我在 latex 源文件中使用双列布局,并且有一系列(不等式)方程式要显示,我想将它们保留在左列内。但是,使用 \begin{align*} 环境,它会使方程式溢出列,并占用右列的一些额外空间。您可以参考我在此处附加的图片来查看发生了什么。我如何将方程式限制在第一列内?
这是我的乳胶源代码。这是您可以尝试的 MWE。
% \documentclass[conference]{IEEEtran}
\documentclass[10pt,conference,letterpaper]{IEEEtran}
\usepackage{amsmath}
\begin{document}
as abcd dsfe fsafs fkasfkds fasf skfsfj safa; ffk sdfksfjsfsjfsdkfsdfkjsf sfsdfkdf sdfks fksfksdfks fkf sdf sf sf sf sfa fs fsdf asf sfs fsf sf sf sf sf sfsd fs fsfjslfjslfklsfj
as abcd dsfe fsafs fkasfkds fasf skfsfj safa; ffk sdfksfjsfsjfsdkfsdfkjsf sfsdfkdf sdfks fksfksdfks fkf sdf sf sf sf sfa fs fsdf asf sfs fsf sf sf sf sf sfsd fs fsfjslfjslfklsfj
as abcd dsfe fsafs fkasfkds fasf skfsfj safa; ffk sdfksfjsfsjfsdkfsdfkjsf sfsdfkdf sdfks fksfksdfks fkf sdf sf sf sf sfa fs fsdf asf sfs fsf sf sf sf sf sfsd fs fsfjslfjslfklsfj
as abcd dsfe fsafs fkasfkds fasf skfsfj safa; ffk sdfksfjsfsjfsdkfsdfkjsf sfsdfkdf sdfks fksfksdfks fkf sdf sf sf sf sfa fs fsdf asf sfs fsf sf sf sf sf sfsd fs fsfjslfjslfklsfj
\begin{align*}
& \sum\nolimits_{e \in E^*} COST(g(e))\\
&= \sum\nolimits_{e \in S_1} COST(g(e))
+ \sum\nolimits_{e \in S_2} COST(g(e))
+ \sum\nolimits_{e \in S_3} COST(g(e))\\
&\le
2(1+\epsilon) COST(T^* \setminus T)
+ COST(T^* \cap T)
+ 4\epsilon OPT_n
+ 2\epsilon OPT_n\\
&\le 2(1+\epsilon)(COST(T^* \setminus T) + COST(T^* \cap T))
+ 4\epsilon OPT_n
+ 2\epsilon OPT_n\\
&\le 2(1+\epsilon)COST(T^*)
+ 4\epsilon OPT_n
+ 2\epsilon OPT_n\\
&\le 4(1+\epsilon)OPT_n
+ 4\epsilon OPT_n
+ 2\epsilon OPT_n\\
&\le 4+10\epsilon OPT_n
\end{align*}
as abcd dsfe fsafs fkasfkds fasf skfsfj safa; ffk sdfksfjsfsjfsdkfsdfkjsf sfsdfkdf sdfks fksfksdfks fkf sdf sf sf sf sfa fs fsdf asf sfs fsf sf sf sf sf sfsd fs fsfjslfjslfklsfj
as abcd dsfe fsafs fkasfkds fasf skfsfj safa; ffk sdfksfjsfsjfsdkfsdfkjsf sfsdfkdf sdfks fksfksdfks fkf sdf sf sf sf sfa fs fsdf asf sfs fsf sf sf sf sf sfsd fs fsfjslfjslfklsfj
as abcd dsfe fsafs fkasfkds fasf skfsfj safa; ffk sdfksfjsfsjfsdkfsdfkjsf sfsdfkdf sdfks fksfksdfks fkf sdf sf sf sf sfa fs fsdf asf sfs fsf sf sf sf sf sfsd fs fsfjslfjslfklsfj
