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local-search.xml
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<?xml version="1.0" encoding="utf-8"?>
<search>
<entry>
<title>使用Code Server容器部署VS Code Online</title>
<link href="/2021/082307.html"/>
<url>/2021/082307.html</url>
<content type="html"><![CDATA[<h1 id="使用code-server容器部署vs-code-online"><a class="markdownIt-Anchor" href="#使用code-server容器部署vs-code-online"></a> 使用Code Server容器部署VS Code Online</h1><h2 id="前言"><a class="markdownIt-Anchor" href="#前言"></a> 前言</h2><p>考虑到在服务器上直接部署Code Server将端口暴露，非常的不安全。这时候使用Docker将Code Server在容器中运行，相对来说会更加安全。但是在实际配置运行过程中会有各种的问题，如容器权限管理，SSL证书/HTTPS，Code Server更新等。根据实际过程的踩坑，将教程整理为本文。</p><h2 id="开始之前"><a class="markdownIt-Anchor" href="#开始之前"></a> 开始之前</h2><p>首先要准备一台服务器，Code Server文档的最低推荐配置是1GB of RAM，2 CPU Cores。<br />我选用的是腾讯云的轻量云服务器配置为2c4g8m，CentOS 7。</p><h2 id="docker-engine"><a class="markdownIt-Anchor" href="#docker-engine"></a> Docker Engine</h2><p>要在服务器运行Docker需要安装Docker Engine，建议通过Docker Docs给出的说明进行安装，非常不建议直接apt/yum安装仓库中的包（特别是CentOS这种以<s>老旧</s>稳定著称的发行版）。在<a href="https://docs.docker.com/engine/install/">文档</a>中选取对应系统，参照文档进行安装即可。<br />非root用户下运行docker请参考<a href="https://docs.docker.com/engine/install/linux-postinstall/">此文档</a></p><h2 id="code-server"><a class="markdownIt-Anchor" href="#code-server"></a> Code Server</h2><p>有关Code Server的介绍可以参考其<a href="https://coder.com/">官网</a>。从dockerhub中直接拉取最新的<a href="https://hub.docker.com/r/codercom/code-server">Code Server镜像</a>：</p><figure class="highlight bash"><table><tr><td class="gutter"><pre><span class="line">1</span><br></pre></td><td class="code"><pre><code class="hljs bash">docker pull codercom/code-server:latest<br></code></pre></td></tr></table></figure><p>Code Server镜像是基于Debian buster构建，非常干净，需要自己安装所需的软件包。由于我不止部署了一个Code Server（多人使用），考虑到不同的Code Server中版本升级和文件传输备份问题，所以我选择在服务器（宿主机）上每个Code Server容器创建对应的home文件夹，并挂载到容器/home/coder/（Code Server默认的home路径）。同时使用dockerfile来构建我所需的Code Server镜像（A在学习C，B只用Python）。</p><h3 id="dockerfile"><a class="markdownIt-Anchor" href="#dockerfile"></a> Dockerfile</h3><p>我需要分别构建C和Python的两个镜像（当然也可以一个里全装，就是镜像体积会很大）。</p><h4 id="dockerfile-for-python"><a class="markdownIt-Anchor" href="#dockerfile-for-python"></a> Dockerfile for Python</h4><p>多行写入其实可以用cat，但是在dockerfile中似乎语法不支持，只能用echo一行行写了。<br />当然apt在dockerfile的编译环境也是会报错的，要用apt-get。具体区别的话可以Google一下。</p><figure class="highlight dockerfile"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br></pre></td><td class="code"><pre><code class="hljs dockerfile"><span class="hljs-keyword">FROM</span> codercom/code-server<br><span class="hljs-keyword">RUN</span><span class="bash"> sudo mv /etc/apt/sources.list /etc/apt/sources.list.bak \</span><br><span class="bash"> && <span class="hljs-built_in">echo</span> <span class="hljs-string">'deb https://mirrors.tuna.tsinghua.edu.cn/debian/ buster main contrib non-free'</span> >> /home/coder/sources.list \</span><br><span class="bash"> && <span class="hljs-built_in">echo</span> <span class="hljs-string">'deb https://mirrors.tuna.tsinghua.edu.cn/debian/ buster-updates main contrib non-free'</span> >> /home/coder/sources.list \</span><br><span class="bash"> && <span class="hljs-built_in">echo</span> <span class="hljs-string">'deb https://mirrors.tuna.tsinghua.edu.cn/debian/ buster-backports main contrib non-free'</span> >> /home/coder/sources.list \</span><br><span class="bash"> && <span class="hljs-built_in">echo</span> <span class="hljs-string">'deb https://mirrors.tuna.tsinghua.edu.cn/debian-security buster/updates main contrib non-free'</span> >> /home/coder/sources.list \</span><br><span class="bash"> && sudo mv /home/coder/sources.list /etc/apt/ \</span><br><span class="bash"> && sudo apt-get update && sudo apt-get upgrade -y && sudo apt-get install -y fonts-powerline python3 python3-pip vim \</span><br><span class="bash"> && sudo apt-get clean</span><br></code></pre></td></tr></table></figure><h4 id="docker-for-ccpp"><a class="markdownIt-Anchor" href="#docker-for-ccpp"></a> Docker for C/Cpp</h4><figure class="highlight dockerfile"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br></pre></td><td class="code"><pre><code class="hljs dockerfile"><span class="hljs-keyword">FROM</span> codercom/code-server<br><span class="hljs-keyword">RUN</span><span class="bash"> sudo mv /etc/apt/sources.list /etc/apt/sources.list.bak \</span><br><span class="bash"> && <span class="hljs-built_in">echo</span> <span class="hljs-string">'deb https://mirrors.tuna.tsinghua.edu.cn/debian/ buster main contrib non-free'</span> >> /home/coder/sources.list \</span><br><span class="bash"> && <span class="hljs-built_in">echo</span> <span class="hljs-string">'deb https://mirrors.tuna.tsinghua.edu.cn/debian/ buster-updates main contrib non-free'</span> >> /home/coder/sources.list \</span><br><span class="bash"> && <span class="hljs-built_in">echo</span> <span class="hljs-string">'deb https://mirrors.tuna.tsinghua.edu.cn/debian/ buster-backports main contrib non-free'</span> >> /home/coder/sources.list \</span><br><span class="bash"> && <span class="hljs-built_in">echo</span> <span class="hljs-string">'deb https://mirrors.tuna.tsinghua.edu.cn/debian-security buster/updates main contrib non-free'</span> >> /home/coder/sources.list \</span><br><span class="bash"> && sudo mv /home/coder/sources.list /etc/apt/ \</span><br><span class="bash"> && sudo apt-get update && sudo apt-get upgrade -y && sudo apt-get install -y fonts-powerline build-essential gdb vim \</span><br><span class="bash"> && sudo apt-get clean </span><br></code></pre></td></tr></table></figure><h4 id="构建镜像"><a class="markdownIt-Anchor" href="#构建镜像"></a> 构建镜像</h4><p>参考docker build命令</p><figure class="highlight bash"><table><tr><td class="gutter"><pre><span class="line">1</span><br></pre></td><td class="code"><pre><code class="hljs bash">docker build -t 构建的镜像名字 -f dockerfile文件名 --no-cache . <br></code></pre></td></tr></table></figure><p>最后是有一点. 的指当前路径。</p><h2 id="运行code-server"><a class="markdownIt-Anchor" href="#运行code-server"></a> 运行Code Server</h2><p>Code Server是支持ssl证书的，参考其<a href="https://coder.com/docs/code-server/v3.11.1#tls-and-authentication-beta">文档</a>。因为我使用Code Server容器的话，所以直接在Docker运行配置中添加对应参数即可。运行命令如下：</p><figure class="highlight bash"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br></pre></td><td class="code"><pre><code class="hljs bash">docker run -dit --cap-add SYS_PTRACE --name 命名运行的容器 -p 0.0.0.0:8100:8080 \<br> -v /宿主机中的创建的home文件夹路径:/home/coder \<br> -v /宿主机中证书路径/cert.pem:/容器中证书路径/cert.pem \<br> -v /宿主机中公钥路径/key.pem:/容器中公钥路径/key.pem \<br> -u <span class="hljs-string">"<span class="hljs-subst">$(id -u)</span>:<span class="hljs-subst">$(id -g)</span>"</span> \<br> -e PASSWORD=设置的登录密码 \<br> 构建的镜像名字 --cert /容器中证书路径/cert.pem --cert-key /容器中公钥路径/key.pem<br></code></pre></td></tr></table></figure><ul><li>–cap-add SYS_PTRACE 给容器添加权限（否则gdb会无法运行）</li><li>–name 给运行容器命名（需要符合规范：英文字符1-英文字符2）</li><li>-p 0.0.0.0:8100:8080 8100是服务器（宿主机）上的端口也是实际访问的端口，需要在防火墙中放开，自行修改；8080是Code Server默认的运行端口不需要修改。</li></ul><h2 id="升级code-server"><a class="markdownIt-Anchor" href="#升级code-server"></a> 升级Code Server</h2><p>在容器中直接运行Code Server的升级命令应该是可以的，但是我<s>有洁癖</s>不是很喜欢。使用dockerfile构建镜像，home目录本地挂载使得可以直接删除镜像，重复build镜像和run容器（使用与之前完全相同的命令），就可实现更新Code Server，同时保留所有扩展设置和文件。</p><h2 id="references"><a class="markdownIt-Anchor" href="#references"></a> References</h2><ul><li><a href="https://coder.com/docs/code-server/v3.11.1">Coder Docs</a></li><li><a href="https://github.com/cdr/code-server/discussions/2595">Not Serving HTTPS</a></li><li><a href="https://www.cnblogs.com/davis12/p/14453690.html">docker容器权限设置</a></li><li><a href="https://blog.csdn.net/Gamish/article/details/81632862?utm_medium=distribute.pc_relevant.none-task-blog-BlogCommendFromMachineLearnPai2-3.control&depth_1-utm_source=distribute.pc_relevant.none-task-blog-BlogCommendFromMachineLearnPai2-3.control">gdb调试运行中的进程报错</a></li></ul>]]></content>
<tags>
<tag>Cloud</tag>
<tag>Code</tag>
<tag>Container</tag>
</tags>
</entry>
<entry>
<title>Slurm 作业调度系统使用指南</title>
<link href="/2021/031100.html"/>
<url>/2021/031100.html</url>
<content type="html"><![CDATA[<h1 id="slurm-作业调度系统使用指南"><a class="markdownIt-Anchor" href="#slurm-作业调度系统使用指南"></a> Slurm 作业调度系统使用指南</h1><h2 id="1-slurm-命令"><a class="markdownIt-Anchor" href="#1-slurm-命令"></a> 1. Slurm 命令</h2><table><thead><tr><th style="text-align:center">Slurm命令</th><th style="text-align:center">功能</th></tr></thead><tbody><tr><td style="text-align:center">sinfo</td><td style="text-align:center">查看集群分区状态</td></tr><tr><td style="text-align:center">squeue</td><td style="text-align:center">查看作业队列</td></tr><tr><td style="text-align:center">srun, salloc</td><td style="text-align:center">交互式运行作业</td></tr><tr><td style="text-align:center">sbatch</td><td style="text-align:center">提交作业</td></tr><tr><td style="text-align:center">scancel</td><td style="text-align:center">取消作业</td></tr><tr><td style="text-align:center">scontrol</td><td style="text-align:center">查看和修改作业参数</td></tr></tbody></table><h2 id="2-sinfo"><a class="markdownIt-Anchor" href="#2-sinfo"></a> 2. Sinfo</h2><figure class="highlight bash"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br></pre></td><td class="code"><pre><code class="hljs bash">sinfo<span class="hljs-comment">#查看所有分区状态</span><br>sinfo -a<span class="hljs-comment">#查看所有分区状态</span><br>sinfo -N<span class="hljs-comment">#查看节点状态</span><br>sinfo -n node-name<span class="hljs-comment">#查看指定节点状态</span><br>sinfo --<span class="hljs-built_in">help</span><span class="hljs-comment">#查看sinfo的说明</span><br></code></pre></td></tr></table></figure><h3 id="21-节点状态"><a class="markdownIt-Anchor" href="#21-节点状态"></a> 2.1 节点状态</h3><table><thead><tr><th style="text-align:center">alloc</th><th style="text-align:center">idle</th><th style="text-align:center">mix</th><th style="text-align:center">down</th><th style="text-align:center">drain</th></tr></thead><tbody><tr><td style="text-align:center">节点在用</td><td style="text-align:center">节点可用</td><td style="text-align:center">部分占用</td><td style="text-align:center">节点下线</td><td style="text-align:center">节点故障</td></tr></tbody></table><h2 id="3-squeue"><a class="markdownIt-Anchor" href="#3-squeue"></a> 3. Squeue</h2><figure class="highlight bash"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br></pre></td><td class="code"><pre><code class="hljs bash">squeue<span class="hljs-comment">#查看运行中的作业列表</span><br>squeue -l<span class="hljs-comment">#查看列表细节信息</span><br>squene -j job-id<span class="hljs-comment">#查看运行中作业信息</span><br>squeue -u username<span class="hljs-comment">#查看user所有运行中的作业</span><br></code></pre></td></tr></table></figure><h3 id="31-作业状态"><a class="markdownIt-Anchor" href="#31-作业状态"></a> 3.1 作业状态</h3><table><thead><tr><th style="text-align:center">R</th><th style="text-align:center">PD</th><th style="text-align:center">CG</th><th style="text-align:center">CD</th></tr></thead><tbody><tr><td style="text-align:center">正在运行</td><td style="text-align:center">正在排队</td><td style="text-align:center">即将完成</td><td style="text-align:center">已完成</td></tr></tbody></table><h2 id="4-提交作业"><a class="markdownIt-Anchor" href="#4-提交作业"></a> 4. 提交作业</h2><p>Slurm提交作业有3种模式，分别为交互模式，批处理模式，分配模式，这三种方式只是用户使用方式的区别，在管理，调度，记账时同等对待。</p><h3 id="41-参数说明"><a class="markdownIt-Anchor" href="#41-参数说明"></a> 4.1 参数说明</h3><p>以下所有参数在 <code>srun, sbatch, salloc</code> 中均可以使用。更多参数见<code>srun --help</code>, <code>sbatch --help</code>, <code>salloc --help</code>。</p><figure class="highlight bash"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br></pre></td><td class="code"><pre><code class="hljs bash">-c, --cpu-per-task=NCPUs<span class="hljs-comment">#指定每个进程使用核数，不指定默认为1</span><br>-e, --error=error_filename<span class="hljs-comment">#指定错误文件输出</span><br>-J, --job-name=JOBNAME<span class="hljs-comment">#指定作业名称</span><br>--mail-type=END/FAIL/ALL<span class="hljs-comment">#邮件提醒，可选:END,FAIL,ALL</span><br>--mail-user=mail_address<span class="hljs-comment">#通知邮箱地址</span><br>-n, --ntask=NTASKs <span class="hljs-comment">#指定总进程数；不使用cpus-per-task，可理解为进程数即为核数 </span><br>--ntask-per-node=N <span class="hljs-comment">#指定每个节点进程数/核数，使用-n参数后变为每个节点最多运行的进程数</span><br>-N, --nodes=N<span class="hljs-comment">#指定节点数量</span><br>-o, --output=out_filename<span class="hljs-comment">#指定输出文件输出</span><br>-p, --partion=debug<span class="hljs-comment">#指定分区</span><br>-t, --time=dd-hh:mm:ss<span class="hljs-comment">#作业最大运行时间</span><br>-w, --nodelist=node[1,2]<span class="hljs-comment">#指定优先使用节点，不可与避免节点冲突</span><br>-x, --exclude=node[3,5-6]<span class="hljs-comment">#指定避免使用节点，不可与优先节点冲突</span><br>--mem-per-cpu=MB<span class="hljs-comment">#指定计算cpu最大占用内存大小</span><br></code></pre></td></tr></table></figure><h3 id="42-交互模式-srun"><a class="markdownIt-Anchor" href="#42-交互模式-srun"></a> 4.2 交互模式 Srun</h3><p>交互式作业提交，提交命令后，等待作业执行完成之后返回命令行窗口。</p><h4 id="demo-of-srun"><a class="markdownIt-Anchor" href="#demo-of-srun"></a> Demo of srun</h4><figure class="highlight bash"><table><tr><td class="gutter"><pre><span class="line">1</span><br></pre></td><td class="code"><pre><code class="hljs bash">srun -J JOBNAME -p debug -N 2 -c 1 -n 32 --ntasks-per-node=16 -w node[3,4] -x node[1,5-6] --time=dd-hh:mm:ss --output=file_name --error=file_name --mail-user=address --mail-type=ALL mpirun -n 64 ./iPic3D ./inputfile/test.inp<br></code></pre></td></tr></table></figure><p>同 <strong>Demo of sbatch</strong></p><h3 id="43-批处理模式-sbatch"><a class="markdownIt-Anchor" href="#43-批处理模式-sbatch"></a> 4.3 批处理模式 Sbatch</h3><p>批处理作业是指用户编写作业脚本，指定资源需求约束，提交后台执行作业。提交批处理作业的命令为 sbatch，用户提交命令即返回命令行窗口，但此时作业在进入调度状态，在资源满足要求时，分配完计算结点之后，系统将在所分配的第一个计算结点（而不是登录结点）上加载执行用户的作业脚本。批处理作业的脚本为一个文本文件，脚本第一行以 “#!” 字符开头，并制定脚本文件的解释程序，如 sh，bash。由于计算节点为精简环境，只提供 sh 和 bash 的默认支持。</p><p>运行 <code>sbatch filename</code> 来提交任务；计算开始后，工作目录中会生成以 slurm 开头的.out 文件为输出文件（不指定输出的话）。</p><h4 id="demo-of-sbatch"><a class="markdownIt-Anchor" href="#demo-of-sbatch"></a> Demo of sbatch</h4><p>保存在运行程序目录下即可，文件名随意（可以无后缀，内容文本格式即可）；作业提交命令<code>sbatch filename</code></p><figure class="highlight bash"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br></pre></td><td class="code"><pre><code class="hljs bash"><span class="hljs-meta">#!/bin/bash </span><br><span class="hljs-comment">#提交单个作业</span><br><span class="hljs-comment">#SBATCH --job-name=JOBNAME%指定作业名称</span><br><span class="hljs-comment">#SBATCH --partition=debug%指定分区</span><br><span class="hljs-comment">#SBATCH --nodes=2%指定节点数量</span><br><span class="hljs-comment">#SBATCH --cpus-per-task=1%指定每个进程使用核数，不指定默认为1</span><br><span class="hljs-comment">#SBATCH -n 32 %指定总进程数；不使用cpus-per-task，可理解为进程数即为核数</span><br><span class="hljs-comment">#SBATCH --ntasks-per-node=16%指定每个节点进程数/核数,使用-n参数（优先级更高），变为每个节点最多运行的任务数</span><br><span class="hljs-comment">#SBATCH --nodelist=node[3,4]%指定优先使用节点</span><br><span class="hljs-comment">#SBATCH --exclude=node[1,5-6]%指定避免使用节点</span><br><span class="hljs-comment">#SBATCH --time=dd-hh:mm:ss%作业最大运行时长，参考格式填写</span><br><span class="hljs-comment">#SBATCH --output=file_name%指定输出文件输出</span><br><span class="hljs-comment">#SBATCH --error=file_name%指定错误文件输出</span><br><span class="hljs-comment">#SBATCH --mail-type=ALL%邮件提醒,可选:END,FAIL,ALL</span><br><span class="hljs-comment">#SBATCH --mail-user=address%通知邮箱地址</span><br><br><span class="hljs-built_in">source</span> /public/home/yyhua/.bashrc<span class="hljs-comment">#导入环境变量文件</span><br><br>mpirun -n 32 ./iPic3D ./inputfiles/test.inp<span class="hljs-comment">#运行命令</span><br></code></pre></td></tr></table></figure><p>同 <strong>Demo of srun</strong></p><h3 id="44-分配模式-salloc"><a class="markdownIt-Anchor" href="#44-分配模式-salloc"></a> 4.4 分配模式 Salloc</h3><p>结点资源抢占命令。该命令支持用户在提交作业前，抢占所需计算资源（此时开始计算所用机时）。需请求资源，然后在获取节点后登录到计算节点，暂不适用组里服务器。</p><h2 id="5-scontrol"><a class="markdownIt-Anchor" href="#5-scontrol"></a> 5. Scontrol</h2><h3 id="51-信息查看"><a class="markdownIt-Anchor" href="#51-信息查看"></a> 5.1 信息查看</h3><figure class="highlight bash"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br></pre></td><td class="code"><pre><code class="hljs bash">scontrol show job JOBID <span class="hljs-comment">#查看作业的详细信息</span><br>scontrol show node <span class="hljs-comment">#查看所有节点详细信息</span><br>scontrol show node node-name <span class="hljs-comment">#查看指定节点详细信息</span><br>scontrol show node | grep CPU <span class="hljs-comment">#查看各节点cpu状态</span><br>scontrol show node node-name | grep CPU <span class="hljs-comment">#查看指定节点cpu状态</span><br></code></pre></td></tr></table></figure><h3 id="52-更新作业"><a class="markdownIt-Anchor" href="#52-更新作业"></a> 5.2 更新作业</h3><p>在任务开始前却发现作业的属性写错了（例如提交错了分区，修改名字），取消了重新排队似乎很不划算。如果作业恰好 <strong>没在运行</strong>，我们是可以通过 <code>scontrol</code> 命令来更新作业的属性</p><figure class="highlight bash"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br></pre></td><td class="code"><pre><code class="hljs bash">scontrol update jobid=JOBID ... <span class="hljs-comment">#...为下面参数</span><br>reqnodelist=<nodes><br>reqcores=<count><br>name=<name><br>nodelist=<nodes><br>excnodelist=<nodes><br>numcpus=<min_count-max_count><br>numnodes=<min_count-max_count><br>numtasks=<count><br>starttime=yyyy-mm-dd<br>partition=<name><br>timelimit=d-h:m:s<br>mincpusnode=<count><br>minmemorycpu=<megabytes><br>minmemorynode=<megabytes><br></code></pre></td></tr></table></figure><h2 id="references"><a class="markdownIt-Anchor" href="#references"></a> References</h2><ol><li><a href="https://hpc.pku.edu.cn/_book/guide/slurm/slurm.html">作业调度系统 · 北京大学高性能计算使用指南</a></li><li><a href="http://bicmr.pku.edu.cn/~wenzw/pages/slurm.html">SLURM 使用参考</a></li><li><a href="https://docs.hpc.sjtu.edu.cn/job/slurm.html">Slurm 作业调度系统 — 上海交大超算平台用户手册 文档</a></li><li><a href="https://www.hpccube.com/wiki/index.php/SLURM%E4%BD%BF%E7%94%A8%E5%9F%BA%E7%A1%80%E6%95%99%E7%A8%8B">SLURM使用基础教程 - 曙光先进计算</a></li><li><a href="https://arc.umich.edu/greatlakes/slurm-user-guide/">Slurm User Guide for Great Lakes | ITS Advanced Research Computing</a></li></ol>]]></content>
