## Sage Days 64.5

- 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) -- http://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

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

#### 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