当我在 Latex 中编译它时，它不起作用。我必须在这里使用哪个包？一般来说，有人能修复该文件，使其在 Latex 中工作吗？
In general, an isometry of $\mathbb R^2$ is a composition of a rotation, a reflection, and a translation. Every isometry either preserves orientation (so that clockwise loops map to clockwise loops) or reverses it (so that clockwise maps to counterclockwise). In this case, we just have a composition of a translation and a rotation:
\begin{array}{rccc}
x & \mapsto & ax-by & \mapsto & ax-by + c \\
y & \mapsto & bx+ay & \mapsto & bx+ay + d \\[6pt]
& \uparrow & & \uparrow \\
& \text{rotation} & & \text{translation} \\
& (\text{where } \\
& a^2+b^2 \\
& =1.)
\end{array}
In the above, if you find $a$, then you have $b=\pm\sqrt{1-a^2}$ so you've got $b$ except for $\text{“}\pm\text{''}$.
Find two particular points whose images you know: thus $(x_0,y_0)$ maps to $(x_1,y_1)$ and $(x_2,y_2)$ maps to $(x_3,y_3)$, and plug them in to the the system of equations above (including $a^2+b^2=1$), and solve for $a,b,c,d$.
答案1
array必须在数学而不是文本中使用，并且您在数组中使用了 5 列但只声明了 4 列，那么您需要amsfonts(for \mathbb) 和amsmath（或amstextfor \text）
\documentclass{article}
\usepackage{amsfonts,amsmath}
\begin{document}
In general, an isometry of $\mathbb R^2$ is a composition of a rotation, a reflection, and a translation. Every isometry either preserves orientation (so that clockwise loops map to clockwise loops) or reverses it (so that clockwise maps to counterclockwise). In this case, we just have a composition of a translation and a rotation:
\[\begin{array}{rcccc}
x & \mapsto & ax-by & \mapsto & ax-by + c \\
y & \mapsto & bx+ay & \mapsto & bx+ay + d \\[6pt]
& \uparrow & & \uparrow \\
& \text{rotation} & & \text{translation} \\
& (\text{where } \\
& a^2+b^2 \\
& =1.)
\end{array}\]
In the above, if you find $a$, then you have $b=\pm\sqrt{1-a^2}$ so you've got $b$ except for $\text{“}\pm\text{''}$.
Find two particular points whose images you know: thus $(x_0,y_0)$ maps to $(x_1,y_1)$ and $(x_2,y_2)$ maps to $(x_3,y_3)$, and plug them in to the the system of equations above (including $a^2+b^2=1$), and solve for $a,b,c,d$.
\end{document}