Opened 8 years ago
Closed 7 years ago
#17947 closed enhancement (fixed)
implement the cluster fans
Reported by: | chapoton | Owned by: | |
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Priority: | minor | Milestone: | sage-6.10 |
Component: | combinatorics | Keywords: | cluster, fan, Sage Days 64.5 |
Cc: | gmoose05, jipilab | Merged in: | |
Authors: | Frédéric Chapoton | Reviewers: | Jean-Philippe Labbé |
Report Upstream: | N/A | Work issues: | |
Branch: | 97214cf (Commits, GitHub, GitLab) | Commit: | 97214cfb04c33355ec82ff3af0662d96b6502e73 |
Dependencies: | Stopgaps: |
Description
Fans play an important role in cluster algebra theory. Let's have them in.
Change History (31)
comment:1 Changed 8 years ago by
Branch: | → u/chapoton/17947 |
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Cc: | gmoose05 added |
Commit: | → 66173bd0290a13e922a4ca0499f911e0646eb80b |
Keywords: | cluster fan added |
Status: | new → needs_review |
comment:2 Changed 8 years ago by
Commit: | 66173bd0290a13e922a4ca0499f911e0646eb80b → 07cd33c875465cff46f4d46dc3a14691eff85eb6 |
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Branch pushed to git repo; I updated commit sha1. New commits:
07cd33c | trac #17947 details about cluster fan
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comment:3 Changed 8 years ago by
Care to define it in the docstring?
I've always wanted to understand what Nathan is talking about all the time, but I never got over my laziness to read up on it. I guess this is my chance :) Thanks a lot.
comment:4 Changed 8 years ago by
Commit: | 07cd33c875465cff46f4d46dc3a14691eff85eb6 → 9628ba3adff463a4d57a030bd75a57ae2b7aea44 |
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Branch pushed to git repo; I updated commit sha1. New commits:
9628ba3 | trac #17947 more doc
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comment:5 follow-up: 6 Changed 8 years ago by
Thanks -- this makes things a lot less scarier. I feel I need some more help, though. Is a simplicial fan the same as a simplicial complex but with "simplex" replaced by "simplicial cone"? How exactly do the vectors d
in \ZZ^n
give rise to a cone? Is the cone corresponding to a cluster simply the set of all nonnegative linear combinations of the denominator vectors? What is a smooth fan? Why do you require acyclicity; isn't finite-type enough?
comment:6 Changed 8 years ago by
Replying to darij:
Thanks -- this makes things a lot less scarier. I feel I need some more help, though.
Yes. I hope you do not want all these explanations to be written in the doc ?
Is a simplicial fan the same as a simplicial complex but with "simplex" replaced by "simplicial cone"?
Yes, essentially, but not quite because some convexity issues enter the definition. For the exact definition of a fan, see Fulton book on toric varieties for example. A simplicial fan is a fan where every cone is simplicial, namely has the minimal number of generators wrt its dimension.
How exactly do the vectors
d
in\ZZ^n
give rise to a cone?
The d associated with variables in a given cluster span the rays of a cone.
Is the cone corresponding to a cluster simply the set of all nonnegative linear combinations of the denominator vectors?
Yes.
What is a smooth fan?
a smooth fan is a simplicial fan such that each cone is smooth. A smooth cone is a simplicial cone whose rays define a basis of the lattice (they have determinant +-1)
This is related to the smoothness of the toric variety associated to the fan.
Why do you require acyclicity; isn't finite-type enough?
No, with this version of the fan. If you apply it to the cyclic quiver with 3 vertices, the result is not an interesting fan (in particular it is not smooth). There is maybe another version of the fan using the g-vector instead. I do not remember the details right now.
comment:7 Changed 8 years ago by
Branch: | u/chapoton/17947 → public/ticket/17947 |
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Commit: | 9628ba3adff463a4d57a030bd75a57ae2b7aea44 → fb98b4d01681aa841740eef28ae2f1e3490d3793 |
OK, I am not able to review this, but thank you a lot for the explanations. I still don't know what almost positive roots are, how Cone
infers its lattice, etc., so I'll defer to someone more familiar with these things, though the code does look good to me.
