Tutorials

Here you will find tutorials convering all the main aspects of the abelian library.

• Tutorial: LCAs
  • Initializing a LCA
  • Manipulating LCAs
  • Checking if an LCA is a FGA
  • Dual groups
  • Iteration, containment and lengths
  • Ranks and lengths of groups
  • Canonical forms and isomorphic groups
  • Projecting elements to groups
• Tutorial: Homomorphisms
  • Initializing a homomorphism
  • Compositions
  • Slice notation
  • Stacking homomorphisms
  • Calling homomorphisms
  • Calling and composing
• Tutorial: Factoring homomorphisms
  • Initialization and source/target projections
  • The kernel monomorphism
  • The cokernel epimorphism
  • The image/coimage factorization
• Tutorial: Functions on LCAs
  • Initializing a new function
  • Function evaluation
  • Shifts
  • Pullbacks
  • Pushforwards
• Tutorial: Fourier series
  • Overview: \(f(x) = x\) defined on \(T = \mathbb{R}/\mathbb{Z}\)
  • Defining the function
  • Sampling using pullback
  • The DFT
  • Transversal
  • Comparing with analytical solution