Sage: Ticket #28716: Construction of a vector frame from a family of vector fields
https://trac.sagemath.org/ticket/28716
<p>
This ticket modifies <code>DifferentiableManifold.vector_frame()</code> to allow for constructing a vector frame from a spanning family of linearly independent vector fields:
</p>
<pre class="wiki">sage: M = Manifold(2, 'M')
sage: X.<x,y> = M.chart()
sage: e0 = M.vector_field(1+x^2, 1+y^2)
sage: e1 = M.vector_field(2, -x*y)
sage: e = M.vector_frame('e', (e0, e1)); e
Vector frame (M, (e_0,e_1))
sage: e[0].display()
e_0 = (x^2 + 1) d/dx + (y^2 + 1) d/dy
sage: e[1].display()
e_1 = 2 d/dx - x*y d/dy
sage: (e[0], e[1]) == (e0, e1)
True
</pre><p>
Previously, the only way to introduce the vector frame <code>e</code> was to first introduce the automorphism relating the frame <code>(d/dx, d/dy)</code> to <code>(e0, e1)</code> and to pass this automorphism to <code>VectorFrame.new_frame()</code>:
</p>
<pre class="wiki">sage: aut = M.automorphism_field()
sage: aut[:] = [[e0[0], e1[0]], [e0[1], e1[1]]]
sage: e = X.frame().new_frame(aut, 'e')
</pre><p>
<strong>Implementation details:</strong> such functionality already existed for bases of finite rank free modules; the relevant code is extracted from the method <code>FiniteRankFreeModule.basis()</code> and put into the new method <code>FreeModuleBasis._init_from_family()</code>, in order to be used in <code>DifferentiableManifold.vector_frame()</code> as well.
</p>
en-usSagehttps://trac.sagemath.org/chrome/site/logo_sagemath_trac.png
https://trac.sagemath.org/ticket/28716
Trac 1.1.6egourgoulhonMon, 11 Nov 2019 09:39:57 GMTcommit, branch set
https://trac.sagemath.org/ticket/28716#comment:1
https://trac.sagemath.org/ticket/28716#comment:1
<ul>
<li><strong>commit</strong>
set to <em>013fb8b665adaf1339372c457fca851246d30a3c</em>
</li>
<li><strong>branch</strong>
set to <em>public/manifolds/vector_frame_from_family-28716</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=013fb8b665adaf1339372c457fca851246d30a3c"><span class="icon"></span>013fb8b</a></td><td><code>Add construction of a vector frame from a family of vector fields</code>
</td></tr></table>
TicketegourgoulhonMon, 11 Nov 2019 09:41:31 GMTstatus changed; cc set
https://trac.sagemath.org/ticket/28716#comment:2
https://trac.sagemath.org/ticket/28716#comment:2
<ul>
<li><strong>cc</strong>
<em>tscrim</em> added
</li>
<li><strong>status</strong>
changed from <em>new</em> to <em>needs_review</em>
</li>
</ul>
TicketegourgoulhonMon, 11 Nov 2019 09:52:08 GMTdescription changed
https://trac.sagemath.org/ticket/28716#comment:3
https://trac.sagemath.org/ticket/28716#comment:3
<ul>
<li><strong>description</strong>
modified (<a href="/ticket/28716?action=diff&version=3">diff</a>)
</li>
</ul>
TickettscrimMon, 11 Nov 2019 10:41:52 GMT
https://trac.sagemath.org/ticket/28716#comment:4
https://trac.sagemath.org/ticket/28716#comment:4
<p>
Do we need the optional parameter? Basically, can we just use the fact that a tuple/list is being given and then assume it is suppose to be a family of vector fields? If it has to be a keyword, I would change <code>from_family</code> to the more descriptive <code>from_vector_fields</code>.
</p>
Ticketgh-DeRhamSourceMon, 11 Nov 2019 12:22:07 GMT
https://trac.sagemath.org/ticket/28716#comment:5
https://trac.sagemath.org/ticket/28716#comment:5
<p>
This is a great idea and would be very useful for vector bundles, too. Sometimes I got really annoyed by this detour. Would you mind to adapt your code, if working, for vector bundles as-well?
