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---
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layout: "lesson"
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lang: "en"
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title: "More on: Mathematics"
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description: "This lesson show more amsmath alignment environments, how to make math bold, the math extension package mathtools, and using Unicode input for maths."
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toc-anchor-text: "More on: Mathematics"
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lang: "zh"
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title: "更多内容：数学"
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description: "本课展示了更多amsmath对齐环境、如何使数学符号加粗、数学扩展宏包mathtools，以及在数学中使用Unicode输入。"
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toc-anchor-text: "更多内容：数学"
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---
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## 更多`amsmath`对齐
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## Further `amsmath` alignments
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In addition to the `align*` environment shown in the main lesson,
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`amsmath` has several other display math constructs, notably `gather`
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for multi-line displays that do not need alignment, and `multline` for
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splitting a larger single expression over multiple lines, aligning the
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first line to the left, and the last to the right. In all cases the `*`
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form omits the equation numbers by default.
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除了主课程中展示的`align*`环境外，`amsmath`还有几个其他的数学显示结构，特别是`gather`用于不需要对齐的多行显示，以及`multline`用于将较大的单个表达式分成多行，将第一行左对齐，最后一行右对齐。在所有情况下，带`*`的形式默认省略方程编号。
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```latex
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\documentclass[a4paper]{article}
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\usepackage[T1]{fontenc}
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% !TEX program=xelatex
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% 临时patch，否则使用中文标点，TexLive.net会编译错误
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\ExplSyntaxOn
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\clist_map_inline:nn { fp, int, dim, skip, muskip }
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{
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\cs_generate_variant:cn { #1_set:Nn } { NV }
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\cs_generate_variant:cn { #1_gset:Nn } { NV }
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}
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\ExplSyntaxOff
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\documentclass[UTF8]{ctexart}
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\usepackage{xeCJK}
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\usepackage{amsmath}
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\begin{document}
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Gather
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Gather环境
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\begin{gather}
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P(x)=ax^{5}+bx^{4}+cx^{3}+dx^{2}+ex +f\\
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x^2+x=10
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\end{gather}
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Multline
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Multline环境
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\begin{multline*}
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(a+b+c+d)x^{5}+(b+c+d+e)x^{4} \\
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+(c+d+e+f)x^{3}+(d+e+f+a)x^{2}+(e+f+a+b)x\\
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\end{document}
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```
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### Columns in math alignments
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### 数学对齐中的列
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The `amsmath` alignment environments are designed to take pairs of
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columns with the first column of each pair aligned to the right and
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the second aligned to the left. This allows multiple equations to be
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shown, each aligned towards its relation symbol.
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`amsmath`的对齐环境设计为每对列的第一列右对齐，第二列左对齐。这允许显示多个方程，每个方程都围绕其关系符号对齐。
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```latex
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\documentclass{article}
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\usepackage[T1]{fontenc}
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% !TEX program=xelatex
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% 临时patch，否则使用中文标点，TexLive.net会编译错误
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\ExplSyntaxOn
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\clist_map_inline:nn { fp, int, dim, skip, muskip }
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{
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\cs_generate_variant:cn { #1_set:Nn } { NV }
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\cs_generate_variant:cn { #1_gset:Nn } { NV }
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}
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\ExplSyntaxOff
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\documentclass[UTF8]{ctexart}
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\usepackage{xeCJK}
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\usepackage{amsmath}
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\begin{document}
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Aligned equations
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对齐的方程
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\begin{align*}
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a &= b+1 & c &= d+2 & e &= f+3 \\
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r &= s^{2} & t &=u^{3} & v &= w^{4}
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\end{document}
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```
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In addition there are variants of the display environments ending
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in `ed` that make a subterm inside a larger display.
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For example, `aligned` and `gathered` are variants of `align` and `gather` respectively.
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此外，还有以`ed`结尾的显示环境变体，用于在更大的显示中制作子项。
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例如，`aligned`和`gathered`分别是`align`和`gather`的变体。
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```latex
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\documentclass{article}
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\usepackage[T1]{fontenc}
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% !TEX program=xelatex
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% 临时patch，否则使用中文标点，TexLive.net会编译错误
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\ExplSyntaxOn
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\clist_map_inline:nn { fp, int, dim, skip, muskip }
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{
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\cs_generate_variant:cn { #1_set:Nn } { NV }
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\cs_generate_variant:cn { #1_gset:Nn } { NV }
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}
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\ExplSyntaxOff
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\documentclass[UTF8]{ctexart}
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\usepackage{xeCJK}
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\usepackage{amsmath}
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\begin{document}
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Aligned:
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\end{document}
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```
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`aligned` takes a positional optional argument similar to `tabular`.
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This is often useful to align an inline math formula on its top row;
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compare the items in the list in the following example.
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`aligned`接受类似于`tabular`的位置可选参数。
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这在对齐内联数学公式的顶行时经常有用；
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比较下面示例中列表中的项目。
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```latex
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\documentclass{article}
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\usepackage[T1]{fontenc}
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% !TEX program=xelatex
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% 临时patch，否则使用中文标点，TexLive.net会编译错误
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\ExplSyntaxOn
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\clist_map_inline:nn { fp, int, dim, skip, muskip }
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{
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\cs_generate_variant:cn { #1_set:Nn } { NV }
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\cs_generate_variant:cn { #1_gset:Nn } { NV }
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}
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\ExplSyntaxOff
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\documentclass[UTF8]{ctexart}
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\usepackage{xeCJK}
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\usepackage{amsmath}
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\begin{document}
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\begin{itemize}
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\end{document}
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```
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## Bold Math
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Standard LaTeX has two methods to give bold symbols in math. To make
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an entire expression bold, use `\boldmath` before entering the
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expression. The command `\mathbf` is also available to set individual
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letters or words in upright bold roman.
