Sage: Ticket #17160: Finitely generated axiom for (mutiplicative) magmas, semigroups, monoids, groups
https://trac.sagemath.org/ticket/17160
<p>
This introduce an axiom <a class="missing wiki">FinitelyGeneratedAsMagma?</a>, as well as related
categories with axioms for magmas, semigroups and groups::
</p>
<pre class="wiki"> sage: Groups().FinitelyGeneratedAsMagma()
Category of finitely generated groups
</pre><p>
For ease of notations, when there is no ambiguity, one can do::
</p>
<pre class="wiki"> sage: Groups().FinitelyGenerated()
Category of finitely generated groups
</pre><p>
One motivation for this change (for <a class="closed ticket" href="https://trac.sagemath.org/ticket/8678" title="enhancement: Improvements for morphisms of ModulesWithBasis (closed: fixed)">#8678</a>) is that finite semigroups
in Sage used to be automatically endowed with an <code>EnumeratedSets</code>
structure; the default enumeration is then obtained by iteratively
multiplying the semigroup generators. This forced any finite semigroup
to either implement an enumeration, or provide semigroup generators;
this was often inconvenient.
</p>
<p>
Instead, finite semigroups that provide a distinguished finite set of
generators with <code>semigroup_generators</code> should now explicitly declare
themselves in the category of <code>FinitelyGeneratedSemigroups</code>:
</p>
<pre class="wiki"> sage: Semigroups().FinitelyGenerated()
Category of finitely generated semigroups
</pre><p>
This is a backward incompatible change.
</p>
<p>
TODO:
</p>
<ul><li>Use the occasion to migrate <a class="missing wiki">TransitiveIdeal?</a> to <a class="missing wiki">RecursivelyEnumeratedSet?</a>
</li></ul>en-usSagehttps://trac.sagemath.org/chrome/site/logo_sagemath_trac.png
https://trac.sagemath.org/ticket/17160
Trac 1.1.6tscrimWed, 15 Oct 2014 13:48:26 GMTtype, component changed; cc set
https://trac.sagemath.org/ticket/17160#comment:1
https://trac.sagemath.org/ticket/17160#comment:1
<ul>
<li><strong>cc</strong>
<em>tscrim</em> added
</li>
<li><strong>type</strong>
changed from <em>PLEASE CHANGE</em> to <em>enhancement</em>
</li>
<li><strong>component</strong>
changed from <em>PLEASE CHANGE</em> to <em>categories</em>
</li>
</ul>
<p>
Also be good for rings and algebras.
</p>
TicketnthieryWed, 15 Oct 2014 15:28:51 GMTdescription changed
https://trac.sagemath.org/ticket/17160#comment:2
https://trac.sagemath.org/ticket/17160#comment:2
<ul>
<li><strong>description</strong>
modified (<a href="/ticket/17160?action=diff&version=2">diff</a>)
</li>
</ul>
TicketnthieryWed, 15 Oct 2014 15:30:42 GMT
https://trac.sagemath.org/ticket/17160#comment:3
https://trac.sagemath.org/ticket/17160#comment:3
<p>
Replying to <a class="ticket" href="https://trac.sagemath.org/ticket/17160#comment:1" title="Comment 1">tscrim</a>:
</p>
<blockquote class="citation">
<p>
Also be good for rings and algebras.
</p>
</blockquote>
<p>
Yes, and additive magmas as well. And possibly crystals, ... But I'll leave those to a later ticket. And for modules, we alreay have <code>FiniteDimensional</code>.
</p>
<p>
Cheers,
</p>
<blockquote>
<p>
Nicolas
</p>
</blockquote>
TicketnthieryWed, 15 Oct 2014 15:31:43 GMTcc, description changed; author set
https://trac.sagemath.org/ticket/17160#comment:4
https://trac.sagemath.org/ticket/17160#comment:4
<ul>
<li><strong>cc</strong>
<em>sage-combinat</em> <em>darij</em> <em>virmaux</em> added
</li>
<li><strong>description</strong>
modified (<a href="/ticket/17160?action=diff&version=4">diff</a>)
</li>
<li><strong>author</strong>
set to <em>Nicolas M. Thiéry</em>
</li>
</ul>
TicketnthieryWed, 15 Oct 2014 16:25:20 GMTbranch set
https://trac.sagemath.org/ticket/17160#comment:5
https://trac.sagemath.org/ticket/17160#comment:5
<ul>
<li><strong>branch</strong>
set to <em>u/nthiery/categories/finitely-generated-magmas-17160</em>
</li>
</ul>
TickettscrimThu, 16 Oct 2014 01:09:54 GMTcommit set
https://trac.sagemath.org/ticket/17160#comment:6
https://trac.sagemath.org/ticket/17160#comment:6
<ul>
<li><strong>commit</strong>
set to <em>f027ce2b5e1abe22d49bcdc96f2cfeebced8fc16</em>
</li>
</ul>
<p>
I know this isn't set for review yet, but just to note that a finite magma is automatically finitely generated. So I think we should have this reflected in the category structure; in particular, so we don't have lines like this:
</p>
<pre class="wiki">Parent.__init__(self, category = Semigroups().Finite().FinitelyGenerated())
</pre><p>
If you need someone to review it, just let me know when this is ready.
