#8988: Add support for toric varieties
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Reporter: novoselt | Owner: AlexGhitza
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-4.5
Component: algebraic geometry | Keywords:
Author: Andrey Novoseltsev | Upstream: N/A
Reviewer: Volker Braun | Merged:
Work_issues: |
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Comment(by novoselt):
Hi Volker,
I have done some work on the documentation from your patch and got
completely stuck at `Mori_vectors`. Problems from smaller to bigger ones:
* Are we allowed to use non-standard characters? I mean "a with dots" in
Kaehler. I vaguely remember some discussion about it, but don't recall the
result. Personally I prefer to use only characters that are easy to type
and display for everyone. It does mean that some names are not accurately
represented, but having one of such names I can vote in favour of it ;-)
* Your doctest uses toric varieties library which depends on this patch.
It is a good non-trivial doctest, so I have no desire to remove it.
* Why does it return vectors rather than cone (in the same way as
`Kaehler_cone`)?
* Kaehler and Mori cones are supposed to be dual, but they are not.
Because Kaehler cone is given in some coordinates on the class group and
Mori cone is given embedded into a higher dimensional space without a
choice of a basis for its "real space". Both representations are probably
useful and should be available, but it should be done consistently.
So:
* I have removed my `kaehler_cone` method from the main patch, hopefully
now you can give it a positive review together with symbolic doctest fixes
only.
* I have uploaded a new patch which contains your rebased changes and my
edits to the documentation. It should NOT be applied here, I just wanted
to save this code. As a patch it now just contains three new functions and
can be easily moved to other tickets, where the library of toric varieties
will be available to use in doctests. We will also need to take care of
the last two points above.
Let me know what you think of all this.
Andrey
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/8988#comment:26>
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