分支Gr\"obner基;布尔环;zdd数据结构., Open Access Library" />

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BRANCH GR(O)BNER BASES ALGORITHM OVER BOOLEAN RING
布尔环上的分支Gr(o)bner基算法

Keywords: Branch Gr\"obner bases,boolean ring,zdd data structure
分支Gr\"obner基
,布尔环,zdd数据结构.

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Abstract:

It is well known that Gr\"obner bases have extensive applications in many fields.In the recent years, many improvements have been made for the Gr\"obner algorithm,the most famous of which are the F4 and F5 algorithm introduced by Faug\`ere.Although both of the two algorithms have excellent efficiency,they need enormous memories during the computation. So we will present a new branch Gr\"obner bases algorithm based on the zdd data structure overthe boolean ring. This new algorithm not only lowers the usage of memories but also constrains the matrix generated in the computation within a reasonable size.In this paper, we will detail the theory and the proof of this basic algorithm and introduce the zdd data strucure and the branch strategy as well. For many cases, its implementation in Linux is superior to the F4 algorithm implemented by Steel in Magma.

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