</p>
<p>
By the way: We should combine vector bundles and the previous implementations really really soon (in this case inherit vector frames from local frames) otherwise things could get extremly messy.
</p>
<p>
Unfortunately, I am quite busy working at my master thesis right now. I can almost feel the deadline touching my skin. I promise to work on that as soon as I've gained some time back.
</p>
<p>
Even though I don't have the time now, I've opened the corresponding ticket <a class="new ticket" href="https://trac.sagemath.org/ticket/28718" title="task: Smoothly Embed Vector Bundles into Preexisting Code (new)">#28718</a>, just to keep this task in mind.
</p>
TicketegourgoulhonMon, 11 Nov 2019 17:10:54 GMT
https://trac.sagemath.org/ticket/28716#comment:6
https://trac.sagemath.org/ticket/28716#comment:6
<p>
Replying to <a class="ticket" href="https://trac.sagemath.org/ticket/28716#comment:4" title="Comment 4">tscrim</a>:
</p>
<p>
Thanks for your prompt feedback.
</p>
<blockquote class="citation">
<p>
Do we need the optional parameter? Basically, can we just use the fact that a tuple/list is being given and then assume it is suppose to be a family of vector fields?
</p>
</blockquote>
<p>
Good idea, this is much more user-friendly! I am on it...
</p>
TicketegourgoulhonMon, 11 Nov 2019 17:21:03 GMT
https://trac.sagemath.org/ticket/28716#comment:7
https://trac.sagemath.org/ticket/28716#comment:7
<p>
Replying to <a class="ticket" href="https://trac.sagemath.org/ticket/28716#comment:5" title="Comment 5">gh-DeRhamSource</a>:
</p>
<blockquote class="citation">
<p>
This is a great idea and would be very useful for vector bundles, too. Sometimes I got really annoyed by this detour.
</p>
</blockquote>
<p>
Yes, this should have been done sooner...
</p>
<blockquote class="citation">
<p>
Would you mind to adapt your code, if working, for vector bundles as-well?
</p>
</blockquote>
<p>
OK, I'll try to do this (see below).
</p>
<blockquote class="citation">
<p>
By the way: We should combine vector bundles and the previous implementations really really soon (in this case inherit vector frames from local frames) otherwise things could get extremly messy.
</p>
</blockquote>
<p>
Yes, I agree. Note however that this ticket does not touch the class <code>VectorFrame</code>, only the user interface <code>DifferentiableManifold.vector_frame()</code>. I'll perform a similar change to the interfaces <code>TopologicalVectorBundle.local_frame()</code> and <code>TensorBundle.local_frame()</code>.
</p>
<blockquote class="citation">
<p>
Unfortunately, I am quite busy working at my master thesis right now. I can almost feel the deadline touching my skin.
</p>
</blockquote>
<p>
Good luck with your master thesis!
</p>
<blockquote class="citation">
<p>
I promise to work on that as soon as I've gained some time back.
Even though I don't have the time now, I've opened the corresponding ticket <a class="new ticket" href="https://trac.sagemath.org/ticket/28718" title="task: Smoothly Embed Vector Bundles into Preexisting Code (new)">#28718</a>, just to keep this task in mind.
</p>
</blockquote>
<p>
Thanks.
