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| 26b9470e4f |
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<head>
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<h1>Markdown 打字机</h1>
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<p>优雅的打字效果，呈现精美的内容</p>
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const markdownContent = `
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# 高中物理《万有引力定律》视频课程总结
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## 一、课程概述
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本节课围绕**万有引力定律**进行深入探究，重点研究万有引力公式本身的考察和应用，而非天体运动的周期、速度方向等扩展内容。
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## 二、教学目标
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1. **深入理解万有引力定律**：掌握表达式及其适用范围
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2. **应用能力培养**：能够运用万有引力定律解决相关问题
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3. **物理观念建立**：培养正确的物理观念、科学思维和创新精神
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4. **科学态度培养**：增强对客观世界的探究精神
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## 三、典型习题解析
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### 习题1：月地检验证明题
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**题目要求**：通过计算验证苹果落地的力与维持月球绕地球运动的力是同一种性质的力
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**解题思路**：
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1. **理论分析**：如果两种力同性质，应遵循平方反比定律（F ∝ 1/R²）
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2. **力学角度**：
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- 月球轨道加速度：a₁ = g/3600 ≈ 0.0027 m/s²
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- （基于地球半径R，月球轨道半径60R，平方反比关系）
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3. **运动学角度**：
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- 使用向心加速度公式：a₂ = 4π²R/T²
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- 代入月球周期T=27.3天≈2.36×10⁶秒
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- 计算结果：a₂ ≈ 0.0027 m/s²
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4. **结论**：a₁ ≈ a₂，证明两种力性质相同
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**关键点**：不能直接使用万有引力公式证明，需通过独立计算验证
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### 习题2：平抛运动比较
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**题目条件**：
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- 地球质量：月球质量 = 81:1
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- 地球半径：月球半径 = 4:1
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- 相同高度、相同初速度水平抛出
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**求解**：地球与月球表面平抛水平距离之比
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**解题步骤**：
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1. 水平距离公式：x = v₀t
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2. 下落时间：t = √(2h/g)
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3. 通过黄金代换式求重力加速度比：
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- g地/g月 = (M地/R地²)/(M月/R月²) = 81/16
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4. 时间比：t地/t月 = √(g月/g地) = 4/9
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5. 距离比：x地/x月 = t地/t月 = 4/9
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**答案**：地球表面与月球表面的平抛水平距离比为4:9
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### 习题3：伯克效应与引力变化
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**题目要求**：定性画出均匀球体内外各点所受引力随距离变化的函数图像
