[Contents]
Table of contents
- Introduction
- A need for a toolbox for computer exploration in algebraic
combinatorics
- Review of preexisting software
- Specifications
- Structure of this document
- Motivations, history and status
- Combinatorics and Algebra
- The birth of MuPAD-Combinat
- An itch to scratch
- An opportunity
- Development model and plan
- A guided tour through MuPAD-Combinat
- Two examples of combinatorial algebras
- MuPAD-Combinat, step by step
- Using predefined combinatorial functions and classes
- Defining new combinatorial classes
- Using predefined combinatorial algebras
- Defining new combinatorial algebras
- A typical computation
- Current features
- Exercices
- Using existing combinatorial classes
- Using generators
- Implementing new algebras
- The degenerate Hecke Algebra
- The design of the MuPAD-Combinat package
- The choice of the platform
- Naming conventions
- Long names versus abbreviations
- Case of names
- Composite names
- Representing combinatorial objects and classes
- Representing combinatorial objects
- Representing combinatorial classes
- Combinatorial classes and categories
- Further naming comments
- Representing combinatorial algebras
- What is a combinatorial algebra after all?
- Why use strong typing?
- Representing free modules
Dom::FreeModuleTable(R, Basis)
Dom::FreeModulePoly(R, Basis)
Dom::FreeModuleList(R, Basis)
- Representing combinatorial algebras on a given basis
- Representing combinatorial algebras with several bases
- Conversions to and from expressions
- Compact notations
- Reference manual
- The
combinat library
- The
examples library
- The
experimental library
- The
Dom library
- The
Cat library
- The
IPC library
- The
operators library
- The
output library
- The
polylib library
- The
prog library
- The
Type library
- The
muEC library
- The
muEC::PART library for partitions
- The
muEC::COMP library for compositions
- The
muEC::TYP library for type-checking of mu-EC objects
- The
muEC::SG library for the symmetric group
- The
muEC::SYMF library for symmetric functions
- The
muEC::SFA library for symmetric functions on
different alphabets
- The
muEC::SP library for simple and double Schubert
polynomials
- MuPAD-Combinat technical sheet
- MuPAD-Combinat facts
- Structure of the package
[Contents]
MuPAD Combinat,
an open source algebraic combinatorics package