`ntheorem` 和 `thmtools` 似乎不兼容

Question 1

如果您想使用ntheorem而不是amsthm作为后端，那么您将不得不放弃一些可用的格式化功能，amsthm并且必须进行一些其他更改：

命令\NAME、\NUMBER和\NOTE将不再可用。
为了模拟所需的头部格式，您可以使用该headformat=swapnumber选项，但这样您就失去了更改头部格式的灵活性。
qed=\text{\guillemotleft}必须使用 in\declaretheoremstyle而不是 in选项\declaretheorem（无论如何，这都是有意义的）。
您的proof环境必须单独定义。

下面是使用以下方式定义的一个例子ntheorem：

\documentclass[10pt,a4paper]{article}
\usepackage[T1]{fontenc}
\usepackage[utf8x]{inputenc}
\usepackage{amsmath, amssymb}
\usepackage[thmmarks,amsmath]{ntheorem}
\usepackage{thmtools}

\numberwithin{equation}{section}

\declaretheoremstyle[headformat=swapnumber,bodyfont=\normalfont]{theorem}
\declaretheoremstyle[headformat=swapnumber,bodyfont=\normalfont
,qed=\text{\guillemotleft}]{mydefinition}

\declaretheorem[style=theorem,sibling=equation]{theorem}
\declaretheorem[style=theorem,sibling=equation]{proposition}
\declaretheorem[style=theorem,sibling=equation]{lemma}
\declaretheorem[style=mydefinition,sibling=equation]{definition}
\declaretheorem[style=mydefinition,sibling=equation]{exercise}
\declaretheorem[style=mydefinition,sibling=equation]{example}

\newtheorem*{proof}{Proof}

%% Math macro stuff to make this compile
\DeclareMathOperator{\Spec}{Spec}       % Spectrum
\DeclareMathOperator{\M}{M}
\DeclareMathOperator{\Ga}{Ga}
\DeclareMathOperator{\GL}{GL}
\DeclareMathOperator{\Gm}{Gm}
\def\ol{\overline}

\begin{document}

\begin{definition}
A \emph{group variety over $k$} is an integral group scheme of finite type over $\Spec k$.
\end{definition}

\begin{proof}
Test
\end{proof}

\begin{example}
Let $k$ be a field and $R$ a commutative $k$-algebra.
\begin{itemize}
    \item The varieties $\Ga_{k} = \Spec k[x]$ and $\Gm_{k} = \Spec k[x,y]/(xy - 1)$ are group varieties. Indeed, $\Ga_{k}(R)$ is the additive group underlying $R$, and $\Gm_{k}(R) = R^*$ is the group of units in $R$.
    \item The variety $\M_{n,k} = \Spec k[(x_{ij})_{ij}]$ is a group variety. Also the closed sub variety $\GL_{n,k}$ defined by the polynomial $\det \left( (x_{ij})_{ij} \right) - 1$ is a group variety. The $R$-valued points are the $n \times n$-matrices $\M_{n,k}(R)$ with coefficients in $R$, and $\GL_{n,k}(R)$ consists of the invertible matrices respectively. Observe that $\Gm_{k} = \GL_{1,k}$.
    \item The variety $\mu_{n,k} = \Spec k[x]/(x^n -1)$ is a group variety, and $\mu_{n,k}(R)$ consists of the group of $n$-th roots of unity in $R$.
    \item An elliptic curve over $k$ is defined as a proper variety $E/k$ that is smooth of relative dimension $1$, of which the geometric fibre $E_{\ol{k}}$ has genus $1$, together with a given point $0 \in E(k)$. It can be shown that every elliptic curve is a group variety. Actually they form an important class of objects in the study of abelian varieties.
\end{itemize}
\end{example}

\end{document}

在此处输入图片描述

Answer

如果您想使用ntheorem而不是amsthm作为后端，那么您将不得不放弃一些可用的格式化功能，amsthm并且必须进行一些其他更改：

命令\NAME、\NUMBER和\NOTE将不再可用。
为了模拟所需的头部格式，您可以使用该headformat=swapnumber选项，但这样您就失去了更改头部格式的灵活性。
qed=\text{\guillemotleft}必须使用 in\declaretheoremstyle而不是 in选项\declaretheorem（无论如何，这都是有意义的）。
您的proof环境必须单独定义。

