CAJ | 학술논문

目前基于标签的Gr?bner基算法大多是Buchberger型的，涉及矩阵型算法的文献往往是为了进行复杂度分析，而不考虑实际的效率。该文从实际应用出发，给出矩阵型Gao-Vol ny-Wan g(GVW)算法的一个实例，提出算法层次的优化设计方法。同时，该文还给出一个高效的约化准则。通过实验，该文比较了算法可用的各项准则及策略。实验结果表明，该文的矩阵型GVW实例在准则和策略的选取上是最优的。并且，矩阵型GVW在某些多项式系统(例如，Cyclic系列和Katsura系列多项式系统)下比Buchberger型GVW要快2~6倍。
목전기우표첨적Gr?bner기산법대다시Buchberger형적，섭급구진형산법적문헌왕왕시위료진행복잡도분석，이불고필실제적효솔。해문종실제응용출발，급출구진형Gao-Vol ny-Wan g(GVW)산법적일개실례，제출산법층차적우화설계방법。동시，해문환급출일개고효적약화준칙。통과실험，해문비교료산법가용적각항준칙급책략。실험결과표명，해문적구진형GVW실례재준칙화책략적선취상시최우적。병차，구진형GVW재모사다항식계통(례여，Cyclic계렬화Katsura계렬다항식계통)하비Buchberger형GVW요쾌2~6배。
The current signature-based Gr?bner basis algorithms are mostly in Buchberger style and the researches related to matrix style often aim to analyze the complexity of algorithms. From a practical aspect, this paper provides a concrete Gao-Volny-Wang (GVW) algorithm in matrix style and presents optimization at the algorithmic level. Meanwhile, an efficient reduction criterion is given in the paper. Many popular criteria and strategies are compared by some experiments which showthat the matrix version described in the paper is a combination of reasonable criteria and strategies. Moreover, the matrix-GVW is two to six times faster than the Buchberger style for some polynomial systems,e.g. Cyclic series and Katsura series.