TL;DR
This paper introduces a threaded Macaulay2 package implementing Buchberger's algorithm for Gröbner bases, providing detailed lineage information to facilitate algorithm optimization and performance analysis.
Contribution
It presents a novel threaded implementation of Buchberger's algorithm in Macaulay2 with lineage tracking for improved analysis and potential optimization.
Findings
Enhanced understanding of algorithm performance through lineage data
Potential for optimization based on detailed remainders tracking
Threaded implementation improves computational efficiency
Abstract
The complexity of Gr\"{o}bner computations has inspired many improvements to Buchberger's algorithm over the years. Looking for further insights into the algorithm's performance, we offer a threaded implementation of classical Buchberger's algorithm in {\it Macaulay2}. The output of the main function of the package includes information about {\it lineages} of non-zero remainders that are added to the basis during the computation. This information can be used for further algorithm improvements and optimization.
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