<tags>
<tag>Code</tag>
<tag>Notes</tag>
</tags>
</entry>
<entry>
<title>WSL2 中 Fedora Remix 版本升级</title>
<link href="/2020/122110.html"/>
<url>/2020/122110.html</url>
<content type="html"><![CDATA[<h1 id="wsl2-中-fedora-remix-版本升级"><a class="markdownIt-Anchor" href="#wsl2-中-fedora-remix-版本升级"></a> WSL2 中 Fedora Remix 版本升级</h1><h2 id="backup-optional"><a class="markdownIt-Anchor" href="#backup-optional"></a> Backup (Optional)</h2><p>Execute the command in CMD or PowerShell:</p><figure class="highlight livescript"><table><tr><td class="gutter"><pre><span class="line">1</span><br></pre></td><td class="code"><pre><code class="hljs livescript">wsl --<span class="hljs-keyword">export</span> fedoraremix path_u_wanna<span class="hljs-string">\fedoraremix_backup.tar.gz</span><br></code></pre></td></tr></table></figure><h2 id="fresh-up"><a class="markdownIt-Anchor" href="#fresh-up"></a> Fresh Up</h2><figure class="highlight ada"><table><tr><td class="gutter"><pre><span class="line">1</span><br></pre></td><td class="code"><pre><code class="hljs ada">sudo dnf upgrade <span class="hljs-comment">--refresh</span><br></code></pre></td></tr></table></figure><h2 id="install-upgrade-plugin"><a class="markdownIt-Anchor" href="#install-upgrade-plugin"></a> Install Upgrade Plugin</h2><figure class="highlight clean"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br></pre></td><td class="code"><pre><code class="hljs clean">sudo dnf install dnf-plugin-<span class="hljs-keyword">system</span>-upgrade<br><br></code></pre></td></tr></table></figure><h2 id="download-new-release-packages"><a class="markdownIt-Anchor" href="#download-new-release-packages"></a> Download New release Packages</h2><figure class="highlight livecodeserver"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br></pre></td><td class="code"><pre><code class="hljs livecodeserver">sudo dnf <span class="hljs-keyword">system</span>-upgrade download <span class="hljs-comment">--releasever=33 </span><br><br>Optional:<br>% <span class="hljs-comment">--allowerasing 删除依赖损坏的包</span><br>% <span class="hljs-comment">--skip-broken </span><br><br></code></pre></td></tr></table></figure><h2 id="reboot"><a class="markdownIt-Anchor" href="#reboot"></a> Reboot</h2><figure class="highlight clean"><table><tr><td class="gutter"><pre><span class="line">1</span><br></pre></td><td class="code"><pre><code class="hljs clean">sudo dnf <span class="hljs-keyword">system</span>-upgrade reboot<br></code></pre></td></tr></table></figure><p>But it will see a error like this:</p><figure class="highlight vbnet"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br></pre></td><td class="code"><pre><code class="hljs vbnet">System has <span class="hljs-built_in">not</span> been booted <span class="hljs-keyword">with</span> systemd <span class="hljs-keyword">as</span> init system (PID <span class="hljs-number">1</span>). Can<span class="hljs-comment">'t operate.</span><br>Failed <span class="hljs-keyword">to</span> connect <span class="hljs-keyword">to</span> bus: Host <span class="hljs-built_in">is</span> down.<br></code></pre></td></tr></table></figure><p>Don’t worry, and ignore it.</p><h2 id="upgrade"><a class="markdownIt-Anchor" href="#upgrade"></a> Upgrade</h2><figure class="highlight clean"><table><tr><td class="gutter"><pre><span class="line">1</span><br></pre></td><td class="code"><pre><code class="hljs clean">sudo dnf <span class="hljs-keyword">system</span>-upgrade upgrade<br></code></pre></td></tr></table></figure><p>Now, system upgrade is finished.</p><h2 id="rebuild-rpm-database"><a class="markdownIt-Anchor" href="#rebuild-rpm-database"></a> Rebuild RPM Database</h2><figure class="highlight ada"><table><tr><td class="gutter"><pre><span class="line">1</span><br></pre></td><td class="code"><pre><code class="hljs ada">sudo rpmdb <span class="hljs-comment">--rebuilddb</span><br></code></pre></td></tr></table></figure><h2 id="clean-useless-packages-and-depends"><a class="markdownIt-Anchor" href="#clean-useless-packages-and-depends"></a> Clean Useless Packages and Depends</h2><figure class="highlight ada"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br></pre></td><td class="code"><pre><code class="hljs ada">sudo dnf -y autoremove<br>sudo dnf -y clean <span class="hljs-keyword">all</span><br></code></pre></td></tr></table></figure><h2 id="check-version"><a class="markdownIt-Anchor" href="#check-version"></a> Check Version</h2><p>These two commands are all avilable:</p><figure class="highlight awk"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br></pre></td><td class="code"><pre><code class="hljs awk">wslsys<br>cat <span class="hljs-regexp">/etc/</span>fedora-release<br></code></pre></td></tr></table></figure><h2 id="reference"><a class="markdownIt-Anchor" href="#reference"></a> Reference</h2><ol><li><a href="https://www.whitewaterfoundry.com/blog/2019/11/3/upgrade-fedora-remix-for-wsl-to-31">Upgrade Fedora Remix for WSL to 31</a></li><li><a href="https://www.whitewaterfoundry.com/blog/2019/11/3/upgrade-fedora-remix-for-wsl-to-31-2a7z8">Upgrade Fedora Remix for WSL to 32 (for WSL 2 only)</a></li></ol>]]></content>
<tags>
<tag>Linux</tag>
</tags>
</entry>
<entry>
<title>校园网使用指南之教育邮箱</title>
<link href="/2020/032417.html"/>
<url>/2020/032417.html</url>
<content type="html"><![CDATA[<h1 id="校园网使用指南之教育邮箱"><a class="markdownIt-Anchor" href="#校园网使用指南之教育邮箱"></a> 校园网使用指南之教育邮箱</h1><p><strong>------哈尔滨工业大学 电脑110俱乐部 & 网络与信息中心 制------</strong></p><p>众所周知，高校及科研院所拥有edu或ac的域名，并使用其专属的域名邮箱，也称教育邮箱或单位邮箱；该邮箱系统由所属单位自行运行和维护，保证安全性；同时教育邮箱具有身份标识的作用，在邮件交流中，具有一定的便利性。还可以通过教育邮箱来获取软件，购物，出行等的教育优惠。</p><p>本文主要介绍工大教育邮箱的获取，使用，客户端配置，最后会总结一些教育优惠活动。</p><h2 id="工大邮箱的基本情况"><a class="markdownIt-Anchor" href="#工大邮箱的基本情况"></a> 工大邮箱的基本情况</h2><p>工大邮箱由<a href="http://ito.hit.edu.cn/">网络与信息中心</a>提供服务，网页版<a href="mail.hit.edu.cn">邮箱主页</a>，客户端一般需手动配置，老师账号为 <em><a href="mailto:[email protected]">[email protected]</a></em>，学生账号为 <em><a href="mailto:[email protected]">[email protected]</a></em>。学生账号使用期为最长为4年（研究生 2年，博士 NaN年），将在毕业当年12月31日收回邮箱。</p><h2 id="申请流程"><a class="markdownIt-Anchor" href="#申请流程"></a> 申请流程</h2><p>目前可以通过3种方式获取工大的教育邮箱：</p><h3 id="入学激活"><a class="markdownIt-Anchor" href="#入学激活"></a> 入学激活</h3><p>入学迎新系统中，可直接激活邮箱并进行密码设置。</p><h3 id="在校激活"><a class="markdownIt-Anchor" href="#在校激活"></a> 在校激活</h3><p>携带学生卡，至明德楼师生服务大厅的网络中心窗口，办理邮箱开户。（老师仅可在校进行激活，携带工作证件）</p><h3 id="在线激活"><a class="markdownIt-Anchor" href="#在线激活"></a> 在线激活</h3><ol><li><p>关注微信公众号 <strong>哈尔滨工业大学服务号</strong></p></li><li><p>进入 <strong>服务大厅</strong>，并完成统一认证绑定</p></li><li><p>进入 <strong>服务列表</strong></p></li></ol><p><img src="https://i.loli.net/2020/03/25/oPBvDrcShRmTpub.jpg" alt="1.jpg" /></p><ol start="4"><li>在 <strong>服务列表</strong> 中找到 <strong>网络信息</strong> 栏，点击 <strong>学生邮箱激活</strong></li></ol><p><img src="https://i.loli.net/2020/03/25/oQD9dL1hxkPMBFA.jpg" alt="2.jpg" /></p><ol start="5"><li>根据提示设置密码进行激活；由于绑定了统一认证，邮箱账号名会自动生成，设置 邮箱密码激活即可。</li></ol><h2 id="网页版使用"><a class="markdownIt-Anchor" href="#网页版使用"></a> 网页版使用</h2><ol><li>网页版<a href="https://mail.hit.edu.cn/">邮箱主页</a>，进入登录界面，输入账户和密码（邮箱密码由自己单独设置，而非统一认证密码）<br />在灰色打码区域输入学号/用户名，<a href="http://xn--stu-u33et94ayklm64adsqo78a.hit.edu.cn">学生后缀选择stu.hit.edu.cn</a>，<a href="http://xn--hit-u33e396bf8gg86cxxbo58d.edu.cn">老师后缀选择hit.edu.cn</a>。</li></ol><p><img src="https://i.loli.net/2020/03/25/wsXSiWEruv4jzZF.jpg" alt="mail1.jpg" /></p><ol start="2"><li><p>登录后默认进入收件箱，UI界面清晰，进行对应操作即可；左下角为帮助中心和设置。</p><p>帮助中心内有全面的使用指南，设置内可设置签名，过滤规则等</p><p><img src="https://i.loli.net/2020/03/25/Lgtba5jQ3BKFMuo.jpg" alt="mail2.jpg" /></p></li></ol><h2 id="客户端配置"><a class="markdownIt-Anchor" href="#客户端配置"></a> 客户端配置</h2><p>这部分为如何通过客户端（Android/iOS/Windows系统自带的Email，Outlook等邮件软件）使用工大邮箱；在邮件系统的帮助中心中提供了一系列指南，以下内容做个总结。</p><h3 id="协议"><a class="markdownIt-Anchor" href="#协议"></a> 协议</h3><p>目前邮件访问标准协议为 POP3 和 IMAP/SMTP：</p><h4 id="pop3"><a class="markdownIt-Anchor" href="#pop3"></a> POP3</h4><p>POP3是Post Office Protocol 3的简称，即邮局协议的第3个版本，它规定怎样将个人计算机连接到Internet的邮件服务器和下载电子邮件的电子协议。它是因特网电子邮件的第一个离线协议标准，POP3允许用户从服务器上把邮件存储到本地主机（即自己的计算机）上，同时删除保存在邮件服务器上的邮件。</p><h4 id="imap"><a class="markdownIt-Anchor" href="#imap"></a> IMAP</h4><p>IMAP全称是Internet Mail Access Protocol，即交互式邮件存取协议，它是跟POP3类似邮件访问标准协议之一。不同的是，开启了IMAP后，您在电子邮件客户端收取的邮件仍然保留在服务器上，同时在客户端上的操作都会反馈到服务器上，如：删除邮件，标记已读等，服务器上的邮件也会做相应的动作。所以无论从浏览器登录邮箱或者客户端软件登录邮箱，看到的邮件以及状态都是一致的。</p><h4 id="smtp"><a class="markdownIt-Anchor" href="#smtp"></a> SMTP</h4><p>SMTP 的全称是“Simple Mail Transfer Protocol”，即简单邮件传输协议。它是一组用于从源地址到目的地址传输邮件的规范，通过它来控制邮件的中转方式。SMTP 协议属于 TCP/IP 协议簇，它帮助每台计算机在发送或中转信件时找到下一个目的地。</p><h3 id="配置客户端"><a class="markdownIt-Anchor" href="#配置客户端"></a> 配置客户端</h3><p>哈尔滨工业大学电子邮件系统客户端收发服务器及对应端口：</p><figure class="highlight stylus"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br></pre></td><td class="code"><pre><code class="hljs stylus">POP3：pop3<span class="hljs-selector-class">.hit</span><span class="hljs-selector-class">.edu</span><span class="hljs-selector-class">.cn</span> 端口：<span class="hljs-number">110</span> SSL加密端口：<span class="hljs-number">995</span><br>IMAP：imap<span class="hljs-selector-class">.hit</span><span class="hljs-selector-class">.edu</span><span class="hljs-selector-class">.cn</span> 端口：<span class="hljs-number">143</span> SSL加密端口：<span class="hljs-number">993</span><br>SMTP：smtp<span class="hljs-selector-class">.hit</span><span class="hljs-selector-class">.edu</span><span class="hljs-selector-class">.cn</span> 端口：<span class="hljs-number">25</span> SSL加密端口：<span class="hljs-number">465</span><br></code></pre></td></tr></table></figure><p>这里推荐使用IMAP/SMTP，不建议使用POP3；建议开启SSL加密。</p><p>以下以 Outlook 为例，其他客户端操作是一致的。</p><ol><li><p><strong>添加账户</strong></p><p><img src="https://i.loli.net/2020/03/25/oyBL1Te9lVJY2w5.jpg" alt="mail3.jpg" /></p></li><li><p>填写邮箱地址，选择 <strong>IMAP</strong></p><p><img src="https://i.loli.net/2020/03/25/YLg3PlQajAwt2kn.jpg" alt="mail4.jpg" /></p></li><li><p>填写送/收信服务器，加密方式选择 <strong>SSL/TLS</strong>，填写对应 <strong>加密端口</strong>（无加密方式则输入<strong>端口</strong>，部分客户端只需填写服务器地址，无需输入端口）</p><p><img src="https://i.loli.net/2020/03/25/VNm3ACiTZzhwH6B.jpg" alt="mail5.jpg" /></p></li><li><p>等待连接，会显示添加成功</p><p><img src="https://i.loli.net/2020/03/25/zgJQlS8Bf6XMj5G.jpg" alt="mail6.jpg" /></p></li></ol><h2 id="安全设置"><a class="markdownIt-Anchor" href="#安全设置"></a> 安全设置</h2><h3 id="重置密码"><a class="markdownIt-Anchor" href="#重置密码"></a> 重置密码</h3><p>目前重置密码有三种方式：通过绑定手机重置，安全问题重置，线下窗口重置<br /><strong>！！！强烈建议绑定手机，及设置安全问题！！！</strong></p><h4 id="绑定手机"><a class="markdownIt-Anchor" href="#绑定手机"></a> 绑定手机</h4><p>登录网页版后，点击左下角 <strong>设置</strong>，选择 <strong>高级功能 - 手机绑定</strong>，通过短信验证码完成绑定</p><p><img src="https://i.loli.net/2020/03/25/rOjZ8dmvMnfUP29.jpg" alt="mail7.jpg" /></p><h4 id="安全问题"><a class="markdownIt-Anchor" href="#安全问题"></a> 安全问题</h4><p>登录网页版后，点击左下角 <strong>设置</strong>，选择 <strong>个人信息 - 密码保护</strong>，设置密保问题</p><p><img src="https://i.loli.net/2020/03/25/QRIqJthAETox65a.jpg" alt="mail8.jpg" /></p><h4 id="重置密码-2"><a class="markdownIt-Anchor" href="#重置密码-2"></a> 重置密码</h4><p>访问网页版登录界面，点击登录下方 <strong>忘记密码</strong>，根据操作提示进行密码重置</p><p><img src="https://i.loli.net/2020/03/25/WYrMTRh7S6os2gP.jpg" alt="MAIL11.jpg" /></p><h4 id="线下重置"><a class="markdownIt-Anchor" href="#线下重置"></a> 线下重置</h4><p>持学生卡或工作证，至明德楼师生服务大厅网络中心窗口，办理邮箱密码重置。</p><h3 id="二次验证"><a class="markdownIt-Anchor" href="#二次验证"></a> 二次验证</h3><h4 id="二次验证-2"><a class="markdownIt-Anchor" href="#二次验证-2"></a> 二次验证</h4><p>登录网页版后，点击左下角 <strong>设置</strong>，选择 <strong>安全设置 - 二次验证设置</strong>，通过短信验证码<br />每次网页版登录邮箱时，需要通过“帐号密码验证”和“安全验证”两步才能登录邮箱，提高安全性（不影响客户端收发信；建议完成客户端配置后，在开启二次验证）</p><p><img src="https://i.loli.net/2020/03/25/CdsecHWJDX2YVKZ.jpg" alt="mail9.jpg" /></p><h4 id="可信任设备"><a class="markdownIt-Anchor" href="#可信任设备"></a> 可信任设备</h4><p>在开启二次验证情况下，可在<strong>安全设置 - 登录设备查询</strong> 中，添加 <strong>可信任设备</strong>，登录时则无需二次验证</p><p><img src="https://i.loli.net/2020/03/25/TevW5BE1ZcIoqJn.jpg" alt="mail10.jpg" /></p><h2 id="问题反馈"><a class="markdownIt-Anchor" href="#问题反馈"></a> 问题反馈</h2><p>如果在邮箱使用中遇到问题，可参考提供的<a href="https://mail.hit.edu.cn/coremail/help/index_zh_CN.jsp">帮助文档</a>；自主无法解决，请发送邮件至[email protected]，或拨打 0451-86414659 进行反馈和处理。</p><p>客户端收发信问题，请在网页版进行再次尝试，如再次出现，请上报反馈；仅客户端问题，请参考<a href="https://mail.hit.edu.cn/coremail/help/index_zh_CN.jsp">帮助文档</a>；或联系客户端开发人员，网上查找解决方案，客户端不在网络中心技术支持范围。</p><h2 id="教育优惠"><a class="markdownIt-Anchor" href="#教育优惠"></a> 教育优惠</h2><ul><li><p><a href="https://www.apple.com.cn/cn-k12/shop">Apple教育商店</a></p><p>95折优惠，暑假活动购买赠送Beats耳机</p></li><li><p><a href="https://support.apple.com/zh-cn/HT205928">Apple Music 教育优惠</a></p><p>￥5/月，半价订阅，有效期3年</p></li><li><p><a href="https://www.microsoftstore.com.cn/student">Microsoft 教育优惠</a></p><p>教育专区硬件及软件 原价9折优惠</p></li><li><p><a href="https://www.microsoft.com/zh-cn/education/products/office">Office 356 A1</a></p><p>在线版Office，1T OneDrive，工大的目前由微软管理，有效期13年（继续使用需要验证邮箱）</p></li><li><p><a href="https://azureforeducation.microsoft.com/zh-cn/Institutions">Microsoft Azure</a></p><p>$100 额度，有效期1年</p></li><li><p><a href="https://www.jetbrains.com/zh/student/">JetBrains 学生开发授权</a></p><p>JetBrains全部产品免费，有效期1年，到期再次申请即可</p></li><li><p><a href="https://education.github.com/pack">GitHub 学生开发工具包</a></p><ul><li>AWS $75 - 150 额度</li><li>DigitalOcean $50 额度</li><li>Namecheap .me域名 1年免费及SSL证书服务</li><li>…</li></ul></li><li><p><a href="https://www.autodesk.com.cn/education/free-software/featured">AutoDesk 教育社区</a></p><p>AutoDesk全部产品的教育版许可，有效期3年</p></li><li><p><a href="https://www.ansys.com/zh-CN/academic/free-student-products">Ansys Student</a></p><p>包含 Discovery Live, Discovery AIM, Ansys, SCADE</p></li><li><p><a href="https://software.intel.com/zh-cn/articles/qualify-for-free-software">Intel® Software Development Tools</a></p><p>高性能计算，Intel开发套件，包含 Parallel Studio XE, Distribution for Python,System Studio</p></li><li><p><a href="https://www.tableau.com/zh-cn/academic/students">Tableau 学生版</a></p><p>数据可视化软件，1年许可；教师使用 <a href="https://www.tableau.com/zh-cn/academic/teaching">教学版</a> 免费</p></li><li><p><a href="https://www.lindo.com/index.php/ls-downloads/try-lingo">Lingo 教育版</a></p><p>无法在线获取许可，需要使用教育邮箱给 <a href="mailto:[email protected]">[email protected]</a> 发送申请邮件，一个邮箱只能获取1次4个月许可</p></li><li><p><a href="https://www.originlab.com/OriginProLearning.aspx">OriginPro</a></p><p>单台设备，6个月许可，窗口限制数12</p></li><li><p><a href="https://www.altium.com.cn/solutions/academic-programs/student-licenses">Altium Designer</a></p><p>许可证每6个月验证一次</p></li><li><p><a href="https://www.ti.com/">TI 开发板申请</a></p><p>现在限制的很严了，应该是一个账户只能申请一张</p></li><li><p><a href="https://camscanner.com/">全能扫描王</a></p><p>使用教育邮箱注册，并登录应用，自动获取教育专享权益，有效期1年（到期延长期限需要验证教育邮箱）；没有内置广告，pdf无水印，OCR，额外200M云储存</p></li><li><p>还有很多专业软件Adobe，CATIA，SolidWorks，Mathematica等均提供教育优惠购买</p></li><li><p>吃住行的优惠，一般不需要教育邮箱，再次不做赘述了</p></li></ul><h2 id="have-fun-in-hit-_"><a class="markdownIt-Anchor" href="#have-fun-in-hit-_"></a> Have Fun in HIT ! >_<</h2>]]></content>
