Module: spdaot

(sage probably does all of this)

Alexander Ellis, 2016

This module replaces the following deprecated modules:

• symmetric
• manin_schechtman
• nc_polynomial
• mystic
• odd_code
• zero_hecke

I've removed the above modules from Github. But until spdaot catches up and re-implements all the functonality from those modules, you can email me if you want a copy of the older code.

See SPECIFICATION.md for documentation.

Things already implemented:

• class Op, which allows for quickly computing algebra and group actions
• base code for Variable, VariableWord, Relation, Element classes, which handle free algebra modulo relations; wrapper for quickly creating q-commuting variables; inverses
• class Op, which allows for quickly computing algebra and group actions
• some functional programming tools and decorators
• D_n^-, B_n^+ group actions on S_{-1}(V); braided differentials; isobaric braided differentials
• exact scalar relation finder

Things to do, sooner:

• testing suite
• more documentation (SPECIFICATION.md)
• S_n group action on S_1(V)
• add better type checking and error protection to class Op, especially in Op.__init__()
• rank-based relation finder

Things to do, later:

• Young cosets and their minimal/maximal representatives
• pickling routines for caching combinatorial data
• convert between reduced Coxeter expression and one-line notation for permutations
• generate Manin-Schechtman graph
• q-bilinear form on quantum noncommutative symmetric polynomials; generalizations of this
• combinatorial data on permutations: descent set, descent compositon, inversions
• classes for Young diagrams and tableaux
• elementary, complete, power sum, schur, schubert polynomials; odd analogues of these, both twisted and untwisted
• Grothendieck polynomials
• RSK, partitions, compositions
• profile and optimize

Contact

Email: apellis@gmail.com

Github: https://github.com/apellis/spdaot