很长的方程式自动分页

Question

我有一个超长的方程式。我尝试使用，dmath但出现错误“Overfull \hbox”，并且它无法在我的主代码中运行。我甚至尝试将和更改\left(为\right)和\biggl(，\biggr)但仍然不起作用。我可以使用，但手动保留数百行的长方程式中的multline换行符是不可能的。请提出一种处理此问题的方法。\\

\documentclass{article}
\usepackage{amsmath}
\usepackage{breqn}
\begin{document}
\maketitle
\section{Introduction}
\begin{dmath}
\lambda _3+\frac{1}{\biggl(a+4 b+p\biggr)^9}2\biggl(-1048576 x_3 k12{}^2 b^{10}-1572864 a x_3 k12{}^2b^9-2359296 p x_3 k12{}^2 b^9+262144 p \epsilon21 k12 b^9-884736 a^2 x_3 k12{}^2 b^8-2359296 p^2 x_3 k12{}^2 b^8-3080192 a p x_3 k12{}^2 b^8+589824 p^2 \epsilon21 k12 b^8+458752 a p \epsilon21 k12 b^8-163840 a^3 x_3 k12{}^2 b^7-1376256 p^3 x_3 k12{}^2 b^7-2621440 a p^2 x_3 k12{}^2 b^7-1572864 a^2 d x_3 k12{}^2 b^7-1417216 a^2 p x_3 k12{}^2 b^7+589824 p^3 \epsilon21 k12 b^7+917504 a p^2 \epsilon21 k12 b^7+344064 a^2 p \epsilon21 k12 b^7+55296 a^4 x_3 k12{}^2 b^6-516096 p^4 x_3 k12{}^2 b^6-1261568 a p^3 x_3 k12{}^2 b^6-931840 a^2 p^2 x_3 k12{}^2 b^6-1310720 a^3 d x_3 k12{}^2 b^6+1310720 a^3 e x_3 k12{}^2 b^6-131072 a^3 p x_3 k12{}^2 b^6-2752512 a^2 d p x_3 k12{}^2 b^6+344064 p^4 \epsilon21 k12 b^6+802816 a p^3 \epsilon21 k12 b^6+602112 a^2 p^2 \epsilon21 k12 b^6+143360 a^3 p \epsilon21 k12 b^6+39936 a^5 x_3 k12{}^2 b^5-372736 a p^4 x_3 k12{}^2 b^5-311808 a^2 p^3 x_3 k12{}^2 b^5+18432 a^3 p^2 x_3 k12{}^2 b^5-2064384 a^2 d p^2 x_3 k12{}^2 b^5-434176 a^4 d x_3 k12{}^2 b^5+573440 a^4 e x_3 k12{}^2 b^5+126464 a^4 p x_3 k12{}^2 b^5-1966080 a^3 d p x_3 k12{}^2 b^5+1966080 a^3 e p x_3 k12{}^2 b^5+129024 p^5 \epsilon21 k12 b^5+401408 a p^4 \epsilon21 k12 b^5+451584 a^2 p^3 \epsilon21 k12 b^5+215040 a^3 p^2 \epsilon21 k12 b^5+35840 a^4 