https://yamayuki.space/posts/Recent content in 文字 on Yamayuki's SpaceHugozh-CNMon, 09 Nov 2026 00:00:00 +0800https://yamayuki.space/posts/073f2db485e0653a75c72bfa92c6f6b2/Mon, 09 Nov 2026 00:00:00 +0800https://yamayuki.space/posts/073f2db485e0653a75c72bfa92c6f6b2/<h2 class="heading" id="一历史渊源"> 一、历史渊源 <a class="anchor" href="#%e4%b8%80%e5%8e%86%e5%8f%b2%e6%b8%8a%e6%ba%90">#</a> </h2> <p>中国剩余定理的英文名称是 <strong>Chinese Remainder Theorem，简称CRT</strong>，中文也称“孙子定理”或“中国余数定理”。它研究的问题是：知道一个整数分别除以几个数的余数，能否确定这个整数，以及怎样把它算出来。从应用来说，这一定理可以用于计算不同天文周期和纪日周期在某个时刻处于什么位置。</p>https://yamayuki.space/posts/eb5f6c51d60a2d2dce4346bd77fed3da/Wed, 14 Oct 2026 00:00:00 +0800https://yamayuki.space/posts/eb5f6c51d60a2d2dce4346bd77fed3da/<h2 class="heading" id="一引入题目"> 一、引入题目 <a class="anchor" href="#%e4%b8%80%e5%bc%95%e5%85%a5%e9%a2%98%e7%9b%ae">#</a> </h2> <p>考虑一道数学题目：<strong>求 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>10</mn><mo stretchy="false">!</mo></mrow><annotation encoding="application/x-tex">10!</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6944em;"></span><span class="mord">10</span><span class="mclose">!</span></span></span></span> 除以 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>11</mn></mrow><annotation encoding="application/x-tex">11</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">11</span></span></span></span> 的余数。</strong></p> <p>我们要算的是 </p> <span class="katex-display"><span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML" display="block"><semantics><mrow><mn>10</mn><mo stretchy="false">!</mo><mo>=</mo><mn>1</mn><mo>⋅</mo><mn>2</mn><mo>⋅</mo><mn>3</mn><mo>⋅</mo><mn>4</mn><mo>⋅</mo><mn>5</mn><mo>⋅</mo><mn>6</mn><mo>⋅</mo><mn>7</mn><mo>⋅</mo><mn>8</mn><mo>⋅</mo><mn>9</mn><mo>⋅</mo><mn>10</mn></mrow><annotation encoding="application/x-tex"> 10!=1\cdot2\cdot3\cdot4\cdot5\cdot6\cdot7\cdot8\cdot9\cdot10 </annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6944em;"></span><span class="mord">10</span><span class="mclose">!</span><span class="mspace" style="margin-right:0.2778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2778em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">1</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">2</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">3</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">4</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">5</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">6</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">7</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">8</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">9</span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin">⋅</span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">10</span></span></span></span></span><p> 除以 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>11</mn></mrow><annotation encoding="application/x-tex">11</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">11</span></span></span></span> 后剩下多少，也就是求 <span class="katex"><span class="katex-mathml"><math xmlns="http://www.w3.org/1998/Math/MathML"><semantics><mrow><mn>10</mn><mo stretchy="false">!</mo><mtext> </mtext><mo lspace="0.22em" rspace="0.22em"><mrow><mi mathvariant="normal">m</mi><mi mathvariant="normal">o</mi><mi mathvariant="normal">d</mi></mrow></mo><mtext> </mtext><mn>11</mn></mrow><annotation encoding="application/x-tex">10!\bmod11</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="katex-base"><span class="katex-strut" style="height:0.6944em;"></span><span class="mord">10</span><span class="mclose">!</span><span class="mspace" style="margin-right:0.0556em;"></span><span class="mspace" style="margin-right:0.2222em;"></span><span class="mbin"><span class="mord"><span class="mord mathrm">mod</span></span></span><span class="mspace" style="margin-right:0.0556em;"></span><span class="mspace" style="margin-right:0.2222em;"></span></span><span class="katex-base"><span class="katex-strut" style="height:0.6444em;"></span><span class="mord">11</span></span></span></span>。</p> <p>这么长的一串乘积，怎样计算更方便？</p>https://yamayuki.space/posts/c45f5382759e56a9824135d28df3194f/Fri, 25 Sep 2026 00:00:00 +0800https://yamayuki.space/posts/c45f5382759e56a9824135d28df3194f/<h2 class="heading" id="一人工智能的价值对齐与认知边界"> 一、人工智能的价值对齐与认知边界 <a class="anchor" href="#%e4%b8%80%e4%ba%ba%e5%b7%a5%e6%99%ba%e8%83%bd%e7%9a%84%e4%bb%b7%e5%80%bc%e5%af%b9%e9%bd%90%e4%b8%8e%e8%ae%a4%e7%9f%a5%e8%be%b9%e7%95%8c">#</a> </h2> <h3 class="heading" id="1-价值对齐与知识生产方式的变化"> 1. 价值对齐与知识生产方式的变化 <a class="anchor" href="#1-%e4%bb%b7%e5%80%bc%e5%af%b9%e9%bd%90%e4%b8%8e%e7%9f%a5%e8%af%86%e7%94%9f%e4%ba%a7%e6%96%b9%e5%bc%8f%e7%9a%84%e5%8f%98%e5%8c%96">#</a> </h3> <p><strong>问题与背景</strong></p> <p>人工智能正在改变知识的生产、传播和使用方式。价值观具有模糊性、隐含性和冲突性，同一项技术可能同时涉及公平、隐私、效率等不同要求；“与谁的价值对齐”“对齐到什么程度”仍需结合具体情境讨论。</p>https://yamayuki.space/posts/ef6b725b0bff723d88b0cbb398db6bc7/Thu, 24 Sep 2026 00:00:00 +0800https://yamayuki.space/posts/ef6b725b0bff723d88b0cbb398db6bc7/<h2 class="heading" id="大模型与程序分析协同的代码审计"> 大模型与程序分析协同的代码审计 <a class="anchor" href="#%e5%a4%a7%e6%a8%a1%e5%9e%8b%e4%b8%8e%e7%a8%8b%e5%ba%8f%e5%88%86%e6%9e%90%e5%8d%8f%e5%90%8c%e7%9a%84%e4%bb%a3%e7%a0%81%e5%ae%a1%e8%ae%a1">#</a> </h2> <h3 class="heading" id="a1-大模型与程序分析技术协同"> A1. 大模型与程序分析技术协同 <a class="anchor" href="#a1-%e5%a4%a7%e6%a8%a1%e5%9e%8b%e4%b8%8e%e7%a8%8b%e5%ba%8f%e5%88%86%e6%9e%90%e6%8a%80%e6%9c%af%e5%8d%8f%e5%90%8c">#</a> </h3> <p><strong>问题与背景</strong></p> <p>任务能否正确完成存在随机性，重复运行结果容易不一致；不同上下文下容易失准，难以适配新语言、新项目。</p>