</p>
<hr />
<p>
Last 10 new commits:
</p>
<table class="wiki">
<tr><td><a class="ext-link" href="http://git.sagemath.org/sage.git/commit/?id=d5d3a97fcfbf3d2316d8096681c39da2996b8096"><span class="icon"></span>d5d3a97</a></td><td><code>10668: improved description of the HomsetsOf class</code>
</td></tr><tr><td><a class="ext-link" href="http://git.sagemath.org/sage.git/commit/?id=5416ba0a866806b9746fd0e46c3888f2c308e73a"><span class="icon"></span>5416ba0</a></td><td><code>Add a note on the MRO used for Homset._abstract_element_class</code>
</td></tr><tr><td><a class="ext-link" href="http://git.sagemath.org/sage.git/commit/?id=23639a9288bdca85482a93ed029b3d1390309141"><span class="icon"></span>23639a9</a></td><td><code>Fix more typos</code>
</td></tr><tr><td><a class="ext-link" href="http://git.sagemath.org/sage.git/commit/?id=02a6a8a4a5984881a12198ed86a4e8cb7ab8c899"><span class="icon"></span>02a6a8a</a></td><td><code>10668: fixed representation of the category of endsets</code>
</td></tr><tr><td><a class="ext-link" href="http://git.sagemath.org/sage.git/commit/?id=477d381a90f7fbb059b3689d618e50de5f884821"><span class="icon"></span>477d381</a></td><td><code>10668: Homsets.Endset.super_category -> extra_super_category + documentation</code>
</td></tr><tr><td><a class="ext-link" href="http://git.sagemath.org/sage.git/commit/?id=877bfdb215628b19c44a66d14ceee54824beaf14"><span class="icon"></span>877bfdb</a></td><td><code>10668: fix: Modules.EndCategory -> Modules.Homsets.Endset + made it functional: endsets of modules are algebras</code>
</td></tr><tr><td><a class="ext-link" href="http://git.sagemath.org/sage.git/commit/?id=f86824ea354a5260b2ee0b8f24f239c8b5178bdd"><span class="icon"></span>f86824e</a></td><td><code>10668: documentation for HomsetsCategory.category_of + fixed typo in doctest nearby</code>
</td></tr><tr><td><a class="ext-link" href="http://git.sagemath.org/sage.git/commit/?id=787f461ff097e860f21ebf990f67e74185f84d53"><span class="icon"></span>787f461</a></td><td><code>10668: proofreading of Homsets.category_of</code>
</td></tr><tr><td><a class="ext-link" href="http://git.sagemath.org/sage.git/commit/?id=5f9668657eb1d04b9acf90afe1ee38ff84807b75"><span class="icon"></span>5f96686</a></td><td><code>17160: Merge branch 'categories/morphism-methods-10668'</code>
</td></tr><tr><td><a class="ext-link" href="http://git.sagemath.org/sage.git/commit/?id=f027ce2b5e1abe22d49bcdc96f2cfeebced8fc16"><span class="icon"></span>f027ce2</a></td><td><code>17610: first draft of finitely generated axiom for magmas/groups/axioms</code>
</td></tr></table>
TicketnthieryThu, 16 Oct 2014 07:41:55 GMT
https://trac.sagemath.org/ticket/17160#comment:7
https://trac.sagemath.org/ticket/17160#comment:7
<p>
Replying to <a class="ticket" href="https://trac.sagemath.org/ticket/17160#comment:6" title="Comment 6">tscrim</a>:
</p>
<blockquote class="citation">
<p>
I know this isn't set for review yet,
</p>
</blockquote>
<p>
Thanks for having looked at it!