p \epsilon21 k12 b^5+10624 a^6 x_3 k12{}^2 b^4-49280 a^2 p^4 x_3 k12{}^2 b^4+56320 a^3 p^3 x_3 k12{}^2 b^4-860160 a^2 d p^3 x_3 k12{}^2 b^4+106240 a^4 p^2 x_3 k12{}^2 b^4-1228800 a^3 d p^2 x_3 k12{}^2 b^4+1228800 a^3 e p^2 x_3 k12{}^2 b^4-75776 a^5 d x_3 k12{}^2 b^4+102400 a^5 e x_3 k12{}^2 b^4+57856 a^5 p x_3 k12{}^2 b^4-542720 a^4 d p x_3 k12{}^2 b^4+716800 a^4 e p x_3 k12{}^2 b^4+32256 p^6 \epsilon21 k12 b^4+125440 a p^5 \epsilon21 k12 b^4+188160 a^2 p^4 \epsilon21 k12 b^4+134400 a^3 p^3 \epsilon21 k12 b^4+44800 a^4 p^2 \epsilon21 k12 b^4+5376 a^5 p \epsilon21 k12 b^4+1536 a^7 x_3 k12{}^2 b^3+26240 a^3 p^4 x_3 k12{}^2 b^3-215040 a^2 d p^4 x_3 k12{}^2 b^3+44480 a^4 p^3 x_3 k12{}^2 b^3-409600 a^3 d p^3 x_3 k12{}^2 b^3+409600 a^3 e p^3 x_3 k12{}^2 b^3+32896 a^5 p^2 x_3 k12{}^2 b^3-271360 a^4 d p^2 x_3 k12{}^2 b^3+358400 a^4 e p^2 x_3 k12{}^2 b^3-7936 a^6 d x_3 k12{}^2 b^3+10240 a^6 e x_3 k12{}^2 b^3+11552 a^6 p x_3 k12{}^2 b^3-75776 a^5 d p x_3 k12{}^2 b^3+102400 a^5 e p x_3 k12{}^2 b^3+5376 p^7 \epsilon21 k12 b^3+25088 a p^6 \epsilon21 k12 b^3+47040 a^2 p^5 \epsilon21 k12 b^3+44800 a^3 p^4 \epsilon21 k12 b^3+22400 a^4 p^3 \epsilon21 k12 b^3+5376 a^5 p^2 \epsilon21 k12 b^3+448 a^6 p \epsilon21 k12 b^3+120 a^8 x_3 k12{}^2 b^2+10040 a^4 p^4 x_3 k12{}^2 b^2-76800 a^3 d p^4 x_3 k12{}^2 b^2+9216 a^5 p^3 x_3 k12{}^2 b^2-67840 a^4 d p^3 x_3 k12{}^2 b^2+89600 a^4 e p^3 x_3 k12{}^2 b^2+4680 a^6 p^2 x_3 k12{}^2 b^2-28416 a^5 d p^2 x_3 k12{}^2 b^2+38400 a^5 e p^2 x_3 k12{}^2 b^2-512 a^7 d x_3 k12{}^2 b^2+640 a^7 e x_3 k12{}^2 b^2+1216 a^7 p x_3 k12{}^2 b^2-5952 a^6 d p x_3 k12{}^2 b^2+7680 a^6 e p x_3 k12{}^2 b^2+576 p^8 \epsilon21 k12 b^2+3136 