Implement generalized cluster algebras

1150906c-a05e-4119-a7ed-67cf7ad87ccf commented 5 years ago

This ticket is being opened to describe proposed work for an coding sprint at the IMA.

In 2011, Chekhov and Shapiro introduced a generalization of cluster algebras in which the exchange polynomials are allowed to have arbitrarily many terms.

We aim to add generalized cluster algebra functionality and related methods necessary to implement the current understanding of these algebras in Sage. This will be accomplished by building upon the framework established by Rupel and Stella's http://doc.sagemath.org/html/en/reference/algebras/sage/algebras/cluster_algebra.html implementation of cluster algebras.

Our major functionality objectives are:

adding the ability to mutate with arbitrary exchange polynomials to the current ClusterAlgebra package;
implementing generalized mutation for coefficients subject to the normalization conditions defined by Tomoki Nakanishi;
creating methods for calculating left and right companion cluster algebras;
creating a method for unfolding cluster algebras.

For more information, see:

https://arxiv.org/abs/1111.3963

https://arxiv.org/abs/1504.06758

https://arxiv.org/pdf/1006.4276.pdf

CC: @tscrim @sagetrac-gmoose05 @stumpc5 @Etn40ff @EBanaian @sagetrac-drupel

Component: combinatorics

Keywords: IMA coding sprints, days99, cluster algebra, generalized cluster algebra

Author: Esther Banaian, Elizabeth Kelley, Dylan Rupel, Gregg Musiker

Branch/Commit: public/ticket-26771 @ 4a523cc

Issue created by migration from https://trac.sagemath.org/ticket/26771

1150906c-a05e-4119-a7ed-67cf7ad87ccf commented 5 years ago

Description changed:

--- 
+++ 
@@ -6,7 +6,7 @@

 Our major functionality objectives are:
 * creating a class for generalized cluster seeds, with analogous attributes to ClusterSeed
-* implementing generalized mutation for arbitrary coefficients
+* implementing generalized mutation for coefficients subject to the normalization conditions defined by [Tomoki Nakanishi](https://arxiv.org/abs/1409.5967).
 * creating methods for calculating left and right companion algebras
 * creating a method for unfolding cluster algebras

1ff04b02-72fb-4ff1-9f33-0df80527afda commented 5 years ago

Description changed:

--- 
+++ 
@@ -2,13 +2,13 @@

 In 2011, [Chekhov and Shapiro](https://arxiv.org/abs/1111.3963) introduced a generalization of cluster algebras in which the exchange polynomials are allowed to have arbitrarily many terms.

-We want to create a new class, GeneralizedClusterSeed, and related methods necessary to implement these algebras in Sage. We plan to build on the framework established by Rupel and Stella's [implementation](http://doc.sagemath.org/html/en/reference/algebras/sage/algebras/cluster_algebra.html) of cluster algebras.
+We aim to add generalized cluster algebra functionality and related methods necessary to implement the current understanding of these algebras in Sage.  This will be accomplished by building upon the framework established by Rupel and Stella's [http://doc.sagemath.org/html/en/reference/algebras/sage/algebras/cluster_algebra.html](http://doc.sagemath.org/html/en/reference/algebras/sage/algebras/cluster_algebra.html) implementation of cluster algebras.

 Our major functionality objectives are:
-* creating a class for generalized cluster seeds, with analogous attributes to ClusterSeed
-* implementing generalized mutation for coefficients subject to the normalization conditions defined by [Tomoki Nakanishi](https://arxiv.org/abs/1409.5967).
-* creating methods for calculating left and right companion algebras
-* creating a method for unfolding cluster algebras
+* adding the ability to mutate with arbitrary exchange polynomials to the current ClusterAlgebra package;
+* implementing generalized mutation for coefficients subject to the normalization conditions defined by [Tomoki Nakanishi](https://arxiv.org/abs/1409.5967);
+* creating methods for calculating left and right companion cluster algebras;
+* creating a method for unfolding cluster algebras.

 For more information, see:

embray commented 5 years ago

comment:4

Ticket retargeted after milestone closed (if you don't believe this ticket is appropriate for the Sage 8.8 release please retarget manually)

embray commented 5 years ago

comment:5

As the Sage-8.8 release milestone is pending, we should delete the sage-8.8 milestone for tickets that are not actively being worked on or that still require significant work to move forward. If you feel that this ticket should be included in the next Sage release at the soonest please set its milestone to the next release milestone (sage-8.9).

4261ab0e-5b91-4268-aad0-6fdfe10f162c commented 5 years ago

comment:6

Attachment: cluster_algebra.py.gz

First step in adding exchange degrees.

1150906c-a05e-4119-a7ed-67cf7ad87ccf commented 5 years ago

Branch: u/gh-kelleye/master

1150906c-a05e-4119-a7ed-67cf7ad87ccf commented 5 years ago

comment:9

Current beta version of the generalized cluster algebra code.

a9a57cdf-9183-46c4-a1f6-41c1b5271dce commented 5 years ago

comment:10

Old attachment can now be ignored.

Last 10 new commits:

`816c665`	`Merge pull request #36 from godfrey-cw/master`
`6fee69e`	`pyflakes cleanup`
`5bb4e04`	`Merge pull request #35 from fchapoton/pyflakes`
`56d9857`	`trying to tell where conflicts lie`
`4169540`	`use splitlines`
`15a2b7d`	`Merge pull request #30 from fchapoton/patch-1`
`4034768`	`Typo: alread -> already`
`2fd52e5`	`Merge pull request #37 from kevinywlui/patch-2`
`c981690`	`Actually install the cheat sheet when using setup.py`
`da5a902`	`Merge pull request #39 from kevinywlui/develop`