</p>
TicketgitMon, 11 Nov 2019 21:50:05 GMTcommit changed
https://trac.sagemath.org/ticket/28716#comment:8
https://trac.sagemath.org/ticket/28716#comment:8
<ul>
<li><strong>commit</strong>
changed from <em>013fb8b665adaf1339372c457fca851246d30a3c</em> to <em>d0ef4d77e44422e25fbdfbc90e9c852387a15033</em>
</li>
</ul>
<p>
Branch pushed to git repo; I updated commit sha1. New commits:
</p>
<table class="wiki">
<tr><td><a class="ext-link" href="https://git.sagemath.org/sage.git/commit/?id=71b5f0f28d69d556ddd3ff5fd9e177ac56c03500"><span class="icon"></span>71b5f0f</a></td><td><code>Replace keyword argument 'from_family' by positional argument in vector_frame()</code>
</td></tr><tr><td><a class="ext-link" href="https://git.sagemath.org/sage.git/commit/?id=d0ef4d77e44422e25fbdfbc90e9c852387a15033"><span class="icon"></span>d0ef4d7</a></td><td><code>Add construction of a local frame from a set of vector fields in TensorBundle.local_frame()</code>
</td></tr></table>
TicketegourgoulhonMon, 11 Nov 2019 22:17:03 GMTdescription changed
https://trac.sagemath.org/ticket/28716#comment:9
https://trac.sagemath.org/ticket/28716#comment:9
<ul>
<li><strong>description</strong>
modified (<a href="/ticket/28716?action=diff&version=9">diff</a>)
</li>
</ul>
<p>
In the latest version (cf. <a class="ticket" href="https://trac.sagemath.org/ticket/28716#comment:8" title="Comment 8">comment:8</a> commits)
</p>
<ul><li><code>vector_frame()</code> accepts a tuple/list of vector fields as a positional argument, the keyword argument <code>from_family</code> being suppressed, following the suggestion made in <a class="ticket" href="https://trac.sagemath.org/ticket/28716#comment:4" title="Comment 4">comment:4</a>.
</li><li>The <code>ZeroDivisionError</code> that occurs if the vector fields are not linearly independent (the exception is raised when computing the inverse of the automorphism relating the new frame to a previous one) is cached with a proper error message.
</li><li>The documentation of the module <code>sage.manifolds.differentiable.vectorframe</code> has been updated to take into account the new functionality.
</li><li><code>TensorBundle.local_frame()</code> has been updated to offer the same functionality, following <a class="ticket" href="https://trac.sagemath.org/ticket/28716#comment:5" title="Comment 5">comment:5</a>.
</li><li>A <code>TODO</code> section has been added to <code>TopologicalVectorBundle.local_frame()</code> for implementing a similar functionality with local sections in the future.
</li></ul><p>
I propose to stay here for this ticket, i.e. to let the modification of <code>TopologicalVectorBundle.local_frame()</code> to a future ticket (<a class="new ticket" href="https://trac.sagemath.org/ticket/28718" title="task: Smoothly Embed Vector Bundles into Preexisting Code (new)">#28718</a> ?). This is mostly to avoid code duplication with <code>DifferentiableManifold.vector_frame()</code>, waiting for a clearer view of <a class="new ticket" href="https://trac.sagemath.org/ticket/28718" title="task: Smoothly Embed Vector Bundles into Preexisting Code (new)">#28718</a>. Besides, I will be extremely busy in the coming weeks and I would like very much the <code>vector_frame()</code> functionality introduced in the current ticket to make its way in Sage 9.0.
</p>
TicketegourgoulhonSun, 17 Nov 2019 10:10:22 GMT
https://trac.sagemath.org/ticket/28716#comment:10
https://trac.sagemath.org/ticket/28716#comment:10
<p>
Do you agree with the above changes (<a class="ticket" href="https://trac.sagemath.org/ticket/28716#comment:9" title="Comment 9">comment:9</a>)?
</p>
Ticketgh-DeRhamSourceSun, 17 Nov 2019 13:44:37 GMT
https://trac.sagemath.org/ticket/28716#comment:11
https://trac.sagemath.org/ticket/28716#comment:11
<p>
Partially. Of course, we can postpone this to another ticket, preferrably to <a class="new ticket" href="https://trac.sagemath.org/ticket/28718" title="task: Smoothly Embed Vector Bundles into Preexisting Code (new)">#28718</a>. However, I think this fits in here perfectly well and enables the feature for vector bundles in Sage 9.0 without too much effort [1] as you already did it for the tensor bundle. But I have no strong opinion on that so just do as you prefer.