<categories>
<category>HIT Network Guide</category>
</categories>
<tags>
<tag>HIT</tag>
<tag>Guide</tag>
</tags>
</entry>
<entry>
<title>LaTeX数学笔记</title>
<link href="/2020/032302.html"/>
<url>/2020/032302.html</url>
<content type="html"><![CDATA[<h1 id="latex-数学笔记"><a class="markdownIt-Anchor" href="#latex-数学笔记"></a> <em>LaTeX</em> 数学笔记</h1><h2 id="希腊字母"><a class="markdownIt-Anchor" href="#希腊字母"></a> 希腊字母</h2><table><thead><tr><th style="text-align:center">语法</th><th style="text-align:center">大写</th><th style="text-align:center">小写</th><th style="text-align:center">语法</th><th style="text-align:center">大写</th><th style="text-align:center">小写</th></tr></thead><tbody><tr><td style="text-align:center">alpha</td><td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi mathvariant="normal">A</mi></mrow><annotation encoding="application/x-tex">\Alpha</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord"><span class="mord mathrm">A</span></span></span></span></span></td><td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>α</mi></mrow><annotation encoding="application/x-tex">\alpha</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord mathdefault" style="margin-right:0.0037em;">α</span></span></span></span></td><td style="text-align:center">beta</td><td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi mathvariant="normal">B</mi></mrow><annotation encoding="application/x-tex">\Beta</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord"><span class="mord mathrm">B</span></span></span></span></span></td><td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>β</mi></mrow><annotation encoding="application/x-tex">\beta</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8888799999999999em;vertical-align:-0.19444em;"></span><span class="mord mathdefault" style="margin-right:0.05278em;">β</span></span></span></span></td></tr><tr><td style="text-align:center">gamma</td><td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi mathvariant="normal">Γ</mi></mrow><annotation encoding="application/x-tex">\Gamma</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord">Γ</span></span></span></span></td><td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>γ</mi></mrow><annotation encoding="application/x-tex">\gamma</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em;"></span><span class="mord mathdefault" style="margin-right:0.05556em;">γ</span></span></span></span></td><td style="text-align:center">delta</td><td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi mathvariant="normal">Δ</mi></mrow><annotation encoding="application/x-tex">\Delta</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord">Δ</span></span></span></span></td><td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>δ</mi></mrow><annotation encoding="application/x-tex">\delta</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.69444em;vertical-align:0em;"></span><span class="mord mathdefault" style="margin-right:0.03785em;">δ</span></span></span></span></td></tr><tr><td style="text-align:center">epsilon</td><td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi mathvariant="normal">E</mi></mrow><annotation encoding="application/x-tex">\Epsilon</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord"><span class="mord mathrm">E</span></span></span></span></span></td><td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>ϵ</mi></mrow><annotation encoding="application/x-tex">\epsilon</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord mathdefault">ϵ</span></span></span></span></td><td style="text-align:center">zeta</td><td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi mathvariant="normal">Z</mi></mrow><annotation encoding="application/x-tex">\Zeta</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord"><span class="mord mathrm">Z</span></span></span></span></span></td><td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>ζ</mi></mrow><annotation encoding="application/x-tex">\zeta</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8888799999999999em;vertical-align:-0.19444em;"></span><span class="mord mathdefault" style="margin-right:0.07378em;">ζ</span></span></span></span></td></tr><tr><td style="text-align:center">eta</td><td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi mathvariant="normal">H</mi></mrow><annotation encoding="application/x-tex">\Eta</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord"><span class="mord mathrm">H</span></span></span></span></span></td><td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>η</mi></mrow><annotation encoding="application/x-tex">\eta</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em;"></span><span class="mord mathdefault" style="margin-right:0.03588em;">η</span></span></span></span></td><td style="text-align:center">theta</td><td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi mathvariant="normal">Θ</mi></mrow><annotation encoding="application/x-tex">\Theta</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord">Θ</span></span></span></span></td><td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>θ</mi></mrow><annotation encoding="application/x-tex">\theta</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.69444em;vertical-align:0em;"></span><span class="mord mathdefault" style="margin-right:0.02778em;">θ</span></span></span></span></td></tr><tr><td style="text-align:center">iota</td><td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi mathvariant="normal">I</mi></mrow><annotation encoding="application/x-tex">\Iota</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord"><span class="mord mathrm">I</span></span></span></span></span></td><td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>ι</mi></mrow><annotation encoding="application/x-tex">\iota</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord mathdefault">ι</span></span></span></span></td><td style="text-align:center">kappa</td><td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi mathvariant="normal">K</mi></mrow><annotation encoding="application/x-tex">\Kappa</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord"><span class="mord mathrm">K</span></span></span></span></span></td><td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>κ</mi></mrow><annotation encoding="application/x-tex">\kappa</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord mathdefault">κ</span></span></span></span></td></tr><tr><td style="text-align:center">lambda</td><td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi mathvariant="normal">Λ</mi></mrow><annotation encoding="application/x-tex">\Lambda</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord">Λ</span></span></span></span></td><td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>λ</mi></mrow><annotation encoding="application/x-tex">\lambda</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.69444em;vertical-align:0em;"></span><span class="mord mathdefault">λ</span></span></span></span></td><td style="text-align:center">mu</td><td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi mathvariant="normal">M</mi></mrow><annotation encoding="application/x-tex">\Mu</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord"><span class="mord mathrm">M</span></span></span></span></span></td><td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>μ</mi></mrow><annotation encoding="application/x-tex">\mu</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em;"></span><span class="mord mathdefault">μ</span></span></span></span></td></tr><tr><td style="text-align:center">nu</td><td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi mathvariant="normal">N</mi></mrow><annotation encoding="application/x-tex">\Nu</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord"><span class="mord mathrm">N</span></span></span></span></span></td><td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>ν</mi></mrow><annotation encoding="application/x-tex">\nu</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord mathdefault" style="margin-right:0.06366em;">ν</span></span></span></span></td><td style="text-align:center">xi</td><td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi mathvariant="normal">Ξ</mi></mrow><annotation encoding="application/x-tex">\Xi</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord">Ξ</span></span></span></span></td><td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>ξ</mi></mrow><annotation encoding="application/x-tex">\xi</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8888799999999999em;vertical-align:-0.19444em;"></span><span class="mord mathdefault" style="margin-right:0.04601em;">ξ</span></span></span></span></td></tr><tr><td style="text-align:center">omicron</td><td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi mathvariant="normal">O</mi></mrow><annotation encoding="application/x-tex">\Omicron</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord"><span class="mord mathrm">O</span></span></span></span></span></td><td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>ο</mi></mrow><annotation encoding="application/x-tex">\omicron</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord mathdefault">ο</span></span></span></span></td><td style="text-align:center">pi</td><td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi mathvariant="normal">Π</mi></mrow><annotation encoding="application/x-tex">\Pi</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord">Π</span></span></span></span></td><td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>π</mi></mrow><annotation encoding="application/x-tex">\pi</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord mathdefault" style="margin-right:0.03588em;">π</span></span></span></span></td></tr><tr><td style="text-align:center">rho</td><td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi mathvariant="normal">P</mi></mrow><annotation encoding="application/x-tex">\Rho</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord"><span class="mord mathrm">P</span></span></span></span></span></td><td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>ρ</mi></mrow><annotation encoding="application/x-tex">\rho</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em;"></span><span class="mord mathdefault">ρ</span></span></span></span></td><td style="text-align:center">sigma</td><td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi mathvariant="normal">Σ</mi></mrow><annotation encoding="application/x-tex">\Sigma</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord">Σ</span></span></span></span></td><td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>σ</mi></mrow><annotation encoding="application/x-tex">\sigma</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord mathdefault" style="margin-right:0.03588em;">σ</span></span></span></span></td></tr><tr><td style="text-align:center">tau</td><td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi mathvariant="normal">T</mi></mrow><annotation encoding="application/x-tex">\Tau</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord"><span class="mord mathrm">T</span></span></span></span></span></td><td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>τ</mi></mrow><annotation encoding="application/x-tex">\tau</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord mathdefault" style="margin-right:0.1132em;">τ</span></span></span></span></td><td style="text-align:center">upsilon</td><td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi mathvariant="normal">Υ</mi></mrow><annotation encoding="application/x-tex">\Upsilon</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord">Υ</span></span></span></span></td><td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>υ</mi></mrow><annotation encoding="application/x-tex">\upsilon</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord mathdefault" style="margin-right:0.03588em;">υ</span></span></span></span></td></tr><tr><td style="text-align:center">phi</td><td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi mathvariant="normal">Φ</mi></mrow><annotation encoding="application/x-tex">\Phi</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord">Φ</span></span></span></span></td><td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>ϕ</mi></mrow><annotation encoding="application/x-tex">\phi</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8888799999999999em;vertical-align:-0.19444em;"></span><span class="mord mathdefault">ϕ</span></span></span></span></td><td style="text-align:center">chi</td><td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi mathvariant="normal">X</mi></mrow><annotation encoding="application/x-tex">\Chi</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord"><span class="mord mathrm">X</span></span></span></span></span></td><td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>χ</mi></mrow><annotation encoding="application/x-tex">\chi</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.625em;vertical-align:-0.19444em;"></span><span class="mord mathdefault">χ</span></span></span></span></td></tr><tr><td style="text-align:center">psi</td><td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi mathvariant="normal">Ψ</mi></mrow><annotation encoding="application/x-tex">\Psi</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord">Ψ</span></span></span></span></td><td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>ψ</mi></mrow><annotation encoding="application/x-tex">\psi</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8888799999999999em;vertical-align:-0.19444em;"></span><span class="mord mathdefault" style="margin-right:0.03588em;">ψ</span></span></span></span></td><td style="text-align:center">omega</td><td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi mathvariant="normal">Ω</mi></mrow><annotation encoding="application/x-tex">\Omega</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord">Ω</span></span></span></span></td><td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>ω</mi></mrow><annotation encoding="application/x-tex">\omega</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord mathdefault" style="margin-right:0.03588em;">ω</span></span></span></span></td></tr></tbody></table><h2 id="二元算符"><a class="markdownIt-Anchor" href="#二元算符"></a> 二元算符</h2><table><thead><tr><th style="text-align:center">语法</th><th style="text-align:center">符号</th><th style="text-align:center">语法</th><th style="text-align:center">符号</th><th style="text-align:center">语法</th><th style="text-align:center">符号</th></tr></thead><tbody><tr><td style="text-align:center">\times</td><td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>×</mo></mrow><annotation