下面是使用以下方式定义的一个例子ntheorem：

\documentclass[10pt,a4paper]{article}
\usepackage[T1]{fontenc}
\usepackage[utf8x]{inputenc}
\usepackage{amsmath, amssymb}
\usepackage[thmmarks,amsmath]{ntheorem}
\usepackage{thmtools}

\numberwithin{equation}{section}

\declaretheoremstyle[headformat=swapnumber,bodyfont=\normalfont]{theorem}
\declaretheoremstyle[headformat=swapnumber,bodyfont=\normalfont
,qed=\text{\guillemotleft}]{mydefinition}

\declaretheorem[style=theorem,sibling=equation]{theorem}
\declaretheorem[style=theorem,sibling=equation]{proposition}
\declaretheorem[style=theorem,sibling=equation]{lemma}
\declaretheorem[style=mydefinition,sibling=equation]{definition}
\declaretheorem[style=mydefinition,sibling=equation]{exercise}
\declaretheorem[style=mydefinition,sibling=equation]{example}

\newtheorem*{proof}{Proof}

%% Math macro stuff to make this compile
\DeclareMathOperator{\Spec}{Spec}       % Spectrum
\DeclareMathOperator{\M}{M}
\DeclareMathOperator{\Ga}{Ga}
\DeclareMathOperator{\GL}{GL}
\DeclareMathOperator{\Gm}{Gm}
\def\ol{\overline}

\begin{document}

\begin{definition}
A \emph{group variety over $k$} is an integral group scheme of finite type over $\Spec k$.
\end{definition}

\begin{proof}
Test
\end{proof}

\begin{example}
Let $k$ be a field and $R$ a commutative $k$-algebra.
\begin{itemize}
    \item The varieties $\Ga_{k} = \Spec k[x]$ and $\Gm_{k} = \Spec k[x,y]/(xy - 1)$ are group varieties. Indeed, $\Ga_{k}(R)$ is the additive group underlying $R$, and $\Gm_{k}(R) = R^*$ is the group of units in $R$.
    \item The variety $\M_{n,k} = \Spec k[(x_{ij})_{ij}]$ is a group variety. Also the closed sub variety $\GL_{n,k}$ defined by the polynomial $\det \left( (x_{ij})_{ij} \right) - 1$ is a group variety. The $R$-valued points are the $n \times n$-matrices $\M_{n,k}(R)$ with coefficients in $R$, and $\GL_{n,k}(R)$ consists of the invertible matrices respectively. Observe that $\Gm_{k} = \GL_{1,k}$.
    \item The variety $\mu_{n,k} = \Spec k[x]/(x^n -1)$ is a group variety, and $\mu_{n,k}(R)$ consists of the group of $n$-th roots of unity in $R$.
    \item An elliptic curve over $k$ is defined as a proper variety $E/k$ that is smooth of relative dimension $1$, of which the geometric fibre $E_{\ol{k}}$ has genus $1$, together with a given point $0 \in E(k)$. It can be shown that every elliptic curve is a group variety. Actually they form an important class of objects in the study of abelian varieties.
\end{itemize}
\end{example}

\end{document}

在此处输入图片描述

Question 2

呃，这是一个不起作用的例子。

第一个问题：\def\ol\overline因“缺失”而导致失败\begin{document}；请使用括号括起来进行纠正\overline。

第二个问题：“\guillemotleft编码 OT1 时命令不可用”。

无论如何，该命令\qedhere是在 2003 年开发的，amsthm用于解决当证明以显示或列表结束时的“换行”问题；它必须在\end{...}嵌入元素（equation和朋友或itemize）的命令之前输入。碰巧的是，thmtools这也适用于定理类对象，但如果您想要预定义框以外的符号，则必须重新定义\qedsymbol

我对不是很熟悉ntheorem，但知道它在一些重要方面与有所不同amsthm，因此如果您想使用thmtools，ntheorem则需要参考thmtools手册。

Answer