arc.lib: A Singular library for jet schemes with fast partial reduction

The arc.lib library provides efficient computation for the equations which define generalized jet schemes of affine algebraic varieties within the Singular computer algebra system. This library represents a significant improvement over previous Sage implementations, offering enhanced speed, reduced memory usage, and a novel iterative reduction approach for studying jet schemes. For demonstrative purposes, three applications are considered: calculating the singular fiber, iteratively calculating the reduced structure, and testing for flatness. The last two applications raise new interesting theoretical questions within singularity theory which further demonstrate the importance of this new Singular library.