#9972: Add toric lattice morphisms
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Reporter: novoselt | Owner: mhampton
Type: enhancement | Status: needs_work
Priority: major | Milestone: sage-4.6
Component: geometry | Keywords:
Author: Andrey Novoseltsev | Upstream: N/A
Reviewer: Volker Braun | Merged:
Work_issues: switch to FanMorphism |
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Comment(by novoselt):
I'll post an updated patch with `FanMorphism` shortly.
Regarding `image_cone` and `preimage_cones` - I guess we want them to work
for arbitrary cones of domain/codomain fans. In this case it is still
clear what to return for `image_cone(cone)` - the smallest cone of the
codomain fan which contains the image. But what about `preimage_cones`?
Should we return all cones that are mapped to it, or only maximal ones?
(We can also consider packing them into a fan, but in this case we loose
connection with the domain fan, so I don't think that it is a good idea.)
I am also not sure what would be an efficient way to determine preimage
cones. I am thinking about determining rays that are mapped into the given
codomain cone and then scanning trough all domain cones to see which are
generated by such rays only. An alternative approach, which is likely to
be better for intensive work with such cones, is to compute full
dictionary for image cones and then revert it to get preimage ones. Any
suggestions?
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/9972#comment:43>
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