</p>
<p>
One personal reformulation:
</p>
<div class="wiki-code"><div class="code"><pre><span class="gd">- any connection with previously defined vector frames or vector fields
- (the connection can be performed later via the method
</span><span class="gi">+ connecting it to previously defined vector frames or vector fields
+ (this can still be performed later via the method
</span></pre></div></div><p>
[1] at least so far as I can see
</p>
TicketgitSun, 17 Nov 2019 23:09:02 GMTcommit changed
https://trac.sagemath.org/ticket/28716#comment:12
https://trac.sagemath.org/ticket/28716#comment:12
<ul>
<li><strong>commit</strong>
changed from <em>d0ef4d77e44422e25fbdfbc90e9c852387a15033</em> to <em>6635fad2f2c51e5b8e99ea4da98e6b9cd26b020c</em>
</li>
</ul>
<p>
Branch pushed to git repo; I updated commit sha1. New commits:
</p>
<table class="wiki">
<tr><td><a class="ext-link" href="https://git.sagemath.org/sage.git/commit/?id=6635fad2f2c51e5b8e99ea4da98e6b9cd26b020c"><span class="icon"></span>6635fad</a></td><td><code>Construction of a local frame on a vector bundle from a family of sections</code>
</td></tr></table>
TicketegourgoulhonSun, 17 Nov 2019 23:14:16 GMT
https://trac.sagemath.org/ticket/28716#comment:13
https://trac.sagemath.org/ticket/28716#comment:13
<p>
Replying to <a class="ticket" href="https://trac.sagemath.org/ticket/28716#comment:11" title="Comment 11">gh-DeRhamSource</a>:
</p>
<blockquote class="citation">
<p>
Partially. Of course, we can postpone this to another ticket, preferrably to <a class="new ticket" href="https://trac.sagemath.org/ticket/28718" title="task: Smoothly Embed Vector Bundles into Preexisting Code (new)">#28718</a>. However, I think this fits in here perfectly well and enables the feature for vector bundles in Sage 9.0 without too much effort [1] as you already did it for the tensor bundle.
</p>
</blockquote>
<p>
OK I've done it in the above commit. I've also improved the catching of the error in case of linearly dependent elements.
</p>
<blockquote class="citation">
<p>
One personal reformulation:
</p>
<div class="wiki-code"><div class="code"><pre><span class="gd">- any connection with previously defined vector frames or vector fields
- (the connection can be performed later via the method
</span><span class="gi">+ connecting it to previously defined vector frames or vector fields
+ (this can still be performed later via the method
</span></pre></div></div></blockquote>
<p>
Done as well.
</p>
Ticketgh-DeRhamSourceMon, 18 Nov 2019 09:15:41 GMT
https://trac.sagemath.org/ticket/28716#comment:14
https://trac.sagemath.org/ticket/28716#comment:14
<p>
Thank you so much! I'll give it a further look this or tomorrow afternoon.
</p>
<p>
It seems, we are at beta6 now.
</p>
Ticketgh-DeRhamSourceMon, 18 Nov 2019 14:04:29 GMT
https://trac.sagemath.org/ticket/28716#comment:15
https://trac.sagemath.org/ticket/28716#comment:15
<p>
I gave it some short tests. This is a huge improvement for using frames! Thanks! :)
</p>
<p>
Just a minor thing:
</p>
<div class="wiki-code"><div class="code"><pre><span class="gd">- ``self`` (`n` being the dimension of ``self``) defining the local
</span><span class="gi">+ ``self`` (`n` being the rank of ``self``) defining the local
</span></pre></div></div><p>
Apart from that it looks fine to me. As soon as you merged the recent develop branch into this one and patchbot says "yes", I could give it a positive review. Travis?
