Sage: Ticket #28600: Use standard notation for pullback and pushforward on manifolds
https://trac.sagemath.org/ticket/28600
<p>
At this stage, the pushforward of a vector field <code>v</code> along a differentiable map <code>Phi</code> reads <code>Phi^*v</code>. This contradicts the common literature where the pushforward usually writes <code>Phi_*v</code>.
</p>
<p>
In this ticket, a discussion is wanted and eventually a correction is performed.
</p>
en-usSagehttps://trac.sagemath.org/chrome/site/logo_sagemath_trac.png
https://trac.sagemath.org/ticket/28600
Trac 1.1.6egourgoulhonMon, 14 Oct 2019 15:50:26 GMT
https://trac.sagemath.org/ticket/28600#comment:1
https://trac.sagemath.org/ticket/28600#comment:1
<p>
It seems to me that in some texts, <code>Phi^*</code> and <code>Phi_*</code> are used to denote respectively the pushforward and the pullback. I'll look for some precise references.
</p>
Ticketgh-DeRhamSourceMon, 14 Oct 2019 18:21:57 GMT
https://trac.sagemath.org/ticket/28600#comment:2
https://trac.sagemath.org/ticket/28600#comment:2
<p>
Yeah, it's always about conventions and historical remains...
</p>
<p>
Basically, this is not completely trustworthy, but <a class="ext-link" href="https://math.stackexchange.com/questions/68788/idea-of-the-star-position-in-pullback-pushforward-notation"><span class="icon"></span>here</a> is an approach of explaination on stackexchange.
</p>
TicketegourgoulhonFri, 18 Oct 2019 13:15:56 GMT
https://trac.sagemath.org/ticket/28600#comment:3
https://trac.sagemath.org/ticket/28600#comment:3
<p>
Replying to <a class="ticket" href="https://trac.sagemath.org/ticket/28600#comment:1" title="Comment 1">egourgoulhon</a>:
</p>
<blockquote class="citation">
<p>
It seems to me that in some texts, <code>Phi^*</code> and <code>Phi_*</code> are used to denote respectively the pushforward and the pullback. I'll look for some precise references.
</p>
</blockquote>
<p>
Well, I could not find any such reference... Moreover, I agree that in the common literature, the pushforward is denoted by <code>Phi_*</code> while the pullback is denoted by <code>Phi^*</code>. In particular, this holds for Lee's textbooks, which we use as references in the documentation of manifolds. So I am fully OK in adopting such notation. By the way, where in the current Sage documentation have you seen the opposite convention?
</p>
TicketegourgoulhonFri, 18 Oct 2019 13:19:03 GMT
https://trac.sagemath.org/ticket/28600#comment:4
https://trac.sagemath.org/ticket/28600#comment:4
<p>
Replying to <a class="ticket" href="https://trac.sagemath.org/ticket/28600#comment:3" title="Comment 3">egourgoulhon</a>:
</p>
<blockquote class="citation">
<p>
By the way, where in the current Sage documentation have you seen the opposite convention?
</p>
</blockquote>
<p>
OK, I found it: it is not in the documentation but in the code of the method <code>pushforward()</code>, in lines 1273 and 1275 of <code>src/sage/manifolds/differentiable/diff_map.py</code>.
</p>
TicketegourgoulhonFri, 18 Oct 2019 13:40:03 GMTstatus changed; commit, branch, author set
https://trac.sagemath.org/ticket/28600#comment:5
https://trac.sagemath.org/ticket/28600#comment:5
<ul>
<li><strong>status</strong>
changed from <em>new</em> to <em>needs_review</em>
</li>
<li><strong>commit</strong>
set to <em>cb3c97ec7d4575725eedfcf12f4b02c48fc35a49</em>
</li>
<li><strong>branch</strong>
set to <em>public/manifolds/pullback_pushforward_notation</em>
</li>
<li><strong>author</strong>
set to <em>Eric Gourgoulhon</em>
</li>
</ul>
<p>
New commits:
</p>
<table class="wiki">
<tr><td><a class="ext-link" href="https://git.sagemath.org/sage.git/commit?id=cb3c97ec7d4575725eedfcf12f4b02c48fc35a49"><span class="icon"></span>cb3c97e</a></td><td><code>Change notation of pullback and pushforward</code>
</td></tr></table>
TicketegourgoulhonFri, 18 Oct 2019 13:42:34 GMTkeywords, summary changed
https://trac.sagemath.org/ticket/28600#comment:6
https://trac.sagemath.org/ticket/28600#comment:6
<ul>
<li><strong>keywords</strong>
<em>pullback</em> added
</li>
<li><strong>summary</strong>
changed from <em>Manifolds: Pushforward</em> to <em>Use standard notation for pullback and pushforward on manifolds</em>
</li>
</ul>
TicketegourgoulhonFri, 18 Oct 2019 13:43:01 GMTpriority, type changed
https://trac.sagemath.org/ticket/28600#comment:7
https://trac.sagemath.org/ticket/28600#comment:7
<ul>
<li><strong>priority</strong>
changed from <em>minor</em> to <em>major</em>
</li>
<li><strong>type</strong>
changed from <em>enhancement</em> to <em>defect</em>
</li>
</ul>
Ticketgh-DeRhamSourceFri, 18 Oct 2019 15:17:50 GMT
https://trac.sagemath.org/ticket/28600#comment:8
https://trac.sagemath.org/ticket/28600#comment:8
<p>
Looks good to me. All tests passed and the docbuild looks fine. The notebooks run fine as well. Remember, you should edit the comments in the notebook files on your homepage, too.
</p>
<p>
Should I give a positive review?
</p>
TicketegourgoulhonFri, 18 Oct 2019 15:37:43 GMT
https://trac.sagemath.org/ticket/28600#comment:9
https://trac.sagemath.org/ticket/28600#comment:9
<p>
Replying to <a class="ticket" href="https://trac.sagemath.org/ticket/28600#comment:8" title="Comment 8">gh-DeRhamSource</a>:
</p>
<blockquote class="citation">
<p>
Looks good to me. All tests passed and the docbuild looks fine. The notebooks run fine as well. Remember, you should edit the comments in the notebook files on your homepage, too.
</p>
<p>
Should I give a positive review?
</p>
</blockquote>
<p>
Given what you said above, I think you may ;-)
</p>
Ticketgh-DeRhamSourceFri, 18 Oct 2019 16:25:14 GMTstatus changed; reviewer set
https://trac.sagemath.org/ticket/28600#comment:10
https://trac.sagemath.org/ticket/28600#comment:10
<ul>
<li><strong>status</strong>
changed from <em>needs_review</em> to <em>positive_review</em>
</li>
<li><strong>reviewer</strong>
set to <em>Michael Jung</em>
</li>
</ul>
TicketvbraunMon, 21 Oct 2019 22:43:53 GMTstatus, branch changed; resolution set
https://trac.sagemath.org/ticket/28600#comment:11
https://trac.sagemath.org/ticket/28600#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>branch</strong>
changed from <em>public/manifolds/pullback_pushforward_notation</em> to <em>cb3c97ec7d4575725eedfcf12f4b02c48fc35a49</em>
</li>
</ul>
Ticket