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## 数学加粗
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标准LaTeX有两种方法使数学符号加粗。要使整个表达式加粗，在进入表达式前使用`\boldmath`。命令`\mathbf`也可用于将单个字母或单词设置为直立粗体罗马字体。
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```latex
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\documentclass[a4paper]{article}
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\usepackage[T1]{fontenc}
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% !TEX program=xelatex
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% 临时patch，否则使用中文标点，TexLive.net会编译错误
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\ExplSyntaxOn
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\clist_map_inline:nn { fp, int, dim, skip, muskip }
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{
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\cs_generate_variant:cn { #1_set:Nn } { NV }
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\cs_generate_variant:cn { #1_gset:Nn } { NV }
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}
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\ExplSyntaxOff
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\documentclass[UTF8]{ctexart}
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\usepackage{xeCJK}
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\begin{document}
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{\boldmath $(x+y)(x-y)=x^{2}-y^{2}$ $\pi r^2$}
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$(x+\mathbf{y})(x-\mathbf{y})=x^{2}-{\mathbf{y}}^{2}$
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$\mathbf{\pi} r^2$ % bad use of \mathbf
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$\mathbf{\pi} r^2$ % 错误使用\mathbf
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\end{document}
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```
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If you want to access bold symbols (as would be used by `\boldmath`)
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within an otherwise normal weight expression, then you can use the
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command `\bm` from the `bm` package. Note that `\bm` also works with
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symbols such as `=` and Greek letters. (Note that `\mathbf` has no effect
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on `\pi` in the example above.)
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如果您想在普通权重表达式中访问粗体符号（就像`\boldmath`使用的那样），可以使用`bm`宏包中的命令`\bm`。注意`\bm`也适用于`=`和希腊字母等符号。（注意在上面的示例中，`\mathbf`对`\pi`没有效果。）
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```latex
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\documentclass[a4paper]{article}
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\usepackage[T1]{fontenc}
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% !TEX program=xelatex
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% 临时patch，否则使用中文标点，TexLive.net会编译错误
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\ExplSyntaxOn
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\clist_map_inline:nn { fp, int, dim, skip, muskip }
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{
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\cs_generate_variant:cn { #1_set:Nn } { NV }
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\cs_generate_variant:cn { #1_gset:Nn } { NV }
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}
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\ExplSyntaxOff
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\documentclass[UTF8]{ctexart}
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\usepackage{xeCJK}
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\usepackage{bm}
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\begin{document}
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```
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## Mathtools
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The package `mathtools` loads `amsmath` and adds several additional
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features, such as variants of the `amsmath` matrix environments that
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allow the column alignment to be specified.
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`mathtools`宏包加载`amsmath`并添加了一些额外功能，比如`amsmath`矩阵环境的变体，允许指定列对齐方式。
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```latex
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\documentclass[a4paper]{article}
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\usepackage[T1]{fontenc}
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% !TEX program=xelatex
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% 临时patch，否则使用中文标点，TexLive.net会编译错误
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\ExplSyntaxOn
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\clist_map_inline:nn { fp, int, dim, skip, muskip }
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{
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\cs_generate_variant:cn { #1_set:Nn } { NV }
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\cs_generate_variant:cn { #1_gset:Nn } { NV }
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}
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\ExplSyntaxOff
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\documentclass[UTF8]{ctexart}
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\usepackage{xeCJK}
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\usepackage{mathtools}
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\begin{document}
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\end{document}
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```
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## Unicode Math
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## Unicode数学
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As will be seen in [Lesson 14](lesson-14), there are variant TeX
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engines that use OpenType fonts. By default, these engines still use
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classic TeX math fonts but you may use the `unicode-math` package
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to use OpenType Math fonts. The details of this package are beyond
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this course and we refer you to the
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[package documentation](https://texdoc.org/pkg/unicode-math).
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However, we give a small example here.
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如[第14课](lesson-14)所述，有一些变体TeX引擎使用OpenType字体。默认情况下，这些引擎仍然使用经典的TeX数学字体，但您可以使用`unicode-math`宏包来使用OpenType数学字体。这个宏包的细节超出了本课程的范围，我们建议您参考[宏包文档](https://texdoc.org/pkg/unicode-math)。
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但是，我们在这里给出一个小示例。
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```latex
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% !TEX lualatex
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\documentclass[a4paper]{article}
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% !TEX program=xelatex
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% 临时patch，否则使用中文标点，TexLive.net会编译错误
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\ExplSyntaxOn
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\clist_map_inline:nn { fp, int, dim, skip, muskip }
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{
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\cs_generate_variant:cn { #1_set:Nn } { NV }
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\cs_generate_variant:cn { #1_gset:Nn } { NV }
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}
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\ExplSyntaxOff
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\documentclass[UTF8]{ctexart}
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\usepackage{xeCJK}
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\usepackage{unicode-math}
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\setmainfont{TeX Gyre Pagella}
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\setmathfont{TeX Gyre Pagella Math}
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\begin{document}
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One two three
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一二三
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\[
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\log \alpha + \log \beta = \log(\alpha\beta)
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\]
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Unicode Math Alphanumerics
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Unicode数学字母数字符号
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\[A + \symfrak{A}+\symbf{A}+ \symcal{A} + \symscr{A}+ \symbb{A}\]
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\end{document}

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