Inequalities of Mixed Volumes on Six Planar Bodies in Two and Three Dimensions

This is the official repository for Mixed volumes of zonoids and the absolute value of the Grassmannian, which contains all of the SageMath code used to produce the computation results in the paper.

BibTex:

coming soon...

Getting Started

Dependencies

Two Dimensions

Three Dimensions

Structure

In addition to the notebooks mentioned above, this project includes mvol_map_problem.sage. This file contains the MVolMapProblem class, which handles the parameters for the problem (number of bodies, number of dimensions, etc.) and provides cached (memoized) functions that generate important SageMath objects (like the polyhedral cone $C_{n,d}$ which is the conic hull of the image of $\Phi$). However, note that this class is unlikely to work for other dimensions.

Contributing

Pull requests are welcome!

License

This code has been released under the MIT License.

Contact

If you have questions or comments feel free to email Ivan Soprunov ([email protected]). For more code-specific questions consider reaching out to Simon Richard ([email protected]) or Gennadiy Averkov ([email protected]).

Tasks

• Check for trivial proofs given duplicate triangles (sum like terms in orbit representations)