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**关键知识**：
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- 伯克效应：质量分布均匀的球壳对内部质点的引力为零
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- 地球密度均匀：ρ = 常数
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**解题分析**：
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1. **球体内部（0 < r < R）**：
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- 有效质量：M_eff = ρ×(4πr³/3)
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- 引力公式：F = GM_effm/r² = (4πGρm/3)·r
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- ∴ F ∝ r （线性增长）
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2. **球体表面（r = R）**：
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- F_max = GMm/R²
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3. **球体外部（r > R）**：
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- F = GMm/r² ∝ 1/r²
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**函数图像特征**：
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- 0→R：过原点的斜直线（线性增长）
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- r = R：达到最大值F_max
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- r > R：平方反比曲线（逐渐减小）
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## 四、重点难点总结
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### 核心概念
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1. **万有引力定律**：F = G·M₁M₂/r²
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2. **黄金代换式**：GM = gR²
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3. **伯克效应**：均匀球壳内部引力为零
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### 易错点提醒
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1. 月地检验题中不能直接使用万有引力公式
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2. 平抛问题要注意重力加速度的变化
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3. 球体内外引力变化需要分段处理
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### 方法技巧
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1. **验证性题目**：通过独立计算进行验证，而非直接使用待证结论
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||||
2. **比例问题**：善用比例关系简化计算
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||||
3. **图像题**：定性分析时抓住关键点（原点、极值点、渐近线）
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## 五、学习建议
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1. 重视基础公式的理解和记忆
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2. 掌握黄金代换式在各种情境下的应用
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||||
3. 理解伯克效应的物理意义
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||||
4. 加强数学计算能力，特别是科学计算
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||||
5. 注重数理结合，提高空间想象能力
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||||
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||||
`;
|
||||
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dsLightRag/static/sum/md/mermaid.min.js
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dsLightRag/static/sum/md/prism-css.min.js
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dsLightRag/static/sum/md/prism-css.min.js
