问题是“在第 357 行检测到 Overfull \hbox (39.27608pt too wide)”，第一个图像的代码是这样的，问题出现在这里：
\[\begin{array}{cl}
= & (x-\delta_{n+1})\left|\begin{array}{cccccc}
\delta_1 - x & \gamma_2 & & & & \\
\gamma_2 & \delta_2 - x & \gamma_3 & & & \\
& \cdot & \cdot & \cdot & & \\
& & \cdot & \cdot & \cdot & \\
& & & \gamma_{n-1} & \delta_{n-1} - x & \gamma_{n} \\
& & & & \gamma_{n} & \delta_{n} - x
\end{array} \right| - \\
- & \gamma_{n+1}^2 \left|\begin{array}{cccccc}
\delta_1 - x & \gamma_2 & & & & \\
\gamma_2 & \delta_2 - x & \gamma_3 & & & \\
& \cdot & \cdot & \cdot & & \\
& & \cdot & \cdot & \cdot & \\
& & & \gamma_n & \delta_n - x & \gamma_{n+1} \\
& & & & \gamma_{n+1} & \delta_{n+1} - x
\end{array} \right| \\
并且手动解决的错误代码是这样的：
\[\begin{array}{cl}
= & (x-\delta_{n+1})\left|\begin{array}{cccccc}
\delta_1 - x & \gamma_2 & & & & \\
\gamma_2 & \delta_2 - x & \gamma_3 & & & \\
& \cdot & \cdot & \cdot & & \\
& & \cdot & \cdot & \cdot & \\
& & & \gamma_{n-1} & \delta_{n-1} - x & \gamma_{n} \\
& & & & \gamma_{n} & \delta_{n} - x
\end{array} \right| - \gamma_{n+1}^2 \left|\begin{array}{cccccc}
\delta_1 - x & \gamma_2 & & & & \\
\gamma_2 & \delta_2 - x & \gamma_3 & & & \\
& \cdot & \cdot & \cdot & & \\
& & \cdot & \cdot & \cdot & \\
& & & \gamma_n & \delta_n - x & \gamma_{n+1} \\
& & & & \gamma_{n+1} & \delta_{n+1} - x
\end{array} \right| \\
= & (x-\delta_{n+1})\left|\begin{array}{cccccc}
\delta_1 - x & \gamma_2 & & & & \\
\gamma_2 & \delta_2 - x & \gamma_3 & & & \\
& \cdot & \cdot & \cdot & & \\
& & \cdot & \cdot & \cdot & \\
& & & \gamma_{n-1} & \delta_{n-1} - x & \gamma_{n} \\
& & & & \gamma_{n} & \delta_{n} - x
\end{array} \right| + \gamma_{n+1}^2 \left|\begin{array}{ccccccc}
\delta_1 - x & \gamma_2 & & & & & \\
\gamma_2 & \delta_2 - x & \gamma_3 & & & & \\
& \cdot & \cdot & \cdot & & & \\
& & \cdot & \cdot & \cdot & & \\
& & & \gamma_n & \delta_n - x & \gamma_{n+1} & \\
& & & & \gamma_{n+1} & \delta_{n+1} - x & 1 \\
& & & & & 1 & 0
\end{array} \right| \\
\end{array}\]
答案1
不确定你需要什么“自动方式”。我强烈建议你使用数学包——具体来说，是包中用于多行数学材料的环境——并array用（a）代替align*“外部”结构的环境array和（b）vmatrix代替的环境来替换嵌套环境\left| \begin{array}{...} ... \end{array}\right|。
\documentclass{article} % or some other suitable class
\usepackage{amsmath} % for 'align*' and 'vmatrix' environments,
% and for '\allowdisplaybreaks' macro
\begin{document}
\allowdisplaybreaks
\begingroup % limit scope of next instruction to current TeX group
\renewcommand\arraystretch{1.25} % default value: 1.0
\begin{align*}
(x-&\delta_{n+1})p_n(x) - \gamma_{n+1}^2p_{n-1}(x) \\
&= (x-\delta_{n+1})\det(J_n-xId) - \gamma_{n+1}^2\det(J_{n+1}-xId) \\
&= (x-\delta_{n+1})
\begin{vmatrix}
\delta_1{-}x & \gamma_2 \\
\gamma_2 & \delta_2{-}x & \gamma_3 \\
& \cdot & \cdot & \cdot \\
& & \cdot & \cdot & \cdot \\
& & & \gamma_{n-1} & \delta_{n-1}{-}x & \gamma_{n} \\
& & & & \gamma_{n} & \delta_{n}{-}x
\end{vmatrix} \\[\jot]
&\qquad\quad -\gamma_{n+1}^2
\begin{vmatrix}
\delta_1{-}x & \gamma_2 \\
\gamma_2 & \delta_2{-}x & \gamma_3 \\
& \cdot & \cdot & \cdot \\
& & \cdot & \cdot & \cdot \\
& & & \gamma_n & \delta_n{-}x & \gamma_{n+1} \\
& & & & \gamma_{n+1} & \delta_{n+1}{-}x
\end{vmatrix} \\[2\jot]
&= (x-\delta_{n+1})
\begin{vmatrix}
\delta_1{-}x & \gamma_2 \\
\gamma_2 & \delta_2{-}x & \gamma_3 \\
& \cdot & \cdot & \cdot \\
& & \cdot & \cdot & \cdot \\
& & & \gamma_{n-1} & \delta_{n-1}{-}x & \gamma_{n} \\
& & & & \gamma_{n} & \delta_{n}{-}x
\end{vmatrix} \\[\jot]
&\qquad\quad +\gamma_{n+1}^2
\begin{vmatrix}
\delta_1{-}x & \gamma_2 \\
\gamma_2 & \delta_2{-}x & \gamma_3 \\
& \cdot & \cdot & \cdot \\
& & \cdot & \cdot & \cdot \\
& & & \gamma_n & \delta_n{-}x & \gamma_{n+1} \\
& & & & \gamma_{n+1} & \delta_{n+1}{-}x & 1 \\
& & & & & 1 & 0
\end{vmatrix}
\end{align*}
\endgroup
\end{document}