a p^7 \epsilon21 k12 b^2+7056 a^2 p^6 \epsilon21 k12 b^2+8400 a^3 p^5 \epsilon21 k12 b^2+5600 a^4 p^4 \epsilon21 k12 b^2+2016 a^5 p^3 \epsilon21 k12 b^2+336 a^6 p^2 \epsilon21 k12 b^2+16 a^7 p \epsilon21 k12 b^2+4 a^9 x_3 k12{}^2 b+1276 a^5 p^4 x_3 k12{}^2 b-8480 a^4 d p^4 x_3 k12{}^2 b+11200 a^4 e p^4 x_3 k12{}^2 b+838 a^6 p^3 x_3 k12{}^2 b-4736 a^5 d p^3 x_3 k12{}^2 b+6400 a^5 e p^3 x_3 k12{}^2 b+320 a^7 p^2 x_3 k12{}^2 b-1488 a^6 d p^2 x_3 k12{}^2 b+1920 a^6 e p^2 x_3 k12{}^2 b-16 a^8 d x_3 k12{}^2 b+20 a^8 e x_3 k12{}^2 b+62 a^8 p x_3 k12{}^2 b-256 a^7 d p x_3 k12{}^2 b+320 a^7 e p x_3 k12{}^2 b+36 p^9 \epsilon21 k12 b+224 a p^8 \epsilon21 k12 b+588 a^2 p^7 \epsilon21 k12 b+840 a^3 p^6 \epsilon21 k12 b+700 a^4 p^5 \epsilon21 k12 b+336 a^5 p^4 \epsilon21 k12 b+84 a^6 p^3 \epsilon21 k12 b+8 a^7 p^2 \epsilon21 k12 b+\biggl(4 b+p\biggr) \biggl(a^9+\biggl(34 b+20 d-35 e+8 p\biggr) a^8+8 \biggl(4 b+p\biggr) \biggl(17 b+26 d-45 e+4 p\biggr) a^7+\biggl(4 b+p\biggr)^2 \biggl(322 b+860 d-1520 e+83 p\biggr) a^6+4 \biggl(4 b+p\biggr)^3 \biggl(119 b+406 d-700 e+37 p\biggr) a^5+\biggl(4 b+p\biggr)^4 \biggl(434 b+1304 d-1680 e+181 p\biggr) a^4+4 \biggl(4 b+p\biggr)^5 \biggl(56 b+64 d+80 e+37 p\biggr) a^3+\biggl(4 b+p\biggr)^6 \biggl(46 b-96 d+77 p\biggr) a^2-\biggl(8 b-23 p\biggr) \biggl(4 b+p\biggr)^7 a-\biggl(4 b-3 p\biggr) \biggl(4 b+p\biggr)^8\biggr) x_3 k11{}^2+56 a^6 p^4 x_3 k12{}^2-296 a^5 d p^4 x_3 k12{}^2+400 a^5 e p^4 x_3 k12{}^2+28 a^7 p^3 x_3 k12{}^2-124 a^6 d p^3 x_3 k12{}^2+160 a^6 e p^3 x_3 k12{}^2+8 a^8 p^2 x_3 k12{}^2-32 a^7 d p^2 x_3 k12{}^2+40 a^7 e p^2 x_3 k12{}^2+a^9 p x_3 k12{}^2\biggl)=0
\end{dmath}
\end{document}