encoding="application/x-tex">\times</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.66666em;vertical-align:-0.08333em;"></span><span class="mord">×</span></span></span></span></td><td style="text-align:center">\div</td><td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>÷</mo></mrow><annotation encoding="application/x-tex">\div</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.66666em;vertical-align:-0.08333em;"></span><span class="mord">÷</span></span></span></span></td><td style="text-align:center">\cap</td><td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>∩</mo></mrow><annotation encoding="application/x-tex">\cap</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.55556em;vertical-align:0em;"></span><span class="mord">∩</span></span></span></span></td></tr><tr><td style="text-align:center">\pm</td><td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>±</mo></mrow><annotation encoding="application/x-tex">\pm</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.66666em;vertical-align:-0.08333em;"></span><span class="mord">±</span></span></span></span></td><td style="text-align:center">\mp</td><td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>∓</mo></mrow><annotation encoding="application/x-tex">\mp</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.66666em;vertical-align:-0.08333em;"></span><span class="mord">∓</span></span></span></span></td><td style="text-align:center">\cup</td><td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>∪</mo></mrow><annotation encoding="application/x-tex">\cup</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.55556em;vertical-align:0em;"></span><span class="mord">∪</span></span></span></span></td></tr><tr><td style="text-align:center">\cdot</td><td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>⋅</mo></mrow><annotation encoding="application/x-tex">\cdot</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.44445em;vertical-align:0em;"></span><span class="mord">⋅</span></span></span></span></td><td style="text-align:center">\ast</td><td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>∗</mo></mrow><annotation encoding="application/x-tex">\ast</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.46528em;vertical-align:0em;"></span><span class="mord">∗</span></span></span></span></td><td style="text-align:center">\odot</td><td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>⊙</mo></mrow><annotation encoding="application/x-tex">\odot</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.66666em;vertical-align:-0.08333em;"></span><span class="mord">⊙</span></span></span></span></td></tr></tbody></table><h2 id="关系符号"><a class="markdownIt-Anchor" href="#关系符号"></a> 关系符号</h2><table><thead><tr><th style="text-align:center">语法</th><th style="text-align:center">符号</th><th style="text-align:center">语法</th><th style="text-align:center">符号</th><th style="text-align:center">语法</th><th style="text-align:center">符号</th><th style="text-align:center">语法</th><th style="text-align:center">符号</th></tr></thead><tbody><tr><td style="text-align:center">\equiv</td><td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>≡</mo></mrow><annotation encoding="application/x-tex">\equiv</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.46375em;vertical-align:0em;"></span><span class="mrel">≡</span></span></span></span></td><td style="text-align:center">\cong</td><td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>≅</mo></mrow><annotation encoding="application/x-tex">\cong</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.589em;vertical-align:0em;"></span><span class="mrel">≅</span></span></span></span></td><td style="text-align:center">\leq</td><td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>≤</mo></mrow><annotation encoding="application/x-tex">\leq</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.7719400000000001em;vertical-align:-0.13597em;"></span><span class="mrel">≤</span></span></span></span></td><td style="text-align:center">\geq</td><td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>≥</mo></mrow><annotation encoding="application/x-tex">\geq</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.7719400000000001em;vertical-align:-0.13597em;"></span><span class="mrel">≥</span></span></span></span></td></tr><tr><td style="text-align:center">\neq</td><td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi mathvariant="normal">≠</mi></mrow><annotation encoding="application/x-tex">\neq</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8888799999999999em;vertical-align:-0.19444em;"></span><span class="mrel"><span class="mrel"><span class="mord"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.69444em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="rlap"><span class="strut" style="height:0.8888799999999999em;vertical-align:-0.19444em;"></span><span class="inner"><span class="mrel"></span></span><span class="fix"></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.19444em;"><span></span></span></span></span></span></span><span class="mrel">=</span></span></span></span></span></td><td style="text-align:center">\simeq</td><td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>≃</mo></mrow><annotation encoding="application/x-tex">\simeq</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.46375em;vertical-align:0em;"></span><span class="mrel">≃</span></span></span></span></td><td style="text-align:center">\leqq</td><td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>≦</mo></mrow><annotation encoding="application/x-tex">\leqq</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.01166em;vertical-align:-0.25583em;"></span><span class="mrel amsrm">≦</span></span></span></span></td><td style="text-align:center">\geqq</td><td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>≧</mo></mrow><annotation encoding="application/x-tex">\geqq</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.01166em;vertical-align:-0.25583em;"></span><span class="mrel amsrm">≧</span></span></span></span></td></tr><tr><td style="text-align:center">\ll</td><td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>≪</mo></mrow><annotation encoding="application/x-tex">\ll</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.5782em;vertical-align:-0.0391em;"></span><span class="mrel">≪</span></span></span></span></td><td style="text-align:center">\approx</td><td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>≈</mo></mrow><annotation encoding="application/x-tex">\approx</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.48312em;vertical-align:0em;"></span><span class="mrel">≈</span></span></span></span></td><td style="text-align:center">\leqslant</td><td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>⩽</mo></mrow><annotation encoding="application/x-tex">\leqslant</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.7733399999999999em;vertical-align:-0.13667em;"></span><span class="mrel amsrm">⩽</span></span></span></span></td><td style="text-align:center">\geqslant</td><td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>⩾</mo></mrow><annotation encoding="application/x-tex">\geqslant</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.7733399999999999em;vertical-align:-0.13667em;"></span><span class="mrel amsrm">⩾</span></span></span></span></td></tr><tr><td style="text-align:center">\gg</td><td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>≫</mo></mrow><annotation encoding="application/x-tex">\gg</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.5782em;vertical-align:-0.0391em;"></span><span class="mrel">≫</span></span></span></span></td><td style="text-align:center">\sim</td><td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>∼</mo></mrow><annotation encoding="application/x-tex">\sim</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.36687em;vertical-align:0em;"></span><span class="mrel">∼</span></span></span></span></td><td style="text-align:center">\thicksim</td><td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>∼</mo></mrow><annotation encoding="application/x-tex">\thicksim</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.36687em;vertical-align:0em;"></span><span class="mrel amsrm">∼</span></span></span></span></td><td style="text-align:center">\backsim</td><td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>∽</mo></mrow><annotation encoding="application/x-tex">\backsim</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.37788em;vertical-align:0em;"></span><span class="mrel amsrm">∽</span></span></span></span></td></tr><tr><td style="text-align:center">\subset</td><td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>⊂</mo></mrow><annotation encoding="application/x-tex">\subset</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.5782em;vertical-align:-0.0391em;"></span><span class="mrel">⊂</span></span></span></span></td><td style="text-align:center">\subsetq</td><td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>⊆</mo></mrow><annotation encoding="application/x-tex">\subseteq</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.7719400000000001em;vertical-align:-0.13597em;"></span><span class="mrel">⊆</span></span></span></span></td><td style="text-align:center">\supset</td><td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>⊃</mo></mrow><annotation encoding="application/x-tex">\supset</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.5782em;vertical-align:-0.0391em;"></span><span class="mrel">⊃</span></span></span></span></td><td style="text-align:center">\supseteq</td><td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>⊆</mo></mrow><annotation encoding="application/x-tex">\subseteq</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.7719400000000001em;vertical-align:-0.13597em;"></span><span class="mrel">⊆</span></span></span></span></td></tr><tr><td style="text-align:center">\because</td><td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>∵</mo></mrow><annotation encoding="application/x-tex">\because</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.69224em;vertical-align:0em;"></span><span class="mrel amsrm">∵</span></span></span></span></td><td style="text-align:center">\therefore</td><td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>∴</mo></mrow><annotation encoding="application/x-tex">\therefore</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.69224em;vertical-align:0em;"></span><span class="mrel amsrm">∴</span></span></span></span></td><td style="text-align:center">\nsupseteq</td><td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>⊉</mo></mrow><annotation encoding="application/x-tex">\nsupseteq</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.09657em;vertical-align:-0.30274em;"></span><span class="mrel amsrm">⊉</span></span></span></span></td><td style="text-align:center">\supsetneq</td><td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>⊋</mo></mrow><annotation encoding="application/x-tex">\supsetneq</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.7719400000000001em;vertical-align:-0.13597em;"></span><span class="mrel amsrm">⊋</span></span></span></span></td></tr><tr><td style="text-align:center">\leftarrow</td><td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>←</mo></mrow><annotation encoding="application/x-tex">\leftarrow</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.36687em;vertical-align:0em;"></span><span class="mrel">←</span></span></span></span></td><td style="text-align:center">\uparrow</td><td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>↑</mo></mrow><annotation encoding="application/x-tex">\uparrow</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8888799999999999em;vertical-align:-0.19444em;"></span><span class="mrel">↑</span></span></span></span></td><td style="text-align:center">\updownarrow</td><td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>↕</mo></mrow><annotation encoding="application/x-tex">\updownarrow</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mrel">↕</span></span></span></span></td><td style="text-align:center">\Longrightarrow</td><td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>⟹</mo></mrow><annotation encoding="application/x-tex">\Longrightarrow</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.549em;vertical-align:-0.024em;"></span><span class="mrel">⟹</span></span></span></span></td></tr></tbody></table><h2 id="常用数学符号"><a class="markdownIt-Anchor" href="#常用数学符号"></a> 常用数学符号</h2><table><thead><tr><th style="text-align:center">语法</th><th style="text-align:center">符号</th><th style="text-align:center">语法</th><th style="text-align:center">符号</th><th style="text-align:center">语法</th><th style="text-align:center">符号</th></tr></thead><tbody><tr><td style="text-align:center">\sum</td><td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>∑</mo></mrow><annotation encoding="application/x-tex">\sum</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.00001em;vertical-align:-0.25001em;"></span><span class="mop op-symbol small-op" style="position:relative;top:-0.0000050000000000050004em;">∑</span></span></span></span></td><td style="text-align:center">\int</td><td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>∫</mo></mrow><annotation encoding="application/x-tex">\int</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.11112em;vertical-align:-0.30612em;"></span><span class="mop op-symbol small-op" style="margin-right:0.19445em;position:relative;top:-0.0005599999999999772em;">∫</span></span></span></span></td><td style="text-align:center">\dagger</td><td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>†</mo></mrow><annotation encoding="application/x-tex">\dagger</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8888799999999999em;vertical-align:-0.19444em;"></span><span class="mord">†</span></span></span></span></td></tr><tr><td style="text-align:center">\prod</td><td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>∏</mo></mrow><annotation encoding="application/x-tex">\prod</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.00001em;vertical-align:-0.25001em;"></span><span class="mop op-symbol small-op" style="position:relative;top:-0.0000050000000000050004em;">∏</span></span></span></span></td><td style="text-align:center">\oint</td><td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>∮</mo></mrow><annotation encoding="application/x-tex">\oint</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.11112em;vertical-align:-0.30612em;"></span><span class="mop op-symbol small-op" style="margin-right:0.19445em;position:relative;top:-0.0005599999999999772em;">∮</span></span></span></span></td><td style="text-align:center">\infty</td><td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi mathvariant="normal">∞</mi></mrow><annotation encoding="application/x-tex">\infty</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.43056em;vertical-align:0em;"></span><span class="mord">∞</span></span></span></span></td></tr><tr><td style="text-align:center">\partial</td><td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi mathvariant="normal">∂</mi></mrow><annotation encoding="application/x-tex">\partial</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.69444em;vertical-align:0em;"></span><span class="mord" style="margin-right:0.05556em;">∂</span></span></span></span></td><td style="text-align:center">\iiint</td><td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>∭</mo></mrow><annotation encoding="application/x-tex">\iiint</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.111em;vertical-align:-0.306em;"></span><span class="mop op-symbol small-op" style="margin-right:0.19445em;position:relative;top:-0.0004999999999999727em;">∭</span></span></span></span></td><td style="text-align:center">\forall</td><td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi mathvariant="normal">∀</mi></mrow><annotation