可以将lemma、theorem、corollary、的标题definition显示为彩色吗？
答案1
通过该包amsthm您可以使用增强的 \newtheorem命令。
\newtheorem{⟨env name⟩}{⟨text⟩}[⟨parent counter⟩]
\newtheorem{⟨env name⟩}[⟨shared counter⟩]{⟨text⟩}
然后添加颜色，如图<text>所示。
请注意，此处使用的环境defn不包含共享计数器，因此它将启动为 <section number>. 1.
\documentclass[12pt,a4paper]{article}
\usepackage{amsmath,amsthm}
\usepackage{xcolor}
%*********************************************** put the colors <<<<<
\newtheorem{thm}{\textcolor{green}{Theorem}}[section]
\newtheorem{cor}[thm]{\textcolor{violet}{Corollary}}
\newtheorem{lem}[thm]{\textcolor{orange}{Lemma}}
\newtheorem{prop}[thm]{\textcolor{blue}{Proposition}}
\newtheorem{defn}{\textcolor{red}{Definition}}[section]
%****************************************************
\DeclareMathOperator{\per}{per}
\newcommand{\A}{\mathcal{A}}
\newcommand{\eval}[2][\right]{\relax
\ifx#1\right\relax \left.\fi#2#1\rvert}
\begin{document}
\section{A color Sampler}
\begin{lem}\label{lem-per}
\begin{equation}
\prod_{i\in\mathbf{n}}
\biggl(\sum_{\,j\in\mathbf{n}}b_{ij}\hat x_i\biggr)
=\biggl(\prod_{\,i\in\mathbf{n}}\hat x_i\biggr)\per \mathbf{B}
\end{equation}
where $\per \mathbf{B}$ is the permanent of $\mathbf{B}$.
\end{lem}
\begin{thm}\label{thm-main}
\begin{equation}\label{detB}
\det\mathbf{B}=
\sum^n_{l =0}\sum_{I_l \subseteq n}
\prod_{i\in I_l}(b_{ii}-\lambda_i)
\det\mathbf{B}^{(\lambda)}(I_l |I_l ),
\end{equation}
where $I_l =\{i_1,\dots,i_l \}$ and $\mathbf{B}^{(\lambda)}(I_l |I_l )$
is the principal submatrix obtained from $\mathbf{B}^{(\lambda)}$
by deleting its $i_1,\dots,i_l $ rows and columns.
\end{thm}
\begin{cor}\label{tripleA}
Let $(\A,\A',\A'')$ be a triple of arrangements. Then
\[ \pi (\A,t) = \pi (\A',t) + t \pi (\A'',t). \]
\end{cor}
\begin{defn}
Let $(\A,\A',\A'')$ be a triple with respect to
the hyperplane $H \in \A$. Call $H$ a \textit{separator}
if $T(\A) \not\in L(\A')$.
\end{defn}
\begin{prop}\label{prop:eg}
\begin{equation}
H_c=\frac1{2n}\sum^n_{l =0}(-1)^{l}
D_{l},
\end{equation}
where
\begin{equation}\label{delta-l}
D_{l}=\eval[2]{\sum_{I_{l}\subseteq \mathbf{n}}
D(t_1,\dots,t_n)}_{t_i=\left\{\begin{smallmatrix}
0,& \text{if }i\in I_{l}\quad\\% \quad added for centering
1,& \text{otherwise}\end{smallmatrix}\right.\;,\;\; i=1,\dots,n}.
\end{equation}
\end{prop}
\end{document}