Thematic tutorial document tree

• Algebraic Combinatorics in Sage
  • Walks in graphs
  • \(n\)-Cube
  • The Tsetlin library
  • RSK algorithm
• Tutorial: Using the Sage notebook, navigating the help system, first exercises
  • Making this help page into a worksheet
  • Entering, Editing and Evaluating Input
  • Help systems
  • Completion and contextual documentation
  • Some linear algebra
  • Some Plotting
  • Symbolic Expressions
• Abelian Sandpile Model
  • Introduction
  • 4ti2 installation
  • Usage
  • Contact
• Group Theory and Sage
  • Basic properties of the integers
  • Permutation groups
  • Group functions
  • Subgroups
  • Symmetry groups
  • Normal subgroups
  • Conjugacy
  • Sylow subgroups
  • Groups of small order as permutation groups
  • Acknowledgements
• Lie Methods and Related Combinatorics in Sage
  • The Scope of this Document
  • Lie Group Basics
  • The Weyl Character Ring
  • Maximal Subgroups and Branching Rules
  • Weight Rings
  • Weyl Groups, Coxeter Groups and the Bruhat Order
  • Classical Crystals
  • Affine Finite Crystals
  • Affine Highest Weight Crystals
  • Iwahori Hecke Algebras
  • Kazhdan-Lusztig Polynomials
  • Bibliography
• Linear Programming (Mixed Integer)
  • Definition
  • Mixed integer linear programming
  • Practical
  • Basic linear programs
  • Matching
  • Flows
  • Solvers
  • Using CPLEX or GUROBI through Sage
• Number Theory and the RSA Public Key Cryptosystem
  • Elementary number theory
  • How to keep a secret?
  • Keeping a secret with two keys
  • Generating public and private keys
  • Encryption and decryption
  • Acknowledgements
  • Bibliography
• Tutorial: Programming in Python and Sage
  • Data structures
  • Control structures
  • Functions
  • Exercises
  • Loops and Functions
• Tutorial: Comprehensions, Iterators, and Iterables
  • List comprehensions
  • Iterators
  • Standard Iterables
• Tutorial: Objects and Classes in Python and Sage
  • Foreword: variables, names and objects
  • Other languages have “variables”
  • Python has “names”
  • Object-oriented programming paradigm
  • Inheritance
  • Sage specifics about classes
  • Solutions to the exercises
• Functional Programming for Mathematicians
  • Styles of programming
  • Functional programming using map
  • Define small functions using lambda
  • Reducing a sequence to a value
  • Filtering with filter
  • Further resources
• How to implement new algebraic structures in Sage
  • Sage’s category and coercion framework