Answer 1

描述

如果您使用正常的数学环境（或$...$），则会自动添加分页符。

我使用默认计数器手动添加了方程编号equation。

注意：如果用 和 替换所有括号，则\biggl(和\biggr)没有任何用处。然后，您只需使用普通的 即可()。

代码

\documentclass{article}
\usepackage{amsmath}
\usepackage{breqn}

\begin{document}

\begin{math}
\lambda _3+\frac{1}{\biggl(a+4 b+p\biggr)^9}2\biggl(-1048576 x_3 k12{}^2 b^{10}-1572864 a x_3 k12{}^2b^9-2359296 p x_3 k12{}^2 b^9+262144 p \epsilon21 k12 b^9-884736 a^2 x_3 k12{}^2 b^8-2359296 p^2 x_3 k12{}^2 b^8-3080192 a p x_3 k12{}^2 b^8+589824 p^2 \epsilon21 k12 b^8+458752 a p \epsilon21 k12 b^8-163840 a^3 x_3 k12{}^2 b^7-1376256 p^3 x_3 k12{}^2 b^7-2621440 a p^2 x_3 k12{}^2 b^7-1572864 a^2 d x_3 k12{}^2 b^7-1417216 a^2 p x_3 k12{}^2 b^7+589824 p^3 \epsilon21 k12 b^7+917504 a p^2 \epsilon21 k12 b^7+344064 a^2 p \epsilon21 k12 b^7+55296 a^4 x_3 k12{}^2 b^6-516096 p^4 x_3 k12{}^2 b^6-1261568 a p^3 x_3 k12{}^2 b^6-931840 a^2 p^2 x_3 k12{}^2 b^6-1310720 a^3 d x_3 k12{}^2 b^6+1310720 a^3 e x_3 k12{}^2 b^6-131072 a^3 p x_3 k12{}^2 b^6-2752512 a^2 d p x_3 k12{}^2 b^6+344064 p^4 \epsilon21 k12 b^6+802816 a p^3 \epsilon21 k12 b^6+602112 a^2 p^2 \epsilon21 k12 b^6+143360 a^3 p \epsilon21 k12 b^6+39936 a^5 x_3 k12{}^2 b^5-372736 a p^4 x_3 k12{}^2 b^5-311808 a^2 p^3 x_3 k12{}^2 b^5+18432 a^3 p^2 x_3 k12{}^2 b^5-2064384 a^2 d p^2 x_3 k12{}^2 b^5-434176 a^4 d x_3 k12{}^2 b^5+573440 a^4 e x_3 k12{}^2 b^5+126464 a^4 p x_3 k12{}^2 b^5-1966080 a^3 d p x_3 k12{}^2 b^5+1966080 a^3 e p x_3 k12{}^2 b^5+129024 p^5 \epsilon21 k12 b^5+401408 a p^4 \epsilon21 k12 b^5+451584 a^2 p^3 \epsilon21 k12 b^5+215040 a^3 p^2 \epsilon21 k12 b^5+35840 a^4 p \epsilon21 k12 b^5+10624 a^6 x_3 k12{}^2 b^4-49280 a^2 p^4 x_3 k12{}^2 b^4+56320 a^3 p^3 x_3 k12{}^2 b^4-860160 a^2 d p^3 x_3 k12{}^2 b^4+106240 a^4 p^2 x_3 k12{}^2 b^4-1228800 a^3 d p^2 x_3 k12{}^2 b^4+1228800 a^3 e p^2 x_3 k12{}^2 b^4-75776 a^5 d x_3 k12{}^2 b^4+102400 a^5 e x_3 k12{}^2 b^4+57856 a^5 p x_3 k12{}^2 b^4-542720 a^4 d p x_3 k12{}^2 b^4+716800 a^4 e p x_3 k12{}^2 b^4+32256 p^6 \epsilon21 k12 b^4+125440 a p^5 \epsilon21 k12 b^4+188160 a^2 p^4 \epsilon21 k12 b^4+134400 a^3 p^3 \epsilon21 k12 b^4+44800 a^4 p^2 \epsilon21 k12 b^4+5376 a^5 p \epsilon21 k12 b^4+1536 a^7 x_3 k12{}^2 b^3+26240 a^3 p^4 x_3 k12{}^2 b^3-215040 a^2 d p^4 x_3 k12{}^2 b^3+44480 a^4 p^3 x_3 k12{}^2 b^3-409600 a^3 d p^3 x_3 k12{}^2 b^3+409600 a^3 e p^3 x_3 k12{}^2 b^3+32896 a^5 p^2 x_3 k12{}^2 b^3-271360 a^4 d p^2 x_3 k12{}^2 b^3+358400 a^4 e p^2 x_3 k12{}^2 b^3-7936 a^6 d x_3 k12{}^2 b^3+10240 a^6 e