#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):
Well, instead of "very-very" let me say that `ambient_ray_incices` are as
natural as coordinates. Coordinates may be not very convenient for
definitions, since you need to make sure that the choice of the coordinate
system does not matter. They are in many cases not mathematically natural
in the sense that there are many different choices without any preference.
At the same time they are quite useful both for proofs and for working
with concrete examples.
Now, choosing between `cone.ambient_ray_indices()` and
`fan.ray_indices(cone)` is like choosing between always mentioning which
coordinate system you are using whenever you use coordinates and having
some coordinate system "understood from context." Of course, in the second
case you are risking to encounter a situation when it was not quite clear
and it leads to mistakes since coordinates in one system may have very
little to do with coordinates in another one. People do such mistakes from
time to time, that's just life. But it is very convenient to have this
default and I still vote for it despite the mistake that you have
discovered. (By the way - how did you find it?)
Leaving a function but banning it for internal use is a bit silly - the
way to enforce it is to scan for occurrences of this function and then
replace it with a "safe version". If you do it, then the second step can
be making sure that it is used safely and correctly.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/9972#comment:32>
Sage <http://www.sagemath.org>
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