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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

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

Finalization of the Coxeter3 integration into Sage

Anne Schilling, Nicolas Thiéry

This would bring a faster implementation of Kazhdan-Lusztig polynomials to Sage.

See Trac Ticket 12912.

Finalization of Coxeter and Weyl groups patch

Mark Shimozono, Anne Schilling, Christian Stump

Finalization of the patch Trac Ticket 12774.

Further Kazdhan-Lusztig functionalities

Brant Jones

Quantum Schubert products in general types (in particular type C) for the full flag variety

Liz Beazley

Equivariant puzzle rule

Liz Beazley, Anne Schilling

Implementation of k-tableaux using alpha factorizations

Anne Schilling

Review the root system plot ticket

Nicolas Borie, Nicolas Thiéry

Review the affine ambient space patch

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)

Crystals and rigged configurations code and dependencies

Travis Scrimshaw

Officially deprecate CombinatorialClass

I believe after #13605, there are only a few more left...

Travis Scrimshaw Vincent Delecroix

Implement a general RSK

Travis Scrimshaw

Split and finalize languages

Vincent Delecroix and Travis Scrimshaw

Add more poset functionality (continuing from Sage Days 40)

Alex Csar Kevin Dilks

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 GradedConectedAlgebrasWithBasis (computation of matrices for each graded component, ...) (require point 2)
  • Fix technical detail about composition of linear morphism

Nicolas Borie

The symmetric group as a proper Weyl group

http://trac.sagemath.org/sage_trac/ticket/14095

Iterating through Partitions(n) for n>=1000

http://trac.sagemath.org/sage_trac/ticket/14095