* Version 13-04-11 (First version from discussion in Minneapolis)

== Cluster algebras road map beyond Sage-5.9 ==

 * Infos about [[http://www.ima.umn.edu/2011-2012/SW7.9-13.12/#Schedule|SageDays 40]], Minneapolis July 9-13, 2012
 * Infos about [[http://www.ima.umn.edu/2014-2015/SW6.1-5.15/?event_id=SW6.1-5.15|SageDays 64.5]], Minneapolis June 1-5, 2015
  * [[combinat/clusteralgebras/sagedays64.5|Wiki containing further info]]

This page contains our road map beyond the core implementation of cluster algebras as merged in Sage-5.9, see [[http://trac.sagemath.org/sage_trac/ticket/10298|#10298]].

=== New features ===

==== Finished ====

 * Implement Greedy bases - http://trac.sagemath.org/sage_trac/ticket/14445

 * generalized associahedra from cluster complexes (Christian) - http://trac.sagemath.org/sage_trac/ticket/10817

 * Jim Starx code for Quiver Representations and abilities to work with Auslander-Reiten translates, etc. ([[http://trac.sagemath.org/sage_trac/ticket/12630|#12630]])

==== Easier ====

 * Check why variable_class() is so much slower compared with cluster_class().  This might be because Laurent polynomials are slow in sage. (Christian)

 * Include new Quiver mutation types for Gale-Robinson Quivers (Gregg) - http://trac.sagemath.org/sage_trac/ticket/14444

 * Add sum of quivers/cluster seed as disjoint union (Christian/Gregg) - http://trac.sagemath.org/sage_trac/ticket/14443

 * Include new Quivers/cluster seed for square and triangular products of quivers (as in Keller's work on periodicity) (Christian/Gregg) - http://trac.sagemath.org/sage_trac/ticket/14443

 * Implement snake graph / matrix multiplication formulas for cluster algebras from surfaces and friezes. (Gregg) - http://trac.sagemath.org/ticket/16310
 Also see Dupont's sage code on friezes from http://www.math.jussieu.fr/~dupontg/files/strings.sage 

==== Harder ====

 1. Allow labellings of the vertices of quivers and cluster seeds (i.e., provide a dict that contains this information, and which is used all over to work with cluster seeds)
    
 * in some situations, it might be nice to update variable names. E.g., for Plücker coords and SL[N].

 * Finish mutation type checking for affine D_n (try to dove-tail with student describing all affine B/C/etc. quiver types)

 * Allow inputs of cluster algebras from surfaces (interface from ideal triangulations/bistellar flips as from John Palmeri or Robert Lipshitz) (Gregg?) - look at http://www.math.columbia.edu/~lipshitz/research.html#Programming

 * Work with the improved graph editor (once it exists?)

 * Weiwen Gu Decomposition algorithm - and then use this to classify cluster algebra from surface by genus, number of marked/boundary points, etc. (Emily/Al/Gregg)

 * Quantum cluster algebras - with Dylan Rupel

 * Work with cluster algebras as "algebras" and find bases or express elements in bases 

 * d-vectors (using inductive formulas from Cluster Algebras IV?)

 * LP algebras (Thomas Lam and Pasha Pylyavskyy with Gregg?)

 * Q-system and T-system calculations as in Di Francesco and Kedem's work

=== Changes to the compendium ===

 1. Convert the compendium into an rst file and provide it as a thematic tutorial.

 * Change intro to describe downloading only sage >= 5.9

 * Adding F-polynomials, G-vectors, C-vectors, etc. updates to principal_extension/restrictions, ...

 * Mutation type names (eg. V, W, ...) need to be updated

 * Generalized associahedra from cluster algebra in new ticket so that compendium accurately discusses these features

 * check if all class sizes are correct - see [[http://trac.sagemath.org/sage_trac/ticket/14048|#14048]] by Hugh Thomas and Frederic Chapoton

 * cut out groups_of_mutations() and probably other names need to be deleted or updated