#17386: Enumerate points of bounded height in projective/affine space over
number
fields
-------------------------------------+-------------------------------------
Reporter: gjorgenson | Owner:
Type: enhancement | Status: needs_work
Priority: minor | Milestone: sage-6.5
Component: algebraic | Resolution:
geometry | Merged in:
Keywords: | Reviewers: Ben Hutz
Authors: Grayson Jorgenson | Work issues:
Report Upstream: N/A | Commit:
Branch: | 456c7213880388ca6311348c55a798cf5a9b1187
u/gjorgenson/ticket/17386 | Stopgaps:
Dependencies: |
-------------------------------------+-------------------------------------
Changes (by bhutz):
* status: needs_review => needs_work
* reviewer: => Ben Hutz
Comment:
Here is a first pass at reviewing this.
First you need to be careful with the difference between relative height
and absolute height. The function K.elements_of_bounded_height() is
returning with respect to a bound of relative height (as its documentation
says). I would think most users would be interested in absolute height
rational points for schemes. So you'll need to fix the functionality here,
but also fix the documentation to specify which height in all appropriate
places.
Also, specify whether the bound is <= or <
`numberField` is not a good variable name as CamelCase is reserved for
class names.
In projective_homset.py put the imports near where they are needed so you
only import what you need (this is done correctly in affine_homset.py)
Some examples that I expected to work that didn't
{{{
u = QQ['u'].0
K.<v> = NumberField(u^2 + 3)
A.<x,y> = ProjectiveSpace(K,1)
X=A.subscheme(x-y)
X.rational_points(3)
}}}
same for affine
{{{
from sage.schemes.projective.projective_rational_point import
enum_projective_number_field
enum_projective_number_field(X,3)
}}}
{{{
from sage.schemes.affine.affine_rational_point import
enum_affine_number_field
enum_affine_number_field(X,3)
}}}
I think the issues with the enum_ functions is whether the input should be
the scheme `X` or the point set `X(K)`. Clarify which in the documentation
for the functions. However, the X.rational_points ones seem to actually be
failing.
--
Ticket URL: <http://trac.sagemath.org/ticket/17386#comment:4>
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 unsubscribe from this group and stop receiving emails from it, send an email
to [email protected].
To post to this group, send email to [email protected].
Visit this group at http://groups.google.com/group/sage-trac.
For more options, visit https://groups.google.com/d/optout.