</p>
TicketgitMon, 18 Nov 2019 22:20:44 GMTcommit changed
https://trac.sagemath.org/ticket/28716#comment:16
https://trac.sagemath.org/ticket/28716#comment:16
<ul>
<li><strong>commit</strong>
changed from <em>6635fad2f2c51e5b8e99ea4da98e6b9cd26b020c</em> to <em>81e2f60b2247b473b0d2aa8c059a2211faa4ff63</em>
</li>
</ul>
<p>
Branch pushed to git repo; I updated commit sha1. New commits:
</p>
<table class="wiki">
<tr><td><a class="ext-link" href="https://git.sagemath.org/sage.git/commit/?id=5c9c516df409bcf10555343e92aca101995c2ca1"><span class="icon"></span>5c9c516</a></td><td><code>Merge branch 'public/manifolds/vector_frame_from_family-28716' of git://trac.sagemath.org/sage into Sage 9.0.beta6</code>
</td></tr><tr><td><a class="ext-link" href="https://git.sagemath.org/sage.git/commit/?id=81e2f60b2247b473b0d2aa8c059a2211faa4ff63"><span class="icon"></span>81e2f60</a></td><td><code>Minor fix in the documentation of TopologicalVectorBundle.local_frame()</code>
</td></tr></table>
TicketegourgoulhonMon, 18 Nov 2019 22:24:25 GMT
https://trac.sagemath.org/ticket/28716#comment:17
https://trac.sagemath.org/ticket/28716#comment:17
<p>
Replying to <a class="ticket" href="https://trac.sagemath.org/ticket/28716#comment:15" title="Comment 15">gh-DeRhamSource</a>:
</p>
<blockquote class="citation">
<p>
Just a minor thing:
</p>
<div class="wiki-code"><div class="code"><pre><span class="gd">- ``self`` (`n` being the dimension of ``self``) defining the local
</span><span class="gi">+ ``self`` (`n` being the rank of ``self``) defining the local
</span></pre></div></div></blockquote>
<p>
Thanks for pointing this; it is corrected in the above commit.
</p>
Ticketgh-DeRhamSourceTue, 19 Nov 2019 12:28:20 GMT
https://trac.sagemath.org/ticket/28716#comment:18
https://trac.sagemath.org/ticket/28716#comment:18
<p>
There is one thing I'm not sure about. Namely the line:
</p>
<pre class="wiki"> mat = [[c[[i]] for c in comps] for i in fmodule.irange()]
aut.add_comp(basis)[:] = mat
this --> aut.add_comp(self)[:] = mat
fmodule.set_change_of_basis(basis, self, aut)
</pre><p>
in <code>free_module_basis.py</code>.
</p>
<p>
Shouldn't it be the identity matrix with respect to that basis? Or did I get something wrong?
</p>
TicketegourgoulhonTue, 19 Nov 2019 14:00:28 GMT
https://trac.sagemath.org/ticket/28716#comment:19
https://trac.sagemath.org/ticket/28716#comment:19
<p>
Replying to <a class="ticket" href="https://trac.sagemath.org/ticket/28716#comment:18" title="Comment 18">gh-DeRhamSource</a>:
</p>
<blockquote class="citation">
<p>
There is one thing I'm not sure about. Namely the line:
</p>
<pre class="wiki"> mat = [[c[[i]] for c in comps] for i in fmodule.irange()]
aut.add_comp(basis)[:] = mat
this --> aut.add_comp(self)[:] = mat
fmodule.set_change_of_basis(basis, self, aut)
</pre><p>
in <code>free_module_basis.py</code>.
</p>
<p>
Shouldn't it be the identity matrix with respect to that basis? Or did I get something wrong?
</p>
</blockquote>
<p>
The formula is correct: it should not be the identity matrix but the matrix of the change-of-basis automorphism, which has the same expression in both bases.
</p>
Ticketgh-DeRhamSourceTue, 19 Nov 2019 15:18:55 GMTstatus changed; reviewer set
https://trac.sagemath.org/ticket/28716#comment:20
https://trac.sagemath.org/ticket/28716#comment:20
<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>
<p>
Replying to <a class="ticket" href="https://trac.sagemath.org/ticket/28716#comment:19" title="Comment 19">egourgoulhon</a>:
</p>
<blockquote class="citation">
<p>
The formula is correct: it should not be the identity matrix but the matrix of the change-of-basis automorphism, which has the same expression in both bases.
</p>
</blockquote>
<p>
Yeah, you're absolutely right. I thought it through once again and come to the same conclusion now. Furthermore, some tests on this did work properly. Sorry!
</p>
<p>
So from my perspective, everything is fine. I'll give it a positive review.
</p>
TicketegourgoulhonTue, 19 Nov 2019 15:50:02 GMT
https://trac.sagemath.org/ticket/28716#comment:21
https://trac.sagemath.org/ticket/28716#comment:21
<p>
Thank you for the review!
