Normaliz: development and long term sustainability

• Applicant: Professor Dr. Winfried Bruns
• Subject Area: Mathematics
• Term: from 2020 to 2021
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 440345850

Final Report Abstract

In addition to numerous improvements of the existing implementation, Several goals in the development of Normaliz could be reached within the duration of the project or brought forward considerably: new arithmetic for algebraic polytopes by e-antic 1.0, new algorithms for polytope volumes with applications to social choice, Gröbner and Graver bases, a first application of distributed computation. An important point is the improvement of the build and test infrastructure.

Publications

• Algebraic polytopes in Normaliz. In: A. M. Bigatti, J. Carette, J. H. Davenport, M. Joswig and T. de Wolff (Eds.), Mathematical Software – ICMS 2020, LNCS 12097, Springer 2020, pp. 193–201
  W. Bruns
  (See online at https://doi.org/10.1007/978-3-030-52200-1_19)
• Automorphism groups and normal forms in Normaliz. Preprint
  W. Bruns
  (See online at https://doi.org/10.48550/arXiv.2112.08145)
• Computations of volumes in five candidates elections. Preprint
  W. Bruns and B. Ichim
  (See online at https://doi.org/10.48550/arXiv.2109.00473)
• Polytope volume by descent in the face lattice and applications in social choice. Math. Program. Comput. 13 (2021), 415–442
  W. Bruns and B. Ichim
  (See online at https://doi.org/10.1007/s12532-020-00198-z)