#6214: Polyhedra compute incorrect dimension when defined through inequalities
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Reporter: mhampton | Owner: mhampton
Type: defect | Status: new
Priority: major | Milestone:
Component: geometry | Keywords:
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Not always, but it is possible; the following is from "Drini" on sage-
support:
I was checking the new polytope commands
specifically a polytope in R^2 with points (a,b,c,d,e,f) such that
e+b>= c+d
e+c >= b+d
a+b+c+d+e+f = 31
(this is a polytope I had worked on before so I know it very well)
After several tries (documentation still sparse and incomplete) I
managed to cosntruct it.
Checked vertices:
P.vertices()
[[0, 0, 0, 0, 0, 31], [31, 0, 0, 0, 0, 0], [0, 0, 0, 31/2, 31/2, 0],
[0,
0, 31/2, 0, 31/2, 0], [0, 0, 0, 0, 31, 0], [0, 31/2, 0, 0, 31/2, 0],
[0,
31/2, 31/2, 0, 0, 0]]
That's right, 7 vertices, the right ones (again this is a polytope I
knew before)
P.ambiend_dim()
6
P.dim()
6
!!!!!
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The ambient dimension is indeed 6 (we're after all in R^6) but the
polytope has dimension 5 for it's contained in the a+b+c+d+e+f=31
hyperplane (and thus its dimension is 1 less than ambient) Notice all
vertices have coordinates adding 31, therefore it's indeed contained
in the hyperplane
Polymake verified this as well saying dimension is 5
Now I don't know how or where to submit a bug, but I suppose people
involved with development here know
so the least I can do is comment there's a bug so it's known and
forwarded (and then stop doing polytope computations in sagemath for a
bit longer)
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/6214>
Sage <http://sagemath.org/>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
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