Android完美支持MathML显示公式方程

Android完美支持MathML显示公式方程

历经3个开发阶段《Android实现方程编辑器》、《Android完美解决LaTeX中文显示问题》、《Android判断LaTeX是否为空方程》后,『神马笔记』的方程编辑器现已经完美支持LaTeX,接下来尝试支持MathML。

一、目标

神马笔记』支持MathML显示公式方程。

二、设计思路

在MathML之前,『神马笔记』已经完美支持LaTeX。

最快速实现支持MathML的方式是将MathML转化为LaTeX语言。

这样一来,后续的解析渲染就可以复用LaTeX的实现,不需要再次开发。

三、实现过程

1. 实现方案

方案 描述 参考资料
JMathTeX The library uses the typesetting algorithms of the well-known TeX and LaTeX systems and therefore displays formulas in a very professional looking way. Formulas are Java-objects that can be built from scratch (by combining smaller formulas in several ways) and from LaTeX strings. There is also limited support for MathML. http://jmathtex.sourceforge.net/
MathParser MathParser is a freeware tool that converts MathML into LaTeX. It processes pure MathML code as well as HTML with embedded MathML. It also offers a special built-in parser for Mathcad HTML/MathML files. You do not have to retype all equations for publishing anymore. http://www.tilman.de/programme/mathparser/index_en.html
fMath FMATH is a FREE solution to display mathematics on web pages, desktop app or mobile devices using MathML, LaTeX or OMML (Microsoft Word) standards. http://www.fmath.info/
XSLT MathML Library The XSLT MathML Library, xsltml, provides the XSLT developer with a set of XSLT templates for MathML 2.0 to LaTeX translation. These are implemented purely in XSLT, that is they do not use any extensions. http://xsltml.sourceforge.net/

2. 参考文章

文章 地址
数学公式:使用xsltml将MathML转LaTex https://www.jianshu.com/p/b4caef5bf1ab
java使用XSL+XML生成HTML文件 http://www.blogjava.net/yangxiang/archive/2009/08/11/290688.html

3. 测试结果

方案 结果
JMathTeX 根据JMathTeX介绍,对MathML提供了有限支持。
后来的项目转换过程中JMathTeX->JLaTeXMath->jlatexmath-android
似乎移除了对MathML的支持。
后续有待查证。
MathParser 采用替换的方式进行转换。
未达到预期效果,放弃之。
fMath 使用JDOM2解析XML并进行转换,部分公式效果未达到预期,但可用。
备选方案。
XSLT MathML Library 使用XSL方式转换,部分公式无法显示,但似乎优于fMath。
推荐方案。

4. 检测MathML

因为LaTeX和MathML使用同一个编辑框。因此需要自动检查用户输入的语言。

通过检索math><math两个关键字区分LaTeX和MathML。

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public static final boolean isMathML(String text) {
if (TextUtils.isEmpty(text)) {
return false;
}

{
int pos = text.lastIndexOf("math>");
if (pos >= 0) {
return true;
}
}

{
int pos = text.indexOf("<math");
if (pos >= 0) {
return true;
}
}

return false;
}

四、遗留问题

附录中的公式来自于文章《Android完美解决LaTeX中文显示问题》,通过工具将LaTeX转换为MathML。

发现LaTeX能显示为多行的公式,使用MathML只显示一行。

未来有待查找问题根源。

五、Next

神马笔记』的方程编辑器开发至此,已经实现了以下功能。

  1. 支持LaTeX和MathML
  2. 支持无效方程判断
  3. 支持空方程判定
  4. 支持LaTeX快捷输入栏

可能是Android平台最强大的方程编辑器了。

接下来将把方程编辑器整合到『神马笔记』中,以实现在笔记中插入方程。

六、Finally

~第一是早早归来~怕红萼无人为主~

七、Appendix

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<mi>O</mi>
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</munderover>
</mrow>
</math>

2.

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3.

