A combination of three separate repos from a project from Summer, 2019. The inspiration was that not all integers can be formed by the sum of three squares, yet energy levels in a 3D potential well can only be formed by the sum of three squared intgers. It may therefore be a possibility that some levels are inaccessible.
main.py calculates and prints the combinations of each integer that is the sum of three squares, as well as determining a and b for the equation n = (8^a)(b+7), where n is the integer for which n = x^2 + y^2 + z^2.
The degeneracy_plotter.py graphically shows the degeneracy combinations for a given integer.
The probility sctipt is used to determine the probability of getting a degeneracy of 0 when determining the sum-of-three-squares degeneracy along Z.
The C++ implementation is simply a faster calculation for combinations, and does not offer any additional functionality. Additioanlly, it does not plot frequencies/probabilities of different combinations.
The python portion of this project uses the numpy, scipy and matplotlib packages, as well as the MIDACO solver, available here
As well as MIDACO, the C++ requires Lava's implementation of matplotlib for C++ which is to be added as a header.