type(s) for -=: 'NoneType' and 'int'

There are two tiny fixes to it:

• Make sure to special-case the empty polyhedron in Polyhedron_base.__init__.
• Add a trivial inequality for initialization of the universe polyhedron with backend cdd.

We add doctests for each fix. Note that #29907 will also indirectly test this.

CC: @jplab @LaisRast

Component: geometry

Keywords: polyhedra, dilation

Author: Jonathan Kliem

Branch: 0bb6413

Reviewer: Matthias Koeppe

Issue created by migration from https://trac.sagemath.org/ticket/29899

[kliem]

New commits:

e41d698	fix universe from Hrep for cdd
e055bc7	correctly detect the empty polyhedron

[kliem]

Commit: e055bc7

[kliem]

Branch: public/29899

[kliem]

comment:2

What also doesn't work for cdd and this is how the TestSuite detected the problem is 2*Polyhedron(backend='cdd'). The problem is that it tries to discover the action via

parent(Polyhedron(backend='cdd')).an_element(), which is Polyhedron([[]], backend='cdd').

[kliem]

comment:3

There is no thing as a trivial equation of course.

[sagetrac-git]

Changed commit from e055bc7 to 7eba64d

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

7eba64d

trivial inequality

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

067fb16

also fix it for initialization from Hrep and Vrep

[sagetrac-git]

Changed commit from 7eba64d to 067fb16

[kliem]

comment:6

Again, the branch that I push into public/29842 in a second really tests those things. Otherwise, I wouldn't have discovered this stuff in the first place.

[mkoeppe]

comment:8

I think you should add a doctest that more specifically illustrates this subtle point of the behavior of Polyhedron_base.__init__ when generators are involved.

[sagetrac-git]

Changed commit from 067fb16 to e94f71c

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

e94f71c

add doctests

[mkoeppe]

comment:11

inequalites -> inequalities.

Also could you rephrase/expand the comment involving "The damage is limited." I don't fully understand it

[kliem]

comment:12

I will improve this.

The reason for using generators is that we don't have to build a list/tuple that is possibly discarded. Once we are there, we need to generate all the generators. Of course it might be better if you can really just generate them, when you feed them to the backend, but the backends require that you don't call _init_from_Vrepresentation, when vertices and rays and lines are empty. So we should respect that.

[kliem]

Changed commit from e94f71c to 0bb6413

[kliem]

Changed branch from public/29899 to public/29899-reb

[kliem]

New commits:

53a64b0	Merge branch 'public/29899' of git://trac.sagemath.org/sage into public/29899-reb
0bb6413	documentation

[mkoeppe]

Reviewer: Matthias Koeppe

[kliem]

comment:16

Thank you.

[vbraun]

Changed branch from public/29899-reb to 0bb6413

[slel]

Changed commit from 0bb6413 to none