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<mrow class="MJX-TeXAtom-ORD">
<mn>2</mn>
</mrow>
</msub>
<mi mathvariant="normal">O</mi>
<mover>
<mrow class="MJX-TeXAtom-OP">
<mstyle scriptlevel="1">
<mtable rowspacing="0.1em" columnspacing="0em" displaystyle="false">
<mtr>
<mtd>
<mo>=</mo>
<mspace width="negativethinmathspace" />
<mo>=</mo>
<mspace width="negativethinmathspace" />
<mo>=</mo>
<mspace width="negativethinmathspace" />
<mo>=</mo>
<mspace width="negativethinmathspace" />
<mo>=</mo>
<mspace width="negativethinmathspace" />
<mo>=</mo>
</mtd>
</mtr>
</mtable>
</mstyle>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mrow class="MJX-TeXAtom-ORD">
<mo>&#x7535;</mo>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mo>&#x89E3;</mo>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mphantom>
<mrow class="MJX-TeXAtom-ORD">
<mo>&#x7535;</mo>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mo>&#x89E3;</mo>
</mrow>
</mphantom>
</mrow>
</mrow>
</mover>
<mo>&#x2061;<!-- ⁡ --></mo>
<mn>2</mn>
<msub>
<mi mathvariant="normal">H</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>2</mn>
</mrow>
</msub>
<mo stretchy="false">&#x2191;<!-- ↑ --></mo>
<mo>+</mo>
<msub>
<mi mathvariant="normal">O</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>2</mn>
</mrow>
</msub>
<mo stretchy="false">&#x2191;<!-- ↑ -->&#x223C;<!-- ∼ --></mo>
<mn>4</mn>
<msup>
<mi mathvariant="normal">e</mi>
<mrow class="MJX-TeXAtom-ORD">
<mo>&#x2212;<!-- − --></mo>
</mrow>
</msup>
<mrow class="MJX-TeXAtom-ORD">
<mo>&#xFF0C;</mo>
</mrow>
<mspace linebreak="newline" />
<mn>2</mn>
<mn>1</mn>
<mn>4</mn>
<mspace linebreak="newline" />
<mn>0.2</mn>
<mi mathvariant="normal">m</mi>
<mi mathvariant="normal">o</mi>
<mi mathvariant="normal">l</mi>
<mn>0.1</mn>
<mi mathvariant="normal">m</mi>
<mi mathvariant="normal">o</mi>
<mi mathvariant="normal">l</mi>
<mn>0.4</mn>
<mi mathvariant="normal">m</mi>
<mi mathvariant="normal">o</mi>
<mi mathvariant="normal">l</mi>
<mspace linebreak="newline" />
<mrow class="MJX-TeXAtom-ORD">
<mo>&#x5219;</mo>
</mrow>
<mn>2</mn>
<mi mathvariant="normal">C</mi>
<mi mathvariant="normal">u</mi>
<mi mathvariant="normal">S</mi>
<msub>
<mi mathvariant="normal">O</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>4</mn>
</mrow>
</msub>
<mo>+</mo>
<mn>2</mn>
<msub>
<mi mathvariant="normal">H</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>2</mn>
</mrow>
</msub>
<mi mathvariant="normal">O</mi>
<mover>
<mrow class="MJX-TeXAtom-OP">
<mstyle scriptlevel="1">
<mtable rowspacing="0.1em" columnspacing="0em" displaystyle="false">
<mtr>
<mtd>
<mo>=</mo>
<mspace width="negativethinmathspace" />
<mo>=</mo>
<mspace width="negativethinmathspace" />
<mo>=</mo>
<mspace width="negativethinmathspace" />
<mo>=</mo>
<mspace width="negativethinmathspace" />
<mo>=</mo>
<mspace width="negativethinmathspace" />
<mo>=</mo>
</mtd>
</mtr>
</mtable>
</mstyle>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mrow class="MJX-TeXAtom-ORD">
<mo>&#x7535;</mo>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mo>&#x89E3;</mo>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mphantom>
<mrow class="MJX-TeXAtom-ORD">
<mo>&#x7535;</mo>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mo>&#x89E3;</mo>
</mrow>
</mphantom>
</mrow>
</mrow>
</mover>
<mo>&#x2061;<!-- ⁡ --></mo>
<mn>2</mn>
<mi mathvariant="normal">C</mi>
<mi mathvariant="normal">u</mi>
<mo>+</mo>
<msub>
<mi mathvariant="normal">O</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>2</mn>
</mrow>
</msub>
<mo stretchy="false">&#x2191;<!-- ↑ --></mo>
<mo>+</mo>
<mn>2</mn>
<msub>
<mi mathvariant="normal">H</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>2</mn>
</mrow>
</msub>
<mi mathvariant="normal">S</mi>
<msub>
<mi mathvariant="normal">O</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>4</mn>
</mrow>
</msub>
<mrow class="MJX-TeXAtom-ORD">
<mo>&#xFF0C;</mo>
</mrow>
<mspace linebreak="newline" />
<mn>0.1</mn>
<mi mathvariant="normal">m</mi>
<mi mathvariant="normal">o</mi>
<mi mathvariant="normal">l</mi>
<mn>0.2</mn>
<mi mathvariant="normal">m</mi>
<mi mathvariant="normal">o</mi>
<mi mathvariant="normal">l</mi>
<mspace linebreak="newline" />
<mrow class="MJX-TeXAtom-ORD">