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!function(s){var e=/(?:"(?:\\(?:\r\n|[\s\S])|[^"\\\r\n])*"|'(?:\\(?:\r\n|[\s\S])|[^'\\\r\n])*')/;s.languages.css={comment:/\/\*[\s\S]*?\*\//,atrule:{pattern:RegExp("@[\\w-](?:[^;{\\s\"']|\\s+(?!\\s)|"+e.source+")*?(?:;|(?=\\s*\\{))"),inside:{rule:/^@[\w-]+/,"selector-function-argument":{pattern:/(\bselector\s*\(\s*(?![\s)]))(?:[^()\s]|\s+(?![\s)])|\((?:[^()]|\([^()]*\))*\))+(?=\s*\))/,lookbehind:!0,alias:"selector"},keyword:{pattern:/(^|[^\w-])(?:and|not|only|or)(?![\w-])/,lookbehind:!0}}},url:{pattern:RegExp("\\burl\\((?:"+e.source+"|(?:[^\\\\\r\n()\"']|\\\\[^])*)\\)","i"),greedy:!0,inside:{function:/^url/i,punctuation:/^\(|\)$/,string:{pattern:RegExp("^"+e.source+"$"),alias:"url"}}},selector:{pattern:RegExp("(^|[{}\\s])[^{}\\s](?:[^{};\"'\\s]|\\s+(?![\\s{])|"+e.source+")*(?=\\s*\\{)"),lookbehind:!0},string:{pattern:e,greedy:!0},property:{pattern:/(^|[^-\w\xA0-\uFFFF])(?!\s)[-_a-z\xA0-\uFFFF](?:(?!\s)[-\w\xA0-\uFFFF])*(?=\s*:)/i,lookbehind:!0},important:/!important\b/i,function:{pattern:/(^|[^-a-z0-9])[-a-z0-9]+(?=\()/i,lookbehind:!0},punctuation:/[(){};:,]/},s.languages.css.atrule.inside.rest=s.languages.css;var t=s.languages.markup;t&&(t.tag.addInlined("style","css"),t.tag.addAttribute("style","css"))}(Prism);
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dsLightRag/static/sum/md/prism-javascript.min.js
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dsLightRag/static/sum/md/prism-javascript.min.js
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Prism.languages.javascript=Prism.languages.extend("clike",{"class-name":[Prism.languages.clike["class-name"],{pattern:/(^|[^$\w\xA0-\uFFFF])(?!\s)[_$A-Z\xA0-\uFFFF](?:(?!\s)[$\w\xA0-\uFFFF])*(?=\.(?:constructor|prototype))/,lookbehind:!0}],keyword:[{pattern:/((?:^|\})\s*)catch\b/,lookbehind:!0},{pattern:/(^|[^.]|\.\.\.\s*)\b(?:as|assert(?=\s*\{)|async(?=\s*(?:function\b|\(|[$\w\xA0-\uFFFF]|$))|await|break|case|class|const|continue|debugger|default|delete|do|else|enum|export|extends|finally(?=\s*(?:\{|$))|for|from(?=\s*(?:['"]|$))|function|(?:get|set)(?=\s*(?:[#\[$\w\xA0-\uFFFF]|$))|if|implements|import|in|instanceof|interface|let|new|null|of|package|private|protected|public|return|static|super|switch|this|throw|try|typeof|undefined|var|void|while|with|yield)\b/,lookbehind:!0}],function:/#?(?!\s)[_$a-zA-Z\xA0-\uFFFF](?:(?!\s)[$\w\xA0-\uFFFF])*(?=\s*(?:\.\s*(?:apply|bind|call)\s*)?\()/,number:{pattern:RegExp("(^|[^\\w$])(?:NaN|Infinity|0[bB][01]+(?:_[01]+)*n?|0[oO][0-7]+(?:_[0-7]+)*n?|0[xX][\\dA-Fa-f]+(?:_[\\dA-Fa-f]+)*n?|\\d+(?:_\\d+)*n|(?:\\d+(?:_\\d+)*(?:\\.(?:\\d+(?:_\\d+)*)?)?|\\.\\d+(?:_\\d+)*)(?:[Ee][+-]?\\d+(?:_\\d+)*)?)(?![\\w$])"),lookbehind:!0},operator:/--|\+\+|\*\*=?|=>|&&=?|\|\|=?|[!=]==|<<=?|>>>?=?|[-+*/%&|^!=<>]=?|\.{3}|\?\?=?|\?\.?|[~:]/}),Prism.languages.javascript["class-name"][0].pattern=/(\b(?:class|extends|implements|instanceof|interface|new)\s+)[\w.\\]+/,Prism.languages.insertBefore("javascript","keyword",{regex:{pattern:RegExp("((?:^|[^$\\w\\xA0-\\uFFFF.\"'\\])\\s]|\\b(?:return|yield))\\s*)/(?:(?:\\[(?:[^\\]\\\\\r\n]|\\\\.)*\\]|\\\\.|[^/\\\\\\[\r\n])+/[dgimyus]{0,7}|(?:\\[(?:[^[\\]\\\\\r\n]|\\\\.|\\[(?:[^[\\]\\\\\r\n]|\\\\.|\\[(?:[^[\\]\\\\\r\n]|\\\\.)*\\])*\\])*\\]|\\\\.|[^/\\\\\\[\r\n])+/[dgimyus]{0,7}v[dgimyus]{0,7})(?=(?:\\s|/\\*(?:[^*]|\\*(?!/))*\\*/)*(?:$|[\r\n,.;:})\\]]|//))"),lookbehind:!0,greedy:!0,inside:{"regex-source":{pattern:/^(\/)[\s\S]+(?=\/[a-z]*$)/,lookbehind:!0,alias:"language-regex",inside:Prism.languages.regex},"regex-delimiter":/^\/|\/$/,"regex-flags":/^[a-z]+$/}},"function-variable":{pattern:/#?(?!\s)[_$a-zA-Z\xA0-\uFFFF](?:(?!\s)[$\w\xA0-\uFFFF])*(?