as abcd dsfe fsafs fkasfkds fasf skfsfj safa; ffk sdfksfjsfsjfsdkfsdfkjsf sfsdfkdf sdfks fksfksdfks fkf sdf sf sf sf sfa fs fsdf asf sfs fsf sf sf sf sf sfsd fs fsfjslfjslfklsfj
as abcd dsfe fsafs fkasfkds fasf skfsfj safa; ffk sdfksfjsfsjfsdkfsdfkjsf sfsdfkdf sdfks fksfksdfks fkf sdf sf sf sf sfa fs fsdf asf sfs fsf sf sf sf sf sfsd fs fsfjslfjslfklsfj
as abcd dsfe fsafs fkasfkds fasf skfsfj safa; ffk sdfksfjsfsjfsdkfsdfkjsf sfsdfkdf sdfks fksfksdfks fkf sdf sf sf sf sfa fs fsdf asf sfs fsf sf sf sf sf sfsd fs fsfjslfjslfklsfj
as abcd dsfe fsafs fkasfkds fasf skfsfj safa; ffk sdfksfjsfsjfsdkfsdfkjsf sfsdfkdf sdfks fksfksdfks fkf sdf sf sf sf sfa fs fsdf asf sfs fsf sf sf sf sf sfsd fs fsfjslfjslfklsfj
as abcd dsfe fsafs fkasfkds fasf skfsfj safa; ffk sdfksfjsfsjfsdkfsdfkjsf sfsdfkdf sdfks fksfksdfks fkf sdf sf sf sf sfa fs fsdf asf sfs fsf sf sf sf sf sfsd fs fsfjslfjslfklsfj
as abcd dsfe fsafs fkasfkds fasf skfsfj safa; ffk sdfksfjsfsjfsdkfsdfkjsf sfsdfkdf sdfks fksfksdfks fkf sdf sf sf sf sfa fs fsdf asf sfs fsf sf sf sf sf sfsd fs fsfjslfjslfklsfj
as abcd dsfe fsafs fkasfkds fasf skfsfj safa; ffk sdfksfjsfsjfsdkfsdfkjsf sfsdfkdf sdfks fksfksdfks fkf sdf sf sf sf sfa fs fsdf asf sfs fsf sf sf sf sf sfsd fs fsfjslfjslfklsfj
as abcd dsfe fsafs fkasfkds fasf skfsfj safa; ffk sdfksfjsfsjfsdkfsdfkjsf sfsdfkdf sdfks fksfksdfks fkf sdf sf sf sf sfa fs fsdf asf sfs fsf sf sf sf sf sfsd fs fsfjslfjslfklsfj
as abcd dsfe fsafs fkasfkds fasf skfsfj safa; ffk sdfksfjsfsjfsdkfsdfkjsf sfsdfkdf sdfks fksfksdfks fkf sdf sf sf sf sfa fs fsdf asf sfs fsf sf sf sf sf sfsd fs fsfjslfjslfklsfj
as abcd dsfe fsafs fkasfkds fasf skfsfj safa; ffk sdfksfjsfsjfsdkfsdfkjsf sfsdfkdf sdfks fksfksdfks fkf sdf sf sf sf sfa fs fsdf asf sfs fsf sf sf sf sf sfsd fs fsfjslfjslfklsfj
as abcd dsfe fsafs fkasfkds fasf skfsfj safa; ffk sdfksfjsfsjfsdkfsdfkjsf sfsdfkdf sdfks fksfksdfks fkf sdf sf sf sf sfa fs fsdf asf sfs fsf sf sf sf sf sfsd fs fsfjslfjslfklsfj
as abcd dsfe fsafs fkasfkds fasf skfsfj safa; ffk sdfksfjsfsjfsdkfsdfkjsf sfsdfkdf sdfks fksfksdfks fkf sdf sf sf sf sfa fs fsdf asf sfs fsf sf sf sf sf sfsd fs fsfjslfjslfklsfj
