implement computation of Silverman height bounds

[williamstein]

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!

CC: robertwb cremona

Component: number theory

Author: William Stein

Reviewer: Robert Bradshaw

Merged: sage-4.2.1.alpha0

Issue created by migration from https://trac.sagemath.org/ticket/7266

[williamstein]

comment:1

Attachment: trac_7266.patch.gz

[JohnCremona]

comment:2

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.

[robertwb]

comment:3

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.

[JohnCremona]

comment:4

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!

[mwhansen]

Merged: sage-4.2.1.alpha0

[mwhansen]

Changed author from wstein to William Stein

[mwhansen]

Reviewer: Robert Bradshaw

[williamstein]

comment:6

But I read here that the Sage project "religiously avoiding redundant code.": http://www.metafilter.com/86262/unbump