English

Toric Geometry in OSCAR

Algebraic Geometry 2023-10-24 v1 High Energy Physics - Theory

Abstract

We report on the computer implementation for toric geometry in the computer algebra system OSCAR\texttt{OSCAR}. The main architectural feature of OSCAR\texttt{OSCAR} is that its four fundamental tools Antic\texttt{Antic} (Hecke, Nemo), GAP\texttt{GAP}, Polymake\texttt{Polymake} and Singular\texttt{Singular} are integral components\mathit{integral~components}, rather than external software. Toric geometry benefits greatly from this architecture. Julia\texttt{Julia} is a high-performance programming language designed for numerical and scientific computing. The growing ecosystem of Julia\texttt{Julia} packages ensures its continued viability for scientific computing and data analysis. Indeed, OSCAR\texttt{OSCAR} is written in Julia\texttt{Julia}. This implies that the performance of OSCAR\texttt{OSCAR} should be comparable or even better than many other implementations.

Cite

@article{arxiv.2303.08110,
  title  = {Toric Geometry in OSCAR},
  author = {Martin Bies and Lars Kastner},
  journal= {arXiv preprint arXiv:2303.08110},
  year   = {2023}
}

Comments

6 pages, prepared for the ComputerAlgebraRundbrief (March 2023)

R2 v1 2026-06-28T09:17:05.974Z