x_3 k12{}^2 b^3+11552 a^6 p x_3 k12{}^2 b^3-75776 a^5 d p x_3 k12{}^2 b^3+102400 a^5 e p x_3 k12{}^2 b^3+5376 p^7 \epsilon21 k12 b^3+25088 a p^6 \epsilon21 k12 b^3+47040 a^2 p^5 \epsilon21 k12 b^3+44800 a^3 p^4 \epsilon21 k12 b^3+22400 a^4 p^3 \epsilon21 k12 b^3+5376 a^5 p^2 \epsilon21 k12 b^3+448 a^6 p \epsilon21 k12 b^3+120 a^8 x_3 k12{}^2 b^2+10040 a^4 p^4 x_3 k12{}^2 b^2-76800 a^3 d p^4 x_3 k12{}^2 b^2+9216 a^5 p^3 x_3 k12{}^2 b^2-67840 a^4 d p^3 x_3 k12{}^2 b^2+89600 a^4 e p^3 x_3 k12{}^2 b^2+4680 a^6 p^2 x_3 k12{}^2 b^2-28416 a^5 d p^2 x_3 k12{}^2 b^2+38400 a^5 e p^2 x_3 k12{}^2 b^2-512 a^7 d x_3 k12{}^2 b^2+640 a^7 e x_3 k12{}^2 b^2+1216 a^7 p x_3 k12{}^2 b^2-5952 a^6 d p x_3 k12{}^2 b^2+7680 a^6 e p x_3 k12{}^2 b^2+576 p^8 \epsilon21 k12 b^2+3136 a p^7 \epsilon21 k12 b^2+7056 a^2 p^6 \epsilon21 k12 b^2+8400 a^3 p^5 \epsilon21 k12 b^2+5600 a^4 p^4 \epsilon21 k12 b^2+2016 a^5 p^3 \epsilon21 k12 b^2+336 a^6 p^2 \epsilon21 k12 b^2+16 a^7 p \epsilon21 k12 b^2+4 a^9 x_3 k12{}^2 b+1276 a^5 p^4 x_3 k12{}^2 b-8480 a^4 d p^4 x_3 k12{}^2 b+11200 a^4 e p^4 x_3 k12{}^2 b+838 a^6 p^3 x_3 k12{}^2 b-4736 a^5 d p^3 x_3 k12{}^2 b+6400 a^5 e p^3 x_3 k12{}^2 b+320 a^7 p^2 x_3 k12{}^2 b-1488 a^6 d p^2 x_3 k12{}^2 b+1920 a^6 e p^2 x_3 k12{}^2 b-16 a^8 d x_3 k12{}^2 b+20 a^8 e x_3 k12{}^2 b+62 a^8 p x_3 k12{}^2 b-256 a^7 d p x_3 k12{}^2 b+320 a^7 e p x_3 k12{}^2 b+36 p^9 \epsilon21 k12 b+224 a p^8 \epsilon21 k12 b+588 a^2 p^7 \epsilon21 k12 b+840 a^3 p^6 \epsilon21 k12 b+700 a^4 p^5 \epsilon21 k12 b+336 a^5 p^4 \epsilon21 k12 b+84 a^6 p^3 \epsilon21 k12 b+8 a^7 p^2 \epsilon21 k12 b+\biggl(4 b+p\biggr) \biggl(a^9+\biggl(34 b+20 d-35 e+8 p\biggr) a^8+8 \biggl(4 b+p\biggr) \biggl(17 b+26 d-45 e+4 p\biggr) a^7+\biggl(4 b+p\biggr)^2 \biggl(322 b+860 d-1520 e+83 p\biggr) a^6+4 \biggl(4 b+p\biggr)^3 \biggl(119 b+406 d-700 e+37 p\biggr) a^5+\biggl(4 b+p\biggr)^4 \biggl(434 b+1304 d-1680 e+181 p\biggr) a^4+4 \biggl(4 b+p\biggr)^5 \biggl(56 b+64 d+80 e+37 p\biggr) a^3+\biggl(4 b+p\biggr)^6 \biggl(46 b-96 d+77 p\biggr) a^2-\biggl(8 b-23 p\biggr) \biggl(4 b+p\biggr)^7 a-\biggl(4 b-3 p\biggr) \biggl(4 b+p\biggr)^8\biggr) x_3 k11{}^2+56 a^6 p^4 x_3 k12{}^2-296 a^5 d p^4 x_3 k12{}^2+400 a^5 e p^4 x_3 k12{}^2+28 a^7 p^3 x_3 k12{}^2-124 a^6 d p^3 x_3 k12{}^2+160 a^6 e p^3 x_3 k12{}^2+8 a^8 p^2 x_3 k12{}^2-32 a^7 d p^2 x_3 k12{}^2+40 a^7 e p^2 x_3 k12{}^2+a^9 p x_3 k12{}^2\biggl)=0
\hfill
\refstepcounter{equation}
(\theequation)
\label{eq:myequation}
\end{math}