encoding="application/x-tex">\forall</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.69444em;vertical-align:0em;"></span><span class="mord">∀</span></span></span></span></td></tr><tr><td style="text-align:center">\nabla</td><td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi mathvariant="normal">∇</mi></mrow><annotation encoding="application/x-tex">\nabla</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68333em;vertical-align:0em;"></span><span class="mord">∇</span></span></span></span></td><td style="text-align:center">\oiint</td><td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo>∯</mo></mrow><annotation encoding="application/x-tex">\oiint</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.111em;vertical-align:-0.306em;"></span><span class="mop vlist-t vlist-t2" style="position:relative;top:-0.0005000000000000282em;"><span class="vlist-r"><span class="vlist" style="height:0.8049999999999999em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mop op-symbol small-op" style="margin-right:0.19445em;">∬</span></span><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="overlay" style="height:0.499em;width:0.957em;"><svg width='0.957em' height='0.499em' style='width:0.957em' viewBox='0 0 957 499' preserveAspectRatio='xMinYMin'><path d='M512.6 71.6c272.6 0 320.3 106.8 320.3 178.2 0 70.8-47.7 177.6-320.3 177.6S193.1 320.6 193.1 249.8c0-71.4 46.9-178.2 319.5-178.2zm368.1 178.2c0-86.4-60.9-215.4-368.1-215.4-306.4 0-367.3 129-367.3 215.4 0 85.860.9 214.8 367.3 214.8 307.2 0 368.1-129 368.1-214.8z'/></svg></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.306em;"><span></span></span></span></span></span></span></span></td><td style="text-align:center">\exists</td><td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi mathvariant="normal">∃</mi></mrow><annotation encoding="application/x-tex">\exists</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.69444em;vertical-align:0em;"></span><span class="mord">∃</span></span></span></span></td></tr></tbody></table><h2 id="常用表示"><a class="markdownIt-Anchor" href="#常用表示"></a> 常用表示</h2><table><thead><tr><th style="text-align:center">语法</th><th style="text-align:center">表示</th><th style="text-align:center">语法</th><th style="text-align:center">表示</th></tr></thead><tbody><tr><td style="text-align:center"><code>\vec{A}</code></td><td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mover accent="true"><mi>A</mi><mo>⃗</mo></mover></mrow><annotation encoding="application/x-tex">\vec{A}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.9663299999999999em;vertical-align:0em;"></span><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9663299999999999em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault">A</span></span></span><span style="top:-3.25233em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.09660999999999997em;"><span class="overlay" style="height:0.714em;width:0.471em;"><svg width='0.471em' height='0.714em' style='width:0.471em' viewBox='0 0 471 714' preserveAspectRatio='xMinYMin'><path d='M377 20c0-5.333 1.833-10 5.5-14S391 0 397 0c4.667 0 8.667 1.667 12 53.333 2.667 6.667 9 10 19 6.667 24.667 20.333 43.667 41 57 7.333 4.667 1110.667 11 18 0 6-1 10-3 12s-6.667 5-14 9c-28.667 14.667-53.667 35.667-75 63-1.333 1.333-3.167 3.5-5.5 6.5s-4 4.833-5 5.5c-1 .667-2.5 1.333-4.5 2s-4.333 1-7 1c-4.667 0-9.167-1.833-13.5-5.5S337 184 337 178c0-12.667 15.667-32.333 47-59H213l-171-1c-8.667-6-13-12.333-13-19 0-4.667 4.333-11.333 13-20h359c-16-25.333-24-45-24-59z'/></svg></span></span></span></span></span></span></span></span></span></span></td><td style="text-align:center"><code>\hat{A}</code></td><td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mover accent="true"><mi>A</mi><mo>^</mo></mover></mrow><annotation encoding="application/x-tex">\hat{A}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.9467699999999999em;vertical-align:0em;"></span><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9467699999999999em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault">A</span></span></span><span style="top:-3.25233em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.11110999999999999em;">^</span></span></span></span></span></span></span></span></span></td></tr><tr><td style="text-align:center"><code>\bar{A}</code></td><td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mover accent="true"><mi>A</mi><mo>ˉ</mo></mover></mrow><annotation encoding="application/x-tex">\bar{A}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.8201099999999999em;vertical-align:0em;"></span><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.8201099999999999em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault">A</span></span></span><span style="top:-3.25233em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.11110999999999999em;">ˉ</span></span></span></span></span></span></span></span></span></td><td style="text-align:center"><code>\ddot{A}</code></td><td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mover accent="true"><mi>A</mi><mo>¨</mo></mover></mrow><annotation encoding="application/x-tex">\ddot{A}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.9201900000000001em;vertical-align:0em;"></span><span class="mord accent"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.9201900000000001em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault">A</span></span></span><span style="top:-3.25233em;"><span class="pstrut" style="height:3em;"></span><span class="accent-body" style="left:-0.11110999999999999em;">¨</span></span></span></span></span></span></span></span></span></td></tr><tr><td style="text-align:center"><code>\hbar</code></td><td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi mathvariant="normal">ℏ</mi></mrow><annotation encoding="application/x-tex">\hbar</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.68889em;vertical-align:0em;"></span><span class="mord">ℏ</span></span></span></span></td><td style="text-align:center"><code>\sqrt[n]{a}</code></td><td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mroot><mi>a</mi><mi>n</mi></mroot></mrow><annotation encoding="application/x-tex">\sqrt[n]{a}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.04em;vertical-align:-0.23972em;"></span><span class="mord sqrt"><span class="root"><span class="vlist-t"><span class="vlist-r"><span class="vlist" style="height:0.5516160000000001em;"><span style="top:-2.836336em;"><span class="pstrut" style="height:2.5em;"></span><span class="sizing reset-size6 size1 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">n</span></span></span></span></span></span></span></span><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8002800000000001em;"><span class="svg-align" style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord" style="padding-left:0.833em;"><span class="mord mathdefault">a</span></span></span><span style="top:-2.76028em;"><span class="pstrut" style="height:3em;"></span><span class="hide-tail" style="min-width:0.853em;height:1.08em;"><svg width='400em' height='1.08em' viewBox='0 0 400000 1080' preserveAspectRatio='xMinYMin slice'><path d='M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z M834 80H400000v40H845z'/></svg></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.23972em;"><span></span></span></span></span></span></span></span></span></td></tr><tr><td style="text-align:center"><code>\overline{a+b}</code></td><td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mover accent="true"><mrow><mi>a</mi><mo>+</mo><mi>b</mi></mrow><mo stretchy="true">‾</mo></mover></mrow><annotation encoding="application/x-tex">\overline{a+b}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:0.97777em;vertical-align:-0.08333em;"></span><span class="mord overline"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.89444em;"><span style="top:-3em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault">a</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mbin">+</span><span class="mspace" style="margin-right:0.2222222222222222em;"></span><span class="mord mathdefault">b</span></span></span><span style="top:-3.81444em;"><span class="pstrut" style="height:3em;"></span><span class="overline-line" style="border-bottom-width:0.04em;"></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.08333em;"><span></span></span></span></span></span></span></span></span></td><td style="text-align:center"><code>^4_2He</code></td><td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><msubsup><mrow></mrow><mn>2</mn><mn>4</mn></msubsup><mi>H</mi><mi>e</mi></mrow><annotation encoding="application/x-tex">^4_2He</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.0622159999999998em;vertical-align:-0.24810799999999997em;"></span><span class="mord"><span></span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.8141079999999999em;"><span style="top:-2.4518920000000004em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">2</span></span></span><span style="top:-3.063em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">4</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.24810799999999997em;"><span></span></span></span></span></span></span><span class="mord mathdefault" style="margin-right:0.08125em;">H</span><span class="mord mathdefault">e</span></span></span></span></td></tr><tr><td style="text-align:center"><code>\sum_{i=0}^na_n</code></td><td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><msubsup><mo>∑</mo><mrow><mi>i</mi><mo>=</mo><mn>0</mn></mrow><mi>n</mi></msubsup><msub><mi>a</mi><mi>n</mi></msub></mrow><annotation encoding="application/x-tex">\sum_{i=0}^na_n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1.104002em;vertical-align:-0.29971000000000003em;"></span><span class="mop"><span class="mop op-symbol small-op" style="position:relative;top:-0.0000050000000000050004em;">∑</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.804292em;"><span style="top:-2.40029em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight"><span class="mord mathdefault mtight">i</span><span class="mrel mtight">=</span><span class="mord mtight">0</span></span></span></span><span style="top:-3.2029em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">n</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.29971000000000003em;"><span></span></span></span></span></span></span><span class="mspace" style="margin-right:0.16666666666666666em;"></span><span class="mord"><span class="mord mathdefault">a</span><span class="msupsub"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.151392em;"><span style="top:-2.5500000000000003em;margin-left:0em;margin-right:0.05em;"><span class="pstrut" style="height:2.7em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">n</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.15em;"><span></span></span></span></span></span></span></span></span></span></td><td style="text-align:center"><code>\sum\limits_a^b</code></td><td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><msubsup><mo>∑</mo><mi>a</mi><mi>b</mi></msubsup></mrow><annotation encoding="application/x-tex">\sum\limits_a^b</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:2.4861180000000003em;vertical-align:-0.950005em;"></span><span class="mop op-limits"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.536113em;"><span style="top:-2.149995em;margin-left:0em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">a</span></span></span><span style="top:-3.0000050000000003em;"><span class="pstrut" style="height:3em;"></span><span><span class="mop op-symbol small-op">∑</span></span></span><span style="top:-3.950005em;margin-left:0em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">b</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.950005em;"><span></span></span></span></span></span></span></span></span></td></tr></tbody></table><h3 id="矩阵表示"><a class="markdownIt-Anchor" href="#矩阵表示"></a> 矩阵表示</h3><figure class="highlight gauss"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br></pre></td><td class="code"><pre><code class="hljs gauss">\begin{<span class="hljs-keyword">matrix</span>}<br>a & b\\<br>c & d<br>\<span class="hljs-keyword">end</span>{<span class="hljs-keyword">matrix</span>}<br></code></pre></td></tr></table></figure><table><thead><tr><th style="text-align:center"><strong>matrix</strong></th><th style="text-align:center"><strong>pmartix</strong></th><th style="text-align:center"><strong>bmartix</strong></th><th style="text-align:center"><strong>Bmartix</strong></th><th style="text-align:center"><strong>vmartix</strong></th></tr></thead><tbody><tr><td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mtable rowspacing="0.15999999999999992em" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mi>a</mi></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mi>b</mi></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mi>c</mi></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mi>d</mi></mstyle></mtd></mtr></mtable><annotation encoding="application/x-tex">\begin{matrix} a & b\\c & d\end{matrix}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:2.4000000000000004em;vertical-align:-0.9500000000000004em;"></span><span class="mord"><span class="mtable"><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.45em;"><span style="top:-3.61em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault">a</span></span></span><span style="top:-2.4099999999999997em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault">c</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.9500000000000004em;"><span></span></span></span></span></span><span class="arraycolsep" style="width:0.5em;"></span><span class="arraycolsep" style="width:0.5em;"></span><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.45em;"><span style="top:-3.61em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault">b</span></span></span><span style="top:-2.4099999999999997em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault">d</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.9500000000000004em;"><span></span></span></span></span></span></span></span></span></span></span></td><td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo fence="true">(</mo><mtable rowspacing="0.15999999999999992em" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mi>a</mi></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mi>b</mi></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mi>c</mi></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mi>d</mi></mstyle></mtd></mtr></mtable><mo fence="true">)</mo></mrow><annotation encoding="application/x-tex">\begin{pmatrix} a & b\\c & d\end{pmatrix}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:2.40003em;vertical-align:-0.95003em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;"><span class="delimsizing size3">(</span></span><span class="mord"><span class="mtable"><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.45em;"><span style="top:-3.61em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault">a</span></span></span><span style="top:-2.4099999999999997em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault">c</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.9500000000000004em;"><span></span></span></span></span></span><span class="arraycolsep" style="width:0.5em;"></span><span class="arraycolsep" style="width:0.5em;"></span><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.45em;"><span style="top:-3.61em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault">b</span></span></span><span style="top:-2.4099999999999997em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault">d</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.9500000000000004em;"><span></span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em;"><span class="delimsizing size3">)</span></span></span></span></span></span></td><td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo