#9972: Add fan morphisms
------------------------------------------------+---------------------------
Reporter: novoselt | Owner: mhampton
Type: enhancement | Status: needs_info
Priority: major | Milestone: sage-4.6.1
Component: geometry | Keywords:
Author: Andrey Novoseltsev, Volker Braun | Upstream: N/A
Reviewer: Volker Braun, Andrey Novoseltsev | Merged:
Work_issues: |
------------------------------------------------+---------------------------
Comment(by novoselt):
Why a fan morphism does not define linear maps on individual cones? A fan
morphism is a linear map between lattices, so it can be restricted to any
(compatible) pair of domain/codomain cones and still induce a morphism
between corresponding affine varieties. Just specifying mapping of fans as
finite sets of cones is not sufficient, e.g. identity morphism and
multiplication by 2 are different but obviously would induce the same cone
correspondence. So since the actual linear map does matter, it makes sense
to use preimages under this linear map. I agree that full (potentially
non-strictly convex) preimages are probably of little use, we need to
restrict to the domain fan, but I don't see why something called
"preimage" should ever exclude the origin. In the sense of orbit closures
it does correspond to the whole variety, but in the sense of affine
patches it corresponds to the torus itself which is a part of any toric
variety of the given dimension and always gets mapped to itself.
So I still propose the switch to `cones_mapping_into` for the current
version and adding `cones_mapping_onto` for the version that you want to
have. No `preimage_cones` at all since it is a confusing name in this
context. On the level of toric varieties the corresponding methods may
refer to orbits to make things clear, but here they are not present yet.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/9972#comment:56>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
--
You received this message because you are subscribed to the Google Groups
"sage-trac" group.
To post to this group, send email to [email protected].
To unsubscribe from this group, send email to
[email protected].
For more options, visit this group at
http://groups.google.com/group/sage-trac?hl=en.
