Normaliz cone from precomputed data has lattice messed up

[kliem]

sage: p = Polyhedron(vertices=[(-3,-3), (3,0), (3,3), (0,3)], backend='normaliz')
sage: q = loads(p.dumps)
sage: p
sage: p.ehrhart_series()                                                                                                                                                            
(13*t^2 + 22*t + 1)/(-t^3 + 3*t^2 - 3*t + 1)
sage: p.volume()                                                                                                                                                                    
18
sage: q.ehrhart_series()                                                                                                                                                            
(t^2 + 2*t + 1)/(-t^3 + 3*t^2 - 3*t + 1)
sage: q.volume()                                                                                                                                                                    
2

The problem is that we should take the saturation instead of the basis of the row space. In the example above the quotient of the ambient lattice with the computed basis was not torsion-free.

CC: @jplab @LaisRast @mkoeppe

Component: geometry

Keywords: normaliz, polytope

Author: David Roe, Jonathan Kliem

Branch/Commit: bcc7ea6

Reviewer: Matthias Koeppe

Issue created by migration from https://trac.sagemath.org/ticket/30891

[kliem]

comment:1

Normaliz data for p:

# ----8<---- Equivalent Normaliz input file ----8<----
amb_space 2
cone 0
subspace 0
vertices 4
 -3 -3 1
 3 0 1
 3 3 1
 0 3 1
# ----8<-------------------8<-------------------8<----
# Calling PyNormaliz.NmzCone(cone=[], subspace=[], vertices=[[-3, -3, 1], [3, 0, 1], [3, 3, 1], [0, 3, 1]])

Normaliz data for q:

# ----8<---- Equivalent Normaliz input file ----8<----
amb_space 2
dehomogenization 1
 0 0 1
extreme_rays 4
 -3 -3 1
 0 3 1
 3 0 1
 3 3 1
generated_lattice 3
 3 0 0
 0 3 0
 0 0 1
maximal_subspace 0
support_hyperplanes 4
 -1 0 3
 -1 2 3
 0 -1 3
 2 -1 3
# ----8<-------------------8<-------------------8<----
# Calling PyNormaliz.NmzCone(dehomogenization=[[0, 0, 1]], extreme_rays=[[-3, -3, 1], [0, 3, 1], [3, 0, 1], [3, 3, 1]], generated_lattice=[[3, 0, 0], [0, 3, 0], [0, 0, 1]], maximal_subspace=[], support_hyperplanes=[[-1, 0, 3], [-1, 2, 3], [0, -1, 3], [2, -1, 3]])

The volume is probably a usage error, I did not consider the case where a "cube" in the generated lattice has volume not equal to 1.

Ok, the other issue probably as well.

This raises a simple question in sage: Given rational vectors. How do I calculate integer vectors that generate the induced lattice? Actually the given vectors or integer, but for the mathematical question, I consider them to be rational.

[kliem]

Changed upstream from Not yet reported upstream; Will do shortly. to none

[kliem]

comment:3

I guess the solution to the second part also solves the first part, because in case of the volume the generated lattice is always the entire lattice (otherwise the "ambient" volume is zero anyway).

[kliem]

Author: David Roe, Jonathan Kliem

[kliem]

Branch: public/30891

[kliem]

Commit: cddb6db

[kliem]

New commits:

cddb6db

use saturation to obtain the correct lattice

[kliem]

Changed branch from public/30891 to public/30891-reb

[kliem]

Changed commit from cddb6db to bcc7ea6

[kliem]

comment:7

Forgot the optional flags. I don't know, when I will ever remember (and get it right on the first try).

---

New commits:

c7ed9b5	Merge branch 'public/30891' of git://trac.sagemath.org/sage into public/30891-reb
bcc7ea6	added optional flags

[mkoeppe]

Reviewer: Matthias Koeppe

[kliem]

comment:9

Thank you.

[vbraun]

Changed branch from public/30891-reb to bcc7ea6