#10140: Base sage.geometry.cone on the Parma Polyhedra Library (PPL)
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Reporter: vbraun | Owner: mhampton
Type: enhancement | Status: needs_info
Priority: major | Milestone: sage-4.7
Component: geometry | Keywords: ppl
Author: Volker Braun | Upstream: N/A
Reviewer: Andrey Novoseltsev | Merged:
Work_issues: |
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Comment(by vbraun):
{{{
for y, yv in zip(p.faces(dim=2), p.polar().faces(codim=3))
}}}
This is absolutely terrible and the prime reason why the face lattice
shouldn't make any promises with regards to ordering. Just so that nobody
can use a construct like this. For anybody but the author it is completely
illegible and utterly mysterious that the faces end up being dual. At the
same time, it would be so much easier to write
{{{
for face in p.faces(dim=3):
print face, face.dual()
}}}
Also I'm totally opposed to requiring rays in cones to always be
decorated. The cones of a fan are not the only place that uses `Cone`. In
fact, the main reason for this ticket is that the current (PALP-based)
implementation of cones is unsuitable for Kahler cones because it is
constrained to low dimension.
We could have an `OrderedCone()` function that constructs the cone while
keeping the ray order intact if possible (at a performance penalty). This
function could then even raise a `ValueError` if there is no unique
minimal representation. But I still think that its a bad idea to
implicitly have some particular order.
As far as associating rays with homogeneous variables, I think we really
should subclass the multivariate polynomial ring. Then we can convert rays
to homogeneous variables and properly check homogeneity of polynomials.
Finally, about `QQ['x, x']``: The variable name is just a string and can
be pretty much anything. The issue was raised during the recent bug days
and the real problem is that conversion to e.g. maxima is broken in such a
case. Sage generally only cares about the order of the variables.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/10140#comment:31>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
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