Compute mutation type of a ClusterSeed or ClusterQuiver

[sagetrac-gmoose05]

This ticket implements mutation type checks for cluster seeds and quivers.

Apply to the sage library:

• attachment: trac_13425-mutation_type-gm.patch
• attachment: trac_13425-review-cs.patch
• attachment: trac_13425-review_two-cs.patch
• attachment: trac_13425-small-doc-fix.patch
• attachment: trac_13425-review_four-cs.patch
• attachment: trac_13425-review_five-cs.patch
• attachment: trac_13425-sixth-review-gm.patch

Depends on #13424

Component: combinatorics

Keywords: cluster algebra, quiver, days45

Author: Gregg Musiker, Christian Stump

Reviewer: Christian Stump, Gregg Musiker

Merged: sage-5.9.beta2

Issue created by migration from https://trac.sagemath.org/ticket/13425

[sagetrac-gmoose05]

Dependencies: 13424

[sagetrac-gmoose05]

Changed dependencies from 13424 to #13424

[sagetrac-gmoose05]

Changed author from Gregg Musiker and Christian Stump to Gregg Musiker, Christian Stump

[stumpc5]

comment:4

The tests become much too slow with this patch:

with only #13424 applied:

sage -t  "devel/sage-combinat/sage/combinat/cluster_algebra_quiver/cluster_seed.py"
	 [3.3 s]
sage -t  "devel/sage-combinat/sage/combinat/cluster_algebra_quiver/quiver.py"
	 [2.2 s]

and with this patch applied as well:

sage -t  "devel/sage-combinat/sage/combinat/cluster_algebra_quiver/cluster_seed.py"
	 [33.5 s]
sage -t  "devel/sage-combinat/sage/combinat/cluster_algebra_quiver/quiver.py"
	 [32.8 s]

We should avoid that.

[Etn40ff]

Changed keywords from cluster algebra, quiver to cluster algebra, quiver, days45

[stumpc5]

comment:7

Hi Gregg!

I know you are again working on this patch: it needs to be (almost trivially) rebased agains the newest version of #13424.

[sagetrac-gmoose05]

comment:8

Just uploaded a review patch (although I'm still working through it and this is just partial work).

The bulk of the changes are from mutation_type.py:

I documented and added examples for all methods until the testing
commands near the end, and _connected_mutation_type which I still need
to read and understand.

I also changed auxiliary command names so that they begin with an underscore.

Christian, there were a few places where I had questions for you,
these are indicated by the word "CHECK" in caps.

More to come later as I look through the other .py files in this patch also.

Gregg

[sagetrac-gmoose05]

comment:9

Christian, I just posted a new review patch. I think the ticket is not too far away from being ready. I documented as much of the code as I could with comments, and added explanations and examples for almost all methods.

There are a few outstanding comments or questions marked with CHECK.

Also, I see that in cluster_seed.py we add mutation_type() commands every time the user asks for a Cluster Variable or related command. However, this greatly slows down those methods with the only advantage being the almost_positive_roots command. So I figured we should discuss this over email or skype at some point.

We also discussed at Sage Days about trying to optimize by having the program test for infinite_mutation_type by randomly mutating a few times if more than 6 vertices before trying to test for a recognizable mutation_type. I haven't made such changes.

Gregg

[stumpc5]

comment:10

Hi Gregg -- thanks a lot for the hard work you are putting into my unreadable code! I am about to upload a review patch. Most importantly, I have made the random tests work again and did quite some test to ensure the code does what it is supposed to do.

I solved some of the CHECK's, I think it is better to discuss the others on the phone. Before giving the code a positive review, I think we should have a strong cpu make some tests and random tests for rank 8-12 since I think I never did that (though I also think that the problems should occur already earlier).

Cheers, Christian