#15115: correct set of points at infinity for hyperelliptic curve
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Reporter: mstreng | Owner:
Type: defect | Status: new
Priority: major | Milestone: sage-5.12
Component: geometry | Resolution:
Keywords: hyperelliptic | Merged in:
curve points at infinity | Reviewers:
Authors: Marco Streng | Work issues: doctest the rest of
Report Upstream: N/A | the sage library, check how
Branch: | documentation looks, add example
Dependencies: #15108 | from ticket description to patch
| Commit:
| Stopgaps:
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Comment (by nbruin):
Replying to [comment:7 mstreng]:
> What kind of functionality for places of function fields does Sage have
right now? It is definitely good to have for general curves. But for
hyperelliptic curves we should still switch to weighted projective spaces
at some point anyway.
I was really just thinking about rephrasing the docstrings of the routines
you now claim give mathematically wrong results: either stick with the
zeta function of the singular model (which is going to be confusing now
and wrong in the future) or yield the appropriate zeta function and
document it as "the zeta function of the complete nonsingular curve in the
birationality class of this curve" or "the zeta function of the function
field of this curve" or something similar. You wouldn't particularly need
support for places and function fields to write that in a docstring.
Similarly, document "isomorphic" as "birational isomorphic" if t hat makes
the routine correct.
All the hard work for hyperelliptic curves happens in an affine patch
anyway, so the completion doesn't really matter that much. So perhaps it's
doable to simply use `toric_varieties.WP` as an ambient! (of course, for
performance this stuff should only lazily be there: for many applications,
a hyperelliptic curve is a list of coefficients of the polynomials `f,h`
in `y^2+h(x)y=f(x)`.
--
Ticket URL: <http://trac.sagemath.org/ticket/15115#comment:8>
Sage <http://www.sagemath.org>
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