</p>
TicketvbraunWed, 27 Nov 2019 00:31:55 GMTstatus changed
https://trac.sagemath.org/ticket/28716#comment:22
https://trac.sagemath.org/ticket/28716#comment:22
<ul>
<li><strong>status</strong>
changed from <em>positive_review</em> to <em>needs_work</em>
</li>
</ul>
<p>
Merge conflict
</p>
TicketegourgoulhonWed, 27 Nov 2019 20:02:19 GMT
https://trac.sagemath.org/ticket/28716#comment:23
https://trac.sagemath.org/ticket/28716#comment:23
<p>
Replying to <a class="ticket" href="https://trac.sagemath.org/ticket/28716#comment:22" title="Comment 22">vbraun</a>:
</p>
<blockquote class="citation">
<p>
Merge conflict
</p>
</blockquote>
<p>
There is no conflict with the just released 9.0.beta7. Is it a conflict with <a class="closed ticket" href="https://trac.sagemath.org/ticket/27784" title="enhancement: Characteristic Classes on Vector Bundles (closed: fixed)">#27784</a> (which is not merged yet)?
</p>
Ticketgh-DeRhamSourceThu, 28 Nov 2019 08:51:36 GMT
https://trac.sagemath.org/ticket/28716#comment:24
https://trac.sagemath.org/ticket/28716#comment:24
<p>
Replying to <a class="ticket" href="https://trac.sagemath.org/ticket/28716#comment:23" title="Comment 23">egourgoulhon</a>:
</p>
<blockquote class="citation">
<p>
Replying to <a class="ticket" href="https://trac.sagemath.org/ticket/28716#comment:22" title="Comment 22">vbraun</a>:
</p>
<blockquote class="citation">
<p>
Merge conflict
</p>
</blockquote>
<p>
There is no conflict with the just released 9.0.beta7. Is it a conflict with <a class="closed ticket" href="https://trac.sagemath.org/ticket/27784" title="enhancement: Characteristic Classes on Vector Bundles (closed: fixed)">#27784</a> (which is not merged yet)?
</p>
</blockquote>
<p>
Not sure. But to run some tests for my thesis, I merged these two tickets and a conflict occured. Just a very minor thing about lines if I remember correctly.
</p>
<p>
However, either ticket needs to be merged to be certain.
</p>
TicketegourgoulhonThu, 28 Nov 2019 09:45:20 GMT
https://trac.sagemath.org/ticket/28716#comment:25
https://trac.sagemath.org/ticket/28716#comment:25
<p>
Replying to <a class="ticket" href="https://trac.sagemath.org/ticket/28716#comment:24" title="Comment 24">gh-DeRhamSource</a>:
</p>
<blockquote class="citation">
<p>
Replying to <a class="ticket" href="https://trac.sagemath.org/ticket/28716#comment:23" title="Comment 23">egourgoulhon</a>:
</p>
<blockquote class="citation">
<p>
Replying to <a class="ticket" href="https://trac.sagemath.org/ticket/28716#comment:22" title="Comment 22">vbraun</a>:
</p>
<blockquote class="citation">
<p>
Merge conflict
</p>
</blockquote>
<p>
There is no conflict with the just released 9.0.beta7. Is it a conflict with <a class="closed ticket" href="https://trac.sagemath.org/ticket/27784" title="enhancement: Characteristic Classes on Vector Bundles (closed: fixed)">#27784</a> (which is not merged yet)?
</p>
</blockquote>
<p>
Not sure. But to run some tests for my thesis, I merged these two tickets and a conflict occured. Just a very minor thing about lines if I remember correctly.
</p>
</blockquote>
<p>
Yes most of the time these conflicts due to various developments performed in parallel are very minor and easy to solve.
</p>
<blockquote class="citation">
<p>
However, either ticket needs to be merged to be certain.
</p>
</blockquote>
<p>
Yes. I am afraid we have to wait for the next beta to solve this...
</p>
TickettscrimThu, 28 Nov 2019 10:27:46 GMT
https://trac.sagemath.org/ticket/28716#comment:26
https://trac.sagemath.org/ticket/28716#comment:26
<p>
Since you basically know what ticket, I would just merge that in and set this back to positive review with that as a dependency.
