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

arXiv eprints
 Pub Date:
 March 2023
 DOI:
 10.48550/arXiv.2303.08110
 arXiv:
 arXiv:2303.08110
 Bibcode:
 2023arXiv230308110B
 Keywords:

 Mathematics  Algebraic Geometry;
 High Energy Physics  Theory;
 1404
 EPrint:
 6 pages, prepared for the ComputerAlgebraRundbrief (March 2023)