</p>
<blockquote class="citation">
<p>
but just to note that a finite magma is automatically finitely generated. So I think we should have this reflected in the category structure; in particular, so we don't have lines like this:
</p>
<pre class="wiki">Parent.__init__(self, category = Semigroups().Finite().FinitelyGenerated())
</pre></blockquote>
<p>
As stated in the description, the point of the ticket is precisely to
make a distinction between finite magmas (which are indeed finitely
generated by definition), and finite monoids that are explicitly
endowed with a finite set of generators. The new axiom is about the
latter. So, above, we anyway want something like:
</p>
<blockquote>
<p>
Semigroups().Finite().XXX()
</p>
</blockquote>
<p>
Granted, the current name of the axiom is misleading, and I am
hesitant about it. I also considered:
</p>
<blockquote>
<p>
sage: Groups().Finite().<a class="missing wiki">WithFiniteSetOfGenerators?</a>()
Category of groups with finite set of generators
</p>
</blockquote>
<p>
It's very explicit but feels like heavy notation; and it does not feel
as appealing as "finitely generated" which immediately rings a bell in
a mathematician's head. Also, it seems to me that being "finitely
generated" is rather useless computationally speaking if no finite set
of generators is provided; so we would not be using that nice name for
a weaker purpose anyway.
</p>
<p>
I guess that's the main design decision to be taken in this
ticket. The rest is rather straightforward.
</p>
<p>
Ah, yes, the other design decision is whether it's acceptable to break
backward compatibility. I'll be the first one to be hurt by this
change, and I believe it's worth it ...
</p>
<p>
Opinions anyone?
</p>
<blockquote class="citation">
<p>
If you need someone to review it, just let me know when this is ready.
</p>
</blockquote>
<p>
Ok, thanks! Darij would be a good candidate to give feedback too!
</p>
<p>
Cheers,
</p>
<blockquote>
<p>
Nicolas
</p>
</blockquote>
TicketnthieryThu, 16 Oct 2014 07:43:54 GMTdependencies set
https://trac.sagemath.org/ticket/17160#comment:8
https://trac.sagemath.org/ticket/17160#comment:8
<ul>
<li><strong>dependencies</strong>
set to <em>#10668</em>
</li>
</ul>
<p>
The dependency on <a class="closed ticket" href="https://trac.sagemath.org/ticket/10668" title="defect: Refactor category support for morphisms (Hom is not a functorial ... (closed: fixed)">#10668</a> is mostly for convenience: <a class="closed ticket" href="https://trac.sagemath.org/ticket/10668" title="defect: Refactor category support for morphisms (Hom is not a functorial ... (closed: fixed)">#10668</a> fixes the doctests in c3_controlled to not need to be updated everytime the category hierarchy changes.
</p>
TickettscrimThu, 16 Oct 2014 15:55:41 GMT
https://trac.sagemath.org/ticket/17160#comment:9
https://trac.sagemath.org/ticket/17160#comment:9
<p>
Saying this ticket is for a specified fixed set of generators contracts this statement:
</p>
<blockquote class="citation">
<p>
And for modules, we alreay have <code>FiniteDimensional</code>.
</p>
</blockquote>
<p>
I think we should make an analogy to <code>WithBasis</code> and <code>FiniteDimensional</code> by having 2 axioms, <code>WithGeneratingSet</code> and <code>FinitelyGenerated</code>. This would give <code>FinitelyGenerated</code> a purpose, would still allow the current goal of not having to specify the enumeration, and allow the option for infinitely generated objects.
</p>
TicketnthieryThu, 16 Oct 2014 21:20:22 GMT
https://trac.sagemath.org/ticket/17160#comment:10
https://trac.sagemath.org/ticket/17160#comment:10
<p>
Replying to <a class="ticket" href="https://trac.sagemath.org/ticket/17160#comment:9" title="Comment 9">tscrim</a>:
</p>
<blockquote class="citation">
<p>
I think we should make an analogy to <code>WithBasis</code> and
<code>FiniteDimensional</code> by having 2 axioms, <code>WithGeneratingSet</code> and
<code>FinitelyGenerated</code>. This would give <code>FinitelyGenerated</code> a purpose,
would still allow the current goal of not having to specify the
enumeration, and allow the option for infinitely generated objects.
