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== Cluster algebras road map beyond Sage-5.9 == == Sage Days 64.5 ==
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 * Version 13-04-11 (First version from discussion in Minneapolis)  * Minneapolis, June 1-5, 2015
 * Version 15-01-26
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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]]. The starting point is the core implementation of cluster algebras as merged in Sage-5.9, see [[http://trac.sagemath.org/sage_trac/ticket/10298|#10298]], with possible new features discussen in spring 2013 in Minneapolis.
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=== New features === === Topics ===
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==== Finished ====  Topics and goals for the week will be discussed the first day of the workshop. Below is a list of possible topics:
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 * Implement Greedy bases - http://trac.sagemath.org/sage_trac/ticket/14445 ==== Important features ====
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 * 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].
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==== Easier ====

 1. generalized associahedra from cluster complexes (Christian) - http://trac.sagemath.org/sage_trac/ticket/10817		  * generalized associahedra from cluster complexes (Christian) - http://trac.sagemath.org/sage_trac/ticket/10817
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 * Finish the implementation of finite reflection groups (Christian) -- trac.sagemath.org/ticket/11187

 * Allowing options to work with g-vectors, d-vectors, c-vectors directly rather than with cluster variables

==== Other features ====

 * Scattering diagrams (visualization and algebraic computations of broken lines)

 * Quantum cluster algebras

 * Generalized cluster algebras

 * Visualize ideal triangulations

 * Exotic Belavin-Drinfeld cluster algebras or cluster algebras from Double Bruhat Cells

 * Urban Renewal

 * more on Quiver Representations?

==== Other features, easy ====
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==== 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].		 ==== Other features, hard ====
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 1. Convert the compendium into an rst file and provide it as a thematic tutorial.  * Convert the compendium into an rst file and provide it as a thematic tutorial.

Sage Days 64.5

  • Minneapolis, June 1-5, 2015
  • Version 15-01-26

The starting point is the core implementation of cluster algebras as merged in Sage-5.9, see #10298, with possible new features discussen in spring 2013 in Minneapolis.

Topics

  • Topics and goals for the week will be discussed the first day of the workshop. Below is a list of possible topics:

Important features

  • 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].

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

  • Check why variable_class() is so much slower compared with cluster_class(). This might be because Laurent polynomials are slow in sage. (Christian)
  • Finish the implementation of finite reflection groups (Christian) -- trac.sagemath.org/ticket/11187
  • Allowing options to work with g-vectors, d-vectors, c-vectors directly rather than with cluster variables

Other features

  • Scattering diagrams (visualization and algebraic computations of broken lines)
  • Quantum cluster algebras
  • Generalized cluster algebras
  • Visualize ideal triangulations
  • Exotic Belavin-Drinfeld cluster algebras or cluster algebras from Double Bruhat Cells
  • Urban Renewal
  • more on Quiver Representations?

Other features, easy

Other features, hard

  • 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?)

  • Jim Starx code for Quiver Representations and abilities to work with Auslander-Reiten translates, etc. (#12630)

  • 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

  • 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 #14048 by Hugh Thomas and Frederic Chapoton

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

combinat/clusteralgebras/sagedays64.5 (last edited 2015-05-22 13:13:09 by chapoton)