Ticket #7266 (closed enhancement: fixed)
implement computation of Silverman height bounds
| Reported by: | was | Owned by: | was |
|---|---|---|---|
| Priority: | major | Milestone: | sage-4.2.1 |
| Component: | number theory | Keywords: | |
| Cc: | robertwb cremona | Work issues: | |
| Report Upstream: | Reviewers: | Robert Bradshaw | |
| Authors: | William Stein | Merged in: | sage-4.2.1.alpha0 |
| Dependencies: | Stopgaps: |
Description
The Silverman height bound isn't necessarily as tight at the CPS bound, but it works uniformly over all field extensions, which makes it very useful for some applications, e.g., computing mordell-weil groups over number fields. So let's add it to Sage!
Attachments
-
trac_7266.patch
(5.0 KB) -
added by was 4 years ago.
Change History
comment:2 Changed 4 years ago by cremona
Is there any particular reason for using a native Sage implementation instead of using mwrank/eclib?
I know that #360 has still not been done, but I can't quite see the point of this patch for curves over Q.
comment:3 follow-up: ↓ 4 Changed 4 years ago by robertwb
- Status changed from needs_review to positive_review
Looks good to me. It's a simple enough formula that I'd say the redundant implementation is worth it if just for the ease of introspection.
We're looking at using this for provable computations of Heegner points, where the field of definition is not a priori known.
comment:4 in reply to: ↑ 3 Changed 4 years ago by cremona
Replying to robertwb:
Looks good to me. It's a simple enough formula that I'd say the redundant implementation is worth it if just for the ease of introspection.
We're looking at using this for provable computations of Heegner points, where the field of definition is not a priori known.
Fair point(s). One reason for getting better (usually) bounds for *rational* points via the CPS method is precisely due to this restriction. I have no objection!
comment:5 Changed 4 years ago by mhansen
- Status changed from positive_review to closed
- Reviewers set to Robert Bradshaw
- Resolution set to fixed
- Merged in set to sage-4.2.1.alpha0
- Authors changed from wstein to William Stein
comment:6 Changed 4 years ago by was
But I read here that the Sage project "religiously avoiding redundant code.": http://www.metafilter.com/86262/unbump