</p>
</blockquote>
<p>
I considered this and I agree that this would have the advantage of
being consistent with the basis things. However I don't see what I
would put in the categories with axiom for <code>FinitelyGenerated</code> axiom
besides the subcategories with axioms for <code>WithGeneratingSet</code>, so this
looks like overkill. Besides,
</p>
<blockquote>
<p>
Categories of finitely generated group with generating set
</p>
</blockquote>
<p>
is not great. I am torn.
</p>
<p>
Opinions anyone else?
</p>
<p>
Cheers,
</p>
<blockquote>
<p>
Nicolas
</p>
</blockquote>
TickettscrimThu, 16 Oct 2014 23:43:52 GMT
https://trac.sagemath.org/ticket/17160#comment:11
https://trac.sagemath.org/ticket/17160#comment:11
<p>
Replying to <a class="ticket" href="https://trac.sagemath.org/ticket/17160#comment:10" title="Comment 10">nthiery</a>:
</p>
<blockquote class="citation">
<p>
I considered this and I agree that this would have the advantage of
being consistent with the basis things. However I don't see what I
would put in the categories with axiom for <code>FinitelyGenerated</code> axiom
besides the subcategories with axioms for <code>WithGeneratingSet</code>, so this
looks like overkill. Besides,
</p>
<blockquote>
<p>
Categories of finitely generated group with generating set
</p>
</blockquote>
<p>
is not great. I am torn.
</p>
</blockquote>
<p>
I have things that have infinite (enumerable) distinguished generating sets (ex. free group/monoid with generators indexed by <code>NN</code> or Yangians <a class="closed ticket" href="https://trac.sagemath.org/ticket/15484" title="enhancement: Implement Yangian for gl(n) (closed: fixed)">#15484</a>), so separating these axioms will be useful. In fact, the enumeration could be done in for the general <code>WithGeneratingSet</code> category and would (at least should) error out if the generating set is not enumerable. Although I only know of 1 thing which will be finite dimensional but doesn't come with a distinguished basis. Plus I think we could do an extra case in <code>_repr_object_names_static</code> to change the repr into:
</p>
<pre class="wiki">Category of groups with finite generating set
</pre><p>
Here's another thought, what about we look at the cardinality of the generating set? So we only have <code>WithGeneratingSet</code> which calls <code>is_finitely_generated</code>, whose default is to look at the cardinality of the generating set to determine the output of repr. At least that's the only place where I could see us (currently) using the fact that the generating set is finite. For the enumeration, all we really need is the generating set is enumerable. Although I guess we really want to add <code>EnumeratedSets</code> to the category heirachy, so this probably is not so useful of an idea...
</p>
<blockquote class="citation">
<p>
Opinions anyone else?
</p>
</blockquote>
<p>
Darij, Aladin, or anyone else, your thoughts?
</p>
TicketnthierySat, 18 Oct 2014 11:51:04 GMT
https://trac.sagemath.org/ticket/17160#comment:12
https://trac.sagemath.org/ticket/17160#comment:12
<p>
Replying to <a class="ticket" href="https://trac.sagemath.org/ticket/17160#comment:11" title="Comment 11">tscrim</a>:
</p>
<blockquote class="citation">
<p>
I have things that have infinite (enumerable) distinguished generating sets (ex. free group/monoid with generators indexed by <code>NN</code> or Yangians <a class="closed ticket" href="https://trac.sagemath.org/ticket/15484" title="enhancement: Implement Yangian for gl(n) (closed: fixed)">#15484</a>), so separating these axioms will be useful. In fact, the enumeration could be done in for the general <code>WithGeneratingSet</code> category and would (at least should) error out if the generating set is not enumerable. Although I only know of 1 thing which will be finite dimensional but doesn't come with a distinguished basis.
</p>
</blockquote>
<p>
Another issue: having a distinguished set of generators and being
finitely generated does not necessarily imply that the distinguished
set of generators is finite. So we would actually need three axioms:
"<a class="missing wiki">WithGenerators?</a>", "<a class="missing wiki">FinitelyGenerated?</a>", and "<a class="missing wiki">WithFiniteGeneratingSet?</a>".
So for a finite magma we still would need to do
"Magmas().Finite().<a class="missing wiki">WithFiniteGeneratingSet?</a>()".
</p>
<p>
I am not sure this is worth the complication. Especially since we will
have to do something similar for additive magmas, rings, fields, ...