as abcd dsfe fsafs fkasfkds fasf skfsfj safa; ffk sdfksfjsfsjfsdkfsdfkjsf sfsdfkdf sdfks fksfksdfks fkf sdf sf sf sf sfa fs fsdf asf sfs fsf sf sf sf sf sfsd fs fsfjslfjslfklsfj
as abcd dsfe fsafs fkasfkds fasf skfsfj safa; ffk sdfksfjsfsjfsdkfsdfkjsf sfsdfkdf sdfks fksfksdfks fkf sdf sf sf sf sfa fs fsdf asf sfs fsf sf sf sf sf sfsd fs fsfjslfjslfklsfj
as abcd dsfe fsafs fkasfkds fasf skfsfj safa; ffk sdfksfjsfsjfsdkfsdfkjsf sfsdfkdf sdfks fksfksdfks fkf sdf sf sf sf sfa fs fsdf asf sfs fsf sf sf sf sf sfsd fs fsfjslfjslfklsfj
as abcd dsfe fsafs fkasfkds fasf skfsfj safa; ffk sdfksfjsfsjfsdkfsdfkjsf sfsdfkdf sdfks fksfksdfks fkf sdf sf sf sf sfa fs fsdf asf sfs fsf sf sf sf sf sfsd fs fsfjslfjslfklsfj
as abcd dsfe fsafs fkasfkds fasf skfsfj safa; ffk sdfksfjsfsjfsdkfsdfkjsf sfsdfkdf sdfks fksfksdfks fkf sdf sf sf sf sfa fs fsdf asf sfs fsf sf sf sf sf sfsd fs fsfjslfjslfklsfj
as abcd dsfe fsafs fkasfkds fasf skfsfj safa; ffk sdfksfjsfsjfsdkfsdfkjsf sfsdfkdf sdfks fksfksdfks fkf sdf sf sf sf sfa fs fsdf asf sfs fsf sf sf sf sf sfsd fs fsfjslfjslfklsfj
as abcd dsfe fsafs fkasfkds fasf skfsfj safa; ffk sdfksfjsfsjfsdkfsdfkjsf sfsdfkdf sdfks fksfksdfks fkf sdf sf sf sf sfa fs fsdf asf sfs fsf sf sf sf sf sfsd fs fsfjslfjslfklsfj
as abcd dsfe fsafs fkasfkds fasf skfsfj safa; ffk sdfksfjsfsjfsdkfsdfkjsf sfsdfkdf sdfks fksfksdfks fkf sdf sf sf sf sfa fs fsdf asf sfs fsf sf sf sf sf sfsd fs fsfjslfjslfklsfj
as abcd dsfe fsafs fkasfkds fasf skfsfj safa; ffk sdfksfjsfsjfsdkfsdfkjsf sfsdfkdf sdfks fksfksdfks fkf sdf sf sf sf sfa fs fsdf asf sfs fsf sf sf sf sf sfsd fs fsfjslfjslfklsfj
as abcd dsfe fsafs fkasfkds fasf skfsfj safa; ffk sdfksfjsfsjfsdkfsdfkjsf sfsdfkdf sdfks fksfksdfks fkf sdf sf sf sf sfa fs fsdf asf sfs fsf sf sf sf sf sfsd fs fsfjslfjslfklsfj
as abcd dsfe fsafs fkasfkds fasf skfsfj safa; ffk sdfksfjsfsjfsdkfsdfkjsf sfsdfkdf sdfks fksfksdfks fkf sdf sf sf sf sfa fs fsdf asf sfs fsf sf sf sf sf sfsd fs fsfjslfjslfklsfj
as abcd dsfe fsafs fkasfkds fasf skfsfj safa; ffk sdfksfjsfsjfsdkfsdfkjsf sfsdfkdf sdfks fksfksdfks fkf sdf sf sf sf sfa fs fsdf asf sfs fsf sf sf sf sf sfsd fs fsfjslfjslfklsfj
