liesym 0.1.0

Sympy Lie Algebra extensions powered by rust.

liesym

Lie Algebras using Sympy and backend powered by Rust's pyO3 and ndarray

Overview

In an effort to supply python with the same computer algebra software (CAS) capabilities, SymPy was written. This python library is well written and allows an open source alternative to proprietary choices like Mathematica/WolframLanguage and Maple. Due to the nature of how SymPy was written, certain symbolic calculation can be extremely unoptimized in python. Even using numpy could offer little speed ups as it is not geared towards rational numbers (fractions). Sympy does currently offer a liealgebras module, but due to the performance limitations, certain tradeoffs had to be made such as locking the basis for the classic lie algebras in favor of speed. This is a fair trade off, but would require anyone using a different basis to hand calculate the representations of the algebra all over again. An alternative to solve this problem would be to use a compiled backend that supports generics (and isn't a pain to build with python).

Rust has good python binding support through py03 and allows easy communication through numpy using rust-numpy as well as numpy like api inside rust using ndarray.

Repo Layout

If you are new to how python and rust are tied together with py03, below is a simple top level layout of this repository. When the rust code is build into a lib binary, it is put into into ./liesym so it can be imported in ./liesym/__init__.py

.
├── Cargo.toml          # rust config file
├── README.md           # you are here
├── liesym              # python module
├── notebooks           # jupyter notebooks
├── src                 # rust source code
├── tests               # python tests
└── ...                 # other stuff

Example use

from liesym import A, G2

su3 = A(2)
pr3 = su3.positive_roots

assert pr3 == [Matrix([[1, 1]]), Matrix([[-1, 2]]), Matrix([[2, -1]])]

g2 = G2()
prg = g2.positive_roots

assert prg == [
    Matrix([[0, 1]]),
    Matrix([[3, -1]]),
    Matrix([[1, 0]]),
    Matrix([[-1, 1]]),
    Matrix([[-3, 2]]),
    Matrix([[2, -1]])
]

Docs

Read the documentation at https://npapapietro.github.io/liesym/