</p>
<blockquote class="citation">
<p>
Plus I think we could do an extra case in <code>_repr_object_names_static</code> to change the repr into:
</p>
<pre class="wiki">Category of groups with finite generating set
</pre></blockquote>
<p>
That should be easy indeed.
</p>
<blockquote class="citation">
<p>
Here's another thought, what about we look at the cardinality of the generating set? So we only have <code>WithGeneratingSet</code> which calls <code>is_finitely_generated</code>, whose default is to look at the cardinality of the generating set to determine the output of repr. At least that's the only place where I could see us (currently) using the fact that the generating set is finite.
</p>
</blockquote>
<p>
Well, also all the code to build the Cayley graph, to compute
J/R/L-classes, etc. In short all my finite semigroups code :-)
</p>
<p>
I oppose querying the cardinality, or even just is_finite, for this
can be super expensive if not undecidable. We really want something
declarative here.
</p>
<blockquote class="citation">
<p>
Darij, Aladin, or anyone else, your thoughts?
</p>
</blockquote>
<p>
Yup?
</p>
<p>
We probably should bring the discussion to sage-dev. As usual this
takes a bit of preparation to have an efficient discussion there.
I'll try to do this soon.
</p>
<p>
Cheers,
</p>
<blockquote>
<p>
Nicolas
</p>
</blockquote>
TickettscrimWed, 22 Oct 2014 01:46:09 GMT
https://trac.sagemath.org/ticket/17160#comment:13
https://trac.sagemath.org/ticket/17160#comment:13
<p>
Replying to <a class="ticket" href="https://trac.sagemath.org/ticket/17160#comment:12" title="Comment 12">nthiery</a>:
</p>
<blockquote class="citation">
<p>
Another issue: having a distinguished set of generators and being
finitely generated does not necessarily imply that the distinguished
set of generators is finite. So we would actually need three axioms:
"<a class="missing wiki">WithGenerators?</a>", "<a class="missing wiki">FinitelyGenerated?</a>", and "<a class="missing wiki">WithFiniteGeneratingSet?</a>".
So for a finite magma we still would need to do
"Magmas().Finite().<a class="missing wiki">WithFiniteGeneratingSet?</a>()".
</p>
<p>
I am not sure this is worth the complication. Especially since we will
have to do something similar for additive magmas, rings, fields, ...
</p>
</blockquote>
<p>
...Right... Although I think the right thing is actually <code>WithEnumeratedGeneratingSet</code> as we can do the same thing for infinite enumerated generating sets. However this is mostly an empty category/axiom because we can write generic code for <code>WithGeneratingSet</code> which will error out (at the right spot) for non-enumerated generating sets. In many ways, it's just a join with <code>EnumeratedSets</code>.
</p>
<p>
Another thought, we have 2 axioms <code>FinitelyGenerated</code> and <code>WithGenerators</code> and we create new join categories such as <code>SemigroupWithEnumeratedGeneratingSet</code> which implements an <code>__iter__</code> which calls <code>semigroup_generators</code>. The reasoning would be for monoids, we'd want to <code>monoid_generators</code> and need a separate method to avoid ambiguities similar to <a class="new ticket" href="https://trac.sagemath.org/ticket/15381" title="defect: Comparison of morphisms assumes that a Morphism is determined by its ... (new)">#15381</a>. Or would we use <code>gens</code> in this case and just push everything up to the category?
</p>
<p>
For rings, algebras, fields, I think we get this for free from the axiom magic and that they are subcategories of <code>Magma</code>. Perhaps I'm misunderstanding how things work?
</p>
<blockquote class="citation">
<p>
Well, also all the code to build the Cayley graph, to compute
J/R/L-classes, etc. In short all my finite semigroups code :-)
</p>
<p>
I oppose querying the cardinality, or even just is_finite, for this
can be super expensive if not undecidable. We really want something
declarative here.
</p>
</blockquote>
<p>
Yep, it's a bad idea.
</p>
<blockquote class="citation">
<p>
We probably should bring the discussion to sage-dev. As usual this
takes a bit of preparation to have an efficient discussion there.
I'll try to do this soon.
</p>
</blockquote>
<p>
Probably.
