No need to check, the code is explicitely as I said:
def _is_positive(self, x):
return x >= 1e-6
Here is an example:
sage: P = polytopes.regular_polygon(5, base_ring=RDF)
sage: v0,v1,v2,v3,v4 = [v.vector() for v in P.vertices()]
sage: v = (.5*v0 + .5*v1) - 1e-4*v2
sage: v in P
False
sage: v = (.5*v0 + .5*v1) - 1e-7*v2
sage: v in P
True
Everything is fine with base_ring=AA (and using exact vectors of course).
Vincent
On 13/10/15 08:30, Jan Keitel wrote:
Hi Vincent,
that's actually not true, have you checked it?
The code
elif Vobj.is_vertex():
return (self.polyhedron()._is_positive( self.eval(Vobj) ) and
not self.polyhedron()._is_zero( self.eval(Vobj) ) )
inside interior_contains in representations.py gives
sage: P = polytopes.regular_polygon(5, base_ring=RDF)
sage: sage: a_vertex = P.vertices()[0]
sage: sage: for facet in P.Hrepresentation(): print
facet.contains(a_vertex), facet.interior_contains(a_vertex)
True True
True False
True True
True False
True True
Whether this is the correct way to go is an entirely different question -
all I'm saying is that _is_positive checks (with fuzziness) whether that
the argument is non-negative, but not whether it is non-zero. Maybe that is
what should be changed.
Am Dienstag, 13. Oktober 2015 12:19:50 UTC+2 schrieb vdelecroix:
On 13/10/15 06:48, Jan Keitel wrote:
In this particular case the problem can probably be resolved by being
a bit stricter with the check in interior_contains:
Instead of checking
return self.polyhedron()._is_positive( self.eval(Vobj) )
one should have
return self.polyhedron()._is_positive( self.eval(Vobj) )
> and not
self.polyhedron()._is_zero( self.eval(Vobj) )
This will not solve the problem! _is_positive(x) returns (x >= -1e-6)...
which is exactly the same thing as _is_nonneg(x)... You will also get
False positive and True negative, won't you? For example, you can be out
of the polytope but get from _is_positive that you are inside.
I would go for:
- a warning for non exact rings (using the method .is_exact())
- using _is_positive for non exact rings
Though, using intensively _is_positive or _is_nonneg might significantly
slows down the code (it is one more Python function call).
Vincent
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