#8987: Add support for rational polyhedral fans
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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):
OK, I have implemented 3) with the change "unless `d` is the dimension of
the ambient structure". This allows to work with embedded fans in an
"intuitive" way. I think that changes to the cone module are finished,
coverage is at 100% and all doctests pass. I will go over fan module
tomorrow and see what else has to be documented/fixed there (so far
doctests pass).
Regarding names: `cone.ambient().dim()` and `cone.ambient_dim()` are
different things. The first is the actual dimension of the ambient cone or
fan, while the second is the dimension of the ambient lattice. Are you OK
with this or should we change it? In principle, the second one just
returns `cone.lattice().dim()` and it is not that much more to type, so
`cone.ambient_dim()` can be removed.
Regarding printing using `_repr_`: I think we should have either all short
version (only say what the object is)
{{{
sage: cone
2-dimensional cone
sage: cone_face
1-dimensional cone
sage: fan
Rational polyhedral fan
sage: fan_face
1-dimensional cone
}}}
or all long version (state the ambient structure and the lattice):
{{{
sage: cone
2-dimensional cone in 3-dimensional lattice N
sage: cone_face
1-dimensional face of 2-dimensional cone in 3-dimensional lattice N
sage: fan
Rational polyhedral fan in 3-dimensional lattice N
sage: fan_face
1-dimensional cone of Rational polyhedral fan in 3-dimensional lattice N
}}}
Right now we have something along these lines:
{{{
sage: cone
2-dimensional cone
sage: cone_face
1-dimensional face of 2-dimensional cone
sage: fan
Rational polyhedral fan in 3-dimensional lattice N
sage: fan_face
1-dimensional cone
}}}
I think I was trying to be informative but short, but I find the result
inconsistent and would like to change it to one of the first two options
(probably the second variant is the best, even if it is the longest...)
By the way - I intentionally didn't print the actual dimension of the fan
since it seem to be less relevant than the ambient one: we can have a 2-d
fan generated by 1-d cones in a 3-d space and from the toric varieties
point of view the last dimension is the most important and clear one.
Let me know what you think!
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/8987#comment:39>
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