#17386: Enumerate points of bounded height in projective/affine space over
number
fields
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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: | 003884c155f7fc53bd649617fc5c983e545aefbd
u/gjorgenson/ticket/17386 | Stopgaps:
Dependencies: |
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Changes (by bhutz):
* status: needs_review => needs_work
Comment:
Looks like we are almost there with this one. The functionality all is in
working order. But, I came across a few minor things to fix.
affine_rational_point
example line 168 is a long test so add -> # long time
probably makes more sense to make the bound smaller and get the test < 1s
affine_space -> line 777 not needed, but move the comment to 779
affine_space -> points_of_bounded_height -> add comment that this is using
the Krumm-Doyle algorithm for number fields (get the citation from number
fields where they implemented it).
algebraic_scheme -> line 1502 no longer need is_RationalField(F)
projective_space -> points_of_bounded_height -> add comment that this is
using the Krumm-Doyle algorithm for number fields (get the citation from
number fields where they implemented it).
projective_space -> line 94 not needed -> move comment to 951
There are a few places where the lines in the docs are too long. You need
to wrap those. Such as line 748 in affine_space.py
Another bad example:
{{{
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)
from sage.schemes.affine.affine_rational_point import
enum_affine_number_field
enum_affine_number_field(X,3)
}}}
oops...X is projective and we called enum_affine successfully!! Need a
check in those functions to make sure the ambient space is Affine or
Projective
--
Ticket URL: <http://trac.sagemath.org/ticket/17386#comment:7>
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