as abcd dsfe fsafs fkasfkds fasf skfsfj safa; ffk sdfksfjsfsjfsdkfsdfkjsf sfsdfkdf sdfks fksfksdfks fkf sdf sf sf sf sfa fs fsdf asf sfs fsf sf sf sf sf sfsd fs fsfjslfjslfklsfj
as abcd dsfe fsafs fkasfkds fasf skfsfj safa; ffk sdfksfjsfsjfsdkfsdfkjsf sfsdfkdf sdfks fksfksdfks fkf sdf sf sf sf sfa fs fsdf asf sfs fsf sf sf sf sf sfsd fs fsfjslfjslfklsfj
\end{document}
答案1
这是一种可能的解决方案。使用resizebox
来自graphicx
包和parbox
组合,如下所示。
\resizebox{0.48\textwidth}{!}{\parbox{\linewidth}{ math envrionment}}
或者
{\tiny \begin{align*} ... \end{align*} environment}
代码
\documentclass[10pt,conference,letterpaper]{IEEEtran}
\usepackage{amsmath,graphicx}
\begin{document}
as abcd dsfe fsafs fkasfkds fasf skfsfj safa; ffk sdfksfjsfsjfsdkfsdfkjsf sfsdfkdf sdfks fksfksdfks fkf sdf sf sf sf sfa fs fsdf asf sfs fsf sf sf sf sf sfsd fs fsfjslfjslfklsfj
as abcd dsfe fsafs fkasfkds fasf skfsfj safa; ffk sdfksfjsfsjfsdkfsdfkjsf sfsdfkdf sdfks fksfksdfks fkf sdf sf sf sf sfa fs fsdf asf sfs fsf sf sf sf sf sfsd fs fsfjslfjslfklsfj
as abcd dsfe fsafs fkasfkds fasf skfsfj safa; ffk sdfksfjsfsjfsdkfsdfkjsf sfsdfkdf sdfks fksfksdfks fkf sdf sf sf sf sfa fs fsdf asf sfs fsf sf sf sf sf sfsd fs fsfjslfjslfklsfj
as abcd dsfe fsafs fkasfkds fasf skfsfj safa; ffk sdfksfjsfsjfsdkfsdfkjsf sfsdfkdf sdfks fksfksdfks fkf sdf sf sf sf sfa fs fsdf asf sfs fsf sf sf sf sf sfsd fs fsfjslfjslfklsfj
\resizebox{0.48\textwidth}{!}{\parbox{\linewidth}{
\begin{align*}
& \sum\nolimits_{e \in E^*} COST(g(e))\\
&= \sum\nolimits_{e \in S_1} COST(g(e))
+ \sum\nolimits_{e \in S_2} COST(g(e))
+ \sum\nolimits_{e \in S_3} COST(g(e))\\
&\le
2(1+\epsilon) COST(T^* \setminus T)
+ COST(T^* \cap T)
+ 4\epsilon OPT_n
+ 2\epsilon OPT_n\\
&\le 2(1+\epsilon)(COST(T^* \setminus T) + COST(T^* \cap T))
+ 4\epsilon OPT_n
+ 2\epsilon OPT_n\\
&\le 2(1+\epsilon)COST(T^*)
+ 4\epsilon OPT_n
+ 2\epsilon OPT_n\\
&\le 4(1+\epsilon)OPT_n
+ 4\epsilon OPT_n
+ 2\epsilon OPT_n\\
&\le 4+10\epsilon OPT_n
\end{align*}
}}
as abcd dsfe fsafs fkasfkds fasf skfsfj safa; ffk sdfksfjsfsjfsdkfsdfkjsf sfsdfkdf sdfks fksfksdfks fkf sdf sf sf sf sfa fs fsdf asf sfs fsf sf sf sf sf sfsd fs fsfjslfjslfklsfj