</p>
Ticketgh-DeRhamSourceThu, 28 Nov 2019 10:32:54 GMT
https://trac.sagemath.org/ticket/28716#comment:27
https://trac.sagemath.org/ticket/28716#comment:27
<p>
Replying to <a class="ticket" href="https://trac.sagemath.org/ticket/28716#comment:26" title="Comment 26">tscrim</a>:
</p>
<blockquote class="citation">
<p>
Since you basically know what ticket, I would just merge that in and set this back to positive review with that as a dependency.
</p>
</blockquote>
<p>
Good idea. I'll do that for <a class="closed ticket" href="https://trac.sagemath.org/ticket/27784" title="enhancement: Characteristic Classes on Vector Bundles (closed: fixed)">#27784</a>. I need to add a minor thing into the documentation of characteristic classes anyway.
</p>
Ticketgh-DeRhamSourceThu, 28 Nov 2019 11:32:03 GMT
https://trac.sagemath.org/ticket/28716#comment:28
https://trac.sagemath.org/ticket/28716#comment:28
<p>
Replying to <a class="ticket" href="https://trac.sagemath.org/ticket/28716#comment:27" title="Comment 27">gh-DeRhamSource</a>:
</p>
<blockquote class="citation">
<p>
Replying to <a class="ticket" href="https://trac.sagemath.org/ticket/28716#comment:26" title="Comment 26">tscrim</a>:
</p>
<blockquote class="citation">
<p>
Since you basically know what ticket, I would just merge that in and set this back to positive review with that as a dependency.
</p>
</blockquote>
<p>
Good idea. I'll do that for <a class="closed ticket" href="https://trac.sagemath.org/ticket/27784" title="enhancement: Characteristic Classes on Vector Bundles (closed: fixed)">#27784</a>. I need to add a minor thing into the documentation of characteristic classes anyway.
</p>
</blockquote>
<p>
Done.
</p>
TicketegourgoulhonThu, 28 Nov 2019 12:13:12 GMT
https://trac.sagemath.org/ticket/28716#comment:29
https://trac.sagemath.org/ticket/28716#comment:29
<p>
Replying to <a class="ticket" href="https://trac.sagemath.org/ticket/28716#comment:28" title="Comment 28">gh-DeRhamSource</a>:
</p>
<blockquote class="citation">
<p>
Replying to <a class="ticket" href="https://trac.sagemath.org/ticket/28716#comment:27" title="Comment 27">gh-DeRhamSource</a>:
</p>
<blockquote class="citation">
<p>
Replying to <a class="ticket" href="https://trac.sagemath.org/ticket/28716#comment:26" title="Comment 26">tscrim</a>:
</p>
<blockquote class="citation">
<p>
Since you basically know what ticket, I would just merge that in and set this back to positive review with that as a dependency.
</p>
</blockquote>
<p>
Good idea. I'll do that for <a class="closed ticket" href="https://trac.sagemath.org/ticket/27784" title="enhancement: Characteristic Classes on Vector Bundles (closed: fixed)">#27784</a>. I need to add a minor thing into the documentation of characteristic classes anyway.
</p>
</blockquote>
<p>
Done.
</p>
</blockquote>
<p>
Thanks!
</p>
<p>
I am then setting this ticket back to positive review and will have a look at <a class="closed ticket" href="https://trac.sagemath.org/ticket/27784" title="enhancement: Characteristic Classes on Vector Bundles (closed: fixed)">#27784</a>.
</p>
TicketegourgoulhonThu, 28 Nov 2019 12:14:11 GMTstatus changed
https://trac.sagemath.org/ticket/28716#comment:30
https://trac.sagemath.org/ticket/28716#comment:30
<ul>
<li><strong>status</strong>
changed from <em>needs_work</em> to <em>positive_review</em>
</li>
</ul>
<p>
According to <a class="ticket" href="https://trac.sagemath.org/ticket/28716#comment:29" title="Comment 29">comment:29</a>.
</p>
TicketvbraunSat, 30 Nov 2019 13:36:31 GMTstatus, branch changed; resolution set
https://trac.sagemath.org/ticket/28716#comment:31
https://trac.sagemath.org/ticket/28716#comment:31
<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/vector_frame_from_family-28716</em> to <em>81e2f60b2247b473b0d2aa8c059a2211faa4ff63</em>
</li>
</ul>
Ticket