Thematic tutorial document tree

• Algebraic Combinatorics in Sage
  • Walks in graphs
  • \(n\)-Cube
  • The Tsetlin library
  • Young’s lattice and the RSK algorithm
• Abelian Sandpile Model
  • Introduction
  • 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
  • Weyl Groups, Coxeter Groups and the Bruhat Order
  • Classical Crystals
  • Affine Root System Basics
  • Integrable Highest Weight Representations of Affine Lie algebras
  • Affine Finite Crystals
  • Affine Highest Weight Crystals
  • Elementary crystals
  • Infinity Crystals
  • Iwahori Hecke Algebras
  • Kazhdan-Lusztig Polynomials
  • Bibliography
• Tutorial: Vector Calculus in Euclidean Spaces
  • How to compute a gradient, a divergence or a curl
  • How to perform vector calculus in curvilinear coordinates
  • How to change coordinates
  • Advanced aspects: the Euclidean space as a Riemannian manifold
  • Vector calculus in the Euclidean plane
• Linear Programming (Mixed Integer)
  • Definition
  • Mixed integer linear programming
  • Practical
  • Basic linear programs
  • Matching
  • Flows
  • Solvers (backends)
• 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
• Coding Theory in Sage
  • I. Generic Linear codes and associated methods
  • II. Structured code families and an overview of the encoding and decoding system
  • III. A deeper view of the Encoder and Decoder structure
  • IV. A deeper look at channels
  • V. Codes in General
  • VI. Conclusion - Afterword
• How to write your own classes for coding theory
  • I. Abstract classes
  • II. The repetition code
  • III. Write a new code class
  • IV. Write a new encoder class
  • V. Write a new decoder class
  • VI. Write a new channel class
  • VII. Sort our new elements
  • VIII. Complete code of this tutorial
• Polyhedra
  • A Brief Introduction to Polytopes in Sage
  • A Longer Introduction to Polyhedral Computations in Sage
  • Quick reference for polyhedra in Sage
  • Polyhedra tips and tricks
  • Visualization of polyhedron objects in Sage
  • Draw polytopes in LaTeX using TikZ
• Steenrod Algebra Modules
  • Module elements
  • Module homomorphisms
  • Example: Counting lifts
• 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
• Tutorial: Implementing Algebraic Structures
  • Subclassing free modules and including category information
  • Morphisms
  • Diagonal and Triangular Morphisms
  • Coercions
  • A digression: new bases and quotients of symmetric functions
  • Implementing algebraic structures with several realizations
  • Review
• How to call a C code (or a compiled library) from Sage ?
  • Calling “hello_world()” from hello.c
  • Arguments and return value
  • Calling code from a compiled library
• Numerical Computing with Sage
  • Numerical Tools
  • Using Compiled Code Interactively
  • Parallel Computation
• Three Lectures about Explicit Methods in Number Theory Using Sage
  • Introduction
  • Number Fields
  • A Bird’s Eye View
  • Modular Forms
• Profiling in Sage
  • How long does it take? %time and %timeit
  • Python-level function calls: %prun
  • Python-level line-by-line profiling: %lprun
  • C-level function calls: %crun
  • C-level line-by-line profiling: perf (Linux only)
• Creating a Tutorial from an old Sage Worksheet (.sws)