as abcd dsfe fsafs fkasfkds fasf skfsfj safa; ffk sdfksfjsfsjfsdkfsdfkjsf sfsdfkdf sdfks fksfksdfks fkf sdf sf sf sf sfa fs fsdf asf sfs fsf sf sf sf sf sfsd fs fsfjslfjslfklsfj
as abcd dsfe fsafs fkasfkds fasf skfsfj safa; ffk sdfksfjsfsjfsdkfsdfkjsf sfsdfkdf sdfks fksfksdfks fkf sdf sf sf sf sfa fs fsdf asf sfs fsf sf sf sf sf sfsd fs fsfjslfjslfklsfj
as abcd dsfe fsafs fkasfkds fasf skfsfj safa; ffk sdfksfjsfsjfsdkfsdfkjsf sfsdfkdf sdfks fksfksdfks fkf sdf sf sf sf sfa fs fsdf asf sfs fsf sf sf sf sf sfsd fs fsfjslfjslfklsfj
as abcd dsfe fsafs fkasfkds fasf skfsfj safa; ffk sdfksfjsfsjfsdkfsdfkjsf sfsdfkdf sdfks fksfksdfks fkf sdf sf sf sf sfa fs fsdf asf sfs fsf sf sf sf sf sfsd fs fsfjslfjslfklsfj
as abcd dsfe fsafs fkasfkds fasf skfsfj safa; ffk sdfksfjsfsjfsdkfsdfkjsf sfsdfkdf sdfks fksfksdfks fkf sdf sf sf sf sfa fs fsdf asf sfs fsf sf sf sf sf sfsd fs fsfjslfjslfklsfj
as abcd dsfe fsafs fkasfkds fasf skfsfj safa; ffk sdfksfjsfsjfsdkfsdfkjsf sfsdfkdf sdfks fksfksdfks fkf sdf sf sf sf sfa fs fsdf asf sfs fsf sf sf sf sf sfsd fs
\end{document}
答案2
我建议您不要采取任何会导致数学表达式中使用的字体大小相对于周围文本减小的措施。相反,您可能希望采用以下方法:
不要
\nolimits
在每个\sum
宏后使用修饰符。相反,将\sum{...}
表达式放在指令中\smashoperator
;这样可以减少求和符号前后的空格量。(\smashoperator
宏由包提供mathtools
,它是包的扩展(并加载)amsmath
。)在第 3 行和第 4 行插入额外的换行符。
可选:以罗马(直立)字体呈现“COST”和“OPT”。目前,TeX 将 COST 和 OPT 解释为四字母和三字母变量组,即 和
C
O
S
T
,O
P
T
导致字母间距松散且不理想。(如果您希望以斜体而不是直立字体呈现变量名称,请在定义和的宏中使用\textit
而不是。)\textup
\COST
\OPT
\begin{align*}
& \smashoperator{\sum_{e \in E^*}} \COST(g(e))\\
&= \smashoperator{\sum_{e \in S_1}} \COST(g(e)) +
\smashoperator{\sum_{e \in S_2}} \COST(g(e)) +
\smashoperator{\sum_{e \in S_3}} \COST(g(e))\\
&\le 2(1+\epsilon) \COST(T^* \setminus T) + \COST(T^* \cap T)\\
&\qquad + 4\epsilon \OPT_n + 2\epsilon \OPT_n\\
&\le 2(1+\epsilon)(\COST(T^* \setminus T) + \COST(T^* \cap T))\\
&\qquad + 4\epsilon \OPT_n + 2\epsilon \OPT_n\\
&\le 2(1+\epsilon)\COST(T^*) + 4\epsilon \OPT_n + 2\epsilon \OPT_n\\
&\le 4(1+\epsilon)\OPT_n + 4\epsilon \OPT_n + 2\epsilon \OPT_n\\
&\le 4+10\eps
ilon \OPT_n \end{align*}