#8986: Add support for convex rational polyhedral cones
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Reporter: novoselt | Owner: mhampton
Type: enhancement | Status: needs_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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Changes (by novoselt):
* status: needs_work => needs_review
Comment:
OK, I think I have addressed all the points in the original review except
2) which is pretty much impossible to realize completely (originally I was
thinking of (1,1,1) as vectors, but they are just tuples, see the above
comment for vector behaviour in this situation). I have added a general
warning about tuples in the main `ToricLattice` documentation.
I added `__contains__` to `ToricLattice`, since I discovered that the
inherited implementation is not suitable.
I added `__contains__`, `_contains`, and `contains` to cones. The real job
is done in `_contains`, two others call it. The reason for the third
function is an attempt to make warnings show where the actual potential
mistake was, which requires the same calling depth. Unfortunately, in my
tests it worked as I wanted only if it was triggered by some library code,
in the notebook for created functions and attached files it just shows
`main`. But that may change and maybe the terminal behaves differently.
Now `cone.contains(stuff)` will try its best to return `True` by
interpreting `stuff` as a point in the ambient space of `cone`, i.e. in
`cone.lattice().base_extend(RR)`. However, it will catch points from
foreign lattices first and return `False` with a warning, visible the
first time for each location.
That's how reviewer's code works with the new version of the patch:
{{{
sage: octant = Cone([(1,0,0), (0,1,0), (0,0,1)])
sage: N = octant.lattice()
sage: n = N(1,1,1)
sage: n.set_immutable()
sage: n in octant # True was desired
True
sage: (1,0,0) in octant # True was desired
True
sage: N(1,0,0) in octant.rays() # was and should be True
True
sage: n = N(1,0,0)
sage: n.set_immutable()
sage: n in octant.ray_set() # was and should be True
True
sage: M = N.dual()
sage: M(1,0,0) == N(1,0,0) # Error was desired
False
sage: (1,0,0) == N(1,0,0) # True was desired, but difficult to get
False
sage: M(1,0,0) == (1,0,0) # True was desired, but difficult to get
False
sage: (1,0,0) == (1,0,0) # works as expected
True
sage: (1,0,0) in octant.rays() # True was desired, but difficult to get
False
sage: M(1,0,0) in octant.rays() # Error was desired
False
sage: cone = Cone([[1,0],[0,1]])
sage: (1,1) in cone # Was False
True
sage: M = cone.lattice().dual()
sage: M(1,1) in cone # Now gives warning on the first attempt
__main__:1: UserWarning: you have checked if a cone contains a point from
another lattice, this is always False!
False
}}}
I suppose two lines marked "Error was desired" can also give a warning the
first time they are invoked, if we implement a custom `__eq__` in addition
to `__cmp__` for `ToricLatticeElement`. Should this be done?
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/8986#comment:14>
Sage <http://www.sagemath.org>
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