[Contents]

index - The MuPAD-Combinat handbook

Table of contents

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

[Contents]


MuPAD Combinat, an open source algebraic combinatorics package