English(EN) Generic Characteristic-Zero Equivalence Between Derivative B\'ezout Inversion and Multipoint Evaluation

数学论文将贝祖求逆与多点求值联系起来

作者 PulseAugur 编辑部 · [1 个来源] · 2026-09-17 04:00

研究人员在特征零域中建立了两个复杂数学问题之间的理论等价性：导数贝祖求逆与多点多项式求值。该研究表明，解决传统上计算成本更高的贝祖对问题，可以以与多点求值和插值相同的复杂度来实现。这一发现意义重大，因为它预示着符号计算中可能出现更高效的算法，特别是在通用有理直线程序模型中。 AI

排序理由该条目是发表在arXiv上的研究论文，详细介绍了理论数学进展。[lever_c_demoted from research: ic=1 ai=0.1]

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arXiv cs.LG TIER_1 English(EN) · Zijian Zeng · 2026-09-17 04:00

导数Bézout求逆与多点求值的通用特征零等价性

arXiv:2609.17578v1 Announce Type: cross Abstract: Let $a_1,\ldots,a_m$ be distinct elements of a field $K$, and let $Z(X)=\prod_{i=1}^m (X-a_i)$. We study the arithmetic complexity of computing the unique normalized Bezout pair $s,t$ satisfying $sZ+tZ'=1$, with $\deg t<m><m$ poly…