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Math paper links Bézout inversion to multipoint evaluation

By PulseAugur Editorial · [1 sources] ·

Researchers have established a theoretical equivalence between two complex mathematical problems in characteristic zero fields: derivative Bézout inversion and multipoint polynomial evaluation. The study demonstrates that solving the Bézout pair problem, which traditionally has a higher computational cost, can be achieved with the same complexity as multipoint evaluation and interpolation. This finding is significant because it suggests a potential for more efficient algorithms in symbolic computation, particularly in the generic rational straight-line-program model. AI

RANK_REASON The item is a research paper published on arXiv detailing theoretical mathematical advancements. [lever_c_demoted from research: ic=1 ai=0.1]

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Math paper links Bézout inversion to multipoint evaluation

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The item is a research paper published on arXiv detailing theoretical mathematical advancements. [lever_c_demoted from research: ic=1 ai=0.1]
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COVERAGE [1]

  1. arXiv cs.LG TIER_1 English(EN) · Zijian Zeng ·

    Generic Characteristic-Zero Equivalence Between Derivative B\'ezout Inversion and Multipoint Evaluation

    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…

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