See (\ref{eq:myequation}).

\end{document}

结果

Answer 2

无需大量人工干预：

\documentclass{article}
\usepackage{amsmath}
\usepackage{ragged2e}
\begin{document}

\section{Introduction}

\begingroup
\rightskip=10em minus 10em
\binoppenalty=0
\parfillskip=-\rightskip
$\lambda _3+\frac{1}{(a+4 b+p)^9}2\Bigl(-1048576 x_3 k12{}^2 b^{10}-1572864 a x_3 k12{}^2b^9-2359296 p x_3 k12{}^2 b^9+262144 p \epsilon21 k12 b^9-884736 a^2 x_3 k12{}^2 b^8-2359296 p^2 x_3 k12{}^2 b^8-3080192 a p x_3 k12{}^2 b^8+589824 p^2 \epsilon21 k12 b^8+458752 a p \epsilon21 k12 b^8-163840 a^3 x_3 k12{}^2 b^7-1376256 p^3 x_3 k12{}^2 b^7-2621440 a p^2 x_3 k12{}^2 b^7-1572864 a^2 d x_3 k12{}^2 b^7-1417216 a^2 p x_3 k12{}^2 b^7+589824 p^3 \epsilon21 k12 b^7+917504 a p^2 \epsilon21 k12 b^7+344064 a^2 p \epsilon21 k12 b^7+55296 a^4 x_3 k12{}^2 b^6-516096 p^4 x_3 k12{}^2 b^6-1261568 a p^3 x_3 k12{}^2 b^6-931840 a^2 p^2 x_3 k12{}^2 b^6-1310720 a^3 d x_3 k12{}^2 b^6+1310720 a^3 e x_3 k12{}^2 b^6-131072 a^3 p x_3 k12{}^2 b^6-2752512 a^2 d p x_3 k12{}^2 b^6+344064 p^4 \epsilon21 k12 b^6+802816 a p^3 \epsilon21 k12 b^6+602112 a^2 p^2 \epsilon21 k12 b^6+143360 a^3 p \epsilon21 k12 b^6+39936 a^5 x_3 k12{}^2 b^5-372736 a p^4 x_3 k12{}^2 b^5-311808 a^2 p^3 x_3 k12{}^2 b^5+18432 a^3 p^2 x_3 k12{}^2 b^5-2064384 a^2 d p^2 x_3 k12{}^2 b^5-434176 a^4 d x_3 k12{}^2 b^5+573440 a^4 e x_3 k12{}^2 b^5+126464 a^4 p x_3 k12{}^2 b^5-1966080 a^3 d p x_3 k12{}^2 b^5+1966080 a^3 e p x_3 k12{}^2 b^5+129024 p^5 \epsilon21 k12 b^5+401408 a p^4 \epsilon21 k12 b^5+451584 a^2 p^3 \epsilon21 k12 b^5+215040 a^3 p^2 \epsilon21 k12 b^5+35840 a^4 p \epsilon21 k12 b^5+10624 a^6 x_3 k12{}^2 b^4-49280 a^2 p^4 x_3 k12{}^2 b^4+56320 a^3 p^3 x_3 k12{}^2 b^4-860160 a^2 d p^3 x_3 k12{}^2 b^4+106240 a^4 p^2 x_3 k12{}^2 b^4-1228800 a^3 d p^2 x_3 k12{}^2 b^4+1228800 a^3 e p^2 x_3 k12{}^2 b^4-75776 a^5 d x_3 k12{}^2 b^4+102400 a^5 e x_3 k12{}^2 b^4+57856 a^5 p x_3 k12{}^2 b^4-542720 a^4 d p x_3 k12{}^2 b^4+716800 a^4 e p x_3 k12{}^2 b^4+32256 p^6 \epsilon21 k12 b^4+125440 a p^5 \epsilon21 k12 b^4+188160 a^2 p^4 \epsilon21 k12 b^4+134400 a^3 p^3 \epsilon21 k12 b^4+44800 a^4 p^2 \epsilon21 k12 b^4+5376 a^5 p \epsilon21 k12 b^4+1536 a^7 x_3 k12{}^2 b^3+26240 a^3 p^4 x_3 k12{}^2 b^3-215040 a^2 d p^4 x_3 k12{}^2 b^3+44480 a^4 p^3 x_3 k12{}^2 b^3-409600 a^3 d p^3 x_3 k12{}^2 b^3+409600 a^3 e p^3 x_3 k12{}^2 b^3+32896 a^5 p^2 x_3 k12{}^2 b^3-271360 a^4 d p^2 x_3 k12{}^2 b^3+358400 a^4 e p^2 x_3 k12{}^2 b^3-7936 a^6 d x_3 k12{}^2 b^3+10240 a^6 e x_3 k12{}^2 b^3+11552 a^6 p x_3 k12{}^2 