New commits:
db09838 | Merge branch 'u/chapoton/17947' of git://trac.sagemath.org/sage into fan
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fb98b4d | doc improvements to quiver.py:
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comment:8 Changed 8 years ago by
Commit: | fb98b4d01681aa841740eef28ae2f1e3490d3793 → 82ed22231efa4aa698097a885b43f5fa07b82422 |
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Branch pushed to git repo; I updated commit sha1. New commits:
82ed222 | trivial doc fix
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comment:9 Changed 8 years ago by
Cc: | jipilab added |
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comment:10 Changed 8 years ago by
Milestone: | sage-6.6 → sage-6.7 |
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comment:11 Changed 8 years ago by
Milestone: | sage-6.7 → sage-6.8 |
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comment:12 Changed 8 years ago by
Commit: | 82ed22231efa4aa698097a885b43f5fa07b82422 → df182e500b4723fbf2a87aa4b565293397d8f904 |
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Branch pushed to git repo; I updated commit sha1. New commits:
c3b9534 | Merge branch 'develop' into t/17947/public/ticket/17947
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b6e225a | Add d-vector to ClusterSeed
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d18903f | Add d-matrix to ClusterSeed
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b2a8278 | Removed trailing spaces
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9f56277 | Merge remote-tracking branch 'origin/u/etn40ff/add_d_vectors' into t/17947/public/ticket/17947
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df182e5 | I changed the name of the function fan to d_vector_fan.
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comment:13 Changed 8 years ago by
Dependencies: | → #18588 |
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comment:14 Changed 8 years ago by
Keywords: | Sage Days 64.5 added |
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I attempt my first Sage Days on cluster algebras, and I wanted to implant d-vector fans and g-vector fans. I realized that this was already partially done in this ticket. For the functions d_vector_fan and g_vector_fan to be coherent, I merged with #18588 which implements the d_matrix function.
comment:15 Changed 8 years ago by
Hi!
I would be happy to review this ticket!
It will be quite handy!
comment:16 Changed 8 years ago by
Status: | needs_review → needs_work |
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Duplicate import
+ from cluster_seed import ClusterSeed + from cluster_seed import ClusterSeed
comment:17 Changed 8 years ago by
Commit: | df182e500b4723fbf2a87aa4b565293397d8f904 → 0eea07be8e10af1b0606cc3ecd4c3040e10339b9 |
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Branch pushed to git repo; I updated commit sha1. New commits:
0eea07b | remove duplicate import, as well as a non-necessary import
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comment:18 Changed 8 years ago by
There are blank lines that contain white spaces in the function d_vector_fan in the quiver.py file.
Otherwise it looks good to me.
comment:19 Changed 8 years ago by
Commit: | 0eea07be8e10af1b0606cc3ecd4c3040e10339b9 → 2b1e105e52ff12082a58680b52d8e144aeb51cb0 |
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comment:20 Changed 8 years ago by
Status: | needs_work → needs_review |
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comment:21 Changed 7 years ago by
Commit: | 2b1e105e52ff12082a58680b52d8e144aeb51cb0 → 74a57fc25b2987562510312e0f06c0558a530f4b |
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Branch pushed to git repo; I updated commit sha1. New commits:
74a57fc | Merge branch 'public/ticket/17947' into 6.9.b6
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comment:22 Changed 7 years ago by
Milestone: | sage-6.8 → sage-6.9 |
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comment:23 Changed 7 years ago by
Commit: | 74a57fc25b2987562510312e0f06c0558a530f4b → 97214cfb04c33355ec82ff3af0662d96b6502e73 |
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Branch pushed to git repo; I updated commit sha1. New commits:
97214cf | Merge branch 'public/ticket/17947' into 6.9.rc0
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comment:26 Changed 7 years ago by
Reviewers: | → Jean-Philippe Labbé |
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Status: | needs_review → positive_review |
All test passed on sage-6.9.
This looks good to me. I set this as positive review.
comment:28 Changed 7 years ago by
Milestone: | sage-6.9 → sage-6.10 |
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comment:29 Changed 7 years ago by
Just a PSA: Your ticket will never be merged if it depends on a invalid/wontfix ticket. At least not until that one is being merged into the git tree.
comment:30 Changed 7 years ago by
Dependencies: | #18588 |
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ok, thanks. Let us remove the dependency then. It has been taken care of in another ticket.
comment:31 Changed 7 years ago by
Branch: | public/ticket/17947 → 97214cfb04c33355ec82ff3af0662d96b6502e73 |
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Resolution: | → fixed |
Status: | positive_review → closed |
New commits:
trac #17947 implement the cluster fans