#11429: Count integral points without PALP
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Reporter: vbraun | Owner: AlexGhitza
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-4.7.1
Component: algebraic geometry | Keywords: sd31
Work_issues: | Upstream: N/A
Reviewer: Andrey Novoseltsev | Author: Volker Braun
Merged: | Dependencies: #11312
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Changes (by novoselt):
* keywords: => sd31
* reviewer: => Andrey Novoseltsev
Old description:
> We want our own code to enumerate lattice points in polyhedra because:
> * Going through the PALP pexpect interface is annoyingly slow.
> * no more compile-time bounds
> * It seems like PALP uses a very unsophisticated algorithm:
> {{{
> sage: v = [(1,0,7,-1), (-2,-2,4,-3), (-1,-1,-1,4), (2,9,0,-5),
> (-2,-1,5,1)]
> sage: lp = LatticePolytope(matrix(v).transpose()); lp
> A lattice polytope: 4-dimensional, 5 vertices.
> sage: lp.npoints()
> }}}
> takes forever with PALP but only 500ms with my Python code.
>
> Comparing timings, it seems that PALP always runs over the integral
> points of a rectangular bounding box. This is good for small polytopes
> (low overhead) but bad for large ones. To match PALP's speed for small
> polytopes, I implemented the same algorithm in Cython (the second patch)
> and use it for bounding boxes containing <50k points.
>
> Apply trac_11429_native_enumeration_of_lattice_polytope_points.patch,
> trac_11429_cythonize_lattice_points.patch, trac_11429_fix_doctests.patch
New description:
We want our own code to enumerate lattice points in polyhedra because:
* Going through the PALP pexpect interface is annoyingly slow.
* no more compile-time bounds
* It seems like PALP uses a very unsophisticated algorithm:
{{{
sage: v = [(1,0,7,-1), (-2,-2,4,-3), (-1,-1,-1,4), (2,9,0,-5),
(-2,-1,5,1)]
sage: lp = LatticePolytope(matrix(v).transpose()); lp
A lattice polytope: 4-dimensional, 5 vertices.
sage: lp.npoints()
}}}
takes forever with PALP but only 500ms with my Python code.
Comparing timings, it seems that PALP always runs over the integral points
of a rectangular bounding box. This is good for small polytopes (low
overhead) but bad for large ones. To match PALP's speed for small
polytopes, I implemented the same algorithm in Cython (the second patch)
and use it for bounding boxes containing <50k points.
'''Apply:'''
1.
[attachment:trac_11429_native_enumeration_of_lattice_polytope_points.patch]
1. [attachment:trac_11429_cythonize_lattice_points.patch]
1. [attachment:trac_11429_fix_doctests.patch]
--
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/11429#comment:5>
Sage <http://www.sagemath.org>
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