#8986: Add support for convex rational polyhedral cones
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Reporter: novoselt | Owner: mhampton
Type: enhancement | Status: needs_work
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):
Replying to [comment:5 vbraun]:
> I find `ConvexRationalPolyhedralCone.strict_subcone()` confusing: It
does return a quotient cone, not a subcone. Maybe we can call it
`strict_quotient()`?
Agreed. I just had to construct this object for equivalence checks and
didn't really know how to call it.
> 1) get rid of `IntegralRayCollection.__contains__(ray)`. If you need to
test membership, its easy enough to search `self.rays()` or
`self.rays_set()`:
Agreed.
> 2) tighten the rules for comparison of N/M-lattice objects:
{{{
sage: M(1,0,0) == N(1,0,0) # this should raise an error
False
}}}
Disagreed. Maybe it is silly to ask if an apple is equal to a car, but
there is nothing criminal in it. I think that in general in Python you can
compare any two objects and sort lists containing arbitrary objects. So I
think that `False` is the correct answer in this case.
>
{{{
sage: (1,0,0) == N(1,0,0) # should probably return true
False
sage: M(1,0,0) == (1,0,0) # should probably return true as well
False
}}}
I kind of don't like that we have here a==b and c==a, but b!=c... Do you
really want to have it in? It may be actually non-trivial to implement. I
already had to tweak the coercion system so that sometimes it allows "non-
toric-lattice" objects to be involved and sometimes it does not. In
particular I had to make sure that elements of toric lattices are NOT
coerced into ZZ^n.
So if you insist, I will try to make it work, but I cannot guarantee that
I will be successful and personally I think that we should not change it,
as long as this behaviour is clearly documented. (Probably it is not, but
that's something which definitely can be fixed ;-))
>
{{{
sage: M(1,0,0) in octant.rays() # this should definitely raise an error
False
}}}
Again, I don't think that there should be any errors raised by comparison
operations. `False` is an accurate answer to this question - and octant in
the N-lattice does not contain any points of the M-lattice.
> 3) add methods `contains(n)` to `ConvexRationalPolyhedralCone` to test
whether a N-lattice point is contained in the cone, e.g. (untested)
Agreed. It was on my list of things to do in the future, might as well do
it now.
> 4) `ConvexRationalPolyhedralCone.__contains__()` just calls
`contains()`. This is syntactic sugar, but `__` methods alone don't show
up in the documentation.
Very good point!!! I knew that they don't show up, but didn't think about
just making a "common method" alias.
Please comment on the points of disagreement and I will try to fix the
issues in a couple of days. Thanks for a careful review!
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/8986#comment:6>
Sage <http://www.sagemath.org>
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