Toric Geometry in OSCAR

Abstract

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

6 pages, prepared for the ComputerAlgebraRundbrief (March 2023)