Linear-Programming on As it was https://galoishlee.github.io/tags/linear-programming/ Recent content in Linear-Programming on As it was Hugo zh-CN maocred@gmail.com (Halois) maocred@gmail.com (Halois) This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License. Fri, 14 Aug 2026 14:13:02 +0800 Automated Coppersmith 的渐近界：线性规划对偶与一个精确 SageMath 实现 https://galoishlee.github.io/auto-coppersmith-lp-asymptotics/ Thu, 13 Aug 2026 12:00:00 +0800maocred@gmail.com (Halois) https://galoishlee.github.io/auto-coppersmith-lp-asymptotics/ <blockquote> <p>Reading: Ding et al., ePrint 2026/1027。本文只处理一个问题：Automated Coppersmith 的 shift 选择为什么在缩放后变成线性规划，以及 Theorem 4 中的渐近系数如何写成 \(P\) 上的积分。<sup id="fnref:1"><a href="#fn:1" class="footnote-ref" role="doc-noteref">1</a></sup></p> </blockquote> <p>主链为：shift 可行性 → 逐点 ILP → 缩放 LP → 对偶分片 → Ehrhart 积分。实现部分检查 <code>auto-copper</code> 如何用精确有理数计算对偶顶点、满维单元格与积分，并用有限参数例子核对 Algorithm 2。</p>