=\s*[=:]\s*(?:async\s*)?(?:\bfunction\b|(?:\((?:[^()]|\([^()]*\))*\)|(?!\s)[_$a-zA-Z\xA0-\uFFFF](?:(?!\s)[$\w\xA0-\uFFFF])*)\s*=>))/,alias:"function"},parameter:[{pattern:/(function(?:\s+(?!\s)[_$a-zA-Z\xA0-\uFFFF](?:(?!\s)[$\w\xA0-\uFFFF])*)?\s*\(\s*)(?!\s)(?:[^()\s]|\s+(?![\s)])|\([^()]*\))+(?=\s*\))/,lookbehind:!0,inside:Prism.languages.javascript},{pattern:/(^|[^$\w\xA0-\uFFFF])(?!\s)[_$a-z\xA0-\uFFFF](?:(?!\s)[$\w\xA0-\uFFFF])*(?=\s*=>)/i,lookbehind:!0,inside:Prism.languages.javascript},{pattern:/(\(\s*)(?!\s)(?:[^()\s]|\s+(?![\s)])|\([^()]*\))+(?=\s*\)\s*=>)/,lookbehind:!0,inside:Prism.languages.javascript},{pattern:/((?:\b|\s|^)(?!(?:as|async|await|break|case|catch|class|const|continue|debugger|default|delete|do|else|enum|export|extends|finally|for|from|function|get|if|implements|import|in|instanceof|interface|let|new|null|of|package|private|protected|public|return|set|static|super|switch|this|throw|try|typeof|undefined|var|void|while|with|yield)(?![$\w\xA0-\uFFFF]))(?:(?!\s)[_$a-zA-Z\xA0-\uFFFF](?:(?!\s)[$\w\xA0-\uFFFF])*\s*)\(\s*|\]\s*\(\s*)(?!\s)(?:[^()\s]|\s+(?![\s)])|\([^()]*\))+(?=\s*\)\s*\{)/,lookbehind:!0,inside:Prism.languages.javascript}],constant:/\b[A-Z](?:[A-Z_]|\dx?)*\b/}),Prism.languages.insertBefore("javascript","string",{hashbang:{pattern:/^#!.*/,greedy:!0,alias:"comment"},"template-string":{pattern:/`(?:\\[\s\S]|\$\{(?:[^{}]|\{(?:[^{}]|\{[^}]*\})*\})+\}|(?!\$\{)[^\\`])*`/,greedy:!0,inside:{"template-punctuation":{pattern:/^`|`$/,alias:"string"},interpolation:{pattern:/((?:^|[^\\])(?:\\{2})*)\$\{(?:[^{}]|\{(?:[^{}]|\{[^}]*\})*\})+\}/,lookbehind:!0,inside:{"interpolation-punctuation":{pattern:/^\$\{|\}$/,alias:"punctuation"},rest:Prism.languages.javascript}},string:/[\s\S]+/}},"string-property":{pattern:/((?:^|[,{])[ \t]*)(["'])(?:\\(?:\r\n|[\s\S])|(?!\2)[^\\\r\n])*\2(?=\s*:)/m,lookbehind:!0,greedy:!0,alias:"property"}}),Prism.languages.insertBefore("javascript","operator",{"literal-property":{pattern:/((?:^|[,{])[ \t]*)(?!\s)[_$a-zA-Z\xA0-\uFFFF](?:(?!\s)[$\w\xA0-\uFFFF])*(?=\s*:)/m,lookbehind:!0,alias:"property"}}),Prism.languages.markup&&(Prism.languages.markup.tag.addInlined("script","javascript"),Prism.languages.markup.tag.addAttribute("on(?:abort|blur|change|click|composition(?:end|start|update)|dblclick|error|focus(?:in|out)?|key(?:down|up)|load|mouse(?:down|enter|leave|move|out|over|up)|reset|resize|scroll|select|slotchange|submit|unload|wheel)","javascript")),Prism.languages.js=Prism.languages.javascript;
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dsLightRag/static/sum/md/prism-python.min.js
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dsLightRag/static/sum/md/prism-python.min.js
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Prism.languages.python={comment:{pattern:/(^|[^\\])#.*/,lookbehind:!0,greedy:!0},"string-interpolation":{pattern:/(?:f|fr|rf)(?:("""|''')[\s\S]*?\1|("|')(?:\\.|(?!\2)[^\\\r\n])*\2)/i,greedy:!0,inside:{interpolation:{pattern:/((?:^|[^{])(?:\{\{)*)\{(?!\{)(?:[^{}]|\{(?!\{)(?:[^{}]|\{(?!\{)(?:[^{}])+\})+\})+\}/,lookbehind:!0,inside:{"format-spec":{pattern:/(:)[^:(){}]+(?=\}$)/,lookbehind:!0},"conversion-option":{pattern://,alias:"punctuation"},rest:null}},string:/[\s\S]+/}},"triple-quoted-string":{pattern:/(?:[rub]|br|rb)?("""|''')[\s\S]*?\1/i,greedy:!0,alias:"string"},string:{pattern:/(?:[rub]|br|rb)?