Structure of the Project

This project provides subroutines to compute the Jordan-Chevalley decomposition of integer matrices. The implementation consists of a C++ backend a Python frontend.

C++ Backend

• The backend relies heavily on the C++ libraries Eigen and Boost.Multiprecision. Eigen is a popular algebra library. Boost.Multiprecision is used for variable precision computations and interacts nicely with Eigen. Both are templated header-only libraries and most of their complexity is abstracted away at compile time.

This project contains a small header-only library which provides simple subroutines as well as a selection of more advanced algorithms for polynomial manipulations. It is used to implement the computing the Jordan-Chevalley decomposition.

Python Frontend

The fronted is built using Cython and Eigency. Cython simplifies the process of writing interfaces between Python and C++ by taking care of the low-level implementation. Eigency uses Cython to implement an interface between between NumPy and Eigen datatypes. The interface is first compiled to C++ and into a shared object file using the Python/C API.

Setup Instructions

I tested the setup on

• Ubuntu 18.04 with GCC 7.5 (and clang 6.0 for the backend)
• CentOS 7.5 with GCC 6.3
• Windows 10 version 2004 with MSVC 19.25
• macOS 10.15 with Apple clang 11.0.3

Start by changing the current working directory to the directory containing this document.

Setting up Conda Environment

An easy way to manage Python environments is provided by Conda. A minimal installation of Conda is provided by Miniconda. Please follow the installation instructions. All default settings are reasonable, except auto_activate_base, deactivate it with:

conda config --set auto_activate_base false

Now, set up the conda environment

1. Update conda and all packages

   conda update conda
   conda update --all

2. Create a conda environment with the packages specified in conda-env.yml.

   I recommend to store the environment in the project folder

         conda env create -p ./conda-env --file conda-env.yml

   and to set the promt to (conda):

         conda config --set env_prompt '(conda)'

3. Activate the virtual environment with

   conda activate ./conda-env 

4. Since eigency is not in the conda repositories, we need to install it manually

   pip install eigency

5. If you wish to deactivate the enviroment, use

   conda deactivate

Find more information on managing conda environments here.

Installing Eigen and Boost

There are many ways to install Eigen and Boost, but Conda provides an easy way to install the latest versions of both libraries. Activate the Conda environment, then run

conda install -c conda-forge eigen boost-cpp

Note that Boost >=1.68 required.

Installing the Python Frontend

Assuming that a C++ compiler is available, activate the Conda environment and install with

pip install libjordanchevalley/

This will compile and install the python extension in the installation into the environment directory and takes roughly 2 minutes.

Uninstalling

If you want to just the extension, use

pip uninstall jordanchevalley

Everything is stored in the Conda environment. Remove it with

conda remove -p ./conda-env --all

Then, follow the instructions to uninstall Miniconda.

Using the Extension

Please refer to demo.py for examples on how to use the extension.