fence="true">[</mo><mtable rowspacing="0.15999999999999992em" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mi>a</mi></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mi>b</mi></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mi>c</mi></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mi>d</mi></mstyle></mtd></mtr></mtable><mo fence="true">]</mo></mrow><annotation encoding="application/x-tex">\begin{bmatrix} a & b\\c & d\end{bmatrix}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:2.40003em;vertical-align:-0.95003em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;"><span class="delimsizing size3">[</span></span><span class="mord"><span class="mtable"><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.45em;"><span style="top:-3.61em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault">a</span></span></span><span style="top:-2.4099999999999997em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault">c</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.9500000000000004em;"><span></span></span></span></span></span><span class="arraycolsep" style="width:0.5em;"></span><span class="arraycolsep" style="width:0.5em;"></span><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.45em;"><span style="top:-3.61em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault">b</span></span></span><span style="top:-2.4099999999999997em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault">d</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.9500000000000004em;"><span></span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em;"><span class="delimsizing size3">]</span></span></span></span></span></span></td><td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo fence="true">{</mo><mtable rowspacing="0.15999999999999992em" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mi>a</mi></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mi>b</mi></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mi>c</mi></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mi>d</mi></mstyle></mtd></mtr></mtable><mo fence="true">}</mo></mrow><annotation encoding="application/x-tex">\begin{Bmatrix} a & b\\c & d\end{Bmatrix}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:2.40003em;vertical-align:-0.95003em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;"><span class="delimsizing size3">{</span></span><span class="mord"><span class="mtable"><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.45em;"><span style="top:-3.61em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault">a</span></span></span><span style="top:-2.4099999999999997em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault">c</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.9500000000000004em;"><span></span></span></span></span></span><span class="arraycolsep" style="width:0.5em;"></span><span class="arraycolsep" style="width:0.5em;"></span><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.45em;"><span style="top:-3.61em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault">b</span></span></span><span style="top:-2.4099999999999997em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault">d</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.9500000000000004em;"><span></span></span></span></span></span></span></span><span class="mclose delimcenter" style="top:0em;"><span class="delimsizing size3">}</span></span></span></span></span></span></td><td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo fence="true">∣</mo><mtable rowspacing="0.15999999999999992em" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mi>a</mi></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mi>b</mi></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mi>c</mi></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mi>d</mi></mstyle></mtd></mtr></mtable><mo fence="true">∣</mo></mrow><annotation encoding="application/x-tex">\begin{vmatrix} a & b\\c & d\end{vmatrix}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:2.424em;vertical-align:-0.9500199999999999em;"></span><span class="minner"><span class="mopen"><span class="delimsizing mult"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.47398em;"><span style="top:-1.65598em;"><span class="pstrut" style="height:2.606em;"></span><span class="delimsizinginner delim-size1"><span>∣</span></span></span><span style="top:-2.26198em;"><span class="pstrut" style="height:2.606em;"></span><span class="delimsizinginner delim-size1"><span>∣</span></span></span><span style="top:-2.86798em;"><span class="pstrut" style="height:2.606em;"></span><span class="delimsizinginner delim-size1"><span>∣</span></span></span><span style="top:-3.47398em;"><span class="pstrut" style="height:2.606em;"></span><span class="delimsizinginner delim-size1"><span>∣</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.9500199999999999em;"><span></span></span></span></span></span></span><span class="mord"><span class="mtable"><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.45em;"><span style="top:-3.61em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault">a</span></span></span><span style="top:-2.4099999999999997em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault">c</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.9500000000000004em;"><span></span></span></span></span></span><span class="arraycolsep" style="width:0.5em;"></span><span class="arraycolsep" style="width:0.5em;"></span><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.45em;"><span style="top:-3.61em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault">b</span></span></span><span style="top:-2.4099999999999997em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault">d</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.9500000000000004em;"><span></span></span></span></span></span></span></span><span class="mclose"><span class="delimsizing mult"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.47398em;"><span style="top:-1.65598em;"><span class="pstrut" style="height:2.606em;"></span><span class="delimsizinginner delim-size1"><span>∣</span></span></span><span style="top:-2.26198em;"><span class="pstrut" style="height:2.606em;"></span><span class="delimsizinginner delim-size1"><span>∣</span></span></span><span style="top:-2.86798em;"><span class="pstrut" style="height:2.606em;"></span><span class="delimsizinginner delim-size1"><span>∣</span></span></span><span style="top:-3.47398em;"><span class="pstrut" style="height:2.606em;"></span><span class="delimsizinginner delim-size1"><span>∣</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.9500199999999999em;"><span></span></span></span></span></span></span></span></span></span></span></td></tr></tbody></table><figure class="highlight llvm"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br></pre></td><td class="code"><pre><code class="hljs llvm">\left(<br>\<span class="hljs-keyword">begin</span>{array}{<span class="hljs-keyword">cc</span>|<span class="hljs-keyword">c</span>} % l/<span class="hljs-keyword">c</span>/r means left/center/right<br>a & b & <span class="hljs-keyword">c</span>\\ % <span class="hljs-keyword">cc</span>|<span class="hljs-keyword">c</span> means extended matrix (katex not support)<br>e & f & g<br>\<span class="hljs-keyword">end</span>{array}<br>\right)<br></code></pre></td></tr></table></figure><table><thead><tr><th style="text-align:center">()</th><th style="text-align:center">[]</th><th style="text-align:center">{}</th></tr></thead><tbody><tr><td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo fence="true">(</mo><mtable rowspacing="0.15999999999999992em" columnalign="center center center" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mi>a</mi></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mi>b</mi></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mi>c</mi></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mi>e</mi></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mi>f</mi></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mi>g</mi></mstyle></mtd></mtr></mtable><mo fence="true">)</mo></mrow><annotation encoding="application/x-tex">\left(\begin{array}{ccc}a & b & c\\e & f & g\end{array}\right)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:2.40003em;vertical-align:-0.95003em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;"><span class="delimsizing size3">(</span></span><span class="mord"><span class="mtable"><span class="arraycolsep" style="width:0.5em;"></span><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.45em;"><span style="top:-3.61em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault">a</span></span></span><span style="top:-2.4099999999999997em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault">e</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.9500000000000004em;"><span></span></span></span></span></span><span class="arraycolsep" style="width:0.5em;"></span><span class="arraycolsep" style="width:0.5em;"></span><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.45em;"><span style="top:-3.61em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault">b</span></span></span><span style="top:-2.4099999999999997em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.10764em;">f</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.9500000000000004em;"><span></span></span></span></span></span><span class="arraycolsep" style="width:0.5em;"></span><span class="arraycolsep" style="width:0.5em;"></span><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.45em;"><span style="top:-3.61em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault">c</span></span></span><span style="top:-2.4099999999999997em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em;">g</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.9500000000000004em;"><span></span></span></span></span></span><span class="arraycolsep" style="width:0.5em;"></span></span></span><span class="mclose delimcenter" style="top:0em;"><span class="delimsizing size3">)</span></span></span></span></span></span></td><td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo fence="true">[</mo><mtable rowspacing="0.15999999999999992em" columnalign="center center center" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mi>a</mi></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mi>b</mi></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mi>c</mi></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mi>e</mi></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mi>f</mi></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mi>g</mi></mstyle></mtd></mtr></mtable><mo fence="true">]</mo></mrow><annotation encoding="application/x-tex">\left[\begin{array}{ccc}a & b & c\\e & f & g\end{array}\right]</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:2.40003em;vertical-align:-0.95003em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;"><span class="delimsizing size3">[</span></span><span class="mord"><span class="mtable"><span class="arraycolsep" style="width:0.5em;"></span><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.45em;"><span style="top:-3.61em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault">a</span></span></span><span style="top:-2.4099999999999997em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault">e</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.9500000000000004em;"><span></span></span></span></span></span><span class="arraycolsep" style="width:0.5em;"></span><span class="arraycolsep" style="width:0.5em;"></span><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.45em;"><span style="top:-3.61em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault">b</span></span></span><span style="top:-2.4099999999999997em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.10764em;">f</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.9500000000000004em;"><span></span></span></span></span></span><span class="arraycolsep" style="width:0.5em;"></span><span class="arraycolsep" style="width:0.5em;"></span><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.45em;"><span style="top:-3.61em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault">c</span></span></span><span style="top:-2.4099999999999997em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em;">g</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.9500000000000004em;"><span></span></span></span></span></span><span class="arraycolsep" style="width:0.5em;"></span></span></span><span class="mclose delimcenter" style="top:0em;"><span class="delimsizing size3">]</span></span></span></span></span></span></td><td style="text-align:center"><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mo fence="true">{</mo><mtable rowspacing="0.15999999999999992em" columnalign="center center center" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mi>a</mi></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mi>b</mi></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mi>c</mi></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mi>e</mi></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mi>f</mi></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mi>g</mi></mstyle></mtd></mtr></mtable><mo fence="true">}</mo></mrow><annotation encoding="application/x-tex">\left\{\begin{array}{ccc}a & b & c\\e & f & g\end{array}\right\}</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:2.40003em;vertical-align:-0.95003em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;"><span class="delimsizing size3">{</span></span><span class="mord"><span class="mtable"><span class="arraycolsep" style="width:0.5em;"></span><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.45em;"><span style="top:-3.61em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault">a</span></span></span><span style="top:-2.4099999999999997em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault">e</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.9500000000000004em;"><span></span></span></span></span></span><span class="arraycolsep" style="width:0.5em;"></span><span class="arraycolsep" style="width:0.5em;"></span><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.45em;"><span style="top:-3.61em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault">b</span></span></span><span style="top:-2.4099999999999997em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.10764em;">f</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.9500000000000004em;"><span></span></span></span></span></span><span class="arraycolsep" style="width:0.5em;"></span><span class="arraycolsep" style="width:0.5em;"></span><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.45em;"><span style="top:-3.61em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault">c</span></span></span><span style="top:-2.4099999999999997em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault" style="margin-right:0.03588em;">g</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.9500000000000004em;"><span></span></span></span></span></span><span class="arraycolsep" style="width:0.5em;"></span></span></span><span class="mclose delimcenter" style="top:0em;"><span class="delimsizing size3">}</span></span></span></span></span></span></td></tr></tbody></table><h3 id="分段函数"><a class="markdownIt-Anchor" href="#分段函数"></a> 分段函数</h3><p><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>f</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo>=</mo><mrow><mo fence="true">{</mo><mtable rowspacing="0.15999999999999992em" columnalign="center center" columnspacing="1em"><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mi mathvariant="normal">∣</mi><mi>x</mi><mi mathvariant="normal">∣</mi></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mi>x</mi><mo>≤</mo><mn>0</mn></mrow></mstyle></mtd></mtr><mtr><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mi>s</mi><mi>i</mi><mi>n</mi><mfrac><mn>1</mn><mi>x</mi></mfrac></mrow></mstyle></mtd><mtd><mstyle scriptlevel="0" displaystyle="false"><mrow><mi>x</mi><mo>></mo><mn>0</mn></mrow></mstyle></mtd></mtr></mtable></mrow></mrow><annotation encoding="application/x-tex">f(x)=\left\{\begin{array}{cc}|x| & x\leq0 \\sin \frac 1x & x>0\end{array}\right.