("|')(?:\\.|(?!\1)[^\\\r\n])*\1/i,greedy:!0},function:{pattern:/((?:^|\s)def[ \t]+)[a-zA-Z_]\w*(?=\s*\()/g,lookbehind:!0},"class-name":{pattern:/(\bclass\s+)\w+/i,lookbehind:!0},decorator:{pattern:/(^[\t ]*)@\w+(?:\.\w+)*/m,lookbehind:!0,alias:["annotation","punctuation"],inside:{punctuation:/\./}},keyword:/\b(?:_(?=\s*:)|and|as|assert|async|await|break|case|class|continue|def|del|elif|else|except|exec|finally|for|from|global|if|import|in|is|lambda|match|nonlocal|not|or|pass|print|raise|return|try|while|with|yield)\b/,builtin:/\b(?:__import__|abs|all|any|apply|ascii|basestring|bin|bool|buffer|bytearray|bytes|callable|chr|classmethod|cmp|coerce|compile|complex|delattr|dict|dir|divmod|enumerate|eval|execfile|file|filter|float|format|frozenset|getattr|globals|hasattr|hash|help|hex|id|input|int|intern|isinstance|issubclass|iter|len|list|locals|long|map|max|memoryview|min|next|object|oct|open|ord|pow|property|range|raw_input|reduce|reload|repr|reversed|round|set|setattr|slice|sorted|staticmethod|str|sum|super|tuple|type|unichr|unicode|vars|xrange|zip)\b/,boolean:/\b(?:False|None|True)\b/,number:/\b0(?:b(?:_?[01])+|o(?:_?[0-7])+|x(?:_?[a-f0-9])+)\b|(?:\b\d+(?:_\d+)*(?:\.(?:\d+(?:_\d+)*)?)?|\B\.\d+(?:_\d+)*)(?:e[+-]?\d+(?:_\d+)*)?j?(?!\w)/i,operator:/[-+%=]=?|!=|:=|\*\*?=?|\/\/?=?|<[<=>]?|>[=>]?|[&|^~]/,punctuation:/[{}[\];(),.:]/},Prism.languages.python["string-interpolation"].inside.interpolation.inside.rest=Prism.languages.python,Prism.languages.py=Prism.languages.python;
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dsLightRag/static/sum/md/prism-tomorrow.min.css
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dsLightRag/static/sum/md/prism-tomorrow.min.css
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code[class*=language-],pre[class*=language-]{color:#ccc;background:0 0;font-family:Consolas,Monaco,'Andale Mono','Ubuntu Mono',monospace;font-size:1em;text-align:left;white-space:pre;word-spacing:normal;word-break:normal;word-wrap:normal;line-height:1.5;-moz-tab-size:4;-o-tab-size:4;tab-size:4;-webkit-hyphens:none;-moz-hyphens:none;-ms-hyphens:none;hyphens:none}pre[class*=language-]{padding:1em;margin:.5em 0;overflow:auto}:not(pre)>code[class*=language-],pre[class*=language-]{background:#2d2d2d}:not(pre)>code[class*=language-]{padding:.1em;border-radius:.3em;white-space:normal}.token.block-comment,.token.cdata,.token.comment,.token.doctype,.token.prolog{color:#999}.token.punctuation{color:#ccc}.token.attr-name,.token.deleted,.token.namespace,.token.tag{color:#e2777a}.token.function-name{color:#6196cc}.token.boolean,.token.function,.token.number{color:#f08d49}.token.class-name,.token.constant,.token.property,.token.symbol{color:#f8c555}.token.atrule,.token.builtin,.token.important,.token.keyword,.token.selector{color:#cc99cd}.token.attr-value,.token.char,.token.regex,.token.string,.token.variable{color:#7ec699}.token.entity,.token.operator,.token.url{color:#67cdcc}.token.bold,.token.important{font-weight:700}.token.italic{font-style:italic}.token.entity{cursor:help}.token.inserted{color:green}
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dsLightRag/static/sum/md/prism.min.js
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dsLightRag/static/sum/md/prism.min.js
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