burnsidelib

burnsidelib is a small, single-file SageMath library for computations in Burnside rings of finite groups.

Quick start

With burnsidelib.py in the same directory as your notebook or .sage file:

sage: load("burnsidelib.py")
sage: C2 = gap("CyclicGroup(2)")
sage: A = BurnsideRing(C2)
sage: A.basis_names()
('[C2/1]', '[C2/C2]')
sage: 3*A.gen(0) - 4*A.one()
3*[C2/1] - 4*[C2/C2]

The main object is burnsidelib.BurnsideRing, whose elements support marks, restriction, transfer, norms, and several power operations.

Contents

• Installation
  • Requirements
  • Building these docs locally
• Tutorial
  • Creating a Burnside ring
  • Creating elements
  • Restriction, transfer, and norm
  • Matrices
  • Power operations
  • Pickling
• API reference
  • Burnside rings
  • Elements