</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut" style="height:1em;vertical-align:-0.25em;"></span><span class="mord mathdefault" style="margin-right:0.10764em;">f</span><span class="mopen">(</span><span class="mord mathdefault">x</span><span class="mclose">)</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">=</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span></span><span class="base"><span class="strut" style="height:2.4051080000000002em;vertical-align:-0.9525540000000003em;"></span><span class="minner"><span class="mopen delimcenter" style="top:0em;"><span class="delimsizing size3">{</span></span><span class="mord"><span class="mtable"><span class="arraycolsep" style="width:0.5em;"></span><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.452554em;"><span style="top:-3.612554em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord">∣</span><span class="mord mathdefault">x</span><span class="mord">∣</span></span></span><span style="top:-2.4074459999999998em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault">s</span><span class="mord mathdefault">i</span><span class="mord mathdefault">n</span><span class="mord"><span class="mopen nulldelimiter"></span><span class="mfrac"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:0.845108em;"><span style="top:-2.6550000000000002em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mathdefault mtight">x</span></span></span><span style="top:-3.23em;"><span class="pstrut" style="height:3em;"></span><span class="frac-line" style="border-bottom-width:0.04em;"></span></span><span style="top:-3.394em;"><span class="pstrut" style="height:3em;"></span><span class="sizing reset-size6 size3 mtight"><span class="mord mtight">1</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.345em;"><span></span></span></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.9525540000000003em;"><span></span></span></span></span></span><span class="arraycolsep" style="width:0.5em;"></span><span class="arraycolsep" style="width:0.5em;"></span><span class="col-align-c"><span class="vlist-t vlist-t2"><span class="vlist-r"><span class="vlist" style="height:1.452554em;"><span style="top:-3.612554em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault">x</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">≤</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord">0</span></span></span><span style="top:-2.4074459999999998em;"><span class="pstrut" style="height:3em;"></span><span class="mord"><span class="mord mathdefault">x</span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mrel">></span><span class="mspace" style="margin-right:0.2777777777777778em;"></span><span class="mord">0</span></span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="vlist" style="height:0.9525540000000003em;"><span></span></span></span></span></span><span class="arraycolsep" style="width:0.5em;"></span></span></span><span class="mclose nulldelimiter"></span></span></span></span></span></p><figure class="highlight livescript"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br></pre></td><td class="code"><pre><code class="hljs livescript">f(x)=<span class="hljs-string">\left\{</span> % {需要`<span class="hljs-string">\`转义</span><br><span class="hljs-string">\begin{array}{lc}</span><br>|x| & x <span class="hljs-string">\leq</span> <span class="hljs-number">0</span> <span class="hljs-string">\\</span><br>sin <span class="hljs-string">\frac</span> <span class="hljs-number">1x</span> & x > <span class="hljs-number">0</span><br><span class="hljs-string">\end{array}\right.</span> % .替代不显示括号<br></code></pre></td></tr></table></figure>]]></content>
<tags>
<tag>Code</tag>
<tag>Notes</tag>
</tags>
</entry>
<entry>
<title>白嫖和低价ECS的评测</title>
<link href="/2020/031208.html"/>
<url>/2020/031208.html</url>
<content type="html"><![CDATA[<h1 id="白嫖和低价ecs的评测"><a class="markdownIt-Anchor" href="#白嫖和低价ecs的评测"></a> 白嫖和低价ECS的评测</h1><p>手上目前有有阿里云轻量应用服务器（1C2G5M，CentOS 7.7，学生机），阿里云ECS T5（2C4G1M，CentOS 7.7，高校在家计划送的），华为云弹性云服务器ECS（1C2G1M，Fodera 30，学生机），华为云耀ECS（1C2G1M，CentOS 7.7，牛客网活动白嫖），由于需求和提供的镜像不同，对比其镜像，控制台服务，CPU对比，同带宽网络，硬盘的I/O能力。 u1s1，同等配置硬件差距应该不大，主要是服务上吧。（结果是打脸了QAQ）</p><h2 id="镜像"><a class="markdownIt-Anchor" href="#镜像"></a> 镜像</h2><p>云服务器商，提供的镜像如下：</p><table><thead><tr><th style="text-align:center">服务器 \ 镜像</th><th style="text-align:center">CentOS</th><th style="text-align:center">Debian</th><th style="text-align:center">Ubuntu</th><th style="text-align:center">OpenSUSE</th><th style="text-align:center">FreeBSD</th><th style="text-align:center">Fodera</th><th style="text-align:center">Windows</th></tr></thead><tbody><tr><td style="text-align:center">阿里轻量应用服务器</td><td style="text-align:center">7.3</td><td style="text-align:center">8.9/9.9</td><td style="text-align:center">16.04/18.04</td><td style="text-align:center">42.3</td><td style="text-align:center">X</td><td style="text-align:center">X</td><td style="text-align:center">2016数据中心版</td></tr><tr><td style="text-align:center">阿里ECS</td><td style="text-align:center">6.8 - 7.7, 8.0</td><td style="text-align:center">8.9 - 10.3</td><td style="text-align:center">14.04/16.04/18.04</td><td style="text-align:center">15.1/42.3</td><td style="text-align:center">11.2</td><td style="text-align:center">支持RedHat 7.6 - 7.7, 8</td><td style="text-align:center">2008 - 2019</td></tr><tr><td style="text-align:center">华为ECS</td><td style="text-align:center">6.5 - 7.6</td><td style="text-align:center">8.2/8.8/9.0/10.0</td><td style="text-align:center">16.04/18.04</td><td style="text-align:center">15.0</td><td style="text-align:center">11.0</td><td style="text-align:center">30</td><td style="text-align:center">2008 - 2019</td></tr><tr><td style="text-align:center">华为云耀</td><td style="text-align:center">7.2 - 7.6</td><td style="text-align:center">X</td><td style="text-align:center">16.04/18.04</td><td style="text-align:center">X</td><td style="text-align:center">X</td><td style="text-align:center">X</td><td style="text-align:center">2012 - 2019</td></tr></tbody></table><ul><li>均可更换系统镜像</li><li>阿里均提供Aliyun Linux，阿里ECS提供CoreOS & SUSE Linux；华为ECS提供CoreOS，EulerOS</li></ul><p>华为云耀服务器提供的镜像是最少的，正常使用还是可以，打算折腾的话还是不太够，以及CentOS能够更新到7.7。根据不完全使用体验和群里的吐槽，腾讯的仓库东西版本最落后，阿里和华为CentOS仓库也挺落后的，不是很推荐。</p><h2 id="控制台服务"><a class="markdownIt-Anchor" href="#控制台服务"></a> 控制台服务</h2><p>各家控制台UI都大同小异，阿里轻量应用服务器极度简洁（感觉不好看，但唯一可以控制台添加密钥）；两家ECS服务器区别不大，小机器和单台主机的话过于繁杂；华为云耀的话，感觉不错，简洁，小机器使用体验不错。</p><p>对比图：</p><p><strong>华为云耀</strong>:</p><p><img src="https://i.loli.net/2020/03/12/ZNULM3Gz5mgq9uF.jpg" alt="hwyy1.jpg" /></p><p><strong>华为ECS</strong>：</p><p><img src="https://i.loli.net/2020/03/12/5pc16KsSmZLQDBo.jpg" alt="hwecs1.jpg" /></p><p><strong>阿里轻量</strong>：</p><p><img src="https://i.loli.net/2020/03/12/C17YXbjaPN2G5AM.jpg" alt="ali1.jpg" /></p><p><strong>阿里ECS</strong>：</p><p><img src="https://i.loli.net/2020/03/12/pi9ds6jPZzHOJhU.jpg" alt="aliecs1.jpg" /></p><p>使用体验的话，华为云耀控制台常用的二级菜单，个人感觉更容易找到，阿里的不是很好找。</p><h2 id="cpu对比"><a class="markdownIt-Anchor" href="#cpu对比"></a> CPU对比</h2><p><strong>华为云耀</strong>：</p><p><img src="https://i.loli.net/2020/03/12/OroiWFAx913y8sI.jpg" alt="hwyy3.jpg" /></p><p><strong>华为ECS</strong>：</p><p><img src="https://i.loli.net/2020/03/12/ovFBitdODzqbGMc.jpg" alt="hwecs3.jpg" /></p><p><strong>阿里ECS</strong>：</p><p><img src="https://i.loli.net/2020/03/12/cXVukCjBLl4SrvM.jpg" alt="aliecs3.jpg" /></p><p>使用的U都是Skylake架构，阿里是铂金系列，华为是金牌系列；不过云耀使用的是定制版第二代U，阿里轻量应用服务器U和阿里ECS相同。由于是单核，单从主频上看华为云耀 > 阿里ECS > 华为ECS；不过 云耀步进更大（对于这种小机器，影响并不大）。</p><h2 id="同带宽网络测试"><a class="markdownIt-Anchor" href="#同带宽网络测试"></a> 同带宽网络测试</h2><p>这里就对比测试阿里ECS，华为ECS，华为云耀：</p><h3 id="测试入站"><a class="markdownIt-Anchor" href="#测试入站"></a> 测试入站</h3><figure class="highlight awk"><table><tr><td class="gutter"><pre><span class="line">1</span><br></pre></td><td class="code"><pre><code class="hljs awk">wget http:<span class="hljs-regexp">//</span>cachefly.cachefly.net/<span class="hljs-number">100</span>mb.test<br></code></pre></td></tr></table></figure><p>华为ECS（9.76 MB/s）最快，华为云耀（6.66 MB/s）其次，阿里ECS（219 KB/s）最弟弟（QAQ 完全被吊打）。看起来华为云并未限制入站带宽（上限应该是100Mbps），阿里云是限制了的。</p><p><strong>华为云耀</strong>:</p><p><img src="https://i.loli.net/2020/03/12/2KfLzN8ChaEmciG.jpg" alt="hwyy2.jpg" /></p><p><strong>华为ECS</strong>：</p><p><img src="https://i.loli.net/2020/03/12/7MhraxcXtnLGODY.jpg" alt="hwecs2.jpg" /></p><p><strong>阿里ECS</strong>：</p><p><img src="https://i.loli.net/2020/03/12/bu5BORMi4dWXPlK.jpg" alt="aliecs2.jpg" /></p><h3 id="测试出站"><a class="markdownIt-Anchor" href="#测试出站"></a> 测试出站</h3><p>简洁点，就通过不带参数的scp来测试：</p><p>阿里云ECS（130 KB/s）继续垫底，被吊打。华为云耀和华为相当（192 KB/s）。</p><p><strong>华为云耀</strong>：</p><p><img src="https://i.loli.net/2020/03/12/Cm178qR9KJ5Qxsh.jpg" alt="hwyy4.jpg" /></p><p><strong>华为ECS</strong>：</p><p><img src="https://i.loli.net/2020/03/12/U4jawHyN9T2poen.jpg" alt="hwecs4.jpg" /></p><p><strong>阿里ECS</strong>：</p><p><img src="https://i.loli.net/2020/03/12/c7zWXG5wHkSLJUC.jpg" alt="aliecs4.jpg" /></p><p>总的来说，华为云耀入站略慢于华为ECS，出入都吊打阿里ECS。</p><h2 id="硬盘io性能"><a class="markdownIt-Anchor" href="#硬盘io性能"></a> 硬盘I/O性能</h2><p>使用dd命令进行测试：</p><p><strong>华为云耀</strong>：</p><p><img src="https://i.loli.net/2020/03/12/FVBvtT5zrUaPObc.jpg" alt="hwyy6.jpg" /></p><p><img src="https://i.loli.net/2020/03/12/Q7jEqKkurbNp283.jpg" alt="hwyy5.jpg" /></p><p><strong>华为ECS</strong>：</p><p><img src="https://i.loli.net/2020/03/12/923ke6x7gufiMCo.jpg" alt="hwecs6.jpg" /></p><p><img src="https://i.loli.net/2020/03/12/cR34pAFE8UviHwP.jpg" alt="hwecs5.jpg" /></p><p><strong>阿里ECS</strong>：</p><p><img src="https://i.loli.net/2020/03/12/nOlmZkjWULuAR6f.jpg" alt="aliecs6.jpg" /></p><p><img src="https://i.loli.net/2020/03/12/95Ifbcamy6RtATs.jpg" alt="aliecs5.jpg" /></p><p>在写方面，华为云耀 > 阿里ECS > 华为ECS，华为云耀和阿里ECS差距不大，华为ECS被吊打。<br />在物理写方面，阿里ECS > 华为ECS > 华为云耀，不过都是菜鸡互啄，2333。差距不大，实际体验差不多。<br />在读方面，华为ECS > 华为云耀 > 阿里ECS，华为ECS比华为云耀高些，阿里ECS完全被吊打。</p><p>总体来说，华为云耀 > 华为ECS > 阿里ECS。</p><h2 id="unixbench"><a class="markdownIt-Anchor" href="#unixbench"></a> UnixBench</h2><p>使用UB跑个分，测试整体性能。</p><p><strong>华为云耀</strong>：</p><p><img src="https://i.loli.net/2020/03/12/OgPw9YmqDp5jMSb.jpg" alt="hwyy7.jpg" /></p><p><strong>华为ECS</strong>:</p><p><img src="https://i.loli.net/2020/03/12/2LRCEgfMrD8SFWx.jpg" alt="hwecs7.jpg" /></p><p>由于阿里ECS是2c，所以换成了1c2g的<strong>阿里轻量应用服务器</strong>：（u是一样的）</p><p><img src="https://i.loli.net/2020/03/12/yDgrzhi7Q26T8JS.jpg" alt="ali2.jpg" /></p><p>华为云耀得分 <strong>1758.6</strong> 要比华为ECS高约 29%，阿里轻量应用 <strong>418.3</strong> ，这是被按在地上摩擦。。呃。。我也没想到会这么差。</p><h2 id="lemonbench"><a class="markdownIt-Anchor" href="#lemonbench"></a> LemonBench</h2><p>在跑个LB：</p><table><thead><tr><th style="text-align:center">服务器 \ 项目</th><th style="text-align:center">单核分数</th><th style="text-align:center">内存性能</th><th style="text-align:center">硬盘性能 100MB-4k</th><th style="text-align:center">硬盘性能 1GB-1M</th></tr></thead><tbody><tr><td style="text-align:center">华为云耀</td><td style="text-align:center">1111</td><td style="text-align:center">Read 20.9GB/s, Write 14.9GB/s</td><td style="text-align:center">Read 9.4MB/s, Write 6.1MB/s</td><td style="text-align:center">Read 172MB/s, Write 156MB/s</td></tr><tr><td style="text-align:center">华为ECS</td><td style="text-align:center">888</td><td style="text-align:center">Read 17.6GB/s, Write 12.4GB/s</td><td style="text-align:center">Read 8.6MB/s, Write 4.1MB/s</td><td style="text-align:center">Read 177MB/s, Write 85.7MB/s</td></tr><tr><td style="text-align:center">阿里轻量应用</td><td style="text-align:center">813</td><td style="text-align:center">Read 16.2GB/s, Write 10.9GB/s</td><td style="text-align:center">Read 5.9MB/s, Write 5.7MB/s</td><td style="text-align:center">Read 143MB/s, Write 136MB/s</td></tr><tr><td style="text-align:center">阿里ECS</td><td style="text-align:center">872</td><td style="text-align:center">Read 17.0GB/s, Write 10.5GB/s</td><td style="text-align:center">Read 7.9MB/s, Write 6.7MB/s</td><td style="text-align:center">Read 106MB/s, Write 106MB/s</td></tr></tbody></table><p>华为云耀单核性能，远超另外三个，读写情况和前面测试情况相似。</p><h2 id="总结"><a class="markdownIt-Anchor" href="#总结"></a> 总结</h2><p>综上，同等配置下，华为云耀的整体性能和体验，是比华为弹性云服务器好的，性能上吊打阿里的。</p>]]></content>
<tags>
<tag>Cloud</tag>
</tags>
</entry>
<entry>
<title>面向纯小白开箱即用的VSCode</title>
<link href="/2020/022609.html"/>
<url>/2020/022609.html</url>
<content type="html"><![CDATA[<h1 id="面向纯小白开箱即用的-vscode"><a class="markdownIt-Anchor" href="#面向纯小白开箱即用的-vscode"></a> 面向纯小白开箱即用的 VSCode</h1><h2 id="写在最前面的"><a class="markdownIt-Anchor" href="#写在最前面的"></a> 写在最前面的</h2><p>最近挺多学习c/cpp的学弟（可能有学妹.QAQ.）在群里询问CodeBlocks和编译器的安装，大伙都是推荐VSCode，但还是并没有多少人去尝试。想起我大一的时候，VSCode才出来不久，一个纯小白，在网上查资料自己配置c/cpp，还是有一点难度和懵逼的。</p><p>现在网上的教程，几乎都是教你如何配置，对于有点基础的还是很友好的，纯小白（或者有点懒的people），还是不容易接受。正好我的VSCode一直没有配置c/cpp，于是就有了这个教程，说是教程也谈不上，几乎都是点击鼠标的操作，严格来说算是安装指南。即这是面对没有编程基础的，实现简单的编译和调试，对于c/cpp课程还是足够了。</p><p>BTW 有人觉得教程太长懒得读，直接文末下载压缩包，解压后参考Readme.txt，安装步骤即可。</p><h2 id="那就开始啦"><a class="markdownIt-Anchor" href="#那就开始啦"></a> 那就开始啦</h2><p><strong>环境：</strong> Win10 Enterprise 19041.1165<br /><strong>编辑器：</strong> VSCode 1.59.1<br /><strong>编译器：</strong> mingw-w64-x86_64-8.1.0-release-win32-seh-rt_v6-rev0</p><p>考虑到简易性，编译和调试均采用mingw-w64，对于课程学习是足够的，需要性能和效率，可自行学习配置clang编译。</p><h2 id="安装与配置-mingw-w64"><a class="markdownIt-Anchor" href="#安装与配置-mingw-w64"></a> 安装与配置 mingw-w64</h2><p>请将 <strong>文末</strong> 提供的压缩包 <strong>解压</strong> 出来 (mingw-w64已打包在内) <strong>! ! !</strong></p><p><strong>双击 install.bat 运行</strong><br />会弹出 UAC 请求窗口，<strong>允许</strong> 即可；运行无误，将会显示：（根据系统语言，也会是中文）<br /><img src="https://i.loli.net/2020/02/26/io916PAHDGTn8cR.jpg" alt="" /></p><p>正常情况，mingw-w64已安装和配置好，不放心可以 <strong>win+r</strong> 键，输入 <strong>cmd</strong>，<br />运行 <code>gcc -v</code> 命令，将会显示：（非必须操作）<br /><img src="https://i.loli.net/2020/03/26/VymhjGLbZlcX2v3.jpg" alt="" /></p><h2 id="安装-vscode"><a class="markdownIt-Anchor" href="#安装-vscode"></a> 安装 VSCode</h2><p>双击 <strong>VSCodeSetup-x64-1.59.1</strong>，开始安装</p><ul><li><ol><li>同意协议<br /><img src="https://i.loli.net/2020/02/26/rySI8q19tuobKRC.jpg" alt="" /></li></ol></li><li><ol start="2"><li>设置安装路径（ <strong>建议是默认路径！！！</strong>，C:\任意纯英文路径也可，其他磁盘分区路径未测试）<br /><img src="https://i.loli.net/2020/02/26/S2FwojMEPkp6ViO.jpg" alt="" /><img src="https://i.loli.net/2020/02/26/TCkYUx6Mu2c3sWb.jpg" alt="" /></li></ol></li><li><ol start="3"><li>附加选项，勾选 <strong>Other</strong> 中四项<br /><img src="https://i.loli.net/2020/02/26/gWAV2fOL4DZPydN.jpg" alt="" /></li></ol></li><li><ol start="4"><li>完成，VSCode被打开<br /><img src="https://i.loli.net/2020/02/26/HmIP9fd3uKNoeXk.jpg" alt="" /></li></ol></li></ul><h2 id="安装与配置-vscode-插件"><a class="markdownIt-Anchor" href="#安装与配置-vscode-插件"></a> 安装与配置 VSCode 插件</h2><p>VSCode只是一个编辑器，要想进行编程，除了配置编译器外，还需要依靠插件；同时VSCode拥有丰富的插件，美化类插件，开发类插件等，有兴趣可以去了解下。</p><p>在点击左侧插件图标，即可在搜索框中，查找对应插件，点击“Install”，即可安装。<br />这里我们需要安装3个插件：</p><ul><li><ol><li><strong>C/C++</strong>，来自Microsoft官方<br /><img src="https://i.loli.net/2020/02/26/HgDj5RuSI87olBQ.jpg" alt="" /><br />点击安装后会提示正在下载和安装，完成后消息会自动消失<br /><img src="https://i.loli.net/2020/02/26/ULWXzY42PhQtw6S.jpg" alt="" /></li></ol></li><li><ol start="2"><li><strong>Code Runner</strong>，来自开发者Jun Han<br /><img src="https://i.loli.net/2020/02/26/v725VxcRXJ4YQdo.jpg" alt="" /></li></ol></li><li><ol start="3"><li><strong>Chinese (Simplified) Language Pack for Visual Studio Code</strong> 语言包，来自Microsoft官方<br /><img src="https://i.loli.net/2020/02/26/U8SMry1IFimHEgK.jpg" alt="" />点击安装语言包后，会提示重新加载，“Yes” 后，VSCoode会重新加载，界面将会切换为简体中文 <img src="https://i.loli.net/2020/02/26/d84fs7Q5JcHSBKn.jpg" alt="" /></li></ol></li></ul><p>接下来使用bat文件配置VSCode设置<br /><strong>关闭VSCode</strong>，然后<strong>双击 settings.bat 运行</strong><br />运行无误，将会显示：（根据系统语言，也会是中文）<img src="https://i.loli.net/2020/02/26/nRyEo3TlupcJZs9.jpg" alt="" /></p><h2 id="build-debug"><a class="markdownIt-Anchor" href="#build-debug"></a> Build & Debug</h2><p>现在依靠Code Runner插件，用VSCode是可以编译运行c/cpp单文件的（文件所在文件夹目录不能存在中文），输出结果会显示在VSCode下方内置终端中，<strong>但还不能进行调试</strong>。