Sage: Ticket #13953: (non)archimedian_local_height of a torsion points always gives 0
https://trac.sagemath.org/ticket/13953
<p>
For torsion points of elliptic curves over number fields, nonarchimedian_local_height incorrectly returns 0, and archimedian_local_height raises an error:
</p>
<pre class="wiki">sage: K.<i> = QuadraticField(-1)
sage: E = EllipticCurve([0, 0, 0, K(1), 0])
sage: P = E(i, 0)
sage: P.nonarchimedian_local_height()
0
sage: P.archimedian_local_height()
NameError: global name 'QQ' is not defined
</pre><p>
The correct behaviour (for the normalisation used in Sage) is
</p>
<pre class="wiki">sage: P.nonarchimedian_local_height()
-1/2*log(2)
sage: P.archimedian_local_height()
0.346573590279973
</pre><p>
Note: the same would happen for rational points on elliptic curves over Q, but computing local heights over Q is broken (see <a class="closed ticket" href="https://trac.sagemath.org/ticket/13951" title="defect: (non)archimedian_local_height broken for rational points on elliptic ... (closed: fixed)">#13951</a>).
</p>
<p>
Apply: trac13953-local_heights_torsion.patch
</p>
en-usSagehttps://trac.sagemath.org/chrome/site/logo_sagemath_trac.png
https://trac.sagemath.org/ticket/13953
Trac 1.1.6pbruinMon, 14 Jan 2013 18:12:42 GMTstatus, description changed; author set
https://trac.sagemath.org/ticket/13953#comment:1
https://trac.sagemath.org/ticket/13953#comment:1
<ul>
<li><strong>status</strong>
changed from <em>new</em> to <em>needs_review</em>
</li>
<li><strong>description</strong>
modified (<a href="/ticket/13953?action=diff&version=1">diff</a>)
</li>
<li><strong>author</strong>
set to <em>Peter Bruin</em>
</li>
</ul>
TicketcremonaMon, 14 Jan 2013 20:37:26 GMT
https://trac.sagemath.org/ticket/13953#comment:2
https://trac.sagemath.org/ticket/13953#comment:2
<p>
2 quick questions: (1) is this patch based on <a class="closed ticket" href="https://trac.sagemath.org/ticket/12509" title="defect: computation of height of point on elliptic curve over Q(sqrt(5)) is WRONG (closed: fixed)">#12509</a>? (2) is your fix just to remove the wrong quick exit for torsion points (as appears)?
</p>
TicketpbruinMon, 14 Jan 2013 20:50:08 GMT
https://trac.sagemath.org/ticket/13953#comment:3
https://trac.sagemath.org/ticket/13953#comment:3
<p>
Replying to <a class="ticket" href="https://trac.sagemath.org/ticket/13953#comment:2" title="Comment 2">cremona</a>:
</p>
<blockquote class="citation">
<p>
(1) is this patch based on <a class="closed ticket" href="https://trac.sagemath.org/ticket/12509" title="defect: computation of height of point on elliptic curve over Q(sqrt(5)) is WRONG (closed: fixed)">#12509</a>?
</p>
</blockquote>
<p>
No, but I have another branch where I made the same patch based on <a class="closed ticket" href="https://trac.sagemath.org/ticket/12509" title="defect: computation of height of point on elliptic curve over Q(sqrt(5)) is WRONG (closed: fixed)">#12509</a>; would it be better to upload that one?
</p>
<blockquote class="citation">
<p>
(2) is your fix just to remove the wrong quick exit for torsion points (as appears)?
</p>
</blockquote>
<p>
Yes, the rest of the patch just adds a doctest.
</p>
TicketcremonaMon, 14 Jan 2013 22:38:36 GMT
https://trac.sagemath.org/ticket/13953#comment:4
https://trac.sagemath.org/ticket/13953#comment:4
<p>
Replying to <a class="ticket" href="https://trac.sagemath.org/ticket/13953#comment:3" title="Comment 3">pbruin</a>:
</p>
<blockquote class="citation">
<p>
Replying to <a class="ticket" href="https://trac.sagemath.org/ticket/13953#comment:2" title="Comment 2">cremona</a>:
</p>
<blockquote class="citation">
<p>
(1) is this patch based on <a class="closed ticket" href="https://trac.sagemath.org/ticket/12509" title="defect: computation of height of point on elliptic curve over Q(sqrt(5)) is WRONG (closed: fixed)">#12509</a>?
