SemiSimpleRootSystem

Work in progress... (The algorithms in this code are not optimized completely).

The main.py shows and example of how this its used.

RootSystem

As of now it can generate the entire positive roots and all the roots of the root system. It also can plot the roots in A 2D plane but is only avaliable for root systems having only 2 simple roots. Also, it finds the relationships of the roots other than simple roots interms of commutatators of simple roots. This generated dictionary contains the constant and the commutator as a list. This can be used with Jacobi identity to find the commutator with any other root. The main.py shows the $SU(3)$ root system.

DynkinDraw

It attempts to draw the dynkin diagrams of the given RootSystem object with matplotlib under the hood. The 2 generated dynkin diagrams from main.py are shown below:

TheAlgebra

This class computes the commutators adnd the necessary information such as structure constants for the Lie Algebra.

Important Note

Having python version greater than 3.7 is a must since this version assmues that the python dictionaries would maintain the same order after all insertion is done. This was a implemetation effect in the previous versions but it is a must here! The other details of package versions used for the modules are shown below from conda list command:

_libgcc_mutex             0.1                        main  
_openmp_mutex             5.1                       1_gnu  
bzip2                     1.0.8                h7b6447c_0  
ca-certificates           2022.4.26            h06a4308_0  
certifi                   2022.6.15       py310h06a4308_0  
iteration-utilities       0.11.0                   pypi_0    pypi
ld_impl_linux-64          2.38                 h1181459_1  
libffi                    3.3                  he6710b0_2  
libgcc-ng                 11.2.0               h1234567_1  
libgomp                   11.2.0               h1234567_1  
libstdcxx-ng              11.2.0               h1234567_1  
libuuid                   1.0.3                h7f8727e_2  
mpmath                    1.2.1                    pypi_0    pypi
ncurses                   6.3                  h5eee18b_3  
numpy                     1.23.0                   pypi_0    pypi
openssl                   1.1.1p               h5eee18b_0  
packaging                 21.3                     pypi_0    pypi
pillow                    9.2.0                    pypi_0    pypi
pip                       21.2.4          py310h06a4308_0  
pyparsing                 3.0.9                    pypi_0    pypi
python                    3.10.4               h12debd9_0  
readline                  8.1.2                h7f8727e_1  
setuptools                61.2.0          py310h06a4308_0  
six                       1.16.0                   pypi_0    pypi
sqlite                    3.38.5               hc218d9a_0  
sympy                     1.10.1                   pypi_0    pypi
tk                        8.6.12               h1ccaba5_0  
tzdata                    2022a                hda174b7_0  
wheel                     0.37.1             pyhd3eb1b0_0  
xz                        5.2.5                h7f8727e_1  
zlib                      1.2.12               h7f8727e_2