Unified Analytic Solution of Tensor Equations in Differential Algebraic Closure: Theoretical Framework and Computational Realization

Unified Analytic Solution of Tensor Equations in Differential Algebraic Closure: Theoretical Framework and Computational Realization | Authorea try { document.documentElement.classList.add('js'); } catch (e) { } var _gaq = _gaq || []; _gaq.push(['_setAccount', 'G-8VDV14Y67G']); _gaq.push(['_trackPageview']); (function() { var ga = document.createElement('script'); ga.type = 'text/javascript'; ga.async = true; ga.src = ('https:' == document.location.protocol ? 'https://ssl' : 'http://www') + '.google-analytics.com/ga.js'; var s = document.getElementsByTagName('script')[0]; s.parentNode.insertBefore(ga, s); })(); Skip to main content Preprints Collections Wiley Open Research IET Open Research Ecological Society of Japan All Collections About About Authorea FAQs Contact Us Quick Search anywhere Search for preprint articles, keywords, etc. Search Search ADVANCED SEARCH SCROLL This is a preprint and has not been peer reviewed. Data may be preliminary. 6 October 2025 V1 Latest version Share on Unified Analytic Solution of Tensor Equations in Differential Algebraic Closure: Theoretical Framework and Computational Realization Authors : Dongqi Liu 0009-0006-4018-9292 and shifa liu 0009-0003-6570-2812 [email protected] Authors Info & Affiliations https://doi.org/10.22541/au.175977864.49249173/v1 264 views 151 downloads Contents Abstract Supplementary Material Information & Authors Metrics & Citations View Options References Figures Tables Media Share Abstract 本文建立了一个全面的微分代数框架，用于求解任意阶数和维度的张量方程。我们证明了一般张量方程的所有解都可以在张量微分代数闭包 Ktensor 内解析表达，该张量通过张量导数算子及其求值扩展了系数场。求解公式采用统一形式：对于一般高阶张量方程，显式解析解存在于适当扩展的张量微分代数闭包 Ktensor 中。我们还解决了四个关键的开放问题，涉及最优校正项、张量伽罗瓦群的有限性、量子容错阈值和可解性的几何不变量。 Supplementary Material File (tensor_equations (1).pdf) Download 493.61 KB Information & Authors Information Version history V1 Version 1 06 October 2025 Copyright This work is licensed under a Creative Commons Attribution 4.0 International License Keywords abel-ruffini theorem differential algebraic closure explicit solution galois theory geometric invariants quantum computation tensor equations Authors Affiliations Dongqi Liu 0009-0006-4018-9292 View all articles by this author shifa liu 0009-0003-6570-2812 [email protected] View all articles by this author Metrics & Citations Metrics Article Usage 264 views 151 downloads .FvxKWukQNSOunydq8rnd { width: 100px; } Citations Download citation Dongqi Liu, shifa liu. Unified Analytic Solution of Tensor Equations in Differential Algebraic Closure: Theoretical Framework and Computational Realization. Authorea . 06 October 2025. DOI: https://doi.org/10.22541/au.175977864.49249173/v1 If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download. For more information or tips please see 'Downloading to a citation manager' in the Help menu . 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