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]

Description changed:

--- 
+++ 
@@ -17,6 +17,6 @@
 
 There are two tiny fixes to it:
 - Make sure to tell the empty polyhedron appart at `Polyhedron_base.__init__`.
-- Add a trivial equation for initialization of the universe polyhedron with backend `cdd`.
+- Add a trivial inequality for initialization of the universe polyhedron with backend `cdd`.
 
 #29842 will add doctests to this.

[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