</p>
TicketgitThu, 05 Mar 2015 18:21:30 GMTcommit changed
https://trac.sagemath.org/ticket/17160#comment:14
https://trac.sagemath.org/ticket/17160#comment:14
<ul>
<li><strong>commit</strong>
changed from <em>f027ce2b5e1abe22d49bcdc96f2cfeebced8fc16</em> to <em>dabcafd7bb9100fbe325578e5f4a8252b50c90a4</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="http://git.sagemath.org/sage.git/commit/?id=dabcafd7bb9100fbe325578e5f4a8252b50c90a4"><span class="icon"></span>dabcafd</a></td><td><code>Merge branch 'develop' into t/17160/categories/finitely-generated-magmas-17160</code>
</td></tr></table>
TicketnthieryWed, 11 Mar 2015 16:48:16 GMT
https://trac.sagemath.org/ticket/17160#comment:15
https://trac.sagemath.org/ticket/17160#comment:15
<p>
Replying to <a class="ticket" href="https://trac.sagemath.org/ticket/17160#comment:12" title="Comment 12">nthiery</a>:
</p>
<blockquote class="citation">
<p>
We probably should bring the discussion to sage-dev.
</p>
</blockquote>
<p>
Done: <a class="ext-link" href="https://groups.google.com/d/msg/sage-devel/1du_5IhxsUU/j4hr75fBb9IJ"><span class="icon"></span>https://groups.google.com/d/msg/sage-devel/1du_5IhxsUU/j4hr75fBb9IJ</a>
</p>
TicketgitThu, 12 Mar 2015 10:25:22 GMTcommit changed
https://trac.sagemath.org/ticket/17160#comment:16
https://trac.sagemath.org/ticket/17160#comment:16
<ul>
<li><strong>commit</strong>
changed from <em>dabcafd7bb9100fbe325578e5f4a8252b50c90a4</em> to <em>cf9b429455e3330ff76d544bf39bc9ff7c76e514</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="http://git.sagemath.org/sage.git/commit/?id=cf9b429455e3330ff76d544bf39bc9ff7c76e514"><span class="icon"></span>cf9b429</a></td><td><code>Fixed ReST typo</code>
</td></tr></table>
TicketgitTue, 17 Mar 2015 06:44:47 GMTcommit changed
https://trac.sagemath.org/ticket/17160#comment:17
https://trac.sagemath.org/ticket/17160#comment:17
<ul>
<li><strong>commit</strong>
changed from <em>cf9b429455e3330ff76d544bf39bc9ff7c76e514</em> to <em>4b3d74c41cfec35c35ab2262d6dc17dd90ef3472</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="http://git.sagemath.org/sage.git/commit/?id=aff2689ac6a7f6b80c1d4678ff348761f6a38919"><span class="icon"></span>aff2689</a></td><td><code>17160: fixed category for finite set endomaps + minor __init__ refactoring</code>
</td></tr><tr><td><a class="ext-link" href="http://git.sagemath.org/sage.git/commit/?id=4b3d74c41cfec35c35ab2262d6dc17dd90ef3472"><span class="icon"></span>4b3d74c</a></td><td><code>Merge branch 'develop' into categories/finitely-generated-magmas-17160</code>
</td></tr></table>
TicketnthieryThu, 19 Mar 2015 00:03:04 GMTdescription changed
https://trac.sagemath.org/ticket/17160#comment:18
https://trac.sagemath.org/ticket/17160#comment:18
<ul>
<li><strong>description</strong>
modified (<a href="/ticket/17160?action=diff&version=18">diff</a>)
</li>
</ul>
TicketgitFri, 20 Mar 2015 08:02:05 GMTcommit changed
https://trac.sagemath.org/ticket/17160#comment:19
https://trac.sagemath.org/ticket/17160#comment:19
<ul>
<li><strong>commit</strong>
changed from <em>4b3d74c41cfec35c35ab2262d6dc17dd90ef3472</em> to <em>ad5d6c0dc9cf55eed4900ed76df26f4a3e86f73f</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="http://git.sagemath.org/sage.git/commit/?id=ad5d6c0dc9cf55eed4900ed76df26f4a3e86f73f"><span class="icon"></span>ad5d6c0</a></td><td><code>8678: permutation groups are finitely generated, finite fields are enumerated, fixes</code>
