#9972: Add fan morphisms
------------------------------------------------+---------------------------
Reporter: novoselt | Owner: mhampton
Type: enhancement | Status: needs_work
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: |
------------------------------------------------+---------------------------
Changes (by novoselt):
* status: needs_info => needs_work
Comment:
I kind of complained before that I don't quite understand the term "fan
morphism" ;-)
From the beginning of the ticket:
Replying to [comment:6 vbraun]:
> Replying to [comment:5 novoselt]:
> > "it is a morphism between toric lattices with distinguished fans in
the domain and codomain which are compatible with this morphism."
>
> Yes, that is the usual definition. No restriction on the support of the
underlying lattice map.
So, as I understand we have a category with fans being objects. A fan is a
collection of cones, each cone is a set of points. All cones of the fan
sit in the same lattice, so there is also "the lattice of the fan."
Morphisms in this category are morphisms between lattices associated to
fans, which map cones into cones as sets of points. So in particular they
do define linear maps between individual cones as well, and I got lost
when you said that they don't.
But I guess I agree that when we talk about images/preimages of cones, we
should refer to the induced map between cones as a map between two finite
sets, since we do not have a nice correspondence between cones as sets of
points. Let me think a little more about it and post an updated patch.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/9972#comment:58>
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.
