#26363 closed defect (fixed)
Polyhedron_normaliz.save
Reported by:  mkoeppe  Owned by:  

Priority:  major  Milestone:  sage9.1 
Component:  geometry  Keywords:  
Cc:  jipilab, Winfried, tscrim, ghkliem  Merged in:  
Authors:  Jonathan Kliem  Reviewers:  Travis Scrimshaw 
Report Upstream:  N/A  Work issues:  
Branch:  57beae3 (Commits)  Commit:  
Dependencies:  #28639  Stopgaps: 
Description (last modified by )
sage: P = polytopes.dodecahedron(backend='normaliz') sage: P A 3dimensional polyhedron in (Number Field in sqrt5 with defining polynomial x^2  5)^3 defined as the convex hull of 20 vertices sage: P.save('dodecahedron.sobj') TypeError: can't pickle PyCapsule objects
We fix this by removing the cone with __getstate__
on pickling.
On unpickling we use __setstate__
and _cone_from_Vrepresentation_and_Hrepresentation
from #28639 to restore the cone.
Special care has to be taken in the following cases:
 no inequalities (the cone can only be initialized from Vrep),
 the empty polyhedron (cone is
None
in this case).
As the lines are recomputed, there is no guarantee that they appear in the same order in the normaliz cone. However, normaliz sorts the given lines anyway:
sage: P = Polyhedron(lines=[[1,0], [0,1]], backend='normaliz').lines() (A line in the direction (1, 0), A line in the direction (0, 1)) sage: P = Polyhedron(lines=[[0,1], [1,0]], backend='normaliz').lines() (A line in the direction (1, 0), A line in the direction (0, 1)) sage: P = Polyhedron(lines=[[1,1], [1,0]], backend='normaliz').lines() (A line in the direction (1, 0), A line in the direction (0, 1))
Also, even if _normaliz_cone
has the lines somewhat shuffled, this shouldn't be noticable as computations are invariant on which line we choose.
Change History (16)
comment:1 Changed 17 months ago by
 Description modified (diff)
comment:2 Changed 8 months ago by
comment:3 Changed 4 months ago by
 Cc ghkliem added
comment:4 Changed 4 months ago by
I think I know what to do about it.
 As mentioned one can just remove the cone on pickling. Then the loaded object is just as good as changing backend back and forth (and changing backend to normaliz should also work and still give us a cone or a way to retrive the cone).
 Next step would be do allow initialization of a cone from
Vrepresentation
andHrepresentation
. This works by homogenization of the input and explicitly giving a dehomogenization (this is the only way that Normaliz accepts precomputed data).
Note: I'm not proposing to allow to give both representations to normaliz by the user, but when changing fields or loading a stored object I think we should trust them to be correct.
 Once this is done, one can set up normaliz cone to be a lazy attribute.
comment:5 Changed 4 months ago by
 Dependencies set to #28639
In #28639 I will implement a method that generates the cone from both Vrep and Hrep (recomputing the lines, but thats ok I guess). I have tested this with a few polyhedra, but I have no idea, which examples can be tricky.
comment:6 Changed 4 months ago by
 Description modified (diff)
 Milestone changed from sage8.4 to sage9.0
comment:7 Changed 3 months ago by
 Branch set to public/26363
 Commit set to 984cc62eb2b46b245dc93f5ca9dec983ec478531
New commits:
c42c907  method to obtain cone from Vrep and Hrep

cc17f07  added documentation to cone from normaliz data

a54cfd9  Merge branch 'public/28639' of git://trac.sagemath.org/sage into public/28639reb

fc4c596  alignment fix in docs

f42a4e2  removed pickling restriction on normaliz tests

984cc62  fixed pickling/unpickling of normaliz polyhedra

comment:8 Changed 3 months ago by
 Commit changed from 984cc62eb2b46b245dc93f5ca9dec983ec478531 to a75d3b22d3ece100a0cdfa925644d9bd040cba3c
Branch pushed to git repo; I updated commit sha1. New commits:
a75d3b2  take care of special cases

comment:9 Changed 3 months ago by
 Description modified (diff)
 Status changed from new to needs_review
New commits:
a75d3b2  take care of special cases

comment:10 Changed 3 months ago by
 Commit changed from a75d3b22d3ece100a0cdfa925644d9bd040cba3c to 12b90604672457b96b8bb26d4b133478734d4c85
Branch pushed to git repo; I updated commit sha1. New commits:
12b9060  fixing optional flags, added doctest for number field polyhedron pickling

comment:11 Changed 3 months ago by
I plan to extend Normaliz as suggested. The essential point is that Normaliz can skip a convex hull computation, but nevertheless can produce the facet/ectreme ray incidence vectors and keep them for further operations, like the modification of the original cone.
I am not sure whether one can give up the requirement to input the precomputed data in homogenized form with an added dehomogenization if they come from an inhomogeneous computation.
comment:12 Changed 6 weeks ago by
 Milestone changed from sage9.0 to sage9.1
Ticket retargeted after milestone closed
comment:13 Changed 3 weeks ago by
 Branch changed from public/26363 to public/26363reb
 Commit changed from 12b90604672457b96b8bb26d4b133478734d4c85 to 57beae33ef606c604a22fffabd1cfaa02765e091
comment:14 Changed 3 weeks ago by
 Reviewers set to Travis Scrimshaw
 Status changed from needs_review to positive_review
If there are any extensions to Normaliz that can be utilized in the future (as per comment:11), we can do further changes then. This is a nice improvement. LGTM.
comment:15 Changed 2 weeks ago by
 Branch changed from public/26363reb to 57beae33ef606c604a22fffabd1cfaa02765e091
 Resolution set to fixed
 Status changed from positive_review to closed
comment:16 Changed 2 weeks ago by
 Commit 57beae33ef606c604a22fffabd1cfaa02765e091 deleted
Meanwhile I have implemented the use of precomputed data. Version 3.8.4 will very soon be published. Normaliz accepts
Type::extreme_rays
and
Type::support_hyperplanes
as precomputed data.
Howevber, these do not always define the cone (or polyhedron) in which we want to compute since nontrivial coordinate transformations may come into play. These are restored via
Type::generated_lattice
(also in the algebraic case) and
Type::maximal_subspace
It is also important that these precomputed data are considered homogeneous input types so that the polyhedron must be defined via Type::dehomogenization or Type::grading.
See Sections 6.21 and D.8.16 in Normaliz.pdf (as of today).
One could define in
Polyhedron_normaliz
:This constructs an object just as
(but saving computed results)
However, one would need a method to recover
_normaliz_cone
(this method is needed anyway, to make the second thing work).