Sage Days 45 Coding Sprint Projects
This is the project page for Sage Days 45, and more generaly ICERM's semester on Automorphic Forms, Combinatorial Representation Theory and Multiple Dirichlet Series.
Below is a list of proposed projects. You are welcome to add more projects or add yourself as participant for existing projects! The following feature request guidelines may help you specify useful and realistic project descriptions; if you are at ICERM, you are more than welcome to come discuss about those with the Sage fans there!
Extended affine Weyl groups, affine Iwahori Hecke algebras, and nonsymmetric Macdonald polynomials
Dan Bump, Anne Schilling, Mark Shimozono, Nicolas Thiéry, Viviane Pons
See Trac Ticket 14102.
This project was started during Sage Days 40 by Dan Bump, Dan Orr, Anne Schilling, Mark Shimozono, and Nicolas Thiéry and preliminary patches are in the sage-combinat queue (see extended_affine_weyl_groups_sd40.patch and affine_iwahori_hecke_algebras.patch).
Viviane Pons: I have some programs already in sage-combinat on non symmetric Macdonald polynomials, see trac_6629_abstract_ring_of_multivariate_polynomials_with_several_bases_vp.patch
Viviane : patch is now on trac and ready to be reviewed !
Finalization of the Coxeter3 integration into Sage
Anne Schilling, Nicolas Thiéry, Martina Lanini, Dan Bump
This would bring a faster implementation of Kazhdan-Lusztig polynomials to Sage.
See Trac Ticket 12912.
Status: - Anne : worked on 12912
Finalization of Coxeter and Weyl groups patch
Mark Shimozono, Anne Schilling, Christian Stump
Finalization of the patch Trac Ticket 12774. Done!
Status: - Mark finalized patch and addressed reviewer concerns - Anne : reviewed Mark's patch -
Further Kazdhan-Lusztig functionalities
Brant Jones, Chris Berg, Dan Bump
- Brant : - refactoring the current implementation to take advantage of WithRealizations - implemented KL basis for the Iwahori-Hecke algebra - implemented third basis for the algebra - not on trac yet, but will create a ticket ????
Quantum Schubert products in general types (in particular type C) for the full flag variety
- Expose existing functionality from lrcalc: http://trac.sagemath.org/sage_trac/ticket/14107
- Sage rim-hook implementation (only as an interesting exercise, unless the implementation in lrcalc causes trouble)
- Puzzle rule (see below)
- From k-schur functions using substitution rule
(Equivariant) puzzle rule
Liz Beazley, Anne Schilling, Allen Knutson, Franco Saliola
- Using Knuth's Dancing Links data structure: sage.combinat.matrices.dancing_links?
- Using hive model and counting of integer points in a polytope (Using Latte? or ?)
Status: - - Avinash : constructed Bellkale-Kumar puzzle pieces ; to be uploaded to sage-combinat
Implementation of k-tableaux using alpha factorizations
Review the root system plot ticket
Nicolas Borie, Nicolas Thiéry
Review the affine ambient space patch
Mark Shimozono, Nicolas Thiéry
Finalization of Denton's affine symmetric group patch
And possibly generic implementation of (affine) Coxeter groups as (affine) permutation groups, using (affine) permutations of the roots or the ambient space.
Chris Berg, Nicolas Thiéry
Finalization of the partition options patch
Travis Scrimshaw and Andrew Mathas (and Nicolas)
Status: - Travis : finalized patch - Andrew : reviewing patch (almost done)
Crystals and rigged configurations code and dependencies
Travis Scrimshaw, Anne
Officially deprecate CombinatorialClass
I believe after #13605, there are only a few more left...
Travis Scrimshaw Vincent Delecroix
- Vincent : Reviewed one patch on compositions
Implement a general RSK
RSK for biwords, integer matrices, ...
Travis Scrimshaw, Sara, Kevin Dilks
Split and finalize languages
Vincent Delecroix and Travis Scrimshaw
status : - Vincent : worked on pre-requisites. - Travis : reviewed Vincent's patch
- adding functionality to poset elements--what does this mean?
- iterate over lattices
- zeta, order, characteristic polynomials
- characteristic polynomial done naively
- zeta polynomial from Stembridge's posets code
- W polynomial coming--relabel the poset and then look at permutations
- more examples of posets
- Young diagrams
- Semistandard tableaux
- interval posets
- disjoint union, ordinal sum, product
Alex Csar, Kevin Dilks
- Greene-Kleitman partition of posets (Darij) ; prototype algorithm ready, needs to be correctly formatted.
