#8986: Add support for convex rational polyhedral cones
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Reporter: novoselt | Owner: mhampton
Type: enhancement | Status: positive_review
Priority: major | Milestone: sage-4.4.4
Component: geometry | Keywords:
Author: Andrey Novoseltsev | Upstream: N/A
Reviewer: Volker Braun | Merged:
Work_issues: |
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Comment(by novoselt):
Thank you!
Dimension limit is exactly why I started using `Polyhedra`, however I
didn't quite like the timings. For example, this is what I get on
geom.math with toric patches applied:
{{{
sage: %time
sage: o = lattice_polytope.octahedron(6) # no PALP calls
CPU time: 0.00 s, Wall time: 0.00 s
sage: %time
sage: len(o.faces()) # PALP call to get incidences (no Hasse diagram)
6
CPU time: 0.07 s, Wall time: 0.13 s
sage: %time
sage: f = FaceFan(o)
CPU time: 0.03 s, Wall time: 0.06 s
sage: %time
sage: f.cone_lattice() # some calls to PALP
Finite poset containing 730 elements
CPU time: 0.18 s, Wall time: 0.32 s
sage: %time
sage: p = Polyhedron(vertices=o.vertices().columns()) # almost all time is
in cdd
CPU time: 0.02 s, Wall time: 3.84 s
sage: %time
sage: p.face_lattice() # all time in Sage
Finite poset containing 730 elements
CPU time: 8.36 s, Wall time: 8.36 s
}}}
Given the construction time of `p`, I am not even sure if calling cdd as a
library will help a lot, but you mentioned that you also had some other
library in mind. So while I am definitely interested in going to
dimensions higher than 6, so far PALP seems to be the way to go. One
possible modification for the future is to use PALP when possible and
switch to alternatives when it does not work.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/8986#comment:18>
Sage <http://www.sagemath.org>
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