This project implemented a module in SymPy which provides the ability to integrate arbitrary polynomials over 2D, 3D polytopes. Using Generalized Stokes’ Theorem and Euler’s Theorem the integration over a given polytope is reduced to integration over its faces and then edges. This technique avoids using a 3D quadrature which would otherwise be computationally expensive.
Project link: https://github.com/sympy/sympy/wiki/GSoC-2017-Report-Arif-Ahmed-:-Integration-over-Polytopes