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*-combinat Days Project Idea Page

Implement a generic FactoredElement class

PEOPLE: Burcin Erocal

• In many combinatorics applications we work with rational functions whose numerator/denominator factor into nice components where the factorization is also known beforehand. The current representation of rational functions in Sage use the expanded form of the numerator and denominator. The goal is to implement a generic wrapper to store elements in a factored representation.

• sage-devel thread about working with factored denominators

• another thread

• code mentined above is here

An example of adding a new basis to an algebra

PEOPLE: Franco Saliola, CoryBrunson

• This should be a nice exercise in adding a new basis (the seminormal basis) to an algebra (the group algebra of the symmetric group). We don't even have to introduce any new code to construct the basis since it already exists in Sage, thanks to Mike Hansen. On the other hand, I do have a better implementation based on a method that Alain Lascoux explained to me, so we could use that instead.

Try out Nathann Cohen new interface to Mixed Integer Linear Programming software

PEOPLE Nicolas Thiéry

Bug squashing!

PEOPLE: Franco Saliola, Jason Bandlow, Florent Hivert

• There are bugs in Sage that need fixin':

  1. Bugs in Partitions

  2. The wiki page quirks and weirdness in sage-combinat contains a list of quirks and weirdness in sage-combinat.

  3. The sage-combinat milestone lists all tickets labelled sage-combinat.

Categories

100% doctest and review for all patches up to sagecombinat 4.1

Functorial constructions: subquotient, cartesian_product

FlorentHivert, FrancoSaliola, AnneSchilling, NicolasThiéry

Categorification of RootSystems and Crystals

And application to parabolic subroot-systems

NicolasBorie, AnneSchilling, NicolasThiéry, CoryBrunson

graph layout using graphviz / dot2tex optional package

Anne Schilling, FrancoSaliola, NicolasThiéry

Quickref card for sage.combinat

JasonBandlow, FrancoSaliola, NicolasThiéry

Refactoring of symmetric functions

• Patch Symmetrica
• Make LRcalc spkg

• Bring all symmetric functions under the SymmetricFunctions umbrella

• Improve documentation

JasonBandlow, CoryBrunson

Improve Nonsymmetric Macdonald polynomials

• Add doctests with examples on specifying q, t, and the basement pi
• Add input checks for pi. Maybe accept a list as input, and make it into an appropriate permutation
• Maybe implement:

        sage: F = QQ['q,t']; (q,t) = F.gens(); F.rename('QQ(q,t)')
        sage: P = AbstractPolynomialRing(F, 'x0,x1,x2'); P
        The abstract ring of multivariate polynomials in x0, x1, x2 over QQ(q,t)
        sage: m = Macdo.m; m
        Multivariate Polynomial Ring in x0, x1, x2 over QQ(q,t)
        sage: Macdo = P.MacdonaldPolynomials(q, t)
        sage: E = Macdo.E(pi = [3,1,2]); E
        Multivariate Polynomial Ring in x0, x1, x2 over QQ(q,t), in the Macdonald E basis, with basement [3,1,2]
        sage: E[1,0,0]
        E[1,0,0]
        sage: m(E[1,0,0])
        x0

People: Jeff

Module for generate integer list up to the action of a permutation group

• Integrate a StabChain from Gap to sage

• Finalise the module and submit it

NicolasBorie