b^3-75776 a^5 d p x_3 k12{}^2 b^3+102400 a^5 e p x_3 k12{}^2 b^3+5376 p^7 \epsilon21 k12 b^3+25088 a p^6 \epsilon21 k12 b^3+47040 a^2 p^5 \epsilon21 k12 b^3+44800 a^3 p^4 \epsilon21 k12 b^3+22400 a^4 p^3 \epsilon21 k12 b^3+5376 a^5 p^2 \epsilon21 k12 b^3+448 a^6 p \epsilon21 k12 b^3+120 a^8 x_3 k12{}^2 b^2+10040 a^4 p^4 x_3 k12{}^2 b^2-76800 a^3 d p^4 x_3 k12{}^2 b^2+9216 a^5 p^3 x_3 k12{}^2 b^2-67840 a^4 d p^3 x_3 k12{}^2 b^2+89600 a^4 e p^3 x_3 k12{}^2 b^2+4680 a^6 p^2 x_3 k12{}^2 b^2-28416 a^5 d p^2 x_3 k12{}^2 b^2+38400 a^5 e p^2 x_3 k12{}^2 b^2-512 a^7 d x_3 k12{}^2 b^2+640 a^7 e x_3 k12{}^2 b^2+1216 a^7 p x_3 k12{}^2 b^2-5952 a^6 d p x_3 k12{}^2 b^2+7680 a^6 e p x_3 k12{}^2 b^2+576 p^8 \epsilon21 k12 b^2+3136 a p^7 \epsilon21 k12 b^2+7056 a^2 p^6 \epsilon21 k12 b^2+8400 a^3 p^5 \epsilon21 k12 b^2+5600 a^4 p^4 \epsilon21 k12 b^2+2016 a^5 p^3 \epsilon21 k12 b^2+336 a^6 p^2 \epsilon21 k12 b^2+16 a^7 p \epsilon21 k12 b^2+4 a^9 x_3 k12{}^2 b+1276 a^5 p^4 x_3 k12{}^2 b-8480 a^4 d p^4 x_3 k12{}^2 b+11200 a^4 e p^4 x_3 k12{}^2 b+838 a^6 p^3 x_3 k12{}^2 b-4736 a^5 d p^3 x_3 k12{}^2 b+6400 a^5 e p^3 x_3 k12{}^2 b+320 a^7 p^2 x_3 k12{}^2 b-1488 a^6 d p^2 x_3 k12{}^2 b+1920 a^6 e p^2 x_3 k12{}^2 b-16 a^8 d x_3 k12{}^2 b+20 a^8 e x_3 k12{}^2 b+62 a^8 p x_3 k12{}^2 b-256 a^7 d p x_3 k12{}^2 b+320 a^7 e p x_3 k12{}^2 b+36 p^9 \epsilon21 k12 b+224 a p^8 \epsilon21 k12 b+588 a^2 p^7 \epsilon21 k12 b+840 a^3 p^6 \epsilon21 k12 b+700 a^4 p^5 \epsilon21 k12 b+336 a^5 p^4 \epsilon21 k12 b+84 a^6 p^3 \epsilon21 k12 b+8 a^7 p^2 \epsilon21 k12 b+\left(4 b+p\right) \bigl(a^9+\left(34 b+20 d-35 e+8 p\right) a^8+8 \left(4 b+p\right) \left(17 b+26 d-45 e+4 p\right) a^7+\left(4 b+p\right)^2 \left(322 b+860 d-1520 e+83 p\right) a^6+4 \left(4 b+p\right)^3 \left(119 b+406 d-700 e+37 p\right) a^5+\hfil\break \left(4 b+p\right)^4 \left(434 b+1304 d-1680 e+181 p\right) a^4+\hfil\break 4 \left(4 b+p\right)^5 \left(56 b+64 d+80 e+37 p\right) a^3+\left(4 b+p\right)^6 \left(46 b-96 d+77 p\right) a^2-\left(8 b-23 p\right) \left(4 b+p\right)^7 a-\left(4 b-3 p\right) \left(4 b+p\right)^8\bigr) x_3 k11{}^2+56 a^6 p^4 x_3 k12{}^2-296 a^5 d p^4 x_3 k12{}^2+400 a^5 e p^4 x_3 k12{}^2+28 a^7 p^3 x_3 k12{}^2-124 a^6 d p^3 x_3 k12{}^2+160 a^6 e p^3 x_3 k12{}^2+8 a^8 p^2 x_3 k12{}^2-32 a^7 d p^2 x_3 k12{}^2+40 a^7 e p^2 x_3 k12{}^2+a^9 p x_3 k12{}^2\Bigr)=0$
\unskip\nobreak\hfill\stepcounter{equation}(\theequation)\par
\endgroup

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这些\left(...\right)位将括号内的部分放在一起。有些部分\hfil\break必须手动插入。