On the bit-size of non-radical triangular sets
On the bit-size of non-radical triangular sets
复制标题
关于非根式三角形集的位大小
DOI：
10.1007/978-3-319-72453-9_19
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
Xavier Dahan
中科院分区：
文献类型：
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作者：
Masayuki Fukumitsu;Shingo Hasegawa;Xavier Dahan
我们提出了零维非激进纯词典编纂的 Gröbner 基（三角形集）的系数位大小的上限。这扩展了之前的工作 [4]，仅限于激进三角形集；它遵循基于插值的相同技术步骤。然而，对于具有重数的点，簇高度的关键概念不可用；因此，所获得的界限不太通用，并且取决于某些输入数据。我们还介绍了一系列相关的非单调多项式，它们具有较小的系数和较小的界限。然而，从初始三角形集计算它们并不明显。
We present upper bounds on the bit-size of coefficients of non-radical purely lexicographical Gröbner bases (triangular sets) in dimension zero. This extends a previous work [4], constrained to radical triangular sets; it follows the same technical steps, based on interpolation. However, key notion of height of varieties is not available for points with multiplicities; therefore the bounds obtained are thus less universal and depend on some input data. We also introduce a related family of non-monic polynomials that have smaller coefficients, and smaller bounds. It is not obvious to compute them from the initial triangular set though.