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| * Why is variable_class() so much slower compared with cluster_class() ?? (might be because Laurent polynomials are so slow in sage) | * Check why variable_class() is so much slower compared with cluster_class(). This might be because Laurent polynomials are slow in sage. |
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| * Quiver mutation types for Gale-Robinson Quivers | * Include new Quiver mutation types for Gale-Robinson Quivers |
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| * Quiver mutation types for products of quivers (as in Keller's work on periodicity) | * Include new Quiver mutation types for square and triangular products of quivers (as in Keller's work on periodicity) |
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| * snake graph / matrix multiplication formulas for cluster algebras from surfaces. Also see Dupont's sage code on friezes from http://www.math.jussieu.fr/~dupontg/files/strings.sage | * Implement snake graph / matrix multiplication formulas for cluster algebras from surfaces and friezes. Also see Dupont's sage code on friezes from http://www.math.jussieu.fr/~dupontg/files/strings.sage |
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| * d-vectors (using inductive formulas from Cluster Algebras IV? | * d-vectors (using inductive formulas from Cluster Algebras IV?) |
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| * Jim Starx code for Quiver Representations and abilities to work with Auslander-Reiten translates, etc. | * Jim Starx code for Quiver Representations and abilities to work with Auslander-Reiten translates, etc. (Sage Trac 12630) |
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| * LP algebras (Thomas Lam and Pasha) | * LP algebras (Thomas Lam and Pasha Pylyavskyy) |
Cluster algebras road map beyond Sage-5.9
- Version 13-04-11 (First version from discussion in Minneapolis)
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.
New features
Easier
- generalized associahedra from cluster complexes
- Check why variable_class() is so much slower compared with cluster_class(). This might be because Laurent polynomials are slow in sage.
- Include new Quiver mutation types for Gale-Robinson Quivers
- Include new Quiver mutation types for square and triangular products of quivers (as in Keller's work on periodicity)
- Implement Greedy bases - should already have this essentially done from the fall.
- Implement snake graph / matrix multiplication formulas for cluster algebras from surfaces and friezes.
Also see Dupont's sage code on friezes from http://www.math.jussieu.fr/~dupontg/files/strings.sage
Harder
- 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)
- 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.
- 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. (Sage Trac 12630)
- LP algebras (Thomas Lam and Pasha Pylyavskyy)
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 Hugh/Chapoton's 14048 ticket
- cut out groups_of_mutations() and probably other names need to be deleted or updated