</td></tr></table>
TicketgitFri, 20 Mar 2015 08:12:49 GMTcommit changed
https://trac.sagemath.org/ticket/17160#comment:20
https://trac.sagemath.org/ticket/17160#comment:20
<ul>
<li><strong>commit</strong>
changed from <em>ad5d6c0dc9cf55eed4900ed76df26f4a3e86f73f</em> to <em>839200e376b595f7bfe3247c55fc31adf0693ef3</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="http://git.sagemath.org/sage.git/commit/?id=839200e376b595f7bfe3247c55fc31adf0693ef3"><span class="icon"></span>839200e</a></td><td><code>8678: More doctest updates. Should almost pass all tests.</code>
</td></tr></table>
TicketnthieryFri, 20 Mar 2015 08:13:36 GMTstatus changed
https://trac.sagemath.org/ticket/17160#comment:21
https://trac.sagemath.org/ticket/17160#comment:21
<ul>
<li><strong>status</strong>
changed from <em>new</em> to <em>needs_review</em>
</li>
</ul>
TicketgitFri, 20 Mar 2015 08:14:50 GMTcommit changed
https://trac.sagemath.org/ticket/17160#comment:22
https://trac.sagemath.org/ticket/17160#comment:22
<ul>
<li><strong>commit</strong>
changed from <em>839200e376b595f7bfe3247c55fc31adf0693ef3</em> to <em>919a215d94e8e14eb75818021fa3af38831daf5e</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="http://git.sagemath.org/sage.git/commit/?id=919a215d94e8e14eb75818021fa3af38831daf5e"><span class="icon"></span>919a215</a></td><td><code>Merge branch 'develop = sage 6.6 beta6' into categories/finitely-generated-magmas-17160</code>
</td></tr></table>
TicketgitSat, 21 Mar 2015 06:58:06 GMTcommit changed
https://trac.sagemath.org/ticket/17160#comment:23
https://trac.sagemath.org/ticket/17160#comment:23
<ul>
<li><strong>commit</strong>
changed from <em>919a215d94e8e14eb75818021fa3af38831daf5e</em> to <em>ef01ef0288027084170f033b8cb8b46fa2d47be6</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="http://git.sagemath.org/sage.git/commit/?id=5e6c7078420b02aa70be3aa8aeaf8c259357b3fd"><span class="icon"></span>5e6c707</a></td><td><code>Do not build the Jinja2 docs</code>
</td></tr><tr><td><a class="ext-link" href="http://git.sagemath.org/sage.git/commit/?id=ef01ef0288027084170f033b8cb8b46fa2d47be6"><span class="icon"></span>ef01ef0</a></td><td><code>Merge branch 't/18012/sphinx_depends_on_jinja2' into categories/finitely-generated-magmas-17160</code>
</td></tr></table>
TicketnthierySat, 21 Mar 2015 06:59:21 GMT
https://trac.sagemath.org/ticket/17160#comment:24
https://trac.sagemath.org/ticket/17160#comment:24
<p>
This ticket does not really depend on <a class="closed ticket" href="https://trac.sagemath.org/ticket/17160" title="enhancement: Finitely generated axiom for (mutiplicative) magmas, semigroups, ... (closed: fixed)">#17160</a>, but the build tends to fail without it, so I merged it in.
</p>
TickettscrimSat, 21 Mar 2015 17:03:25 GMTstatus changed; reviewer set
https://trac.sagemath.org/ticket/17160#comment:25
https://trac.sagemath.org/ticket/17160#comment:25
<ul>
<li><strong>status</strong>
changed from <em>needs_review</em> to <em>positive_review</em>
</li>
<li><strong>reviewer</strong>
set to <em>Travis Scrimshaw</em>
</li>
</ul>
<p>
LGTM.
