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arXiv · 2303.08110

Toric Geometry in OSCAR

Martin Bies·Lars Kastner
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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 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.

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Martin Bies, Lars Kastner. 2023-03-14. Toric Geometry in OSCAR. https://arxiv.org/abs/2303.08110

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