Opened 14 years ago
Closed 10 years ago
#727 closed enhancement (fixed)
find rational points on plane conic curves
Reported by: | was | Owned by: | mstreng |
---|---|---|---|
Priority: | major | Milestone: | sage-4.6.2 |
Component: | geometry | Keywords: | rational point points conic quadratic form |
Cc: | ncalexan, justin, mstreng, rlm, pbruin | Merged in: | sage-4.6.2.alpha2 |
Authors: | Nick Alexander, Marco Streng | Reviewers: | David Loeffler |
Report Upstream: | N/A | Work issues: | |
Branch: | Commit: | ||
Dependencies: | Stopgaps: |
Description (last modified by )
Implement a Conic class that is able to
- find rational points on plane conic curves over QQ, finite fields, RR, CC.
- given a conic with a point over a field, compute a parametrization.
Attachments (13)
Change History (34)
comment:1 Changed 13 years ago by
- Component changed from basic arithmetic to algebraic geometry
- Owner changed from somebody to was
comment:2 Changed 13 years ago by
- Cc ncalexan added
- Keywords rational point points conic quadratic form added
comment:3 Changed 13 years ago by
- Component changed from algebraic geometry to quadratic forms
- Owner changed from was to justin
comment:4 Changed 13 years ago by
- Cc justin added
comment:5 Changed 12 years ago by
- Cc mstreng added
comment:6 Changed 12 years ago by
- Component changed from quadratic forms to geometry
- Owner changed from justin to mhampton
- Summary changed from find rational points on ternary quadratic forms -- volunteer needed to find rational points on plane conic curves [with patch, needs work]
The patches I just uploaded were part of ncalexan's patch for ticket 6341, implementing Mestre's algorithm. They implement a Conic class and allow one to find points over the rationals. This Conic class needs to be expanded to provide much more functionality, such as finding points and/or rational parametrizations over other fields. If the original question is only for the rationals, then that at least is answered.
comment:7 Changed 12 years ago by
- Owner changed from mhampton to mstreng
- Status changed from new to assigned
I'll work on the Conic class.
Changed 11 years ago by
comment:8 Changed 11 years ago by
- Cc rlm added
- Report Upstream set to N/A
- this is being revived at Sage Days 23
- trac_727-conic-extcode.patch should be removed: it updates Denis Simon's code from 2005 to 2007, while 2009 is already shipped with the latest Sage
- trac_727_more_conic_files.patch implements a Conic class that uses Denis Simon's code and can find points on conics over number fields and finite fields. It includes most of trac_727-conic.patch and works by itself on 4.4.4. Some doctests fail. It includes an incomplete and incorrect implementation of Hilbert symbols that should be replaced by the Hilbert symbols of #9334
comment:9 Changed 11 years ago by
- I missed the file sage/schemes/plane_conics/init.py (which is empty), so the patch in its current form doesn't work
Changed 11 years ago by
apply after trac_727_more_conic_files1,2,3; requires trac_9334-hilbert.patch to work
Changed 11 years ago by
apply on sage 4.4.4 after trac_727_more_conic_files1,2,3,4, shouldn't require trac_9334-hilbert.patch
comment:10 Changed 11 years ago by
- Cc pbruin added
- Description modified (diff)
- Work issues set to documentation formatting, reviewing
comment:11 Changed 11 years ago by
- Description modified (diff)
- Work issues documentation formatting, reviewing deleted
I'm running a doctest right now. I'll fold them when I get the time. Who wants to review it?
comment:12 Changed 11 years ago by
- Status changed from needs_work to needs_review
"All tests passed!", and I combined the patches into one file
comment:13 Changed 11 years ago by
- Description modified (diff)
comment:14 Changed 11 years ago by
- Summary changed from find rational points on plane conic curves [with patch, needs work] to find rational points on plane conic curves [with patch, needs review]
comment:15 Changed 11 years ago by
- Summary changed from find rational points on plane conic curves [with patch, needs review] to find rational points on plane conic curves
Those [with patch, needs review]
bits in the description are no longer necessary, thanks to the workflow.
comment:16 Changed 11 years ago by
- Status changed from needs_review to needs_work
The patch applies fine to 4.6.alpha0, but not all the tests in the new directory pass:
sage -t -long "devel/sage-main/sage/schemes/plane_conics/con_field.py" sage -t -long "devel/sage-main/sage/schemes/plane_conics/con_number_field.py" sage -t -long "devel/sage-main/sage/schemes/plane_conics/con_rational_field.py" sage -t -long "devel/sage-main/sage/schemes/plane_conics/rnfisnorm.py"
I feared that it would be worse after the new Pari upgrade (which is in 4.6.alpha0). But it does need looking into.
comment:17 Changed 11 years ago by
comment:18 Changed 10 years ago by
- Description modified (diff)
- Work issues set to needs serious retesting after #9334 and #2329
Changed 10 years ago by
Apply only this latest file (works on sage 4.6.1.rc0 without any other patches)
comment:19 Changed 10 years ago by
- Description modified (diff)
- Status changed from needs_work to needs_review
- Work issues needs serious retesting after #9334 and #2329 deleted
I moved all number field functionality to #10621. Because of this, no patches from other tickets are needed, you only need to apply trac_727_conics_without_number_fields.patch
comment:20 Changed 10 years ago by
- Reviewers set to David Loeffler
- Status changed from needs_review to positive_review
This looks really good. It's embarrassing that we've been shipping Denis Simon's scripts with Sage for years but nobody's sat down and written the interface code necessary to make it accessible.
Patch applied fine to 4.6.2.alpha1, all doctests in sage/schemes passed, the ref manual built OK, and all the examples I tried worked.
I have one minor gripe: there are one or two cases where the new Conic classes inherit methods from the generic plane curve classes that perhaps ought to be replaced with more appropriate conic-specific implementations (e.g the method "rational_points"). But that can come in future tickets if people feel it's needed.
comment:21 Changed 10 years ago by
- Merged in set to sage-4.6.2.alpha2
- Resolution set to fixed
- Status changed from positive_review to closed
This is so random -- I have written code to do this. We already distribute Denis Simon's code to solve such systems, and I have have integrated a little of it. Patch coming up. Please talk to me before implementing this.