<mo>&#x5373;</mo>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mo>&#x5F53;</mo>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mo>&#x7535;</mo>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mo>&#x8DEF;</mo>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mo>&#x4E2D;</mo>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mo>&#x901A;</mo>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mo>&#x8FC7;</mo>
</mrow>
<mn>0.4</mn>
<mi mathvariant="normal">m</mi>
<mi mathvariant="normal">o</mi>
<mi mathvariant="normal">l</mi>
<mrow class="MJX-TeXAtom-ORD">
<mo>&#x7535;</mo>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mo>&#x5B50;</mo>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mo>&#x65F6;</mo>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mo>&#xFF0C;</mo>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mo>&#x9634;</mo>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mo>&#x9633;</mo>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mo>&#x4E24;</mo>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mo>&#x6781;</mo>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mo>&#x4EA7;</mo>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mo>&#x751F;</mo>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mo>&#x76F8;</mo>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mo>&#x540C;</mo>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mo>&#x4F53;</mo>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mo>&#x79EF;</mo>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mo>&#x7684;</mo>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mo>&#x6C14;</mo>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mo>&#x4F53;</mo>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mo>&#x65F6;</mo>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mo>&#xFF0C;</mo>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mo>&#x751F;</mo>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mo>&#x6210;</mo>
</mrow>
<mi mathvariant="normal">n</mi>
<mo stretchy="false">(</mo>
<msub>
<mi mathvariant="normal">H</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>2</mn>
</mrow>
</msub>
<mi mathvariant="normal">S</mi>
<msub>
<mi mathvariant="normal">O</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>4</mn>
</mrow>
</msub>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mn>0.2</mn>
<mi mathvariant="normal">m</mi>
<mi mathvariant="normal">o</mi>
<mi mathvariant="normal">l</mi>
<mrow class="MJX-TeXAtom-ORD">
<mo>&#xFF0C;</mo>
</mrow>
<mspace linebreak="newline" />
<mrow class="MJX-TeXAtom-ORD">
<mo>&#x6240;</mo>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mo>&#x4EE5;</mo>
</mrow>
<mi mathvariant="normal">n</mi>
<mo stretchy="false">(</mo>
<msup>
<mi mathvariant="normal">H</mi>
<mrow class="MJX-TeXAtom-ORD">
<mo>+</mo>
</mrow>
</msup>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mn>0.4</mn>
<mi mathvariant="normal">m</mi>
<mi mathvariant="normal">o</mi>
<mi mathvariant="normal">l</mi>
<mrow class="MJX-TeXAtom-ORD">
<mo>&#xFF0C;</mo>
</mrow>
<mspace linebreak="newline" />
<mrow class="MJX-TeXAtom-ORD">
<mo>&#x5219;</mo>
</mrow>
<mi mathvariant="normal">c</mi>
<mo stretchy="false">(</mo>
<msup>
<mi mathvariant="normal">H</mi>
<mrow class="MJX-TeXAtom-ORD">
<mo>+</mo>
</mrow>
</msup>
<mo stretchy="false">)</mo>
<mo>=</mo>
<mstyle displaystyle="true" scriptlevel="0">
<mfrac>
<mrow>
<mn>0.4</mn>
<mi mathvariant="normal">m</mi>
<mi mathvariant="normal">o</mi>
<mi mathvariant="normal">l</mi>
</mrow>
<mrow>
<mn>4</mn>
<mi mathvariant="normal">L</mi>
</mrow>
</mfrac>
</mstyle>
<mo>=</mo>
<mn>0.1</mn>
<mi mathvariant="normal">m</mi>
<mi mathvariant="normal">o</mi>
<mi mathvariant="normal">l</mi>
<mrow class="MJX-TeXAtom-ORD">
<mo>/</mo>
</mrow>
<mi mathvariant="normal">L</mi>
<mrow class="MJX-TeXAtom-ORD">
<mo>&#xFF0C;</mo>
</mrow>
<mspace linebreak="newline" />
<mrow class="MJX-TeXAtom-ORD">
<mo>&#x6240;</mo>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mo>&#x4EE5;</mo>
</mrow>
<mi mathvariant="normal">p</mi>
<mi mathvariant="normal">H</mi>
<mo>=</mo>
<mn>1</mn>
<mrow class="MJX-TeXAtom-ORD">
<mo>&#xFF0C;</mo>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mo>&#x6545;</mo>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mo>&#x9009;</mo>
</mrow>
<mi mathvariant="normal">D</mi>
<mrow class="MJX-TeXAtom-ORD">
<mo>&#xFF0E;</mo>
</mrow>
</math>

