具有语言依赖性的 Declarematoperator

Question

我想为线性函数的范围定义一个新的运算符。因为我是德国人，所以我想以一种根据所用语言而变化的方式来定义它。

\documentclass{scrartcl}
\usepackage[english]{babel}
\usepackage{amsmath}
\DeclareMathOperator{\range}{ran}
\DeclareMathOperator{\kernel}{ker}
% The following should be used if german or ngerman are defined for babel
% \DeclareMathOperator{\range}{Bild}
% \DeclareMathOperator{\kernel}{Kern}
\begin{document}
\begin{align}
  T &: V \rightarrow W \\
  \dim(V) &= \dim(\range(T)) + \dim(\kernel(T))
\end{align}
\end{document}

有没有简单的方法可以实现这一点？

Answer 1

在我看来，定义应该是这样的，即使语言发生变化，操作员也不会在整个文档中发生改变。

因此，如果主要语言是德语，\ker则在英语中也应解析为“Kern”。但是，也很容易提供“变量”类型。

\documentclass{scrartcl}
\usepackage[english,ngerman]{babel}
\usepackage{amsmath}
\usepackage{xparse}

\ExplSyntaxOn
\NewDocumentCommand\DeclareBabelMathOperator{mmO{???}}
 {
  \DeclareMathOperator{#1}
   {
    \str_case:xnF { \use:c { bbl@main@language } } { #2 } { #3 }
   }
 }
\NewDocumentCommand\DeclareVariableBabelMathOperator{mmO{???}}
 {
  \DeclareMathOperator{#1}
   {
    \str_case:xnF { \languagename }{ #2 } { #3 }
   }
 }
\cs_generate_variant:Nn \str_case:nnF { x }
\ExplSyntaxOff


\DeclareBabelMathOperator{\range}{
  {english}{ran}
  {ngerman}{Bild}
}
\DeclareBabelMathOperator{\kernel}{
  {english}{ker}
  {ngerman}{Kern}
}[ker]
\DeclareVariableBabelMathOperator{\vrange}{
  {english}{ran}
  {ngerman}{Bild}
}
\DeclareVariableBabelMathOperator{\vkernel}{
  {english}{ker}
  {ngerman}{Kern}
}[ker]

\begin{document}

\section{Fixed names}
\[
  \dim(V) = \dim(\range(T)) + \dim(\kernel(T))
\]
\begin{otherlanguage*}{english}
\[
  \dim(V) = \dim(\range(T)) + \dim(\kernel(T))
\]
\end{otherlanguage*}

\section{Variable names}
\[
  \dim(V) = \dim(\vrange(T)) + \dim(\vkernel(T))
\]
\begin{otherlanguage*}{english}
\[
  \dim(V) = \dim(\vrange(T)) + \dim(\vkernel(T))
\]
\end{otherlanguage*}

\end{document}

可选参数用于与先前选择中未包含的语言一起使用的字符串。

english如果和ngerman被交换，则输出如下。

Answer 2

\documentclass{scrartcl}
\usepackage[german,english]{babel}
\usepackage{amsmath}

\DeclareMathOperator{\range}{\rangename}
\DeclareMathOperator{\kernel}{\kernelname}

\addto\extrasenglish{%
\def\rangename{range}%
\def\kernelname{ker}%
}

\addto\extrasgerman{%
\def\rangename{Bild}%
\def\kernelname{Kern}%
}
\begin{document}

\selectlanguage{english}
english
\begin{align}
  T &: V \rightarrow W \\
  \dim(V) &= \dim(\range(T)) + \dim(\kernel(T))
\end{align}

\selectlanguage{german}
Und jetzt etwas auf Deutsch
\begin{align}
  T &: V \rightarrow W \\
  \dim(V) &= \dim(\range(T)) + \dim(\kernel(T))
\end{align}
\end{document}

Answer 3

我会坚持旧的\operatorname并将它与babel的结合起来\extrasLANGUAGE：

\documentclass{scrartcl}
\usepackage[german,english]{babel}
\usepackage{amsmath}

\addto\extrasenglish{%
    \def\range{\operatorname{ran}}%
    \def\kernel{\operatorname{ker}}%
}

\addto\extrasgerman{%
    \def\range{\operatorname{Bild}}%
    \def\kernel{\operatorname{Kern}}%
}
\begin{document}

English
\begin{align}
  T &: V \rightarrow W \\
  \dim(V) &= \dim(\range(T)) + \dim(\kernel(T))
\end{align}

\selectlanguage{german}
Und jetzt etwas auf Deutsch
\begin{align}
  T &: V \rightarrow W \\
  \dim(V) &= \dim(\range(T)) + \dim(\kernel(T))
\end{align}
\end{document}