- Eric : poset avoidance (patch on trac 14099)
- Alejandro : fixing interface to graph colouring
- Kevin : first patch successfully uploaded to trac, now to post rest of code to trac
Preparing technical details for Combinatorial Hopf Algebras
Main points are :
- Finalizing GradedEnumeratedSet
- Categories for Graded Connected Hopf Algebras With Basis (require point 1)
- Improve linear morphisms between GradedConnectedAlgebrasWithBasis (computation of matrices for each graded component, ...) (require point 2)
- Fix technical detail about composition of linear morphism
Nicolas Borie, Vincent Delecroix, Saliola
Status: - Vincent : finalized patch 10193 (under review; small things to fix) - Nicolas Borie : reviewing trac 10193 - Andrew : patch on indexed matrices trac 14103 - Nicolas Borie : tested Andrew's patch on indexed matrices trac 14103 - Nicolas Borie : patch for graded modules on the way
The symmetric group as a proper Weyl group
Iterating through Partitions(n) for n>=1000
Finalize more thematic tutorials and get them into Sage
- Discuss the layout for exercises, ...
Nicolas Thiéry, Franco Saliola, ... We need proof readers!
Cluster algebra package
3 tickets that need review/finalization
Gregg Musiker, Christian Stump, Salvatore
Status: - reviewed one patch (positive review) - almost done second patch (today!) - 3rd patch work in progress (to be finalized within a week)
B infinity crystals
Ben, Mary Elisabeth, Travis
General Coxeter groups
Finalization and review
Implementing (and optimizing) Sheicher and Thuswaldner algorithm for finding neighbors of an integral self-affine tile
Quasi symmetric functions / Combinatorial Hopf Algebras
Chris, Sara, Franco, Nicolas^2, Darij
Here are some possible topics:
- QSym tutorial (see the Sym tutorial for inspiration ; use Sym tutorial as a pre-requiste)
- QSym documentation improvements : for instance, include "inject_shorthands"
- product_on_basis for the F-basis
- P-partition enumerators (Darij)
- chromatic quasi-symmetric functions (Alejandro, Eric)
- P-partition enumerators (Darij) [.py files on trac, ready for review]
- Sara Billey : QSym tutorial (first draft ; ready for review)
- Sara Billey and Chris Berg : nicer documentation for inject_shorthands (essentially done)
Quiver algebras and representations
#11111: Finite dimensional vector spaces and algebras
Gabe, Mathas, Mary Elizabeth, Travis
Matrices indexed by whatever (and displayed as html)
Generalized Specht modules
Sara, Alejandro, Darij, Chris, Franco
Chromatic quasi-symmetric functions
Number theory and automorphic forms
List to do for crystals from Crystal Session on Tuesday
- Plotting for Littelmann paths, performance check between Reda's and Mark/Anne's LS implementation (Reda, Mark, ...)
- B-infinity for finite types (Ben Salisbury, ...)
- MV polytopes (Mary, Dinakhar, ...)
- GLn action on crystals (Gautam, Anne, ...)
Let's get to work and have fun!
Arthur L : alcove paths working in all affine types ; visualizations working for type A ; and working through technicalities for other types
Findstat : - Viviane Pons is now the official web developer ; she got findstat working on her machine ! - Christian : new implementation is almost finished (Findstat-2.0 beta; available on github) - Chris Berg : adding new statistics - Sara Billey : adding new statistics
Trees : - (Viviane) patch for combinatorial maps between trees and other objects - patch almost ready for uploading to trac
Tutorials (presentations): - Chris Berg - Franco - Vincent - Nicolas - Viviane - Anne
Crystals: - Reda : plotting rank 2 crystals including latex output (for Littelmann Path model and tableaux) - Ben : finalized the implementation of generalized Young Walls (Anne and Travis reviewed the patch 14130)
Coxeter groups: - Ed Richmond : learning way around Sage ; started working on initial implementation of a class for arbitrary Coxeter groups
2+2==5: - Travis : created a patch so that Sage answers 5 to 2+2 (passes all doctests in integers and integer rings)
- Anne : finalized 14089, 14009, 14052
- Anne : reviewed 12774, 14130, 12912
Polynomials: - Travis : 14120 Laurent Polynomials - Travis : speed up of conversion of polynomials to finite fields 13257