Monomial divisibility diagrams represent monomial ideals as compact DAGs via maximal subtree sharing, enabling faster membership queries than generator lists with divmasks and delivering speed-ups in Gröbner basis algorithms.
Practical Groebner Basis Computation
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abstract
We report on our experiences exploring state of the art Groebner basis computation. We investigate signature based algorithms in detail. We also introduce new practical data structures and computational techniques for use in both signature based Groebner basis algorithms and more traditional variations of the classic Buchberger algorithm. Our conclusions are based on experiments using our new freely available open source standalone C++ library.
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2026 1verdicts
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A data structure for monomial ideals with applications to signature Gr\"obner bases
Monomial divisibility diagrams represent monomial ideals as compact DAGs via maximal subtree sharing, enabling faster membership queries than generator lists with divmasks and delivering speed-ups in Gröbner basis algorithms.