4.

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<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mi>C</mi>
<mi>u</mi>
<mi>S</mi>
<msub>
<mi>O</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>4</mn>
</mrow>
</msub>
<mo>&#x22C5;<!-- ⋅ --></mo>
<mn>5</mn>
<msub>
<mi>H</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>2</mn>
</mrow>
</msub>
<mi>O</mi>
</math>

5.

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5
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7
8
9
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<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mi mathvariant="normal">&#x0025;<!-- % --></mi>
<mi mathvariant="normal">&#x0394;<!-- Δ --></mi>
<mi>p</mi>
<mi>r</mi>
<mi>i</mi>
<mi>c</mi>
<mi>e</mi>
<mo>=</mo>
<mn>100</mn>
<mo>&#x00D7;<!-- × --></mo>
<mo stretchy="false">[</mo>
<mi>exp</mi>
<mo>&#x2061;<!-- ⁡ --></mo>
<mo stretchy="false">(</mo>
<mi>a</mi>
<mrow class="MJX-TeXAtom-ORD">
<mi>g</mi>
</mrow>
<mi>e</mi>
<mo stretchy="false">)</mo>
<mo>&#x2212;<!-- − --></mo>
<mn>1</mn>
<mo stretchy="false">]</mo>
<mo>=</mo>
<mn>100</mn>
<mo>&#x00D7;<!-- × --></mo>
<mo stretchy="false">[</mo>
<mi>exp</mi>
<mo>&#x2061;<!-- ⁡ --></mo>
<mo stretchy="false">(</mo>
<mo>&#x2212;<!-- − --></mo>
<mn>0.008</mn>
<mo stretchy="false">)</mo>
<mo>&#x2212;<!-- − --></mo>
<mn>1</mn>
<mo stretchy="false">]</mo>
<mo>=</mo>
<mo>&#x2212;<!-- − --></mo>
<mn>0.8</mn>
<mi mathvariant="normal">&#x0025;<!-- % --></mi>
</math>

6.

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5
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74
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mi>C</mi>
<mi>u</mi>
<mrow class="MJX-TeXAtom-REL">
<munderover>
<mrow class="MJX-TeXAtom-OP MJX-fixedlimits">
<mspace width="0pt" />
<mo stretchy="false">&#x27F6;<!-- ⟶ --></mo>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mi mathvariant="normal">&#x25B3;<!-- △ --></mi>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<msub>
<mi>H</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>2</mn>
</mrow>
</msub>
<mi>S</mi>
<msub>
<mi>O</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>4</mn>
</mrow>
</msub>
<mo stretchy="false">(</mo>
<mrow class="MJX-TeXAtom-ORD">
<mo>&#x6D53;</mo>
</mrow>
<mo stretchy="false">)</mo>
</mrow>
</munderover>
</mrow>
<mi>C</mi>
<mi>u</mi>
<mi>S</mi>
<msub>
<mi>O</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>4</mn>
</mrow>
</msub>
<mrow class="MJX-TeXAtom-REL">
<mover>
<mrow class="MJX-TeXAtom-OP MJX-fixedlimits">
<mo stretchy="false">&#x27F6;<!-- ⟶ --></mo>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mi>N</mi>
<mi>a</mi>
<mi>O</mi>
<mi>H</mi>
<mrow class="MJX-TeXAtom-ORD">
<mo>&#x6EB6;</mo>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mo>&#x6DB2;</mo>
</mrow>
</mrow>
</mover>
</mrow>
<mi>C</mi>
<mi>u</mi>
<mo stretchy="false">(</mo>
<mi>O</mi>
<mi>H</mi>
<msub>
<mo stretchy="false">)</mo>
<mrow class="MJX-TeXAtom-ORD">
<mn>2</mn>
</mrow>
</msub>
</math>

7.

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<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mfrac>
<mrow class="MJX-TeXAtom-ORD">
<mrow class="MJX-TeXAtom-ORD">
<mo>&#x6EB6;</mo>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mo>&#x89E3;</mo>
</mrow>
</mrow>
<mrow>
<mo stretchy="false">&#x27F6;<!-- ⟶ --></mo>
<mrow class="MJX-TeXAtom-ORD">
<mo>&#x9ECF;</mo>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mo>&#x6DB2;</mo>
</mrow>
<mo stretchy="false">&#x2192;<!-- → --></mo>
<mrow class="MJX-TeXAtom-ORD">
<mo>&#x4F53;</mo>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mo>&#x58C1;</mo>
</mrow>
<mo stretchy="false">&#x2192;<!-- → --></mo>
<mrow class="MJX-TeXAtom-ORD">
<mo>&#x6BDB;</mo>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mo>&#x7EC6;</mo>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mo>&#x8840;</mo>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mo>&#x7BA1;</mo>
</mrow>
<mo stretchy="false">&#x2192;<!-- → --></mo>
</mrow>
</mfrac>
</math>

8.

