#18454: New `random_cone()` function
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Reporter: mjo | Owner:
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-6.8
Component: geometry | Resolution:
Keywords: | Merged in:
Authors: Michael Orlitzky | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
u/mjo/ticket/18454 | 55da704f2f101cfdc25ba1c0b35f38072cb0e7f3
Dependencies: | Stopgaps:
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Comment (by novoselt):
Well, it would be helpful to know in what sense the cone is "random". If
it is a cone on a random set of rays, then dimension+1 is the only
sensible upper bound to me - such a cone always can be constructed. In
R^2^ it may be possible to force construction of cones with more than 4
rays - given that the code can handle 4 instead of 3 for the whole space,
probably it can live with 100. But if we are talking about the minimal
number of extremal rays, then for R^1,2^ maximum is the dimension and for
all others we can do anything - generate a random n-gon in a plane and
lift it.
In most cases I think you would want a strictly convex cone, so that's
exactly what you want with bonus points if primitive generators are not
necessarily in the same hyperplane. Algorithm: generate random vectors
with positive last component. There may be an extra switch to allow linear
subspaces in cones.
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Ticket URL: <http://trac.sagemath.org/ticket/18454#comment:5>
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