abelian
A Python library for locally compact Abelian (LCA) groups.
Note
This software is being built, and is not ready to be used yet.
Project Goals
- Classical groups \(\mathbb{R}\), \(\mathbb{T}\), \(\mathbb{Z}\) and \(\mathbb{Z}_n\) and computations on these.
- Relationship between continuous and discrete should be ‘pretty’.
- FFT computations on discrete, compact groups (and their products),
e.g. \(\mathbb{Z}_{n_{1}} \oplus \mathbb{Z}_{n_{2}} \oplus \dots \oplus \mathbb{Z}_{n_{r}}\).
- The software should build on the mathematical theory.
Todo
- Create skeleton for project
- Factorizations of homomorphisms between FGAs (tests, docs, implementation)
Software specification
All public classes with methods
__init__ (representation, domain) |
Create a function. |
call (list_arg, *args, **kwargs) |
Evaluate the function. |
compose (func) |
Compose with C -> C function. |
convolve (other) |
Convolution (if domain is discrete + compact). |
dft () |
Discrete fourier transform (if domain is discrete + compact). |
pointwise (func, operator) |
Pointwise mult/add/... |
pullback (morphism) |
Pullback. |
pushfoward (morphism) |
Pushfoward. |