#11312: Speed up the computation of the Hilbert basis of a cone
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Reporter: vbraun | Owner: mhampton
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-4.7.1
Component: geometry | Keywords:
Work_issues: | Upstream: N/A
Reviewer: | Author: Volker Braun
Merged: | Dependencies:
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Changes (by vbraun):
* cc: novoselt (added)
* status: new => needs_review
Old description:
> My first implementation of the Hilbert basis eventually uses PALP to
> compute the points in the parallelotope spanned by the rays of a
> simplicial cone. This can be done much faster with just the Smith normal
> form of the ray matrix.
>
> This makes it easy to compute the points in the semi-open parallelotope,
> so the actual number of semigroup generators is sometimes less than the
> PALP version (which computed the integral points in the closure).
New description:
My first implementation of the Hilbert basis eventually uses PALP to
compute the points in the parallelotope spanned by the rays of a
simplicial cone. This can be done much faster with just the Smith normal
form of the ray matrix.
This makes it easy to compute the points in the semi-open parallelotope,
so the actual number of semigroup generators is sometimes less than the
PALP version (which computed the integral points in the closure). As a
pleasant side effect, arbitrary dimension cones work now as we are no
longer limited to PALP's compile-time bounds.
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/11312#comment:1>
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