</p>
</blockquote>
<p>
No, but I have another branch where I made the same patch based on <a class="closed ticket" href="https://trac.sagemath.org/ticket/12509" title="defect: computation of height of point on elliptic curve over Q(sqrt(5)) is WRONG (closed: fixed)">#12509</a>; would it be better to upload that one?
</p>
</blockquote>
<p>
I think it would: you can add that ticket as a dependency of this one. Then they should get merged together.
</p>
TicketpbruinTue, 15 Jan 2013 00:22:40 GMTdependencies set
https://trac.sagemath.org/ticket/13953#comment:5
https://trac.sagemath.org/ticket/13953#comment:5
<ul>
<li><strong>dependencies</strong>
set to <em>#12509</em>
</li>
</ul>
TicketwuthrichSat, 04 May 2013 19:24:18 GMTstatus changed; reviewer set
https://trac.sagemath.org/ticket/13953#comment:6
https://trac.sagemath.org/ticket/13953#comment:6
<ul>
<li><strong>status</strong>
changed from <em>needs_review</em> to <em>positive_review</em>
</li>
<li><strong>reviewer</strong>
set to <em>Chris Wuthrich</em>
</li>
</ul>
<p>
The patch applies cleanly to 5.9 after <a class="closed ticket" href="https://trac.sagemath.org/ticket/12509" title="defect: computation of height of point on elliptic curve over Q(sqrt(5)) is WRONG (closed: fixed)">#12509</a>. The tests pass and it does what it should do.
</p>
TicketwuthrichTue, 14 May 2013 09:37:41 GMTstatus changed
https://trac.sagemath.org/ticket/13953#comment:7
https://trac.sagemath.org/ticket/13953#comment:7
<ul>
<li><strong>status</strong>
changed from <em>positive_review</em> to <em>needs_work</em>
</li>
</ul>
TicketpbruinTue, 14 May 2013 10:09:40 GMTattachment set
https://trac.sagemath.org/ticket/13953
https://trac.sagemath.org/ticket/13953
<ul>
<li><strong>attachment</strong>
set to <em>trac13953-local_heights_torsion.patch</em>
</li>
</ul>
<p>
based on 5.9 + three patches of <a class="closed ticket" href="https://trac.sagemath.org/ticket/12509" title="defect: computation of height of point on elliptic curve over Q(sqrt(5)) is WRONG (closed: fixed)">#12509</a>
</p>
TicketpbruinTue, 14 May 2013 10:31:00 GMTstatus changed
https://trac.sagemath.org/ticket/13953#comment:8
https://trac.sagemath.org/ticket/13953#comment:8
<ul>
<li><strong>status</strong>
changed from <em>needs_work</em> to <em>needs_review</em>
</li>
</ul>
TicketwuthrichTue, 14 May 2013 16:29:02 GMTstatus changed
https://trac.sagemath.org/ticket/13953#comment:9
https://trac.sagemath.org/ticket/13953#comment:9
<ul>
<li><strong>status</strong>
changed from <em>needs_review</em> to <em>positive_review</em>
</li>
</ul>
<p>
Thanks for rebasing it. (Sorry for not commenting, the browser in my office decided to log me out permanently so I could not post a comment on what needs to be done).
</p>
<p>
I tested it again and it is again all fine.
</p>
TicketpbruinWed, 15 May 2013 13:40:40 GMT
https://trac.sagemath.org/ticket/13953#comment:10
https://trac.sagemath.org/ticket/13953#comment:10
<p>
Thanks! And no problem, it was clear what had to be done.
</p>
TicketjdemeyerFri, 17 May 2013 06:32:41 GMTstatus changed; resolution, merged set
https://trac.sagemath.org/ticket/13953#comment:11
https://trac.sagemath.org/ticket/13953#comment:11
<ul>
<li><strong>status</strong>
changed from <em>positive_review</em> to <em>closed</em>
</li>
<li><strong>resolution</strong>
set to <em>fixed</em>
</li>
<li><strong>merged</strong>
set to <em>sage-5.10.beta4</em>
</li>
</ul>
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