</p>
TickettscrimSat, 21 Mar 2015 17:18:37 GMTmilestone changed; keywords set
https://trac.sagemath.org/ticket/17160#comment:26
https://trac.sagemath.org/ticket/17160#comment:26
<ul>
<li><strong>keywords</strong>
<em>days64</em> added
</li>
<li><strong>milestone</strong>
changed from <em>sage-6.4</em> to <em>sage-6.6</em>
</li>
</ul>
TicketgitThu, 02 Apr 2015 02:49:39 GMTstatus, commit changed
https://trac.sagemath.org/ticket/17160#comment:27
https://trac.sagemath.org/ticket/17160#comment:27
<ul>
<li><strong>status</strong>
changed from <em>positive_review</em> to <em>needs_review</em>
</li>
<li><strong>commit</strong>
changed from <em>ef01ef0288027084170f033b8cb8b46fa2d47be6</em> to <em>975c008ade2bc70319c286d9eb09eacdc75cafed</em>
</li>
</ul>
<p>
Branch pushed to git repo; I updated commit sha1 and set ticket back to needs_review. New commits:
</p>
<table class="wiki">
<tr><td><a class="ext-link" href="http://git.sagemath.org/sage.git/commit/?id=7488127709c9e9d5c55dc9eb1c542f5007b009f2"><span class="icon"></span>7488127</a></td><td><code>Merge branch 'develop=6.6rc2' into categories/finitely-generated-magmas-17160</code>
</td></tr><tr><td><a class="ext-link" href="http://git.sagemath.org/sage.git/commit/?id=975c008ade2bc70319c286d9eb09eacdc75cafed"><span class="icon"></span>975c008</a></td><td><code>Merge branch 'u/nthiery/categories/finitely-generated-magmas-17160' of trac.sagemath.org:sage into categories/finitely-generated-magmas-17160</code>
</td></tr></table>
TickettscrimThu, 02 Apr 2015 04:42:05 GMTstatus changed
https://trac.sagemath.org/ticket/17160#comment:28
https://trac.sagemath.org/ticket/17160#comment:28
<ul>
<li><strong>status</strong>
changed from <em>needs_review</em> to <em>positive_review</em>
</li>
</ul>
<p>
Simple merge.
</p>
TicketvbraunFri, 10 Apr 2015 16:35:02 GMTstatus changed
https://trac.sagemath.org/ticket/17160#comment:29
https://trac.sagemath.org/ticket/17160#comment:29
<ul>
<li><strong>status</strong>
changed from <em>positive_review</em> to <em>needs_work</em>
</li>
</ul>
<p>
conflicts with <a class="closed ticket" href="https://trac.sagemath.org/ticket/15852" title="enhancement: uncouple Sequence from categories (closed: fixed)">#15852</a>
</p>
TickettscrimSat, 11 Apr 2015 22:19:39 GMTstatus, commit, dependencies, branch changed
https://trac.sagemath.org/ticket/17160#comment:30
https://trac.sagemath.org/ticket/17160#comment:30
<ul>
<li><strong>status</strong>
changed from <em>needs_work</em> to <em>positive_review</em>
</li>
<li><strong>commit</strong>
changed from <em>975c008ade2bc70319c286d9eb09eacdc75cafed</em> to <em>19ceb8124d27ba0124fb08a232c05924bb7114b0</em>
</li>
<li><strong>dependencies</strong>
changed from <em>#10668</em> to <em>#10668 #15852</em>
</li>
<li><strong>branch</strong>
changed from <em>u/nthiery/categories/finitely-generated-magmas-17160</em> to <em>public/categories/finitely_generated_magma-17160</em>
</li>
</ul>
<p>
Trivial rebase.
</p>
<hr />
<p>
New commits:
</p>
<table class="wiki">
<tr><td><a class="ext-link" href="http://git.sagemath.org/sage.git/commit/?id=dbadd6a6c65a3700fc9bb4dec6ab8534a5f10d63"><span class="icon"></span>dbadd6a</a></td><td><code>15852: uncouple Sequence from categories</code>
</td></tr><tr><td><a class="ext-link" href="http://git.sagemath.org/sage.git/commit/?id=1f9c338257b8b551acb3038aae7014ad8c2abaa8"><span class="icon"></span>1f9c338</a></td><td><code>Merge branch 'develop' into t/15852/15852</code>
</td></tr><tr><td><a class="ext-link" href="http://git.sagemath.org/sage.git/commit/?id=6b12bda32fbe8a146fbfc546b84a8671aa93b8bd"><span class="icon"></span>6b12bda</a></td><td><code>Merge branch 'u/rws/15852' of trac.sagemath.org:sage into public/categories/finitely_generated_magma-17160</code>
</td></tr><tr><td><a class="ext-link" href="http://git.sagemath.org/sage.git/commit/?id=19ceb8124d27ba0124fb08a232c05924bb7114b0"><span class="icon"></span>19ceb81</a></td><td><code>Merge branch 'u/nthiery/categories/finitely-generated-magmas-17160' of trac.sagemath.org:sage into public/categories/finitely_generated_magma-17160</code>
</td></tr></table>
TicketvbraunTue, 14 Apr 2015 19:43:50 GMTstatus, branch changed; resolution set
https://trac.sagemath.org/ticket/17160#comment:31
https://trac.sagemath.org/ticket/17160#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/categories/finitely_generated_magma-17160</em> to <em>19ceb8124d27ba0124fb08a232c05924bb7114b0</em>
</li>
</ul>
Ticket