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 high-performance 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.
Categories: math.AG hep-th