与CodeBlocks一样，需要将c/cpp文件所在文件夹，添加到左侧工作区。不同的是，CodeBlocks会自动添加，且无需额外配置文件；VSCode需要手动添加文件夹到工作区，且需要配置文件，才可以进行调试。如果是自己进行配置，能体会到整个.c文件到.exe文件的编译流程，这里个人觉得VSCode更为直观（其实CB设置里也有，不过颜值在这…QAQ）。</p><h3 id="创建并配置工作区文件夹"><a class="markdownIt-Anchor" href="#创建并配置工作区文件夹"></a> 创建并配置工作区文件夹</h3><p>在解压得到的文件夹demo内，已经分别准备好了c/cpp的调试文件。<img src="https://i.loli.net/2020/02/26/4U6BrhtN1w8m2jP.jpg" alt="" /><br />此时需要你在任一英文路径下新建未来存放.c/.cpp文件的文件夹。例如在C:\下创建Code，（若用户名不为中文，可在桌面创建存放文件夹），然后将对应demo\c或demo\cpp内 <strong>.vscode</strong> 文件夹复制到Code文件夹内，<img src="https://i.loli.net/2020/02/26/nZGUclSqXbTp1k7.jpg" alt="" /> 并右键Code文件夹-用Code打开，将存放（项目）文件夹添加到VSCode的工作区，现在Code文件夹中的c/cpp文件就可以进行编译调试了。<img src="https://i.loli.net/2020/02/26/DaGyBvAJEjtq3sN.jpg" alt="" /><img src="https://i.loli.net/2020/02/26/EzXBCoP1eN8vxbc.jpg" alt="" /></p><h3 id="测试"><a class="markdownIt-Anchor" href="#测试"></a> 测试</h3><p>下面以.c为例，创建测试文件（demo/c和demo/cpp中准备有.c和.cpp用于测试，将其复制到工作区文件夹即可）进行测试：<img src="https://i.loli.net/2020/02/26/B4kSMQlOvGHJdmg.jpg" alt="" /></p><h4 id="编译运行"><a class="markdownIt-Anchor" href="#编译运行"></a> 编译运行</h4><p>在.c文件中右键，可对代码进行格式化，点击 <strong>Run Code</strong> 直接编译运行代码，输出结果会在下方<strong>输出</strong>中显示:（也可在Code Runner扩展设置中修改，用外部cmd弹窗显示）<img src="https://i.loli.net/2020/02/26/r3yNFmPeHZIfJak.jpg" alt="" /><span id="jump1"></p><h4 id="编译调试"><a class="markdownIt-Anchor" href="#编译调试"></a> 编译调试</h4><p>先设置在代码中设置 <strong>断点</strong> <img src="https://i.loli.net/2020/02/26/jlhAvap4Nn9HkSq.jpg" alt="" />点击任务栏中<strong>调试</strong>或按<strong>F5</strong>键，均可启动调试 <img src="https://i.loli.net/2020/02/26/Uk4HMQ7lmRGEoJP.jpg" alt="" />左侧为调试信息显示，有变量，堆栈，断点等信息，上方为控制栏，可进行<strong>继续</strong>，<strong>跳过</strong>，<strong>停止</strong>等操作（均有快捷按键）。<img src="https://i.loli.net/2020/02/26/PHiSsAfxM1q9mdl.jpg" alt="" /><span id="jump2"></p><h3 id="交互式文件的输入"><a class="markdownIt-Anchor" href="#交互式文件的输入"></a> 交互式文件的输入</h3><p>交互式文件的输出与输入，默认设置为调用 VSCode 内置终端（可在设置中更改为外部cmd窗口），位于下方（当然，也可以设置为其他位置）</p><h4 id="编译运行-2"><a class="markdownIt-Anchor" href="#编译运行-2"></a> 编译运行：</h4><p>输入输出均在 <strong>终端</strong> 中进行，而无输入的文件，其运行结果在 <strong>输出</strong> 中显示（见上节 <a href="#jump1">测试</a>）<img src="https://i.loli.net/2020/02/27/YEzdJOXsNM6gb4K.jpg" alt="" /></p><h4 id="编译调试-2"><a class="markdownIt-Anchor" href="#编译调试-2"></a> 编译调试：</h4><p>与编译运行相同，依然在 <strong>终端</strong> 进行输入，断点，变量等信息仍然在左侧，调试信息显示在 <strong>终端</strong> 左侧的 <strong>调试控制台</strong>（见上节 <a href="#jump2">测试</a>）<img src="https://i.loli.net/2020/02/27/icXthIbOMj8TBkP.jpg" alt="" /></p><h3 id="warning"><a class="markdownIt-Anchor" href="#warning"></a> Warning</h3><ul><li><ol><li>代码文件所在文件夹一定要包含 <strong>.vscode</strong> 与其中的配置文件</li></ol></li><li><ol start="2"><li>代码文件所在文件夹一定是纯英文路径，不包含中文和任何特殊字符（如 “ ”空格）</li></ol></li><li><ol start="3"><li>代码文件所在文件夹一定要添加到VSCode工作区内，可以右键 <strong>用Code打开</strong> 添加，也可在VSCode工作区右键添加</li></ol></li><li><ol start="4"><li>（建议小白）严格遵守1 - 3，是可以正常进行编译调试的，避免出现奇怪错误。</li></ol></li></ul><h2 id="some-scripts"><a class="markdownIt-Anchor" href="#some-scripts"></a> Some Scripts</h2><p>这部分没兴趣可以直接跳过。<br />安装mingw-w64与添加系统环境变量命令的 <strong>install.bat</strong>：</p><figure class="highlight awk"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br></pre></td><td class="code"><pre><code class="hljs awk">@echo off<br><span class="hljs-regexp">//</span>检查路径是否冲突<br><span class="hljs-keyword">if</span> exist <span class="hljs-string">"C:\Program Files\mingw64"</span> echo Please remove the folder <span class="hljs-keyword">in</span> this path <span class="hljs-string">"C:\Program Files\mingw64"</span> and try again... && pause && <span class="hljs-keyword">exit</span><br><br><span class="hljs-regexp">//</span>调用管理员权限<br>%<span class="hljs-number">1</span> mshta vbscript:CreateObject(<span class="hljs-string">"Shell.Application"</span>).ShellExecute(<span class="hljs-string">"cmd.exe"</span>,<span class="hljs-string">"/c %~s0 ::"</span>,<span class="hljs-string">""</span>,<span class="hljs-string">"runas"</span>,<span class="hljs-number">1</span>)(window.close)&&<span class="hljs-keyword">exit</span><br>cd /d <span class="hljs-string">"%~dp0"</span><br><br><span class="hljs-regexp">//</span>安装mingw-w64<br>mkdir <span class="hljs-string">"C:\Program Files\mingw64"</span><br>xcopy mingw64 <span class="hljs-string">"C:\Program Files\mingw64"</span> /e<br><br><span class="hljs-regexp">//</span>添加系统环境变量<br>setx PATH <span class="hljs-string">"%PATH%;C:\Program Files\mingw64\bin"</span> /m<br><br>echo Do <span class="hljs-keyword">next</span> step!<br><br>pause<br></code></pre></td></tr></table></figure><p>配置VSCode设置的 <strong>settings.bat</strong>:</p><figure class="highlight dos"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br></pre></td><td class="code"><pre><code class="hljs dos">@<span class="hljs-built_in">echo</span> off<br><span class="hljs-built_in">cd</span> demo<br><span class="hljs-built_in">copy</span> settings.json <span class="hljs-variable">%APPDATA%</span>\Code\User<br><br><span class="hljs-built_in">pause</span><br></code></pre></td></tr></table></figure><h2 id="happy-coding"><a class="markdownIt-Anchor" href="#happy-coding"></a> Happy Coding</h2><p><img src="https://yyhua.cn-sh2.ufileos.com/fluid/post/happy-coding1.jpg" alt="" /> <img src="https://yyhua.cn-sh2.ufileos.com/fluid/post/happy-coding2.png" alt="" /></p><h2 id="download"><a class="markdownIt-Anchor" href="#download"></a> Download</h2><p>压缩包内Readme.txt，为简略安装步骤，可忽略，参考本教程即可。<br />若链接失效，工大同学可通过主页加入<a href="https://www.hitdn110.club/">电脑110义诊群</a>，从群文件中下载安装包。<br /><strong>>_> <a href="https://hiteducn0-my.sharepoint.com/:u:/g/personal/yyhua_hit_edu_cn/EeF_FS92YUVGr0H3k1rKm7sBidmpIi8VUaJvpgKdGe9Iiw">点此下载</a> <_<</strong><br /><strong>>_> <a href="https://yyhua.cn-sh2.ufileos.com/VSCode-1.59.1.7z">备用下载</a> <_<</strong></p><h2 id="the-end"><a class="markdownIt-Anchor" href="#the-end"></a> The End</h2><p>以上是教程（指南）的所有内容啦，VSCode只是一个编辑器，不同编辑器的组合，你可以写很多语言Python, R, Go, PHP等，还有Markdown, LaTeX等文本，强烈推荐去了解学习。</p><p>最后谈一下，关于考试使用CodeBlocks的担忧，IDE的操作逻辑和界面基本大同小异，课程会有上机实验，和考试是完全一样的，足够去熟悉CodeBlocks啦，所有不用担心。以及老师推荐用Codeblocks的问题，简言之CB集成mingw作为IDE所有都是配置好的，上手就用，这样更方便，老师教学也更容易；其实有能力老师也鼓励你去使用类似VSCode等轻量级编辑器（<s>高颜值</s>）、Xcode等IDE的。</p><p>如果有问题可下评论区留言，或查看 <strong>About</strong> 联系方式反馈.<br />本校同学可通过主页加入<a href="https://www.hitdn110.club/">哈工大电脑110俱乐部义诊群</a>询问和反馈。</p><h2 id="references"><a class="markdownIt-Anchor" href="#references"></a> References</h2><ul><li><a href="https://zhuanlan.zhihu.com/p/35178331">VS Code 搭建 C/C++ 编译运行环境的四种方案</a></li><li><a href="https://zhuanlan.zhihu.com/p/84258079">在windows系统中搭建基于VSCode的C开发环境</a></li></ul>]]></content>
<tags>
<tag>Code</tag>
<tag>Guide</tag>
</tags>
</entry>
<entry>
<title>校园网使用指南</title>
<link href="/2019/082407.html"/>
<url>/2019/082407.html</url>
<content type="html"><![CDATA[<h1 id="校园网使用指南"><a class="markdownIt-Anchor" href="#校园网使用指南"></a> 校园网使用指南</h1><p><strong>------哈尔滨工业大学 电脑110俱乐部 & 网络与信息中心 制------</strong></p><h2 id="a-校园网概况"><a class="markdownIt-Anchor" href="#a-校园网概况"></a> A. 校园网概况</h2><p>我校校园网由无线网络和有线网络（寝室网线端口）组成，学校无线网络（SSID：HIT-WLAN）覆盖了校内所有学生公寓、教学区域以及图书馆和部分公共区域，用户接入后会自动分配（DHCP）IP地址。<br />学校的校园有线网网络覆盖了学校所有学生公寓，光纤万兆到楼宇，千兆交换到桌面，每个寝室内包含两个网线端口，通过锐捷认证使用校园网服务。</p><h2 id="b-校园网开户"><a class="markdownIt-Anchor" href="#b-校园网开户"></a> B. 校园网开户</h2><p>办理校园网账号：</p><h3 id="i-终端"><a class="markdownIt-Anchor" href="#i-终端"></a> i. 终端</h3><ol><li>学生可使用 <strong>饭卡/金穗校园卡</strong> 在公寓内自助缴费机上办理开户，按提示输入网络登录密码、公寓信息及电话号码后即完成校园网账号办理。</li><li>在自助缴费机上点击 <strong>缴网费</strong> 按钮，放入饭卡点击 <strong>缴费</strong> 按钮完成缴费。完成交费后就可以利用注册的网络账号在公寓内使用校园网及校园无线网了。</li></ol><h3 id="ii-微信端"><a class="markdownIt-Anchor" href="#ii-微信端"></a> ii. 微信端</h3><ol><li><p>关注 <strong>哈尔滨工业大学服务号</strong> ，进入服务号首页，点击**服务大厅-账号绑定。<br /><img src="https://i.loli.net/2020/03/23/2OpKqIX17P9E3Gv.jpg" alt="fuwuhao.jpg" /><br /><img src="https://i.loli.net/2020/03/23/NZR4OtdVwP1qpGK.png" alt="dating.png" /><br /><img src="https://i.loli.net/2020/03/23/ABPRdHWxqUptMYa.png" alt="bangding.png" /></p></li><li><p>使用统一认证账号绑定后，进入 <strong>个人中心</strong> ，选择服务列表中 <strong>网络信息</strong> 分类下的 <strong>网络自助</strong> 。<br /><img src="https://i.loli.net/2020/03/23/Z8EnJwrQkHlLOPI.png" alt="zizhu.png" /></p></li><li><p>进入 <strong>网络自助</strong> 首页，你可以选择进行 <strong>网络开户</strong> 或 <strong>修改密码</strong> 操作。由于是新用户，点击 <strong>网络开户</strong> 进行开户操作。首先需要阅读 <strong>网络使用协议</strong> ，在10秒之后可以点击同意按钮进入网络开户详情页，并选择套餐。选择完套餐后点击下一步，输入网络密码和手机号，并点击网络开户按钮进行开户操作。<br /><img src="https://i.loli.net/2020/03/23/wNMGhSqy3e4P1xv.png" alt="kaihu.png" /><br /><img src="https://i.loli.net/2020/03/23/pHQg7oRD6mPKU5q.jpg" alt="xieyi.jpg" /><br /><img src="https://i.loli.net/2020/03/23/F2SngdfxmYe1kKs.png" alt="taocan.png" /><br /><img src="https://i.loli.net/2020/03/23/Lgn35S9QhxolZHw.jpg" alt="kaihu1.jpg" /></p></li><li><p>开户成功后，就会跳到成功页面，这时我们就可以根据成功页的提示信息进行缴费啦。回到哈工大微信 <strong>服务大厅</strong> ，在服务类别菜单中选择 <strong>网络信息</strong> 分类下的 <strong>缴费大厅</strong> 进行网费缴纳。<br /><img src="https://i.loli.net/2020/03/23/sTMJQfRx4cbhvO7.png" alt="ok.png" /><br /><img src="https://i.loli.net/2020/03/23/bGBKOZXijSt9flM.png" alt="jiaofei.png" /><br /><img src="https://i.loli.net/2020/03/23/rdaV2yu9j6BsSGO.png" alt="jiaofei1.png" /></p></li></ol><h2 id="c-校园网套餐计费"><a class="markdownIt-Anchor" href="#c-校园网套餐计费"></a> C. 校园网套餐计费</h2><h3 id="i-计费策略"><a class="markdownIt-Anchor" href="#i-计费策略"></a> i. 计费策略</h3><p>目前学校园网服务仅支持<strong>包月套餐</strong>，每月30元，<strong>流量不限</strong>；每个账户有线与无线总计支持<strong>4台设备</strong>同时上网</p><h3 id="ii-套餐网速"><a class="markdownIt-Anchor" href="#ii-套餐网速"></a> ii. 套餐网速</h3><p>有线与无线网速一致，每个联网设备分配 <strong>30Mbps</strong> 公网带宽，校内局域不限制速度，夜间（23:00 - 6:00）解除公网速度限制（<strong>8Mbps = 1MB/s</strong>）</p><h3 id="tips"><a class="markdownIt-Anchor" href="#tips"></a> Tips</h3><ul><li>下载热门资源或内网资源，巧遇校内服务器缓存，下行网速将超过公网带宽限制</li><li>对网络稳定性和延迟有需求的用户，建议使用有线网，以获得更好的网络使用体验</li><li>系统中每位同学存在3个相互独立的账号，统一身份认证账号，校园网账号（已开户，否则无），邮箱账号（同上）</li></ul><h2 id="d-无线接入说明"><a class="markdownIt-Anchor" href="#d-无线接入说明"></a> D. 无线接入说明</h2><p><span id="jump"></span></p><h3 id="i-无线网络使用须知"><a class="markdownIt-Anchor" href="#i-无线网络使用须知"></a> i. 无线网络使用须知</h3><ol><li>当您打开笔记本或手机搜索无线信号时，可能检测到不止一个无线信号，哈尔滨工业大学网络与信息中心提供的无线信号为“<strong>HIT-WLAN</strong>”。</li><li>无线网带宽资源有限，为了满足大多数人的正常使用，严禁通过无线网 P2P 下载、流媒体视频点播等，一经发现，网络信息中心有关闭其无线上网的权利。（by 网络与信息中心）</li><li><strong>HIT-WLAN</strong>是一个开放的网络，你在网络上传输的信息极易被周围人捕获，因此在使用校园无线网络进行敏感操作时，请做好应用层安全防护（https等）。</li><li>请做好计算机安全防护，打好操作系统补丁和防病毒软件，防止认证用户名和密码等个人信息的泄露。</li><li>坚决禁止通过校园网，在学校所购买文献数据库量大批量下载或爬取。</li><li>坚决禁止在校园网上以任何形式使用或传播涉密信息。</li></ol><h3 id="ii-无线网络覆盖区域"><a class="markdownIt-Anchor" href="#ii-无线网络覆盖区域"></a> ii. 无线网络覆盖区域</h3><p>一校区，二校区所有建筑楼宇，所有公寓，大部分公共区域</p><h4 id="a-一校区"><a class="markdownIt-Anchor" href="#a-一校区"></a> a. 一校区</h4><p><img src="https://i.loli.net/2020/03/23/l6jYLcFgvJk4pm9.jpg" alt="campus1.jpg" /></p><h4 id="b-二校区"><a class="markdownIt-Anchor" href="#b-二校区"></a> b. 二校区</h4><p><img src="https://i.loli.net/2020/03/23/djlS9uOmo1E8F72.jpg" alt="campus2.jpg" /></p><h3 id="iii-无线网络使用方法"><a class="markdownIt-Anchor" href="#iii-无线网络使用方法"></a> iii. 无线网络使用方法</h3><ol><li><p>使用WIFI连接名字为“<strong>HIT-WLAN</strong>”的SSID。</p></li><li><p>连接成功后，将会自动弹出认证界面（若未弹出，请运行浏览器，在地址栏中输入任意非https网址，例如 123.123.123.123，网页会自动跳转到无线网络认证页面）<br /><img src="https://i.loli.net/2020/03/23/cCxPBE2ko6fIXOZ.jpg" alt="net web1.jpg" /></p></li><li><p>按提示输入相应的用户名、密码，最后点击 <strong>连接Login</strong> 完成认证。</p></li></ol><p><span id="jump1"></span></p><h3 id="tips-2"><a class="markdownIt-Anchor" href="#tips-2"></a> Tips</h3><ol><li><p>建议使用默认（网络）设置，尤其是不要进行修改（DNS等）。</p></li><li><p>可在无线网登陆界面，进入自助管理界面进行设备下线和报修。<br /><img src="https://i.loli.net/2020/03/23/cCxPBE2ko6fIXOZ.jpg" alt="net web1.jpg" /><br /><img src="https://i.loli.net/2020/03/23/kHuLeglU895OvBQ.jpg" alt="net self.jpg" /><br /><img src="https://i.loli.net/2020/03/23/dqKgDZwIoB2S6WA.jpg" alt="net self1.jpg" /></p></li><li><p>如需进行报修或设备解绑请致电 0451-86414659。</p></li></ol><h2 id="e-有线接入说明"><a class="markdownIt-Anchor" href="#e-有线接入说明"></a> E. 有线接入说明</h2><h3 id="i-有线网络使用须知"><a class="markdownIt-Anchor" href="#i-有线网络使用须知"></a> i. 有线网络使用须知</h3><p>同<a href="#jump">无线网络使用须知</a></p><h3 id="ii-有线网络覆盖区域"><a class="markdownIt-Anchor" href="#ii-有线网络覆盖区域"></a> ii. 有线网络覆盖区域</h3><p>学校所有公寓，每个寝室包含2个网线端口，距离地面高度均约1m。由于寝室结构不同，可能出现端口被柜子等遮盖情况。<br />有的寝室需要装交换机（被上任学长带走的）请联系报修，以及不要把网线插到AP的口上。</p><h3 id="iii-有线网络使用方法"><a class="markdownIt-Anchor" href="#iii-有线网络使用方法"></a> iii. 有线网络使用方法</h3><p>使用锐捷802.1x认证客户端进行上网认证</p><h4 id="a-直连pc"><a class="markdownIt-Anchor" href="#a-直连pc"></a> a. 直连PC</h4><p><span id="jump2"></span></p><ol><li>请在网络中心官网下载<a href="http://ito.hit.edu.cn/2016/0425/c5452a154329/page.htm">锐捷认证客户端</a>或加入电脑110义诊QQ群（见文末）</li><li>安装锐捷认证客户端后，插入网线<br /><img src="https://i.loli.net/2020/03/23/9FRzPl2xosQhHbi.jpg" alt="install.jpg" /></li><li>打开客户端，输入相应用户名，密码点击<strong>连接</strong>即可连接校园网<br /><img src="https://i.loli.net/2020/03/23/RVHSFAwiadgUXQ6.jpg" alt="run.jpg" /></li></ol><p><span id="router"></span></p><h4 id="b-使用路由"><a class="markdownIt-Anchor" href="#b-使用路由"></a> b. 使用路由</h4><p>见续篇：<a href="https://www.hitdn110.club/2019/12/539.html">使用路由器连接有线网</a></p><h3 id="tips-3"><a class="markdownIt-Anchor" href="#tips-3"></a> Tips</h3><ol><li>解绑管理和报修同<a href="#jump1">无线Tips</a></li><li>不建议修改DNS or hosts等网络设置，使用默认设置即可</li><li>由于校园网带宽是分配到接入设备，这为实现带宽叠加（即多拨）提供了可能性，相关信息可加入<a href="#jump2">电脑110义诊QQ群</a>了解</li></ol><h2 id="f-工大vpn"><a class="markdownIt-Anchor" href="#f-工大vpn"></a> F. 工大VPN</h2><h3 id="i-介绍"><a class="markdownIt-Anchor" href="#i-介绍"></a> i. 介绍</h3><p>可在外网环境（例如校外，家中，交流学校等），访问校内网站。支持多平台，包含Windows，MacOS，Linux，Android，iOS。<br />目前师生<strong>免费使用</strong>，且<strong>不限流量</strong>，限制仅<strong>一台设备</strong>登录，具体详情请访问<a href="http://static.hit.edu.cn/vpn/">工大vpn官网</a></p><h3 id="ii-使用方式"><a class="markdownIt-Anchor" href="#ii-使用方式"></a> ii. 使用方式</h3><h4 id="a-web版"><a class="markdownIt-Anchor" href="#a-web版"></a> a. Web版</h4><ol><li>浏览器访问 <a href="http://ivpn.hit.edu.cn">http://ivpn.hit.edu.cn</a></li><li>使用统一认证登录即可<br /><img src="https://i.loli.net/2020/03/26/ayxsZBMtzbvjLH5.jpg" alt="vpn.png" /></li></ol><h4 id="b-客户端"><a class="markdownIt-Anchor" href="#b-客户端"></a> b. 客户端</h4><ol><li><p>从<a href="http://static.hit.edu.cn/vpn/">工大vpn官网</a>下载并安装对应客户端<br /><img src="https://i.loli.net/2020/03/26/V539swZxdO6nKGp.jpg" alt="vpn1.png" /></p></li><li><p>认证方式为：<br />服务器名称：<a href="http://ivpn.hit.edu.cn">ivpn.hit.edu.cn</a><br />用户名口令为统一身份认证账号及密码</p></li></ol><h4 id="tips-4"><a class="markdownIt-Anchor" href="#tips-4"></a> Tips</h4><ul><li>如果无需要连接校内服务器的需求，建议不要安装客户端，使用web版即可</li></ul><h2 id="工大教育邮箱"><a class="markdownIt-Anchor" href="#工大教育邮箱"></a> 工大教育邮箱</h2><p>见 <a href="https://www.hitdn110.club/2020/03/649.html">哈工大邮箱使用指南</a></p><h2 id="not-end"><a class="markdownIt-Anchor" href="#not-end"></a> Not End</h2><p>后续版本将更新：</p><ul><li><p><a href="http://eduroam.cstnet.cn/">Eduroam网络</a> （不一定有）</p></li><li><p>开启路由器访问ipv6网站的功能（酌情）</p></li><li><p>OpenWrt路由器固件的编译、插件开发（酌情）</p></li><li><p>······<br />如果大家有其他想了解的以及校园网相关问题，可加入电脑110义诊QQ群304067847，向我们反馈。</p><p><img src="https://i.loli.net/2020/03/23/YZgxuBrSmGWClpE.jpg" alt="yizhen.jpg" /><br /><br/></p></li></ul><h2 id="welcome-to-hit_"><a class="markdownIt-Anchor" href="#welcome-to-hit_"></a> Welcome to HIT！>_<</h2>]]></content>
<categories>
<category>HIT Network Guide</category>
</categories>
<tags>
<tag>HIT</tag>
<tag>Guide</tag>
</tags>
</entry>
</search>