#18860: Faster Poyhedron.graph()
-------------------------+-------------------------------------------------
Reporter: | Owner:
ncohen | Status: new
Type: | Milestone: sage-6.8
enhancement | Resolution:
Priority: major | Merged in:
Component: | Reviewers:
geometry | Work issues:
Keywords: | Commit:
Authors: | 3b5eabb9735a867678c2c6a13dc7700c24d82732
Nathann Cohen | Stopgaps:
Report Upstream: N/A |
Branch: |
public/18860 |
Dependencies: |
#18779 |
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Comment (by dimpase):
{{{
+ # Why 26 ?? I was expecting 'd-1'. Are there some useless
inequalities
+ # in the list?
}}}
well, you have 26 facets on each edge - none are more useless than the
others. You can do the
following (note that 0th and 1st vertices are adjacent).
{{{
sage: p=polytopes.Gosset_3_21()
sage: M=p.incidence_matrix()
sage: a=0; b=1;
sage: vv=[i for i in [0..702] if M[a,i]*M[b,i]>0]
sage: matrix([p.inequalities()[j].vector() for j in vv]).T.kernel()
Free module of degree 9 and rank 1 over Integer Ring
Echelon basis matrix:
[0 1 0 0 0 0 0 0 0]
}}}
or just
{{{
sage: m=matrix([p.inequalities()[j].vector() for j in vv])
sage: m.rank()
8
}}}
which makes sense, as `m` is of size 27x9. (27, as there is not full-
dimensional).
General code for adjacency of two vertices `a` and `b` of a polytope in
`d`-dimensional space
should check that `m` has corank `1`.
(There could be special cases when one of the vertices is the origin, or
some inequalities are homogeneous).
--
Ticket URL: <http://trac.sagemath.org/ticket/18860#comment:4>
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