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<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mi>a</mi>
<mo>+</mo>
<mi>b</mi>
<mrow class="MJX-TeXAtom-ORD">
<mi mathvariant="bold">i</mi>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mo>&#x548C;</mo>
</mrow>
<mi>a</mi>
<mo>+</mo>
<mi>b</mi>
<mrow class="MJX-TeXAtom-ORD">
<mi mathvariant="bold">i</mi>
</mrow>
</math>

9.

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<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mfrac>
<mrow>
<mrow class="MJX-TeXAtom-ORD">
<mo>&#x7535;</mo>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mo>&#x68AF;</mo>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mo>&#x4E0A;</mo>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mo>&#x5347;</mo>
</mrow>
<mn>10</mn>
<mrow class="MJX-TeXAtom-ORD">
<mo>&#x7C73;</mo>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mo>&#x91CC;</mo>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mo>&#x505A;</mo>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mo>&#x7684;</mo>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mo>&#x529F;</mo>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mphantom>
<mrow class="MJX-TeXAtom-ORD">
<mo>&#x7535;</mo>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mo>&#x68AF;</mo>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mo>&#x4E0A;</mo>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mo>&#x5347;</mo>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mo>&#x7C73;</mo>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mo>&#x91CC;</mo>
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<mo>&#x505A;</mo>
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<mo>&#x7684;</mo>
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<mo>&#x529F;</mo>
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<mo>&#x7535;</mo>
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<mo>&#x68AF;</mo>
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<mo>&#x82B1;</mo>
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<mo>&#x7684;</mo>
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<mrow class="MJX-TeXAtom-ORD">
<mo>&#x65F6;</mo>
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<mo>&#x95F4;</mo>
</mrow>
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<mphantom>
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<mo>&#x7535;</mo>
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<mrow class="MJX-TeXAtom-ORD">
<mo>&#x68AF;</mo>
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<mrow class="MJX-TeXAtom-ORD">
<mo>&#x4E0A;</mo>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mo>&#x5347;</mo>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mo>&#x7C73;</mo>
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<mrow class="MJX-TeXAtom-ORD">
<mo>&#x82B1;</mo>
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<mrow class="MJX-TeXAtom-ORD">
<mo>&#x7684;</mo>
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<mrow class="MJX-TeXAtom-ORD">
<mo>&#x65F6;</mo>
</mrow>
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<mo>&#x95F4;</mo>
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10.

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<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mn>3</mn>
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<mi>e</mi>
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<mi>O</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>2</mn>
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</msub>
<mover>
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<mtable rowspacing="0.1em" columnspacing="0em" displaystyle="false">
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<mtd>
<mo>=</mo>
<mspace width="negativethinmathspace" />
<mo>=</mo>
<mspace width="negativethinmathspace" />
<mo>=</mo>
<mspace width="negativethinmathspace" />
<mo>=</mo>
<mspace width="negativethinmathspace" />
<mo>=</mo>
<mspace width="negativethinmathspace" />
<mo>=</mo>
</mtd>
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<mrow class="MJX-TeXAtom-ORD">
<mrow class="MJX-TeXAtom-ORD">
<mo>&#x70B9;</mo>
</mrow>
<mrow class="MJX-TeXAtom-ORD">
<mo>&#x71C3;</mo>
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<msub>
<mi>e</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>3</mn>
</mrow>
</msub>
<msub>
<mi>O</mi>
<mrow class="MJX-TeXAtom-ORD">
<mn>4</mn>
</mrow>
</msub>
</math>

11.

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<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mi mathvariant="normal">C</mi>
<msub>
<mi mathvariant="normal">O</mi>
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</msub>
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<msub>
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<mspace width="thickmathspace" />
<munderover>
<mrow class="MJX-TeXAtom-OP">
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<mspace width="negativethinmathspace" />
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<mo>&#x2212;<!-- − --></mo>
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<mo>&#x2212;<!-- − --></mo>
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<mn>2</mn>
<msub>
<mi mathvariant="normal">H</mi>
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<mi mathvariant="normal">O</mi>
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12.

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<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<munderover>
<mrow class="MJX-TeXAtom-OP">
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<mo>&#x2212;<!-- − --></mo>
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<mtr>
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<mo>&#x5242;</mo>
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13.

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<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
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