Work in progress... (The algorithms in this code are not optimized completely).
The main.py shows and example of how this its used.
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
.png "Roots of SU(3)")
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:
This class computes the commutators adnd the necessary information such as structure constants for the Lie Algebra.
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